MUSIC

THE art of combining sounds in a manner agreeable to the ear. This combination may be either simultaneous or successive: in the first case, it constitutes harmony; in the last, melody. But though the same sounds, or intervals of sound, which give pleasure when heard in succession, will not always produce the same effect in harmony; yet the principles which constitute the simpler and more perfect kinds of harmony, are almost, if not entirely, the same with those of melody. By perfect harmony, we do not here mean that plenitude, those complex modifications of harmonic sound, which are admired in practice; but that harmony which is called perfect by theoreticians and artists; that harmony which results from the coalescence of simultaneous sounds produced by vibrations in the proportions of thirds, fifths, and octaves, or their duplicates.

The principles upon which these various combinations of sound are founded, and by which they are regulated, constitute a science, which is not only extensive but profound, when we would investigate the principles from whence these happy modifications of sound result, and by which they are determined; or when we would explore the sensations, whether mental or corporeal, with which they affect us. The ancient definitions of music are not proportioned in their extent to our present ideas of that art; but M. Rousseau betrays a temerity highly inconsistent with the philosophical character, when from thence he infers, that their ideas were vague and undetermined. Every soul susceptible of refinement and delicacy in taste or sentiment, must be conscious that there is a music in action as well as in sound; and that the ideas of beauty and decorum, of harmony and symmetry, are, if we may use the expression, equally constituent of visible as of audible music. Those illustrious minds, whose comprehensive prospects in every science where taste and propriety prevail took in nature at a single glance, would behold with contempt and ridicule those narrow and microscopic views of which alone their successors in philosophy have discovered themselves conscious. With these definitions, however, we are less concerned, as they bear no proportion to the ideas which are now entertained of music. Nor can we follow M. Rousseau, from whatever venerable sources his authority may be derived, in adopting his Egyptian etymology for the word music. The established derivation from Musa could only be questioned by a paradoxical genius. That music had been practised in Egypt before it was known as an art in Greece, is indeed a fact which cannot be questioned; but it does not thence follow that the Greeks had borrowed the name as well as the art from Egypt. If the art of music be so natural to man that vocal melody is practised wherever articulate sounds are used, there can be little reason for deducing the idea of music from the whistling of winds through the reeds that grew on the river Nile. And indeed, when we reflect with how easy a transition we

may pass from the accents of speaking to diatonic sounds; when we observe how early children adapt the language of their amusements to measure and melody, however rude; when we consider how early and universally these practices take place—there is no avoiding the conclusion, that the idea of music is connatural to man, and implied in the original principles of his constitution. We have already said, that the principles on which it is founded, and the rules by which it is conducted, constitute a science. The same maxims when applied to practice form an art: hence its first and most capital division is into speculative and practical music.

Speculative music is, if we may be permitted to use the expression, the knowledge of the nature and use of those materials which compose it; or, in other words, of all the different relations between the high and low, between the harsh and the sweet, between the swift and the slow, between the strong and the weak, of which sounds are susceptible: relations which, comprehending all the possible combinations of music and sounds, seem likewise to comprehend all the causes of the impressions which their succession can make upon the ear and upon the soul.

Practical music is the art of applying and reducing to practice those principles which result from the theory of agreeable sounds, whether simultaneous or successive; or, in other words, to conduct and arrange sounds according to the proportions resulting from consonance, from duration and succession, in such a manner as to produce upon the ear the effect which the composer intends. This is the art which we call composition. * See Composition. With respect to the actual production of sounds by voices or instruments, which is called execution, this department is merely mechanical and operative: which, only presupposing the powers of sounding the intervals true, of exactly proportioning their degrees of duration, of elevating or depressing sounds according to those gradations which are prescribed by the tone, and to the value required by the time, demands no other knowledge but a familiar acquaintance with the characters used in music, and a habit of expressing them with promptitude and facility.

Speculative music is likewise divided into two departments; viz. the knowledge of the proportions of sounds or their intervals, and that of their relative durations; that is to say, of measure and of time.

The first is what among the ancients seems to have been called harmonical music. It shows in what the nature of air or melody consists; and discovers what is consonant or discordant, agreeable or disagreeable, in the modulation. It discovers, in a word, the effects which sounds produce on the ear by their nature, by their force, and by their intervals; which is equally applicable to their consonance and their succession.

The second has been called rhythmic, because it treats of sounds with regard to their time and quantity. It contains the explication of their continuance, of their proportions, of their measures whether long or

short, quick or slow, of the different modes of time and the parts into which they are divided, that to these the succession of sounds may be conformed.

Practical music is likewise divided into two departments, which correspond to the two preceding.

That which answers to harmonical music, and which the ancients called melopée, teaches the rules for combining and varying the intervals, whether consonant or dissonant, in an agreeable and harmonious manner.

The second, which answers to the rhythmical music, and which they called rhythmo-pée, contains the rules for applying the different modes of time, for understanding the feet by which verses were scanned, and the diversities of measure; in a word, for the practice of the rhythmus.

Music is at present divided more simply into melody and harmony; for since the introduction of harmony the proportion between the length and shortness of sounds, or even that between the distance of returning cadences, are of less consequence amongst us. For it often happens in modern languages, that the verses assume their measures from the musical air, and almost entirely lose the small share of proportion and quantity which in themselves they possess.

By melody the successions of sound are regulated in such a manner as to produce pleasing airs. See MELODY.

Harmony consists in uniting to each of the sounds, in a regular succession, two or more different sounds, which simultaneously striking the ear soothe it by their concurrence. See HARMONY.

Music, according to Rousseau, may be, and perhaps likewise ought to be, divided into the physical and the imitative. The first is limited to the mere mechanism of sounds, and reaches no farther than the external senses, without carrying its impressions to the heart, and can produce nothing but corporeal sensations more or less agreeable. Such is the music of songs, of hymns, of all the airs which only consist in combinations of melodious sounds, and in general all music which is merely harmonious.

It may, however, be questioned, whether every sound, even to the most simple, is not either by nature or by early and confirmed association, imitative. If we may trust our own feelings, there is no such thing in nature as music which gives mechanical pleasure alone. For if so, it must give such pleasure as we receive from tastes, from odours, or from other grateful titillations; but we absolutely deny that there are any musical sensations or pleasures in the smallest degree analogous to these. Let any piece of music be resolved into its elementary parts and their proportions, it will then easily appear from this analysis, that sense is no more than the vehicle of such perceptions, and that mind alone can be susceptible of them. It may indeed happen, from the number of the performers and the complication of the harmony, that meaning and sentiment may be lost in the multiplicity of sounds; but this, though it may be harmony, loses the name of music.

The second department of this division, by lively and accented inflections, and by sounds which may be said to speak, expresses all the passions, paints every possible picture, reflects every object, subjects the whole of nature to its skilful imitations, and impresses even on the heart and soul of man sentiments

proper to affect them in the most sensible manner. This, continues he, which is the genuine lyric and theatrical music, was what gave double charms and energy to ancient poetry; this is what, in our days, we exert ourselves in applying to the drama, and what our fingers execute on the stage. It is in this music alone, and not in harmonics or the resonance of nature, that we must expect to find accounts of those prodigious effects which it formerly produced.

But, with M. Rousseau's permission, all music which is not in some degree characterized by these pathetic and imitative powers, deserves no better name than that of a musical jargon, and can only be effectuated by such a complication and intricacy of harmony, as may confound, but cannot entertain the audience. This character, therefore, ought to be added as essential to the definition of music; and it must be attributed to our neglect of this alone, whilst our whole attention is bestowed on harmony and execution, that the best performances of our artists and composers are heard with listless indifference and oscitation, nor ever can conciliate any admirers, but such as are induced, by pedantry and affectation, to pretend what they do not feel. Still may the curse of indifference and inattention pursue and harrow up the souls of every composer or performer, who pretends to regale our ears with this musical legerdemain, till the grin of scorn, or the hiss of infamy, teach them to correct this depravity of taste, and entertain us with the voice of nature!

Whilst moral effects are sought in the natural effects of sound alone, the scrutiny will be vain, and disputes will be maintained without being understood: but sounds, as representatives of objects, whether by nature or association, introduce new scenes to the fancy and new feelings to the heart; not from their mechanical powers, but from the connection established by the Author of our frame between sounds and the objects which either by natural resemblance or unavoidable association they are made to represent.

It would seem that music was one of those arts which were first discovered: and that vocal was prior to instrumental music, if in the earliest ages there was any music which could be said to be purely instrumental. For it is more than probable, that music was originally formed to be the vehicle of poetry; and of consequence, though the voice might be supported and accompanied by instruments, yet music was never intended for instruments alone.

We are told by ancient authors, that all the laws, whether human or divine, exhortations to virtue, the knowledge of the characters and actions of gods and heroes, the lives and achievements of illustrious men, were written in verse, and sung publicly by a choir to the sound of instruments; and it appears from the Scriptures, that such from the earliest times was the custom among the Israelites. Nor was it possible to find means more efficacious for impressing on the mind of man the principles of morals, and inspiring the love of virtue. Perhaps, however, this was not the result of a premeditated plan; but inspired by sublime sentiments and elevation of thought, which in accents that were suited and proportioned to their celestial nature endeavoured to find a language worthy of themselves and expressive of their grandeur.

It merits attention, that the ancients were duly sensible

visible of the value and importance of this divine art, not only as a symbol of that universal order and symmetry which prevails through the whole frame of material and intelligent nature, but as productive of the most momentous effects both in moral and political life. Plato and Aristotle, who disagreed almost in every other maxim of politics, are unanimous in their approbation of music, as an efficacious instrument in the formation of the public character and in conducting the state; and it was the general opinion, that whilst the gymnastic exercises rendered the constitution robust and hardy, music humanised the character, and softened those habits of roughness and ferocity by which men might otherwise have degenerated into savages. The gradations by which voices were exerted and tuned, by which the invention of one instrument succeeded to another, or by which the principles of music were collected and methodised in such a manner as to give it the form of an art and the dignity of a science, are topics so fruitful of conjecture and so void of certainty, that we must leave them to employ minds more speculative and inventions more prolific than ours, or transfer them to the History of Music as a more proper place for such disquisitions. For the amusement of the curious, Rousseau in his Musical Dictionary, Plates C and N, has transcribed some fragments of Grecian, Persian, American, Chinese, and Swiss music, with which performers may entertain themselves at leisure. When they have tried the pieces, it is imagined they will be less sanguinely fond than that author of ascribing the power of music to its affinity with the national accents where it is composed. This may doubtless have its influence; but there are other causes more permanent and less arbitrary to which it owes its most powerful and universal charms.

The music now most generally celebrated and practised is that of the Italians, or their successful imitators. The English, from the invasion of the Saxons, to that more late though lucid era in which they imbibed the art and copied the manner of the Italians, had a music which neither pleased the soul nor charmed the ear. The primitive music of the French deserves no higher panegyric. Of all the barbarous nations, the Scots and Irish seem to have possessed the most affecting original music. The first consists of a melody characterised by tenderness: it melts the soul to a pleasing pensive languor. The other is the native expression of grief and melancholy. Tassoni informs us, that in his time a prince from Scotland had imported into Italy a lamentable kind of music from his own country; and that he himself had composed pieces in the same spirit. From this expressive though laconic description, we learn, that the character of our national music was even then established; yet so gross is our ignorance and credulity, that we ascribe the best and most impassioned airs which are extant among us to David Rizzio; as if an Italian Lutanist, who had lived so short a time in Scotland, could at once, as it were by inspiration, have imbibed a spirit and composed in a manner so different from his own. It is yet more surprising that Geminiani should have entertained and published the same prejudice, upon the miserable authority of popular tradition alone; for the fact is authenticated by no better credentials. The primitive music of the Scots may be divided into the

martial, the pastoral, and the festive. The first consists either in marches, which were played before the chieftains, in imitation of the battles which they fought, or in lamentations for the catastrophes of war and the extinction of families. These wild effusions of natural melody preserve several of the rules prescribed for composition. The strains, though rude and untutored, are frequently terrible or mournful in a very high degree. The port or march is sometimes in common, sometimes in treble time; regular in its measures, and exact in the distance between its returning cadences; most frequently, though not always, loud and brisk. The pi-broch, or imitation of battles, is wild, and abrupt in its transitions from interval to interval and from key to key; various and desultory in its movements; frequently irregular in the return of its cadences; and in short, through the whole, seems inspired with such fury and enthusiasm, that the hearer is irresistibly infected with all the rage of precipitate courage, notwithstanding the rudeness of the accents by which it is kindled. To this the pastoral forms a striking contrast. Its accents are plaintive, yet soothing; its harmony generally flat; its modulations natural and agreeable; its rhythmus simple and regular; its returning cadences at equal distance; its transitions from one concinnous interval to another, at least for the most part; its movements slow, and may be either in common or treble time. It scarcely admits of any other harmony than that of a simple bass. A greater number of parts would cover the air and destroy the melody. To this we shall add what has been said upon the same subject by Dr Franklin. Writing to Lord K——, he proceeds thus:

"Give me leave, on this occasion, to extend a little the sense of your position, 'That melody and harmony are separately agreeable, and in union delightful'; and to give it as my opinion, that the reason why the Scotch tunes have lived so long, and will probably live for ever (if they escape being lifted in modern affected ornament), is merely this, that they are really compositions of melody and harmony united, or rather that their melody is harmony. I mean, the simple tunes sung by a single voice. As this will appear paradoxical, I must explain my meaning. In common acceptance, indeed, only an agreeable succession of sounds is called melody; and only the concurrence of agreeable sounds, harmony. But since the memory is capable of retaining for some moments a perfect idea of the pitch of a past sound, so as to compare it with the pitch of a succeeding sound, and judge truly of their agreement or disagreement, there may and does arise from thence a sense of harmony between the present and past sounds, equally pleasing with that between two present sounds. Now the construction of the old Scotch tunes is this, that almost every succeeding emphatical note, is a third, a fifth, an octave, or in short some note that is in concord with the preceding note. Thirds are chiefly used, which are very pleasing concords. I use the word emphatical, to distinguish those notes which have a stress laid on them in singing the tune, from the lighter connecting notes that serve merely, like grammar-articles in common speech, to tack the whole together.

"That we have a most perfect idea of a sound just past, I might appeal to all acquainted with music,

who know how easy it is to repeat a sound in the same pitch with one just heard. In tuning an instrument, a good ear can as easily determine that two strings are in unison by sounding them separately, as by sounding them together; their disagreement is also as easily, I believe, I may say more easily and better distinguished when sounded separately; for when sounded together, though you know by the beating that one is higher than the other, you cannot tell which it is. I have ascribed to memory the ability of comparing the pitch of a present tone with that of one past. But if there should be, as possibly there may be, something in the ear similar to what we find in the eye, that ability would not be entirely owing to memory. Possibly the vibrations given to the auditory nerves by a particular sound may actually continue for some time after the cause of these vibrations is past, and the agreement or disagreement of a subsequent sound become by comparison with them more discernible. For the impression made on the visual nerves by a luminous object will continue for 20 or 30 seconds."

After some experiments to prove the permanency of visible impressions, he continues thus:

"Further, when we consider by whom these ancient tunes were composed, and how they were first performed, we shall see that such harmonical successions of sounds was natural and even necessary in their construction. They were composed by the minstrels of those days, to be played on the harp accompanied by the voice. The harp was strung with wire, which gives a sound of long continuance; and had no contrivance like that of the modern harpsichord, by which the sound of the preceding note can be stopped the moment a succeeding note begins. To avoid actual discord, it was therefore necessary that the succeeding emphatic note should be a cord with the preceding, as their sounds must exist at the same time. Hence arose that beauty in those tunes that has so long pleased, and will please for ever, though men scarce know why. That they were originally composed for the harp, and of the most simple kind, I mean a harp without any half-notes but those in the natural scale, and with no more than two octaves of strings, from C to C, I conjecture from another circumstance; which is, that not one of these tunes, really ancient, has a single artificial half-note in it; and that in tunes where it is most convenient for the voice to use the middle notes of the harp, and place the key in F, there the B, which if used should be a B flat, is always omitted, by passing over it with a third. The connoisseurs in modern music will say I

have no taste: but I cannot help adding, that I believe our ancestors, in having a good song, distinctly articulated, sung to one of those tunes, and accompanied by the harp, felt more real pleasure than is communicated by the generality of modern operas, exclusive of that arising from the scenery and dancing. Most tunes of late composition, not having this natural harmony united with their melody, have recourse to the artificial harmony of a bass, and other accompanying parts. This support, in my opinion, the old tunes do not need, and are rather confused than aided by it. Whoever has heard James Oswald play them on his violincello, will be less inclined to dispute this with me. I have more than once seen tears of pleasure in the eyes of his auditors: and yet I think, even his playing those tunes would please more if he gave them less modern ornament."

As these observations are for the most part true and always ingenious, we need no other apology for quoting them at length. It is only proper to remark, that the transition in Scots music by consonant intervals, does not seem, as Dr Franklin imagines, to arise from the nature of the instruments upon which they played. It is more than probable, that the ancient British harp was not strung with wire, but with the same materials as the Welsh harps at present. These strings have not the same permanency of tone as metal; so that the sound of a preceding emphatic note must have expired before the subsequent accented note could be introduced. Besides, they who are acquainted with the manufacture of the Irish harp, know well that there is a method of discontinuing sounds no less easy and effectual than upon the harpsichord. When the performer finds it proper to interrupt a note, he has no more to do but return his finger gently upon the string immediately struck, which effectually stops its vibration.

That species of Scots music which we have distinguished by the name of festive seems now limited to reels and country-dances. These may be either in common or treble time. They most frequently consist of two strains: each of these contains eight or twelve bars. They are truly rhythmical; but the mirth which they excite seems rather to be inspired by the vivacity of the movement, than either by the force or variety of the melody. They have a manner and expression peculiar to themselves, which it is impossible to describe, and which can only be exhibited by good performers.

Thus far we have pursued the general idea of music. We shall, after the history, give a more particular detail of the science from Monsieur D'Alembert.

HISTORY OF MUSIC.

MUSIC is capable of a variety so infinite, so greatly does the most simple differ from the most complex, and so multiplied are the degrees between these two extremes, that in no age could the incidents respecting that fascinating art have been few or uninteresting. But, that accounts of these incidents should have been handed down to us, scanty and imperfect, is no matter of surprise, when we recollect that the history of music is the history only of sounds, of which writing is a very inadequate

medium; and that men would long employ themselves in the pleasing exercise of cultivating music before they possessed either the ability or the inclination to record their exertions.

No accurate traces, therefore, of the actual state of music, in the earlier ages of the world, can be discerned. Our ideas on the subject have no foundation firmer than conjecture and analogy.

It is probable, that among all barbarous nations some degree of similarity is discernible in the style of their

their music. Neither will much difference appear during the first dawns of civilization. But in the more advanced periods of society, when the powers of the human mind are permitted without obstacle to exert their native activity and tendency to invention, and are at the same time affected by the infinite variety of circumstances and situations which before had no existence, and which in one case accelerate, and in another retard; then that similarity, once so distinguishable, gives place to the endless diversity of which the subject is capable.

³ Music not the invention of any one man. The practice of music being universal in all ages and all nations, it would be absurd to attribute the invention of the art to any one man. It must have suffered a regular progression, through infancy, childhood, and youth, before it could arrive at maturity. The first attempts must have been rude and attless; perhaps the first flute was a reed of the lake.

No nation has been able to produce proofs of antiquity so indisputable as the Egyptians; it would be vain, therefore, to attempt tracing music higher than the history of Egypt.

⁴ Egyptian music. By comparing the accounts of Diodorus Siculus and of Plato, there is reason to suppose, that in very ancient times the study of music in Egypt was confined to the priesthood, who used it only on religious and solemn occasions; that, as well as sculpture, it was circumscribed by law; that it was esteemed sacred, and forbidden to be employed on light or common occasions; and that innovation in it was prohibited: but what the style or relative excellence of this very ancient music was, there are no traces by which we can form an accurate judgment. After the reigns of the Pharaohs, the Egyptians fell by turns under the dominion of the Ethiopians, the Persians, the Greeks, and the Romans. By such revolutions, the manners and amusements of the people, as well as their form of government, must have been changed. In the age of the Ptolemies, the musical games and contests instituted by those monarchs were of Greek origin, and the musicians who performed were chiefly Greek.

⁵ An Egyptian musical instrument. The most ancient monuments of human art and industry, at present extant at Rome, are the obelisks brought thither from Egypt, two of which are said to have been erected by Sesostris at Heliopolis, about 400 years before the siege of Troy. These were by the order of Augustus brought to Rome after the conquest of Egypt. One of them called guglia rotta, or the broken pillar, which during the sacking of the city in 1527 was thrown down and broken, still lies in the Campus Martius. On it is seen the figure of a musical instrument of two strings, and with a neck. It resembles much the calascione still used in the kingdom of Naples.

This curious relic of antiquity is mentioned, because it affords better evidence than, on the subject of ancient music, is usually to be met with, that the Egyptians, at so very early a period of their history, had advanced to a considerable degree of excellence in the cultivation of the arts. By means of its neck, this instrument was capable, with only two strings, of producing a great number of notes. These two strings, if tuned fourths to each other, would furnish that series of sounds called by the ancients heptachord,

which consists of a conjunct tetrachord as B, C, D, E; E, F, G, A; if tuned fifths, they would produce an octave, or two disjunct tetrachords. The calascione is tuned in this last manner. The annals of no nation other than Egypt, for many ages after the period of the obelisk at Heliopolis, exhibit the vestige of any contrivance to shorten strings during performance by a neck or finger-board. Father Montfaucon observes, that after examining 500 ancient lyres, harps, and citharas, he could discover no such thing.

Egypt indeed seems to have been the source of human intelligence, and the favourite residence of genius and invention. From that celebrated country did the Greeks derive their knowledge of the first elements of those arts and sciences in which they afterwards so eminently excelled. From Greece again did the Romans borrow their attainments in the same pursuits. And from the records of those different nations have the moderns been enabled to accomplish an improvement so wonderful in literature.

⁶ The Hermes or Mercury of the Egyptians, named Trismegistus, or thrice illustrious, who was, according to Sir Isaac Newton, the secretary of Osiris, is celebrated as the inventor of music. It has already been observed, that no one person ought strictly to be called the inventor of an art which seems to be natural to, and coeval with, the human species; but the Egyptian Mercury is without doubt intitled to the praise of having made striking improvements in music, as well as of having advanced in various respects the civilization of the people, whose government was chiefly committed to his charge. The account given by Apollodorus of the manner in which he accidentally invented the lyre, is at once entertaining and probable. "The Nile (says Apollodorus), after having overflowed the whole country of Egypt, when it returned within its natural bounds, left on the shore a great number of dead animals of various kinds, and among the rest a tortoise; the flesh of which being dried and wasted by the sun, nothing remained within the shell but nerves and cartilages, and these being braced and contracted by the drying heat became sonorous. Mercury, walking along the banks of the Nile, happened to strike his foot against this shell; and was so pleased with the sound produced, that the idea of a lyre started into his imagination. He constructed the instrument in the form of a tortoise, and strung it with the dried sinews of dead animals."

How beautiful to conceive the energetic powers of the human mind in the early ages of the world, exploring the yet undiscovered capabilities of nature, and directed to the inexhaustible store by the finger of God, in the form of accident!

The monaulos, or single flute, called by the Egyptians phoinix, was probably one of the most ancient instruments used either by them or any other nation. From various remains of ancient sculpture, it appears to have been shaped like a bull's horn, and was at first, it may be supposed, no other than the horn itself. Before the invention of flutes, as no other instrument except those of percussion were known, music must have been little more than metrical. When the art of refining and lengthening sounds was first discovered,

the power of music over mankind, from the agreeable surprise occasioned by soft and extended notes, was probably irresistible. At a time when all the rest of the world was involved in savage ignorance, the Egyptians were possessed of musical instruments capable of much variety and expression—Of this the astonishing remains of the city Thebes still subsisting afford ample evidence. In a letter from Mr Bruce, ingrossed in Dr Burney's History of Music, there is given a particular description of the Theban harp, an instrument of extensive compass, and exquisite elegance of form. It is accompanied with a drawing taken from the ruins of an ancient sepulchre at Thebes, supposed by Mr Bruce to be that of the father of Sesostris.

On the subject of this harp, Mr Bruce makes the following striking observation. "It overturns all the accounts of the earliest state of ancient music and instruments in Egypt, and is altogether, in its form, ornaments, and compass, an incontestable proof, stronger than a thousand Greek quotations, that geometry, drawing, mechanics, and music, were at the greatest perfection when this harp was made; and that what we think in Egypt was the invention of arts was only the beginning of the era of their restoration."

Indeed, when the beauty and powers of this harp, along with the very great antiquity of the painting which represents it, are considered, such an opinion as that which Mr Bruce hints at, does not seem to be devoid of probability.

It cannot be doubted that during the reigns of the Ptolemies, who were voluptuous princes, music must have been much cultivated and encouraged. The father of Cleopatra, who was the last of that race of kings, derived his title of auletes, or flute-player, from his excessive attachment to the flute. Like Nero, he used to array himself in the dress of a tibiæan, and exhibit his performance in the public musical contests.

Some authors, particularly Am. Marcellinus and M. Pau, refuse to the Egyptians, at any period of their history, any musical genius, or any excellence in the art; but the arguments used to support this opinion seem to be inconclusive, and the evidences of the opposite decision appear to be incontestable.

The sacred Scriptures afford almost the only materials from which any knowledge of Hebrew music can be drawn. In the rapid sketch, therefore, of ancient music which we mean to exhibit, a very few observations are all which can properly be given to that department of our subject.

Moses, who led the Israelites out of Egypt, was educated by Pharaoh's daughter in all the literature and elegant arts cultivated in that country. It is probable, therefore, that the taste and style of Egyptian music would be infused in some degree into that of the Hebrews. Music appears to have been interwoven through the whole tissue of religious ceremony in Palestine. The priesthood seem to have been musicians hereditarily and by office. The prophets appear to have accompanied their inspired effusions with music; and every prophet, like the present improvisatori of Italy, seems to have been accompanied by a musical instrument.

Music, vocal and instrumental, constituted a great part of the funeral ceremonies of the Jews. The pomp and expense used on these occasions advanced by N° 233.

degrees to an excessive extent. The number of flute-players in the processions amounted sometimes to several hundreds, and the attendance of the guests continued frequently for 30 days.

The Hebrew language abounds with consonants, and has so few vowels, that in the original alphabet they had no characters. It must, therefore, have been harsh and unfavourable to music. Their instruments of music were chiefly those of percussion; so that, both on account of the language and the instruments, the music must have been coarse and noisy. The vast numbers of performers too, whom it was the taste of the Hebrews to collect together, could with such language and such instruments produce nothing but clamour and jargon. According to Josephus, there were 200,000 musicians at the dedication of Solomon's temple. Such are the circumstances from which only an idea of Hebrew music can be formed; for the Jews neither ancient nor modern have ever had any characters peculiar to music; and the melodies used in their religious ceremonies have at all times been entirely traditional.

Cadmus, wish the Phœnician colony which he led into Greece, imported at the same time various arts into that country. By the assistance of his Phœnician artificers, that chief discovered gold in Thrace and copper at Thebes. At Thebes that metal is still termed cadmia. Of these materials, and of iron, they formed to themselves armour and instruments of war. These they struck against each other during their dances at sacrifices, by which they first obtained the idea of music. Such is the account given of the origin of that species of music in Greece produced by instruments of percussion. The invention of wind instruments in Greece is attributed to Minerva; and to the Grecian Mercury is assigned, by the poets and historians of that country, the honour of many discoveries probably due to the Egyptian Hermes, particularly the invention of stringed instruments. The lyre of the Egyptian Mercury had only three strings; that of the Grecian seven: the last was perhaps no more than an improvement on the other. When the Greeks desired a prince or hero of their own country, they usually assigned him an Egyptian name, and with the name bestowed on their new divinity all the actions, attributes, and rites of the original.

The Grecian lyre, although said to have been invented by Mercury, was cultivated principally by Apollo, who first played upon it with method, and accompanied it with the voice. The celebrated contest between him and Marsyas is mentioned by various authors; in which, by conjoining the voice with his lyre (a combination never before attempted), his music was declared superior to the flute of Marsyas. The progress of the lyre, according to Diodorus Siculus, is the following. "The muses added to the Grecian lyre the string called mese; Linus that of lichanos; and Orpheus and Thamyras those strings which are the Grecian named hypate and parhypate." It has been already mentioned, that the lyre invented by the Egyptian Mercury had but three strings; by putting these circumstances together, we may perhaps acquire some knowledge of the progress of music, or at least of the extension of its scale in the highest antiquity. Mese, in the Greek music, is the fourth sound of the second tetrachord.

tetrachord of the great system and first tetrachord invented by the ancients, answering to our A, on the fifth line in the base. If this found then was added to the former three, it proves that the most ancient tetrachord was that from E in the base to A; and that the three original strings in the Mercurian and Apollonian lyre were tuned E, F, G; which the Greeks call hypate meson, parhypate meson, and meson diatone; the addition, therefore, of mes to these completed the first and most ancient tetrachord E, F, G, A. The string lichanos again being added to these, and answering to our D on the third line in the base, extended the compass downwards, and gave the ancient lyre a regular series of five sounds. The two strings hypate and parhypate, corresponding with our B and C in the base, completed the heptachord or seven sounds b, c, d, e, f, g, a; a compass which received no addition till after the days of Pindar.

It might perhaps be expected, that in a history of Greek music something ought to be said concerning the muses Apollo, Bacchus, and the other gods and demi-gods, who in the mythology of that country appear to have promoted and improved the art. But such a discussion would be too diffusive, and involve too much foreign matter for the plan we have chosen to adopt. We cannot avoid, however, making a few observations on the poems of Homer, in so far as connected with our subject. It has been imagined, with much appearance of probability, that the occupation of the first poets and musicians of Greece resembled that of the Celtic and German bards and the sculds of Iceland and Scandinavia. They sung their poems in the streets of cities and in the palaces of princes. They were treated with high respect, and regarded as inspired persons. Such was the employment of Homer. His poems, so justly celebrated, exhibit the most authentic picture that can be found in the musals of antiquity, although perhaps somewhat highly coloured, of the times of which he wrote and in which he lived. Music is always named throughout the Iliad and Odyssey with rapture; but as in these poems no mention is made of instrumental music unaccompanied with poetry and singing, a considerable share no doubt of the poet's praises is to be attributed to the poetry. The instruments most frequently named are the lyre, the flute, and the syrinx. The trumpet appears not to have been known at the siege of Troy, although it had come to be in use in the days of Homer himself. From the time of Homer till that of Sappho, there is almost a total blank in literature. Only a few fragments remain of the works of those poets and musicians whose names are preserved as having flourished between those periods (+). During the century which elapsed between the days of Sappho and those of Anacreon, no literary productions are preserved entire.—From Anacreon to Pindar there is another chasm of near a century. Subsequent to this time, the works still extant of the three great tragic poets, Æschylus, Sophocles, and Euripides, together with those of

VOL. XII. Part II.

Plato, Aristotle, Aristoxenus, Euclid, Theocritus, Callimachus, Polybius, and many others, produced all within a space less than 300 years, distinguish this illustrious and uncommon period as that in which the whole powers of genius seem to have been exerted to illuminate and instruct mankind in future ages. Then it was that eloquence, poetry, music, architecture, history, painting, sculpture, like the spontaneous blossoms of nature, flourished without the appearance of labour or of art.

The poets, as well epic as lyric and elegiac, were all likewise musicians; so strictly connected were music and poetry for many ages. It would afford amusement to collect the biographical anecdotes of these favourites of genius, and to assign to each the respective improvements made by him in music and poetry; but our limits do not admit of so extensive a disquisition; for which, therefore, reference must be made to the editors and commentators of these authors, and to the voluminous histories of music lately published.

The invention of notation and musical characters marked a distinguished era in the progress of music. There are a diversity of accounts respecting the person to whom the honour of that invention is due; but the evidences seem to preponderate in favour of Terpander, a celebrated poet and musician, to whose genius music is much indebted. He flourished about the 27th Olympiad, or 671 years before Christ.

Before that valuable discovery, music being entirely traditional, must have depended much on the memory and taste of the performer.

There is an incident mentioned in the accounts handed down to us of the Olympic games, which may serve in some degree to mark the character of music at the time in which it happened. Lucian relates that a young flute-player named Harmonides, at his first public appearance in these games, began a solo with so violent a blast, on purpose to surprise and elevate the audience, that he breathed his last breath into his flute, and died on the spot. When to this anecdote, wonderful to us, and almost incredible, is added the circumstance, that the trumpet-players at these public exhibitions expressed an excess of joy when they found their exertions had neither rent their cheeks nor burst their blood-vessels, some idea may be formed of the noisy and vociferous style of music which then pleased; and from such facts only can any opinion be obtained of the actual state of ancient music.

In whatever manner the flute was played on, there is no doubt that it was long in Greece an instrument of high favour, and that the flute-players were held in much estimation. The flute used by Ismenias, a celebrated Theban musician, cost at Corinth three talents, or L. 581, 5 s. If, says Xenophon, a bad flute-player would pass for a good one, he must, like the great flute-players, expend large sums on rich furniture, and appear in public with a great retinue of servants.

The ancients, it appears, were not less extravagant in gratifying the ministers of their pleasures than our-

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selves

(+) Hesiod lived so near to Homer, that it has been disputed which of them is the most ancient. It is now, we believe, universally admitted, that the palm of antiquity is due to Homer; but we consider them as having both flourished in the same era.

selves. Amœbeus, a harper, was paid an Attic talent, or L. 193, 159. per day for his performance (†).

It is proper to add, that the celebrated musicians of Greece who performed in public were of both sexes; and that the beautiful Lamia, who was taken captive by Demetrius, in the sea engagement in which he vanquished Ptolemy Soter, and who herself captivated her conqueror, as well as many other elevated female spirits, are recorded by ancient authors in terms of admiration, and of whom, did our limits here admit of biography, we would treat with pleasure. The philosophers of Greece, whose capacious minds grasped every other object of human intelligence, were not inattentive to the theory of music, or the philosophy of sound. This department of science became the source of various sects, and of much diversity of opinion.—The founders of the most distinguished sects were Pythagoras and Aristoxenus. Of their theories, mention is made in the Appendix to this article.

Like every other people, the Romans, from their first origin as a nation, were possessed of a species of music which might be distinguished as their own. It appears to have been rude and coarse, and probably was a variation of the music in use among the Etruscans and other tribes around them in Italy: but as soon as they began to open a communication with Greece, from that country, with their arts and philosophy, they borrowed also their music and musical instruments. No account, therefore, of Roman music is to be expected that would not be a repetition of what has been said on the subject of the music of Greece.

The excessive vanity of Nero with respect to music, displayed in his public contentions for superiority with the most celebrated professors of the art in Greece and Rome, is known to every one conversant in the history of Rome. The solicitude with which that detestable tyrant attended to his voice is curious, and will throw some light on the practices of singers in ancient times. He was in use to lie on his back, with a thin plate of lead on his stomach. He took frequent emetics and cathartics, abstained from all kinds of fruit and such meats as were held to be prejudicial to singing. Apprehensive of injuring his voice, he at length desisted from haranguing the soldiery and the senate; and after his return from Greece established an officer (Phonascus) to regulate his tones in speaking.

Most nations have consented in introducing music into their religious ceremonies. That art was early admitted into the rites of the Egyptians and Hebrews; and that it constituted a considerable part of the Grecian and Roman religious service, appears from the writings of many ancient authors. The same pleasing art soon obtained an introduction into the Christian church, as the Acts of the Apostles discover in many passages. There remain no specimens of the music employed in the worship of the primitive Christians; but probably it was at first the same with that used in the Pagan rites of the Greeks and Romans. The practice of chanting the psalms was introduced into the western churches by St. Ambrose, about 350 years after Christ. In the year 600, the method of chant-

ing was improved by St. Gregory the Great. The Ambrosian chant contained four modes. In the Gregorian the number was doubled. So early as the age of Constantine the Great, prior to either of the periods last mentioned, when the Christian religion first obtained the countenance of power, instrumental music came to be introduced into the service of the church. In England, according to bishop Stillingfleet, music introduced was employed in the church-service, first by St. Augustin into the time, and afterwards much improved by St. Dunstan, who was himself an eminent musician, and who is said to have first furnished the English churches and convents with the organ. The organ, the most majestic of all instruments, seems to have been an improvement of the hydraulic or water organ of the Greeks.—The first organ seen in France was sent from Constantinople in 757, as a present to king Pepin from the emperor Constantine Copromymus VI. In Italy, Germany, and England, that instrument became frequent during the 10th century.

During the dark ages no work of genius or taste in any department of science seems to have been produced in any part of Europe; and except in Italy, where the cultivation of music was rather more the object of attention, that art was neglected equally with all others. There has always been observed a correspondence in every country between the progress of music and the cultivation of other arts and sciences. In the middle ages, therefore, when the most fertile provinces of Europe were occupied by the Goths, Huns, Vandals, and other barbarous tribes, whose language was as harsh as their manners were savage, little perfection and no improvement of music is to be looked for. Literature, arts, and refinements, were encouraged more early at the courts of the Roman pontiffs than in any other country; and owing to that circumstance it is, that the scale, the counterpoint, the best melodies, the dramas religious and secular, the chief graces and elegancies of modern music, have derived their origin from Italy. In modern times, Italy has been to the rest of Europe what ancient Greece was to Rome. The Italians have aided the civilization of their conquerors, and enlightened the minds of those whose superior prowess had enslaved them.

Having mentioned counterpoint, it would be improper not to make one or two observations on an invention which is supposed to have been the source of great innovation in the practice of music. Counterpoint, or music in parts, seems to be an invention purely modern. The term harmony meant in the language of antiquity what is now understood by melody. Guido, a monk of Arezzo in Tuscany, is, in the general opinion, supposed to have entertained the first idea of counterpoint about the year 1022: an art which, since his time, has experienced gradual and imperceptible improvements, far exceeding the powers and comprehension of any one individual. The term counterpoint, or contra punctum, denotes its own etymology and import. Musical notation was at one time performed by small points; and the present mode is only

(†) Roscius gained 500 sestertia, or L. 4036: 9: 2 d. Sterling per annum.

only an improvement of that practice. Counterpoint, therefore, denotes the notation of harmony or music in parts, by points opposite to each other. The improvements of this important acquisition to the art of music kept pace at first with those of the organ; an instrument admirably adapted to harmony: And both the one and the other were till the 13th century employed chiefly in sacred music. It was at this period that secular music began to be cultivated.

Before the invention of characters for time, music in parts must have consisted entirely of simple counterpoint, or note against note, as is still practised in psalmody. But the happy discovery of a time-table extended infinitely the powers of combined sounds. The ancients had no other resource to denote time and movement in music except two characters (— ∪), equivalent to a long and a short syllable. But time is of such importance in music, that it can impart meaning and energy to the repetition of the same sound: without it variety of tones has no effect with respect to gravity and acuteness. The invention of the time-table is attributed by almost all the writers on music of the last and present century to John de Muris, who flourished about the year 1330. But in a manuscript of John de Muris himself, bequeathed to the Vatican library by the Queen of Sweden, that honour seems to be yielded to Magister Franco, who appears to have been alive as late as 1083. John de Muris, however, who there is some cause to believe was an Englishman, though not the inventor of the cantus mensurabilis, did certainly by his numerous writings greatly improve it. His tract on the Art of Counterpoint is the most clear and useful essay on the subject of which those times can boast.

In the 11th century, during the first crusade, Europe began to emerge from the barbarous stupidity and ignorance which had long overwhelmed it. While its inhabitants were exercising in Asia every species of rapine and pious cruelty, art, ingenuity, and reason, insensibly civilized and softened their minds. Then it was that the poets and songsters, known by the name of Troubadours, who first appeared in Provence, instituted a new profession; which obtained the patronage of the count of Poictou, and many other princes and barons, who had themselves cultivated music and poetry with success. At the courts of their munificent patrons the troubadours were treated with respect. The ladies, whose charms they celebrated, gave them the most generous and flattering reception. The success of some inspired others with hopes, and excited exertions in the exercise of their art; impelling them towards perfection with a rapidity which the united force alone of emulation and emolument could occasion. These founders of modern versification, construing their songs on plans of their own Classical authority, either through ignorance or design, was entirely disregarded. It does not appear, however, during the cultivation and favour of Provençal literature, that any one troubadour so far outstripped the rest as to become a model of imitation. The progress of taste must ever be impeded by the ignorance and caprice of those who cultivate an art without science or principles.

During almost two centuries after the arrangement of the scale attributed to Guido, and the invention of

the time-table ascribed to Franco, no remains of secular music can be discovered, except those of the troubadours or Provençal poets. In the simple tunes of these bards no time indeed is marked, and but little variety of notation appears: it is not difficult, however, to discover in them the germs of the future melodies, as well as the poetry of France and Italy. Had the poetry and music of the troubadours been treated of in an agreeable manner by the writers who have chosen that subject, it would have been discovered to be worthy of attention: the poetry, as interesting to literature; the melody to which it was sung, as curious to the musical historian.—Almost every species of Italian poetry is derived from the Provençals. Air, the most captivating part of secular vocal music, seems to have had the same origin. The most ancient strains that have been spared by time, are such as were set to the songs of the troubadours. The Provençal language began to be in favour with poets about the end of the 10th century. In the 12th it became the general vehicle, not only of poetry, but of prose, to all who were ignorant of Latin. And these were not the laity only. At this period violars, or performers on the vielle or viol, juglars or flute-players, musars or players on other instruments, and comics or comedians, abounded all over Europe. This swarm of poet-musicians, who were formerly comprehended in France under the general title of jongleurs, travelled from province to province, singing their verses at the courts of princes. They were rewarded with cloaths, horses, arms, and money. Jongleurs or musicians were employed often to sing the verses of troubadours, who themselves happened to be deficient in voice or ignorant of music. The term troubadour, therefore, implies poetry as well as music. The jongleurs, menetriers, strollers, or minstrels, were frequently musicians, without any pretensions to poetry. These last have been common at all times; but the troubadour or bard has distinguished a particular profession, either in ancient or modern times, only during the early dawns of literature.

In the 13th century the songs were on various subjects; moral, merry, amorous: and at that time melody seems to have been little more than plain song or chanting. The notes were square, and written on four lines only like those of the Romish church in the cliff C, and without any marks for time. The movement and embellishment of the air depended on the abilities of the finger. Since that time, by the cultivation of the voice modern music has been much extended, for it was not till towards the end of St Lewis's reign that the fifth line began to be added to the slave. The finger always accompanied himself with an instrument in unison.

As the lyre is the favourite instrument in Grecian poetry, so the harp held the same place in the estimation of the poets who flourished in the period of which we speak. A poet of the 14th century, Mac-hau, wrote a poem on the subject of the harp alone; in which he assigns to each of its 25 strings an allegorical name; calling one liberality, another wealth, &c.

The instrument which frequently accompanied, and indeed disputed the pre-eminence with the harp, was or viola. Till the 16th century this instrument was furnished with frets; after that period it was reduced

to four strings: and still under the denomination of violin holds the first place among treble instruments. The viol was played with a bow, and differed entirely from the vielle, the tones of which were produced by the friction of a wheel; the wheel performed the part of a bow.

British harpers were famous long before the conquest. The bounty of William of Normandy to his fisculator or bard is recorded in the Doomsday book. The harp seems to have been the favourite instrument in Britain for many ages, under the British, Saxon, Danish, and Norman kings. The fiddle, however, is mentioned so early as 1200 in the legendary life of St. Christopher. The ancient privileges of the minstrels at the fairs of Chester are well known in the history of England.

The extirpation of the bards of Wales by Edward I. is likewise too familiar an incident to be mentioned here. His persecuting spirit, however, seems to have been limited to that principality; for we learn, that at the ceremony of knighting his son, a multitude of minstrels attended.

In 1315, during the reign of Edward II. such extensive privileges were claimed by the minstrels, and so many dissolute persons assumed that character, that it became necessary to restrain them by express laws.

The father of our genuine poetry, who in the 14th century enlarged our vocabulary, polished our numbers, and with acquisitions from France and Italy augmented our store of knowledge (Chaucer), entitles one of his poems The History of St. Cecilia; and the celebrated patroness of music must no doubt be mentioned in a history of the art. Neither in Chaucer, however, nor in any of the histories or legendary accounts of this Saint, does any thing appear to authorise the religious veneration paid to her by the votaries of music; nor is it easy to discover whence it has arisen. As an incident relative to the period of which we speak, it may be mentioned, that, according to Spelmann, the appellation of Doctor was not among the degrees granted to graduates in England sooner than the reign of King John, about 1207; although, in Wood's history of Oxford, that degree is said to have been conferred, even in music, in the reign of Henry II. It is known that the title was created on the continent in the 12th century; and as, during the middle ages, music was always ranked among the seven liberal arts, it is likely that the degree was extended to it.

After the invention of printing, an art which has tended to disseminate knowledge with wonderful rapidity among mankind, music, and particularly counterpoint, became an object of high importance. The names of the most eminent composers who flourished in England, from that time to the Reformation, were, Fairfax, William of Newark, Sheryngham, Turges, Danisler, Tudor, Taverner, Tye, Johnson, Parsons; to whom may be added John Marbeck, who set the whole English cathedral service to music.

Before this period Scottish music had advanced to a high degree of perfection. James I. was a great composer of airs to his own verses; and may be considered as the father of that plaintive melody which in Scotch tunes is so pleasing to a tale not vitiated by modern affectation. Besides the testimony of Forcham

and Majer, who may be suspected of being under the influence of national prejudice, we have that of Alessandro Tessani, to the musical skill of that accomplished prince. "Among us moderns (says this foreigner) we may reckon James king of Scotland, who not only composed many sacred pieces of vocal music, but also of himself invented a new kind of music, plathiree and melanoboly, different from all others; in which he has been imitated by Carlo Gesualdo prince of Venetia, who in our age has improved music with new and admirable inventions."

Under such a genius in poetry and music as king James I. it cannot be doubted that the national music must have been greatly improved. We have seen that he composed several anthems, or vocal pieces of sacred music, which shows that his knowledge of the science must have been very considerable. It is likewise known, that organs were by him introduced into the cathedrals and abbeys of Scotland, and choir-service brought to such a degree of perfection, as to fall little short of that established in any country of Europe.—By an able antiquary † of the present age, the great era of music, as of poetry, in Scotland, is supposed to have been from the beginning of the reign of James I. down to the end of the reign of James V. During that period flourished Gavin Douglas bishop of Dun-
† See Tatler's Dissertation on the Scotch Music, vol. i. of Transactions of the Society of Antiquaries in Scotland.
keld, Ballenden archdeacon of Murray, Dunbar, Henryson, Scott, Montgomery, Sir David Lindsay, and many others, whose fine poems have been preserved in Baron's Collection, and of which several have been published by Alma Ramsay in his Evergreen.

Before the Reformation, as there was but one religion, there was but one kind of sacred music in Europe, plain chant, and the descent built upon it.—That music likewise was applied to one language only, the Latin. On that account, the compositions of Italy, France, Spain, Germany, Flanders, and England, kept pace in a great degree with each other in style and excellence. All the arts seem to have been the companions, if not the produce, of successful commerce, and to have pursued the same course. Like commerce, they appeared first in Italy, then in the Hanseatic towns, next in the Netherlands; and during the 16th century, when commerce became general, in every part of Europe.

In the 16th century music was an indispensable part of polite education; all the princes of Europe were instructed in that art. There is a collection preserved in manuscript called Queen Elizabeth's Virginal Book. If her majesty was able to execute any of the pieces in that book, she must have been a great player; a month's practice would not have been sufficient for any master now in Europe to enable him to play one of them to the end. Tallis, singularly profound in musical composition, and Bird his admirable scholar, were two of the authors of this famous collection.

During the reign of Elizabeth, the genius and learning of the British musicians were not inferior to any on the continent; an observation scarcely applicable at any other period of the history of this country. Sacred music was the principal object of study all over Europe.

The most eminent musical theorists of Italy, who flourished in the 16th century, were, Franchinus Gaffurius, or Gafforio of Lode, Pietro Aaron of Florence,

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St. Cecilia.

27
Origin of the degree of Mus. D.

28
Scottish music.

29
In the 16th century music was an indispensable part of polite education.

³⁰ Eminent musicians in Italy during the 16th century. rence, Lodovico Fogliano, Giov. Spataro, Giov. Maria da Terentio Lanfranco, Stefano Uaneo, Anton. Francifco Done, Luigi Dentice, Nicolo Vicentino, and Giofello Zarlino, the most general, voluminous, and celebrated theorist of that period.

Vincentio Galilei, a Florentine nobleman, and father of the great Galileo Galilei.

Maria Artufe of Bologna, Orafeo Tegrini, Pietro Pontio, and Lodovico Zacconi.

The principal Roman authors were, Giovanni Ammuccia, Giovanni Pierluigi da Palestrina, justly celebrated; Ruggiero Giovanelli, Luca Marcuzio, who brought to perfection madrigals, the most cheerful species of secular music.

Of the Venetians, Adrian Willeri is allowed to be at the head.

At the head of the Neapolitans is deservedly placed Rocco Rodio.

At Naples, too, the illustrious dilettante, Don Carlo Gesualdo prince of Venosa, is highly celebrated. He seems, however, to have owed much of his fame to his high rank.

Lombardy would also furnish an ample list of eminent musicians during the 16th century, of whom our limits will not admit of a particular enumeration:—The chief of them were, Costanzo Porta, Gafoldi, Biffi, Cima, Vocchi, and Monteverde.

At Bologna, besides Artusi already mentioned, Andrea Rota of the same city appears to have been an admirable contrapunctist.

Francifco Corteccia, a celebrated organist and composer, and Alessandro Strigglio, a lutanist and voluminous composer, were the most eminent Florentines.

³¹ In Germany. The inhabitants of the extensive empire of Germany have long made music a part of general education.—They hold the place, next Italy, among the most successful cultivators of the art. During the 16th century, their most eminent composers of music and writers on the subject were, Geo. Reifchius, Michael Roswick, Andreas Ornithorparchus, Paul Hofheimer, Luspeinius, Henry Loris or Lorit, Faber, Fink, Hofman, and many others whom it would be tedious to mention; and for a particular account of whose treatises and compositions we must refer to more voluminous histories of music.

³² In France. In France, during the 16th century, no art except the art of war made much progress in improvement.—Ronsard, Baif, Goudimel, Claud le Jeune, Caurroy, and Maudit, are the chief French musicians of that period.

³³ Spain. In Spain, music was early received into the circle of sciences in the universities. The musical professorship at Salamanca was founded and endowed by Alfonso the Wise, king of Castile.

One of the most celebrated of the Spanish musicians was Francis Salinas, who had been blind from his infancy. He was a native of Burgos.

D. Cristoforo Morales, and Tomaso Lodovico da

Vittorio, deserve likewise to be mentioned; and to mention them is all we can attempt; the purpose of which is, to excite more minute inquiry by those who may choose to investigate the subject particularly.

³⁴ The Netherlands, likewise, during the period of the Netherlands, which we have been speaking, produced many eminent composers; of whom we may mention Verletot, Gombert, Arkadelt, Berehem, Richefort or Ricciafort, Cregodon Le Cock or Le Coq, Canis, Jacob Clemens Non Papa, Pierre Manchicourt, Baiton, Keri. Rore, Orlando di Lasso, and his sons Ferdinand and Rodolph.

³⁵ Musical composers who acquired fame in England, were, Dr. Na-
thanael Giles, Thomas Tomkins, and his son of the same name; Elway Bevin, Orlando Gibbons, Dr. William Child, Adrian Batten, Martin Pierfon, William Lawes, Henry Lawes, Dr. John Wilson, John Hilton, John Playford, Captain Henry Cook, Pelham Humphrey, John Blow, William Turner, Dr. Christopher Gibbons, Benjamin Rogers, and Henry Purcell. Of these, Orlando Gibbons, Pelham Humphrey, and Henry Purcell, far excelled the rest.

About the end of the reign of James I. a music-lecture or professorship was founded in the university of Oxford by Dr. William Hyechin.

In the reign of Charles I. a charter was granted to the musicians of Westminster, incorporating them, as the king's musicians, into a body politic, with powers to prosecute and fine all who, except themselves, should "attempt to make any benefit or advantage of music in England or Wales:" powers which in the subsequent reign were put in execution.

About the end of the reign of Charles II. a passion seems to have been excited in England for the violin, and for pieces expressly composed for it, in the Italian manner (*). Prior to 1600, there was little other music except masses and madrigals, the two principal divisions of sacred and secular music; but from that time to the present, dramatic music becomes the chief object of attention. The music of the church and of the chamber continued indeed to be cultivated in Italy with diligence, and in a learned and elaborate style, till near the middle of the century; yet a revolution in favour of melody and expression was preparing, even in sacred music, by the success of dramatic composition, consisting of recitation and melodies for a single voice. Such melodies began now to be preferred to music of many parts; in which canons, fugues, and full harmony, had been the productions which chiefly employed the master's study and the hearer's attention.

³⁶ So late as the beginning of the present century, according to Riccoboni, the performers in the operas of Germany, particularly at Hamburg, "were all tradesmen or handicrafts; your shoemaker (says he) was often the first performer on the stage; and you might have bought fruit and sweetmeats of the same girls,

(*) The most celebrated violin players of Italy, from the 16th century to the present time, have been Farina, M. Angelo Rossi, Bassani the violin-master of Corelli, the admirable Angelico Corelli himself, Torelli, Alberti, Albenoni, Tefarini, Vivaldi, Geminiani one of the most distinguished of Corelli's scholars, Tartini, Veracini, Barbella, Locatelli, Ferrari, Martini, Boccherini, and Giardini.

girls, whom the night before you had seen in the characters of Armida or Semiramis. Soon, however, the German opera arose to a more respectable situation; and even during the 17th century many eminent composers flourished in that country.

The list of great musicians which France produced during the early part of the same century is not numerous. Music seems to have been but little cultivated in that country, till the operas of Lulli, under the powerful patronage of Louis XIV. excited public attention.

The favourite singing-master and composer of France, about the middle of the 17th century, was Michael Lambert. John Baptist Lulli, soon after this time, rose from the rank of a menial servant to fame, opulence, and nobility, by his skill in musical compositions. The celebrated singer La Rocheis was taught singing and acting by Lulli.

La Maupin the successor of La Rocheis, on account of her extraordinary character and romantic adventures, deserves to be mentioned. She was equally fond of both sexes, fought and loved like a man, resisted and fell like a woman. She eloped from her husband with a fencing-master, of whom she learnt the small sword; she became an excellent fencer. At Marfeilles she became enamoured of a young lady, whom she seduced: on account of this whimsical affection the lady was by her friends confined in a convent. La Maupin obtained admission into the same convent as a novice: she set fire to the convent, and in the confusion carried off her favourite. At Paris, when she appeared on the stage in 1695, DuMont a singer having affronted her, she put on mens clothes, and inflicted on his drawing his sword and fighting her: when he refused, she caned him, and took from him his watch and snuff-box as trophies of her victory. At a ball given by Monsieur brother of Louis XIV. she again put on mens clothes; and having behaved impertinently to a lady, three of the lady's friends, supposing the Maupin to be a man, called her out: she killed them all; and returning coolly to the ball, told the story to Monsieur, who obtained her pardon. She became afterwards mistress to the elector of Bavaria. This prince quitting her for the countess of Arcos, sent her by the count, husband of that lady, a purse of L. 40,000 livres: she threw it at the count's head, telling him, it was a recompence worthy of such a scoundrel and cuckold as himself. At last, seized with a fit of devotion, she recalled her husband, and spent the remainder of her life in piety. She died in 1707 at the age only of 34.

The English musician whom we last mentioned was the celebrated Purcell: after his time the chief composers for the church were Clarke, Dr Holden, Dr Greygton, Tucker, Aldrich, Golwin, Weldon, Dr Crofts, Dr Green, Boyce, and Nares; to whom may be added John Stanley, who attained high proficiency in music, although from two years old totally deprived of sight.

The annals of modern music have hitherto furnished no event so important to the progress of the art as the invention of recitative or dramatic melody; a style of music which resembles the manner of the ancient rhapsodists.

The Orfeo of Politian was the first attempt at mu-

fical drama. It was afterwards perfected by Metastasio. No musical dramas similar to those afterwards known by the names of opera and oratorio, had existence in Italy before the beginning of the 17th century. It was above the 1600, or a little before that time, that eunuchs were first employed for singing in Italy.

There seem to have been no singing eunuchs in ancient times, unless the galli or archigalli, priests of Cybele, were such. Castration has, however, at all times been practised in eastern countries, for the purpose of furnishing to tyrannic jealousy guards of female chastity; but never, so far as modern writers on the subject have discovered, merely to preserve the voice, till about the end of the 16th century.

At Rome, the first public theatre opened for the exhibition of musical dramas, in modern times, was il Torre de Nona, where in 1671 Gialone was performed. In 1679, the opera of Deu è Amore, set by the famous organist Bernardo Pasquini, was represented at Nilla Sala de Signori Capranica; a theatre which still subsists. In the year 1680, L'Onesta negli Amore was exhibited; the first dramatic composition of the elegant, profound, and original Alessandro Scarlatti.

The inhabitants of Venice have cultivated and encouraged the musical drama with more zeal and diligence than the rest of Italy, during the end of the last and beginning of the present century; yet the opera was not established in Venice before the year 1637; in that year the first regular drama was performed: it was Andromeda.

In 1680 the opera of Berenice was exhibited at Padua with such astonishing splendour as to merit notice. There were choruses of 100 virgins, 100 soldiers, 100 horsemen in iron armour, 40 cornets of horse, 6 trumpeters on horseback, 6 drummers, 6 ensigns, 6 sackbuts, 6 great flutes, 6 mistrels playing on Turkish instruments, 6 others on octave flutes, 6 pages, 3 sergeants, 6 cymbalists. There were 12 huntsmen, 12 groom, 6 coachmen for the triumph, 6 others for the procession, 2 lions led by two Turks, 2 elephants by two others; Berenice's triumphal car drawn by 4 horses, 6 other cars with prisoners and spoils drawn by 12 horses, 6 coaches. Among the scenes and representations in the first act were, a vast plain with two triumphal arches, another plain with pavilions and tents, and a forest for the chase: in act third, the royal dressing-room completely furnished, stables with 100 live horses, portico adorned with tapestry, and a stupendous palace in perspective. At the end of the first act were representations of every kind of chase, wild boar, stag, deer, bears. At the end of the third act, an enormous globe, descended as from the sky, divided itself into other globes suspended in the air, and ornamented with emblematical figures of time, fame, honour, &c.

Early in the last century, machinery and decoration usurped the importance due to poetry and music in such exhibitions.

Few instances occur of musical dramas at Naples till the beginning of the present century. Before the time of the elder Scarlatti, it seems as if Naples had been less fertile in great contrapuntists, and less diligent in the cultivation of dramatic music, than any other state of Italy. Since that time all the rest of Europe

Europe has been furnished with composers and performers from that city.

The word opera seems to have been familiar to English poets from the beginning of the last century. Stilo recitativo, a recent innovation even in Italy, is mentioned by Ben Johnson so early as 1617. From this time it was used in masques, occasionally in plays, and in cantatas, before a regular drama wholly set to music was attempted. By the united abilities of Quinault and Lulli, the opera in France had arisen to high favour. This circumstance afforded encouragement to several attempts at dramatic music in England by Sir William D'Avenant and others, before the music, language, or performers of Italy were employed on our stage. Pieces, styled dramatic operas, preceded the Italian opera on the stage of England. These were written in English, and exhibited with a profuse decoration of scenery and habits, and with the best singers and dancers that could be procured: Plyche and Cinco, are entertainments of this kind: the Tempest and Macbeth were acted with the same accompaniments.

During the 17th century, whatever attempts were made in musical drama, the language sung was always English. About the end of that century, however, Italian singing began to be encouraged, and vocal as well as instrumental musicians from that country began to appear in London.

The first musical drama, performed wholly after the Italian manner in recitative for the dialogue or narrative parts, and measured melody for the airs, was Arfinoe queen of Cyprus, translated from an Italian opera of the same name, written by Stanzani of Bologna. The English version of this opera was set to music by Thomas Clayton, one of the royal band, in the reign of William and Mary. The singers were all English, Messrs Hughes, Leveredge, and Cook; Mrs Tofts, Mrs Crofs, and Mrs Lyndsey. The translation of Arfinoe, and the music to which it is set, are execrable; yet such is the charm of novelty, that this miserable performance, deserving neither the name of a drama by its poetry, nor of an opera by its music, sustained 24 representations, and the second year 11.

Operas, notwithstanding their deficiencies in poetry, music, and performance (no foreign composer or eminent singer having yet arrived), became so formidable to our actors at the theatres, that it appears from the Daily Courant, 14th January 1707, a subscription was opened "for the encouragement of the comedians acting in the Haymarket, and to enable them to keep the diversion of plays under a separate interest from operas."

Mr Addison's opera of Rosamond appeared about this time; but the music set by Clayton is so contemptible, that the merit of the poetry, however great, could not of itself long support the piece. The choice of so mean a composer as Clayton, and Mr Addison's partiality to his abilities, betray a want of musical taste in that elegant author.

The first truly great singer who appeared on the stage of Britain was Cavaller Nicolino Grimaldi, commonly known by the name of Nicolini. He was a Neapolitan; and though a beautiful singer indeed, was still more eminent as an actor. In the Tatler, no 115, the elegance and propriety of his action are

particularly described. Recently before his appearance, Valentini Urbani, and a female singer called The Baroness, arrived. Margarita de l'Epini, who afterwards married Dr Pepusch, had been in this country some time before.

The first opera performed wholly in Italian, and by Italian singers, was Almahide. As at present, so at that time, operas were generally performed twice a-week.

The year 1710 is distinguished in the annals of music by the arrival in Britain of George Frederick Handel. Handel had been in the service of the elector of Hanover, and came first to England on a visit of curiosity. The fame of this great musician had penetrated into this country before he himself arrived in it; and Aaron Hill, then in the direction of the Haymarket theatre, instantly applied to him to compose an opera. It was Rinaldo; the admirable music of which he produced entirely in a fortnight. Soon after this period appeared, for the first time as an opera singer, the celebrated Mrs Anastasia Robinson. Mrs Robinson, who was the daughter of a portrait painter, made her first public exhibitions in the concerts at York-buildings; and acquired so much the public favour, that her father was encouraged to take a house in Golden Square, for the purpose of establishing weekly concerts and assemblies, in the manner of Conversazioni, which became the resort of the most polite audiences.

Soon after Mrs Robinson accepted of an engagement at the Opera, where her salary is said to have been L. 1000, and her other emoluments equal to that sum. She quitted the stage in consequence of her marriage with the gallant earl of Peterborough, the friend of Pope and Swift. The eminent virtues and accomplishments of this lady, who died a few years ago at the age of 88, entitled her to be mentioned even in a compend too short for biography. The conducting of the opera having been found to be more expensive than profitable, it was entirely suspended from 1717 till 1720, when a fund of L. 50,000 for supporting and carrying it on was subscribed by the first personages of the kingdom. The subscribers, of whom king George I. was one for L. 1000, were the opera formed into a society, and named The Royal Academy of Music. Handel was commissioned to engage the performers: for that purpose he went to Dresden, where Italian operas were at that time performed in the most splendid manner at the court of Augustus elector of Saxony, then king of Poland. Here Handel engaged Senesino-Berenstadt, Boschi, and the Duranti.

In the 1723, the celebrated Francesca Cuzzoni appeared as a first-rate singer; and two years afterwards arrived her distinguished rival Signora Faustina Bordoni.

In a cantabile air, though the notes Cuzzoni added were few, she never lost an opportunity of enriching the cantilena with the most beautiful embellishments. Her shake was perfect. She possessed a creative fancy; and she enjoyed the power of occasionally accelerating and retarding the measure in the most artificial and able manner, by what is in Italy called tempo rubato. Her high notes were unrivalled in clearness and sweetness. Her intonations were so just and so fixed, that

it seemed as if she had not the power to sing out of tune.

Faustina Bordoni, wife of the celebrated Saxon composer Haffne, invented a new kind of singing, by running divisions, with a neatness and velocity which astonished all who heard her. By taking her breath imperceptibly, she had the art of sustaining a note apparently longer than any other finger. Her beats and trills were strong and rapid; her intonation perfect. Her professional perfections were enhanced by a beautiful face, fine symmetry of figure, and a countenance and gesture on the stage which indicated an entire intelligence and possession of the several parts allotted to her.

These two angelic performers excited so signally the attention of the public, that a party spirit between the abettors of the one and of the other was formed, as violent and as inveterate almost as any of those that had ever occurred relative to matters either theological or political; yet so distinct were their styles of singing, so different their talents, that the praise of the one was no reproach to the other.

In less than seven years, the whole L. 50,000 subscribed by the Royal Academy, besides the produce of admission to non-subscribers, was expended, and the governor and directors of the society relinquished the idea of continuing their engagements; consequently, at the close of the season 1727, the whole band of singers dispersed. The next year we find Senefino, Faustina, Balde, Cuzzoni, Nicolini, Farinelli, and Bosche, at Venice.

Handel, however, at his own risk, after a suspension of about a twelvemonth, determined to recommence the Opera; and accordingly engaged a band of performers entirely new. These were Signor Bernacchi, Signora Merighi, Signora Strada, Signor Annibale Pio Fabri, his wife, Signora Bertoldi, and John Gadfrid Reimschneider.

The sacred musical drama, or oratorio, was invented early in the 15th century. Every nation in Europe seems first to have had recourse to religious subjects for dramatic exhibitions. The oratorios had been common in Italy during the last century; they had never been publicly introduced in England till Handel, stimulated by the rivalry of other adventurers, exhibited in 1732 his oratorios of Esther, and of Acis, and Galatea, the last of which he had composed twelve years before for the duke of Chandos's chapel at Cannons. The most formidable opposition which Handel met with in his conduct of the Italian opera was a new theatre for exhibiting these operas, opened by subscription in Lincoln's Inn Fields, under the conduct of Nicola Porpora, a respectable composer. A difference having occurred between Handel and Senefino, Senefino had for some time deserted the Haymarket, where Handel managed, and was now engaged at the rival theatre of Lincoln's Inn Fields. To supply the place of Senefino, Handel brought over Giovanni Carissimi, a singer of the most extensive powers. His voice was at first a powerful and clear soprano; afterwards it changed into the fullest, finest, deepest, counter-tenor that has perhaps ever been heard. Carissimi's person was tall, beautiful, and majestic. He rendered every thing he sung interesting by energy, taste, and judicious embellishment. In the execution of difficult divisions from the chest,

N° 733.

his manner was articulate and admirable. It was the opinion of Haffne, as well as other eminent professors, that whoever had not heard Carissimi, was unacquainted with the most perfect style of singing. The opera under the direction of Porpora was removed to the Haymarket, which Handel had left. Handel occupied the theatre of Lincoln's Inn Fields; but his rivals now acquired a vast advantage of attraction, by the accession of Carlo Broschi detto Farinelli to their party, who at this time arrived. This renowned singer seems to have transcended the limits of all anterior vocal excellence. No vocal performer of the present century has been so unanimously allowed to possess an uncommon power, sweetness, extent, and agility of voice, as Farinelli. Nicolini, Senefino, and Carissimi, gratified the eye as much by the dignity, grace, and propriety of their action and deportment, as the ear, by the judicious use of a few notes within the limits of a small compass of voice; but Farinelli, without the assistance of significant gestures or graceful attitudes, enchanted and astonished his hearers, by the force, extent, and mellifluous tones of the mere organ, when he had nothing to execute, articulate, or express. Though during the time of singing he was as motionless as a statue, his voice was so active that no intervals were too close, too wide, or too rapid, for his execution.

Handel having lost a great part of his fortune by the opera, was under the necessity of trying the public gratitude in a benefit, which was not disgraced by the event: the theatre, for the honour of the nation, was so crowded, that he is said to have cleared L. 800.

After a fruitless attempt by Heidegger, the coadjutor of Handel in the conduct of the opera, and partentee of the King's Theatre in Haymarket, to procure a subscription for continuing it, it was found necessary to give up the undertaking.

It was about this time that the statue of Handel was erected in Vauxhall, at the expence of Mr Tyers, proprietor of those gardens.

The next year (1739) Handel carried on oratorios at the Haymarket, as the opera there was suspended. The earl of Middlesex now undertook the troublesome office of impresario of the Italian opera. He engaged the King's theatre, with a band of singers from the Continent almost entirely new. Caluzzi was his composer. Handel, almost ruined, retired at this time to Ireland, where he remained a considerable time. In 1744 he again attempted oratorios at the King's theatre, which was then, and till 1746, unoccupied by the opera, on account of the rebellion.

The arrival of Giardini in London this year forms a memorable era in the instrumental music of England. His powers on the violin were unequalled. The same year Dr Croza, then manager of the opera, closed, leaving the performers, and innumerable trades-people, his creditors. This incident put an end to operas of all kinds for some time.

This year a comic opera, entitled Il Filosofo di Chimpagna, composed by Caluzzi, was exhibited, which surpassed in musical merit all the comic operas performed in England till the Bicona Figliula. Signora Paganini acquired such fame by the airs allotted to her in that piece, that the crowds at her benefit were beyond example. Caps were lost, gowns torn in pieces,

pieces, and ladies in full dress, without servants or carriages, were obliged to walk home, amidst the merriment of the spectators on the streets.

48
1764 and
1765.
Manzoli.

At this period the arrival of Giovanni Manzoli marked a splendid era in the annals of musical drama, by conferring on serious opera a degree of importance to which it had seldom yet arisen since its establishment in England. Manzoli's voice was the most powerful and voluminous soprano that had been heard since the time of Farinelli: his manner of singing was grand, and full of taste and dignity.

49
Tenducci.

At this time Tenducci, who had been in England some time before, and was now returned much improved, performed in the station of second man to Manzoli.

50
1769.
Guadagni.

Gaetano Guadagni made a great figure at this time. He had been in this country early in life (1748), as a serious man in a burletta troop of singers. His voice was then a full and well-toned counter-tenor; but he sang wildly and carelessly. The excellence of his voice, however, attracted the notice of Handel, who assigned him the parts in his oratorios the Messiah and Samson, which had been originally composed for Mrs Cibber. He quitted London for the first time about 1753. The highest expectations of his abilities were raised by fame before his second arrival, at the time of which we treat. As an actor he seems to have had no equal on any stage in Europe. His figure was uncommonly elegant and noble; his countenance replete with beauty, intelligence, and dignity; his attitudes were full of grace and propriety. Those who remembered his voice when formerly in England were now disappointed: it was comparatively thin and feeble; he had now changed it to a soprano, and extended its compass from six or seven notes to fourteen or fifteen. The music he sang was the most simple imaginable; a few notes with frequent pauses, and opportunities of being liberated from the composer and the band, were all he required. In these effusions, seemingly extemporaneous, he displayed the native power of melody unaided by harmony or even by unisonous accompaniment: the pleasure he communicated proceeded principally from his artful manner of diminishing the tones of his voice, like the dying notes of the Aolian harp. Most other singers affect a swell, or mezza de voce; but Guadagni, after beginning a note with force, attenuated it so delicately that it possessed all the effect of extreme distance. During the season 1770 and 1771, Tenducci was the immediate successor of Guadagni. This performer, who appeared in England first only as a singer of the second or third class, was during his residence in Scotland and Ireland so much improved as to be well received as first man, not only on the stage of London but in all the great theatres of Italy.

51
1773.
Miss Davies.

It was during this period that dancing seemed first to gain the ascendancy over music by the superior talents of Mademoiselle Heinzel, whose grace and execution were so perfect as to eclipse all other excellence.

In the first opera performed this season (Lucio Vero) appeared Miss Cecilia Davies, known in Italy by the name of L'Ingleseina. Miss Davies had the honour of being the first English woman who had ever been thought worthy of singing on any stage in Italy. She even performed with eclat the principal female charac-

ters on many of the great theatres of that country. Gabrielli only on the Continent was said to surpass her. Her voice, though not of great volume, was clear and perfectly in tune; her shake was open and distinct, without the sluggishness of the French cadence. The flexibility of her throat rendered her execution equal to the most rapid divisons.

Next season introduced Venanzio Ravygini, a beautiful and animated young man; a composer as well as a singer. His voice was sweet, clear, flexible; in compass more than two octaves.

52
The season 1775 and 1776 was rendered memorable Caterina by the arrival of the celebrated Caterina Gabrielli, styled early in life La Guocbetina, being the daughter of a cardinal's cook at Rome. She had, however, in her countenance and deportment no indications of low birth. Her manner and appearance depicted dignity and grace. So great was her reputation before her arrival in England for singing and for caprice, that the public expecting perhaps in both too much, were unwilling to allow her due praise for her performance, and were apt to ascribe every thing she did to pride and insolence. Her voice, though exquisite, was not very powerful. Her chief excellence having been the neatness and rapidity of her execution, the surprise of the public must have been much diminished on hearing her after Miss Davies, who sang many of the same songs in the same style, and with a neatness so nearly equal, that common hearers could distinguish no difference. The discriminating critic, however, might have discovered a superior sweetness in the natural tone of the Gabrielli's voice, an elegance in the finishing of her musical periods or passages, an accent and precision in her divisons, superior not only to Miss Davies, but to every other singer of her time. In slow movements her pathetic powers, like those in general of performers most renowned for agility, were not exquisitely touching. She now resides at Bologna.

53
About the time of which we have been treating, the proprietors of the Pantheon ventured to engage the Agujari at the enormous salary of L. 100 per night, for singing two songs only! Lucrezia Agujari was a truly wonderful performer. The lower part of her voice was full, round, and of excellent quality; its compass amazing. She had two octaves of fair natural voice, from A on the fifth line in the bass to A on the sixth line in the treble, and beyond that in all she had in early youth more than another octave. She has been heard to ascend to Bb in ottissimo. Her shake was open and perfect; her intonation true; her execution marked and rapid; the style of her singing, in the natural compass of her voice, grand and majestic.

54
In 1776 arrived Anna Pozzi, as successor to the Gabrielli. She possessed a voice clear, sweet, and powerful; but her inexperience, both as an actress and as a singer, produced a contrast very unfavourable to her when compared with so celebrated a performer as Gabrielli. Since that time, however, Pozzi, with more study and knowledge, has become one of the best and most admired female singers in Italy.

55
After the departure of Agujari for the second and last time, the managers of the Pantheon engaged the Georgi as her successor. Her voice was exquisitely fine, but

but totally uncultivated. She is now employed as the first woman in the operas of the principal cities of Italy.

During the seasons 1777 and 1778, the principal singers at the opera in London were Erlandesco Roncaglia and Francesca Danze, afterwards Madame Le Brun.

Roncaglia possessed a sweet-toned voice; but of the three great requisites of a complete stage-singer, pathos, grace, and execution, which the Italians call cantabile, graziosa, and bravura, he could lay claim only to the second. His voice, a voce da camera, when confined to the graziosa in a room, leaves nothing to wish for.

Danze had a voice well in tune, a good shake, great execution, prodigious compass, with great knowledge of music; yet the pleasure her performance imparted was not equal to these accomplishments: but her object was not so much pathos and grace, as to surprise by the imitation of the tone and difficulties of instruments.

This year Gasparo Pacchierotti appeared in London, whither his high reputation had penetrated long before. The natural tone of his voice is interesting, sweet, and pathetic. His compass downwards is great, with an ascent up to Bb, and sometimes to C in alt. He possesses an unbounded fancy, and the power not only of executing the most difficult and refined passages, but of inventing embellishment entirely new. Ferdinando Bertoni, a well-known composer, came along with Pacchierotti to Britain.

During the last ten years, dancing has become an important branch of the amusements of the opera-house. Mademoiselle Hemel, M. Vestris le Jeune, Mademoiselle Baccelli, had, during some years, delighted the audience at the opera; but on the arrival of M. Vestris l'Aine, pleasure was exchanged for ecstasy. In the year 1781, Pacchierotti had by this time been so frequently heard that his singing was no impediment to conversation; but while the elder Vestris was on the stage, not a breathing was to be heard. Those lovers of music who talked the loudest while Pacchierotti sung, were in agonies of terror lest the graceful movements of Vestris, le dieu de la danse, should be disturbed by audible approbation. Since that time, the most mute and respectful attention has been paid to the manly grace of Le Pieq, and the light fantastic toe of the younger Vestris; to the Rossis, the Theodores, the Coulons, the Hillingsburgs; while the flighted singers have been disturbed, not by the violence of applause, but the clamour of inattention.

The year 1784 was rendered a memorable era in the annals of music by the splendid and magnificent manner in which the birth and genius of Handel were celebrated in Westminster Abbey and the Pantheon, by five performances of pieces selected from his own works, and executed by a band of more than 500 voices and instruments, in the presence and under the immediate auspices of their majesties and the first personages of the kingdom. The commemoration of Handel has been since established as an annual musical festival for charitable purposes; in which the number of performers and the perfection of the performances have continued to increase. In 1785 the band, vocal and instrumental, amounted to 616; in 1786 to 741; in 1787 to 806.

Dr Burney published An Account of the Musical Performances in Commemoration of Handel, for the benefit of the Musical Fund. The members and guardians of that fund are now incorporated under the title of Royal Society of Musicians. See HANDEL.

This year Pacchierotti and his friend Bertoni left England. About the same time our country was deprived of the eminent composer Sacchini, and Gardini the greatest performer on the violin then in Europe.

As a compensation for these losses, this memorable year is distinguished by the arrival of Madam Mara, whose performance in the commemoration of Handel in Westminster Abbey inspired an audience of 3000 of the first people of the kingdom, not only with pleasure but with ecstasy and rapture.

In 1786 arrived Giovanni Rubinielli. His voice is a Rubinielli, true and full contralto from C in the middle of the scale to the octave above. His style is grand; his execution neat and distinct; his taste and embellishments new, select, and masterly.

In 1788 a new dance, composed by the celebrated M. Noverre, called Cupid and Psyche, was exhibited along with the opera La Locandiera, which produced an effect so uncommon as to deserve notice. So great was the pleasure it afforded to the spectators, that Noverre was unanimously brought on the stage and crowned with laurel by the principal performers. This, though common in France, was a new mark of approbation in England.

This year arrived Signor Luigi Marchesi, a singer whose talents have been the subject of praise and admiration on every great theatre of Europe. Marchesi's style of singing is not only elegant and refined in an uncommon degree, but often grand and full of dignity, particularly in his recitative and occasional low notes. His variety of embellishment and facility of running extempore divisions are wonderful. Many of his graces are elegant and of his own invention.

The three greatest Italian singers of the present times are certainly Pacchierotti, Rubinielli, and Marchesi. In discriminating the several excellencies of these great performers, a very respectable judge, Dr Burney, has particularly praised the sweet and touching voice of Pacchierotti; his fine shake, his exquisite Marchesi, taste, his great fancy, and his divine expression in pathetic songs: Of Rubinielli's voice, the fulness, steadiness, and majesty, the accuracy of his intonations, his judicious graces: Of Marchesi's voice, the elegance and flexibility, his grandeur in recitative, and his boundless fancy and embellishments.—Having mentioned Dr Burney, we are in justice bound to acknowledge the aid we have derived from his history; a work which we greatly prefer to every other modern production on the subject. During the latter part of the present century many eminent composers have flourished on the continent; such as Jomelli, the family of the Bachs, Gluck, Haydn, and many others, whose different styles and excellencies would well deserve to be particularised, would our limits permit. With the same regard to brevity, we can do no more than just mention the late king of Prussia, the late elector of Bavaria, and prince Lobkowitz, as eminent dilettanti of modern times.

Besides the opera-singers whom we have mentioned, our

66 Singers on theatres and in public gardens. our theatres and public gardens have exhibited singers of considerable merit. In 1730 Miss Rafter, afterwards the celebrated Mrs Clive, first appeared on the stage at Drury-lane as a singer. The same year introduced Miss Cecilia Young, afterwards the wife of Dr Arne. Her style of singing was infinitely superior to that of any other English woman of her time.

67 Favourite musicians. Our favourite musicians at this time were, Dubourg, Clegg, Clarke, and Felling, on the violin; Kyte on the hautboy; Jack Felling on the German flute; Balton on the common flute; Karba on the bassoon; Valentine Snow on the trumpet; and on the organ, Roseingrave, Green, Robinson, Magnus, Jack James, and the blind Stanley, who seems to have been preferred. The favourite playhouse singer was Salway; and at concerts Mountier of Chichester.

As composers for our national theatre, Pepusch and Galliard seem to have been unrivalled till 1732; when two competitors appeared, who were long in possession of the public favour: We allude to John Frederick Lampe and Thomas Augustus Arne.

In 1736 Mrs Cibber, who had captivated every hearer of sensibility by her native sweetness of voice and powers of expression as a singer, made her first attempt as a tragic actress. The same year Beard became a favourite singer at Covent-garden. At this time Miss Young, afterwards Mrs Arne, and her two sisters Isabella and Esther, were the favourite English female singers.

68 Fund for decayed musicians. In 1738 was instituted the fund for the support of decayed musicians and their families.

It was in 1745 that Mr Tyers, proprietor of Vauxhall gardens, first added vocal music to the other entertainments of that place. A short time before Ranelagh had become a place of public amusement.

69 Arrival of Gardini. In 1749 arrived Gardini, whose great taste, hand, and style in playing on the violin, procured him universal admiration. A few years after his arrival he formed a morning academia or concert at his house, composed chiefly of his scholars.

About this time San Martini and Charles Avison were eminent composers.

70 Style of Arne. Of near 150 musical pieces brought on our national theatres within these 40 years, 30 of them at least were set by Arne. The style of this composer, if analysed, would perhaps appear to be neither Italian nor English; but an agreeable mixture of both and of Scotch.

71 The earl of Kelly. The late earl of Kelly, who died but a few years ago, deserves particular notice, as possessed of a very eminent degree of musical science, far superior to other dilettanti, and perhaps not inferior to any professor of his time. There was no part of theoretical or practical music in which he was not thoroughly versed: He possessed a strength of hand on the violin, and a genius for composition, with which few professors are gifted.

72 Abel. Charles Frederic Abel was an admirable musician: his performance on the viol da gamba was in every particular complete and perfect. He had a hand which no difficulties could embarrass; a taste the most refined and delicate; a judgment so correct and certain as never to permit a single note to escape him with-

out meaning. His compositions were easy and elegantly simple. In writing and playing an adagio he was superior to all praise; the most pleasing yet learned modulation, the richest harmony, the most elegant and polished melody, were all expressed with the most exquisite feeling, taste, and science. His manner of playing an adagio soon became the model of imitation for all our young performers on bowed instruments. Bartholemon, Cervetto, Cramer, and Crofidi, may in this respect be ranked as of his school. All lovers of music must have lamented that Abel in youth had not attached himself to an instrument more worthy of his genius, taste, and learning, than the viol da gamba, that remnant of the old chest of viols which during the last century was a necessary appendage of a nobleman's or gentleman's family throughout Europe, previous to the admission of violins, tenors, and basses, in private houses or public concerts. Since the death of the late elector of Bavaria, who was next to Abel (the best performer on the viol da gamba in Europe), the instrument seems quite laid aside. It was used longer in Germany than elsewhere; but the place of gambit seems now as much suppressed in the chapels of German princes as that of lutanists. The celebrated performer on the violin, Lolli, came to England in 1785. Such was his caprice, that he was seldom heard; and so eccentric was his style and composition, that by many he was regarded as a madman. He was, however, during his lucid intervals a very great and expressive performer in the serious style.

Mrs Billington, after distinguishing herself in childhood as a neat and expressive performer on the pianoforte, appeared all at once in 1786 as a sweet and captivating singer. In emulation of the Mara and other great bravura singers, she at first too frequently attempted passages of difficulty; now, however, so greatly has she improved, that no song seems too high or too rapid for her execution. The natural tone of her voice is so exquisitely sweet, her knowledge of music so considerable, her shake so true, her closes and embellishments so various, her expressions so grateful, that envy only or apathy could hear her without delight. The present composers, and performers of the first class, are so well known to the lovers of the art, that it would be needless and improper to mention them particularly; and to describe the distinctive powers of Bartholemon, Cramer, Piel-tain, Raimonde, and Salamon, would be too delicate a task for us to undertake.

The Catch-club at the Thatched House, instituted in 1762 by the late earl of Eglinton, the present duke of Queensberry, and others; and the concert of ancient music, suggested by the earl of Sandwich in 1776, have had a beneficial effect in improving the art.

We have been somewhat particular in our account of musical affairs in our own country during the present century, as what would be most interesting to general readers, and of which a well-informed gentleman would not wish to be ignorant. The professor and connoisseur is not to be expected to content himself with disquisitions much more minute than those of which our limits can be supposed to admit.

MUSIC may be considered, either as an art, which has for its object one of the greatest pleasures of which our senses (‡) are susceptible; or as a science, by which that art is reduced to principles. This is the double view in which we mean to treat of music in this work.

It has been the case with music as with all the other arts invented by men: some facts were at first discovered by accident; soon afterwards reflection and observation investigated others; and from these facts, properly disposed and united, philosophers were not slow in forming a body of science, which afterwards increased by degrees.

The first theories of music were perhaps as ancient as the earliest age which we know to have been distinguished by philosophy, even as the age of Pythagoras; nor does history leave us any room to doubt, that from the period when that philosopher taught, the ancients cultivated music, both as an art and as a science, with great assiduity. But there remains to us much uncertainty concerning the degree of perfection to which they brought it. Almost every question which has been proposed with respect to the music of the ancients has divided the learned; and may probably still continue to divide them, for want of monuments sufficient in their number, and incontestable in their nature, from whence we might be enabled to exhibit testimonies and discoveries instead of suppositions and conjectures. In

the preceding history we have stated a few facts respecting the nature of ancient music, and the inventors of the several musical instruments; but it were to be wished, that, in order to elucidate, as much as possible, a point so momentous in the history of the sciences, some person of learning, equally skilled in the Greek language and in music, should exert himself to unite and discuss in the same work the most probable opinions established or proposed by the learned upon a subject so difficult and curious. This philosophical history of ancient music is a work which might highly embellish the literature of our times.

In the mean time, till an author can be found sufficiently instructed in the arts and in history to undertake such a labour with success, we shall content ourselves with considering the present state of music, and limit our endeavours to the explication of those accretions which have accrued to the theory of music in these latter times.

There are two departments in music, melody* and harmony†. Melody is the art of arranging several sounds in succession one to another in a manner agreeable to the ear; harmony is the art of pleasing that organ by the union of several sounds which are heard at one and the same time. Melody has been known and felt through all ages: perhaps the same cannot be affirmed of harmony (§); we know not whether the ancients made any use of it or not, nor at what period it began to be practised.

Not but that the ancients certainly employed in their music

(†) To deliver the elementary principles of music, theoretical and practical, in a manner which may prove at once entertaining and instructive, without protracting this article much beyond the limits prescribed in our plan, appears to us no easy task. We therefore hesitated for some time, whether to try our own strength, or to follow some eminent author on the same subject. Of these the last seemed preferable. Amongst these authors, none appeared to us to have written any thing so fit for our purpose as M. D'Alembert, whose treatise on music is the most methodical, perspicuous, concise, and elegant dissertation on that subject with which we are acquainted. As it was unknown to most English readers before the former edition of this work, it ought to have all the merit of an original. We have given a faithful translation of it; but in the notes, several remarks are added, and many authors quoted, which will not be found in the original. It is a work so systematically composed, that all attempts to abridge it, without rendering it obscure and imperfect, would be impracticable. It is perhaps impossible to render the system of music intelligible in a work of less compass than that with which our readers are now presented; and, in our judgment, a performance of this kind, which is written in such a manner as not to be generally understood, were much better suppressed.

(‡) In this passage, and in the definitions of melody and harmony, our author seems to have adopted the vulgar error, that the pleasures of music terminates in corporeal sense. He would have pronounced it absurd to assert the same thing of painting. Yet if the former be no more than a mere pleasure of corporeal sense, the latter must likewise be ranked in the same predicament. We acknowledge that corporeal sense is the vehicle of sound; but it is plain from our immediate feelings, that the results of sound arranged according to the principles of melody, or combined and disposed according to the laws of harmony, are the objects of a reflex or internal sense.

For a more satisfactory discussion of this matter, the reader may consult that elegant and judicious treatise on Musical Expression by Mr. Avison. In the mean time it may be necessary to add, that, in order to shun the appearance of affectation, we shall use the ordinary terms by which musical sensations, or the mediums by which they are conveyed, are generally denominated.

(§) Though no certainty can be obtained what the ancients understood of harmony, nor in what manner and in what period they practised it; yet it is not without probability, that, both in speculation and practice,

Prelim. Discourse. music those chords which were most perfect and simple; such as the octave, the fifth, and the third; but it seems doubtful whether they knew any of the other consonances or not, or even whether in practice they could deduce the same advantages from the simple chords which were known to them, that have afterwards accrued from experience and combinations.

If that harmony which we now practice owes its origin to the experience and reflection of the moderns, there is the highest probability that the first essays of this art, as of all the others, were feeble, and the progress of its efforts almost imperceptible; and that, in the course of time, improving by small gradations, the successive labours of several geniuses have elevated it to that degree of perfection in which at present we find it.

The first inventor of harmony escapes our investigation, from the same causes which leave us ignorant of those who first invented each particular science; because the original inventors could only advance one step, a succeeding discoverer afterwards made a more sensible improvement, and the first imperfect essays in every kind were lost in the more extensive and striking views to which they led. Thus the arts which we now enjoy, are for the most part far from being due to any particular man, or to any nation exclusively: they are produced by the united and successive endeavours of mankind; they are the results of such continued and united reflections, as have been formed by all men at all periods and in all nations.

It might, however, be wished, that after having ascertained, with as much accuracy as possible, the state of ancient music by the small number of Greek authors which remain to us, the same application were immediately directed to investigate the first incontestable traces of harmony which appear in the succeeding ages, and to pursue those traces from period to period. The products of these researches would doubtless be very imperfect, because the books and monuments of the middle ages are by far too few to enlighten that gloomy and barbarous era; yet these discoveries would still be precious to a philosopher, who delights to observe the human mind in the gradual evolutions of its powers, and the progress of its attainments.

The first compositions upon the laws of harmony which we know, are of no higher antiquity than two ages prior to our own; and they were followed by many others. But none of these essays was capable of satisfying the mind concerning the principles of harmony: they confined themselves almost entirely to the single occupation of collecting rules, without endeavouring to account for them; neither had their analogies one with another, nor their common source, been perceived; a blind and unenlightened experience was the only

compas by which the artist could direct and regulate his course.

M. Rameau was the first who began to transfuse light and order through this chaos. In the different tones produced by the same sonorous body, he found the most probable origin of harmony, and the cause of that pleasure which we receive from it. His principle unfolded, and showed how the different phenomena of music were produced by it: he reduced all the consonances to a small number of simple and fundamental chords, of which the others are only combinations or various arrangements. He has, in short, been able to discover, and render sensible to others, the mutual dependence between melody and harmony.

Though these different topics may be contained in the writings of this celebrated artist, and in these writings may be understood by philosophers who are likewise adept in the art of music; still, however, such musicians as were not philosophers, and such philosophers as were not musicians, have long desired to see these objects brought more within the reach of their capacity: such is the intention of the treatise I now present to the public. I had formerly composed it for the use of some friends. As the work appeared to them clear and methodical, they have engaged me to publish it, persuaded (though perhaps with too much credulity) that it might be useful to facilitate the progress of initiates in the study of harmony.

This was the only motive which could have determined me to publish a book of which I might without hesitation assume the honour, if its materials had been the fruits of my own invention, but in which I can now boast no other merit than that of having developed, elucidated, and perhaps in some respects improved, the ideas of another (c).

The first edition of this essay, published 1732, having been favourably received by the world, and copies no longer to be found in the hands of booksellers, I have endeavoured to render this more perfect. The detail which I mean to give of my labour, will present the reader with a general idea of the principle of M. Rameau, of the consequences deduced from it, of the manner in which I have disposed this principle, and its consequences; in short, of what is still wanting, and might be advantageous to the theory of this amiable art; of what still remains for the learned to contribute towards the perfection of this theory; of the rocks and quicksands which they ought to avoid in this research, and which could serve no other purpose than to retard their progress.

Every sonorous body, besides its principal sound, likewise exhibits to the ear the 12th and 17th major of that sound. This multiplicity of different yet concordant sounds, known for a considerable time, constitutes

they were in possession of what we denominate counterpoint. Without supposing this, there are some passages in the Greek authors which can admit of no satisfactory interpretation. See the Origin and Progress of Language, Vol. II. Besides, we can discover some vestiges of harmony, however rude and imperfect, in the history of the Gothic ages, and amongst the most barbarous people. This they could not have derived from more cultivated countries, because it appears to be incorporated with their national music. The most rational account, therefore, which can be given, seems to be, that it was conveyed in a mechanical or traditional manner through the Roman provinces from a more remote period of antiquity.

(c) See M. Rameau's letter upon this subject, Merc. de Mai 1732.

tutes the basis of the whole theory of M. Rameau, and the foundation upon which he builds the whole superstructure of a musical system*. In these our elements may be seen, how from this experiment one may deduce, by an easy operation of reason, the chief points of melody and harmony; the perfect † chord, as well major as minor; the two ‡ tetrachords employed in ancient music; the formation of our diatonic § scale; the different values ¶ which the same found may have in that scale, according to the turn which is given to the bas*; the alterations † which we observe in that scale, and the reason why they are totally imperceptible to the ear; the rules peculiar to the mode ‡ major; the difficulty in ¶ intonation of forming three tones || in succession; the reason why two perfect chords are prescribed in immediate succession in the diatonic order; the origin of the minor mode, its subordination to the mode major, and its variations; the use of discord §; the causes of such effects as are produced by different kinds of music, whether diatonic, chromatic*, or enharmonic†; the principles and laws of temperament‡. In this discourse we can only point out those different objects, the subsequent essay being designed to explain them with the minuteness and precision which they require.

One end which we have proposed in this treatise, was not only to place the discoveries of M. Rameau in their most conspicuous and advantageous light, but even in particular respects to render them more simple. —For instance, besides the fundamental experiment which we have mentioned above, that celebrated musician, to render the explication of some particular phenomena in music more accessible, had recourse to another experiment; I mean that which shows that a sonorous body struck and put in vibration, forces its 12th and 17th major in descending to divide themselves and produce a tremulous sound. The chief use which M. Rameau made of this second experiment was to investigate the origin of the minor mode, and to give a satisfactory account of some other rules established in harmony; and with respect to this in our first edition we have implicitly followed him: in this we have found means to deduce from the first experiment alone the formation of the minor mode, and besides to disengage that formation from all the questions which were foreign to it.

It is the same case with some other points (as the origin of the chord of the sub-dominant §, and the explication of the seventh in some peculiar respects), upon which it is imagined that we have simplified, and perhaps in some measure extended, the principles of the celebrated artist.

We have likewise banished from this edition, as from the former, every consideration of geometrical, arithmetical, and harmonical proportions and progressions, which authors have endeavoured to find in the mixture and protraction of tones produced by a sonorous body; persuaded as we are, that M. Rameau was under no necessity of paying the least regard to these proportions, which we believe to be not only useless, but even, if we may venture to say so, fallacious when applied to the theory of music. In short, though the relations produced by the octave, the fifth, and the third, &c. were quite different from what they are; though in these chords we should neither remark any progression

nor any law; though they should be incommensurable one with another; the protracted tone of a sonorous body, and the multiplied sounds which result from it, are a sufficient foundation for the whole harmonic system.

But though this work is intended to explain the theory of music, and to reduce it to a system more complete and more luminous than has hitherto been done, we ought to caution those who shall read this treatise, that they may be careful not to deceive themselves, either by misapprehending the nature of our object, or the end which our endeavours pursue.

We must not here look for that striking evidence which is peculiar to geometrical discoveries alone, and which can be so rarely obtained in these mixed disquisitions, where natural philosophy is likewise concerned: into the theory of musical phenomena there must always enter a particular kind of metaphysics, which these phenomena implicitly take for granted, and which brings along with it its natural obscurity. In this subject, therefore, it would be absurd to expect what is called demonstration: it is an achievement of no small importance, to have reduced the principal facts to a system consistent with itself, and firmly connected in its parts; to have deduced them from one simple experiment; and to have established upon this foundation the most common and essential rules of the musical art. But in another view, if here it be improper to require that intimate and unalterable conviction which can only be produced by the strongest evidence, we remain in the mean time doubtful whether it is possible to elucidate this subject more strongly.

After this declaration, one should not be astonished, that, amongst the facts which are deduced from our fundamental experiment, there should be some which appear immediately to depend upon that experiment, and others which are deduced from it in a way more remote and less direct. In disquisitions of natural philosophy, where we are scarcely allowed to use any other arguments, except such as arise from analogy or congruity, it is natural that the analogy should be sometimes more sometimes less sensible: and we will venture to assert, that such a mind must be very improper for philosophy, which cannot recognize and distinguish this gradation and the different circumstances on which it proceeds. It is not even surprising, that in a subject where analogy alone can take place, this conduct should desert us all at once in our attempts to account for certain phenomena. This likewise happens in the subject which we now treat; nor do we conceal the fact, however mortifying, that there are certain points (though their number be but small) which appear still in some degree unaccountable from our principle. Such, for instance, is the procedure of the diatonic scale in descending; the formation of the chord commonly termed the sixth redundant* or superfluous,* See Redundant. and some other facts of less importance, for which as yet we can scarcely offer any satisfactory account except from experience alone.

Thus, though the greatest number of the phenomena in the art of music appear to be deducible in a simple and easy manner from the protracted tone of sonorous bodies, one ought not perhaps with too much temerity to affirm as yet, that this mixed and protracted tone is demonstratively the only original principle

of harmony (b). But in the mean time it would not be less unjust to reject this principle, because certain phenomena appear to be deduced from it with less success than others. It is only necessary to conclude from this, either that by future scrutinies means may be found for reducing these phenomena to this principle; or that harmony has perhaps some other unknown principle, more general than that which results from the protracted and compounded tone of sonorous bodies, and of which this is only a branch; or, lastly, that we ought not perhaps to attempt the reduction of the whole science of music to one and the same principle; which, however, is the natural effect of an impatience so frequent even among philosophers themselves, which induces them to take a part for the whole, and to judge of objects in their full extent by the greatest number of their appearances.

In those sciences which are called physico-mathematical (and amongst this number perhaps the science of sounds may be placed), there are some phenomena which depend only upon one single principle and one single experiment: there are others which necessarily suppose a greater number both of experiments and principles, whose combination is indispensable in forming an exact and complete system; and music perhaps is in this last case. It is for this reason, that, whilst

we bestow on M. Rameau all due praise, we should not at the same time neglect to stimulate the learned in their endeavours to carry them still to higher degrees of perfection, by adding, if it is possible, such improvements as may be wanting to consummate the science.

Whatever the result of their efforts may be, the reputation of this intelligent artist has nothing to fear: he will still have the advantage of being the first who rendered music a science worthy of philosophical attention; to have made its practice more simple and easy; and to have taught musicians to employ in this subject the light of reason and analogy.

We would the more willingly persuade those who are skilled in theory and eminent in practice to extend and improve the views of him who before them pursued and pointed out the career, because many amongst them have already made laudable attempts, and have even been in some measure successful in diffusing new light through the theory of this enchanting art. It Tartini's
86
Tartini's
experi-
ment.
was with this view that the celebrated Tartini has presented us in 1754 with a treatise of harmony, founded on a principle different from that of M. Rameau. This principle is the result of a most beautiful experiment (†). If at once two different sounds are produced from two instruments of the same kind, these two
sounds

(b) The demonstration of the principles of harmony by M. Rameau was not thus intitled in the exposition which he presented in the year 1749 to the Academy of Sciences, and which that Society besides approved with all the eulogiums which the author deserved; the title, as inferred in the register of the academy, was, "A memorial, in which are explained the foundations of a system of music theoretical and practical." It is likewise under this title that it was announced and approved of by the Commissioners, who in their printed report, which the public may read along with M. Rameau's memorial, have never dignified his theory with any other name than that of a system, the only name in reality which is expressive of its nature. M. Rameau, who, after the approbation of the Academy, has thought himself at liberty to adorn his system with the name of a demonstration, did not certainly recollect what the Academy has frequently declared; that, in approving any work, it was by no means implied, that the principles of that work appeared to them demonstrated. In short, M. Rameau himself, in some writings posterior to what he calls his demonstration, acknowledges, that upon particular points in the theory of the musical art, he is under a necessity of having recourse to analogy and aptitude; this excludes every idea of demonstration, and restores the theory of the musical art exhibited by M. Rameau to the class in which it can only be ranked with propriety, I mean the class of probabilities.

(†) Had the utility of the preliminary discourse in which we are now engaged been less important and obvious than it really is, we should not have given ourselves the trouble of translating, nor our readers that of perusing it. But it must be evident to every one, that the cautions here given, and the advices offered, are no less applicable to students than to authors. The first question here decided is, Whether pure mathematics can be successfully applied to the theory of music? The author is justly of a contrary opinion. It may certainly be doubted with great justice, whether the solid contents of sonorous bodies, and their degrees of cohesion or elasticity, can be ascertained with sufficient accuracy to render them the subjects of musical speculation, and to determine their effects with such precision as may render the conclusions deduced from them geometrically true. It is admitted, that sound is a secondary quality of matter, and that secondary qualities have no obvious connection which we can trace with the sensations produced by them. Experience, therefore, and not speculation, is the grand criterion of musical phenomena. For the effects of geometry in illustrating the theory of music (if any will still be so credulous as to pay them much attention), the English reader may consult Smith's Harmonics, Malcom's Dissertation on Music, and Pleydel's Treatise on the same subject inserted in a former edition of this work. Our author next treats of the famous discovery made by Sig. Tartini, of which the reader may accept the following compendious account.

If two sounds be produced at the same time properly tuned and with due force, from their conjunction a third sound is generated, so much more distinctly to be perceived by delicate ears as the relation between the generating sounds is more simple; yet from this rule we must except the unison and octave. From the fifth is produced a sound unison with its lowest generator; from the fourth, one which is an octave lower than the highest of its generators; from the third major, one which is an octave lower than its lowest; and from the
sixth

found to generate * a third different from both the others. They have inserted in the Encyclopédie, under the article Fundamental, a detail of this experiment according to M. Tartini; and we owe to the public an information of which in composing this article we were ignorant: M. Rameau, a member of the Royal Society at Montpellier, had presented to that society in the year 1753, before the work of M. Tartini had appeared, a memorial printed the same year, and where may be found the same experiment displayed at full length. In relating this fact, which it was necessary for us to do, it is by no means our intention to detract in any degree from the reputation of M. Tartini; we are persuaded that he owes this discovery to his own researches alone: but we think ourselves obliged in honour to give public testimony in favour of him who was the first in exhibiting this discovery.

But whatever be the case, it is in this experiment that M. Tartini attempts to find the origin of harmony: his book, however, is written in a manner so obscure, that it is impossible for us to form any judgement of it; and we are told that others distinguished for their knowledge of the science are of the same opinion. It were to be wished that the author would engage some man of letters, equally practised in music and skilled in the art of writing, to unfold these ideas which he has not discovered with sufficient perspicuity, and from whence the art might perhaps derive considerable advantage if they were placed in a proper light. Of this I am so much the more persuaded, that even though this experiment should not be regarded by others in the same view with M. Tartini as the foundation of the musical art, it is nevertheless extremely probable that one might use it with the greatest advantage to enlighten and facilitate the practice of harmony.

In exhorting philosophers and artists to make new attempts for the advancement of the theory of music, we ought at the same time to let them know the danger of mistaking what is the real end of their researches. Experience is the only foundation upon which they can proceed; it is alone by the observation of facts, by bringing them together in one view, by showing their dependency upon one, if possible, or at least upon a very small number of primary facts, N^o 233.

that they can reach the end to which they so ardently aspire, the important end of establishing an exact theory of music, where nothing is wanting, nothing obscure, but every thing discovered in its full extent, and in its proper light. The philosopher who is properly enlightened, will not give himself the trouble to explain such facts as are less essential to his art, because he can discern those on which he ought to expatiate for its proper illustration. If one would estimate them according to their proper value, he will only find it necessary to cast his eyes upon the attempts of natural philosophers who have discovered the greatest skill in their science; to explain, for instance, the multiplicity of tones produced by sonorous bodies. These fages, after having remarked (what is by no means difficult to conclude) that the universal vibration of a musical string is a mixture of several partial vibrations, from thence infer, that a sonorous body ought to produce a multiplicity of tones, as it really does. But why should this multiplied sound only appear to contain three, and why these three preferable to others? Some pretend that there are particles in the air, which, by their different degrees of magnitude and texture, being naturally susceptible of different oscillations, produce the multiplicity of sound in question. But what do we know of all this hypothetical doctrine? And though it should even be granted, that there is such a diversity of tension in these aerial particles, how should this diversity prevent them from being all of them confounded in their vibrations by the motions of a sonorous body? What then should be the result, when the vibrations arrive at our ears, but a confused and inapprehensible† noise, where one could not distinguish any particular sound?

If philosophical musicians ought not to lose their time in searching for mechanical explications of the phenomena in music, explications which will always be found vague and unsatisfactory; much less is it their province to exhaust their powers in vain attempts to rise above their sphere into a region still more remote from the prospect of their faculties, and to lose themselves in a labyrinth of metaphysical speculations upon the causes of that pleasure which we feel from harmony. In vain would they accumulate hypothesis on hypothesis, to find a reason why some chords should please

sixth minor (whose highest note forms an octave with the lowest in the third formerly mentioned) will be produced a sound lower by a double octave than the highest of the lesser sixth; from the third minor, one which is double the distance of a greater third from its lowest; but from the sixth major (whose highest note makes an octave to the lowest in the third minor) will be produced a sound only lower by double the quantity of a greater third than the highest; from the second major, a sound lower by a double octave than the lowest; from a second minor, a sound lower by triple the quantity of a third major than the highest; from the interval of a diatonic or greater semitone, a sound lower by a triple octave than the highest; from that of a minor or chromatic semitone, a sound lower by the quantity of a fifth four times multiplied than the lowest, &c. &c. But that these musical phenomena may be tried by experiments proper to ascertain them, two hautboys tuned with scrupulous exactness must be procured, whilst the musicians are placed at the distance of some paces one from the other, and the hearers in the middle. The violin will likewise give the same chords, but they will be less distinctly perceived, and the experiment more fallacious, because the vibrations of other strings may be supposed to enter into it.

If our English reader should be curious to examine these experiments and the deductions made from them in the theory of music, he will find them clearly explained and illustrated in a treatise called Principles and Power of Harmony, printed at London in the year 1771.

us more than others. The futility of these suppositions accounts must be obvious to every one who has the least penetration. Let us judge of the rest by the most probable which has till now been invented for that purpose. Some ascribe the different degrees of pleasure which we feel from chords, to the more or less frequent coincidence of vibrations; others to the relations which these vibrations have among themselves as they are more or less simple. But why should this coincidence of vibrations, that is to say, their simultaneous impulse on the same organs of sensation, and the accident of beginning frequently at the same time, prove so great a source of pleasure? Upon what is this gratuitous supposition founded? And though one should grant it, would it not follow from thence, that the same chord should successively and rapidly affect us with contrary sensations, since the vibrations are alternately coincident and discrepant? On the other hand, how should the ear be so sensible to the simplicity of relations, whilst for the most part these relations are entirely unknown to him whose organs are notwithstanding sensibly affected with the charms of agreeable music? We may conceive without difficulty how the eye judges of relations; but how does the ear form similar judgments? Besides, why should certain chords which are extremely pleasing in themselves, such as the fifth, lose almost nothing of the pleasure which they give us, when they are altered, and of consequence when the simplicity of their relations are destroyed; whilst other chords, which are likewise extremely agreeable, such as the third, become harsh almost by the smallest alteration; nay, whilst the most perfect and the most agreeable of all chords, I mean the octave, cannot suffer the most inconsiderable change?

Let us in sincerity confess our ignorance concerning the genuine causes of these effects (†). The metaphysical conjectures concerning the acoustic organs are probably in the same predicament with those which are formed concerning the organs of vision, if one may speak so, in which philosophers have even till now made such inconsiderable progress, and in all likelihood will not be surpassed by their successors.

Since the theory of music, even to those who confine themselves within its limits, implies questions from which every wise musician will abstain, with much greater reason should they avoid idle excursions beyond the boundaries of that theory, and endeavours to investigate between music and the other sciences chimerical relations which have no foundation in nature. The singular opinions advanced upon this subject by some even of the most celebrated musicians, deserve not to be rescued from oblivion, nor refuted; and ought only to be regarded as a new proof how far men of genius may deviate from truth and taste, when they engage in subjects of which they are ignorant.

The rules which we have attempted to establish concerning the track which every one ought to pursue in the theory of the musical art, may suffice to show our readers the end which we have proposed, and which we have endeavoured to attain in this Work. We have nothing to do here (for it is proper that we repeat it), we have nothing to do with the mechanical principles of protracted and harmonic tones produced by sonorous bodies; principles which till now have been explored in vain, and which perhaps may be long explored with the same success; we have still left

(†) We have as great an aversion as our author to the explication of musical phenomena from mechanical principles; yet we fear the following observations, deduced from irresistible and universal experience, evidently show that the latter necessarily depend on the former. It is, for instance, universally allowed, that dissonances grate and concords please a musical ear: It is likewise no less unanimously agreed, that in proportion as a chord is perfect, the pleasure is increased; now the perfection of a chord consists in the regularity and frequency of coincident oscillations between two sonorous bodies impelled to vibrate: thus the third is a chord less perfect than the fifth, and the fifth than the octave. Of all these consonances, therefore, the octave is most pleasing to the ear; the fifth next, and the third last. In absolute discords, the vibrations are never coincident, and of consequence a perpetual pulsation or jarring is recognised between the protracted sounds, which exceedingly hurts the ear; but in proportion as the vibrations coincide, those pulsations are superseded, and a kindred formed betwixt the two continued sounds, which delights even the corporeal sense: that relation, therefore, without recognising the aptitudes which produce it, must be the obvious cause of the pleasure which chords give to the ear. What we mean by coincident vibrations is, that while one sonorous body performs a given number of vibrations, another performs a different number in the same time; so that the vibrations of the quickest must sometimes be simultaneous with those of the slowest, as will plainly appear from the following deduction: Between the extremes of a third, the vibrations of the highest are as 5 to 4 of the lowest; those of the fifth as 3 to 2; those of the octave as 2 to 1. Thus it is obvious, that in proportion to the frequent coincidence of periodical vibrations, the compound sensation is more agreeable to the ear. Now, to inquire why that organ should be rather pleased with these than with the pulsation and tremulous motion of encountering vibrations which can never coincide, would be to ask why the touch is rather pleased with polished than rough surfaces? or, why the eye is rather pleased with the waving line of Hogarth than with sharp angles and abrupt or irregular prominences? No alteration of which any chord is susceptible will hurt the ear unless it should violate or destroy the regular and periodical coincidence of vibrations. When alterations can be made without this disagreeable effect, they form a pleasing diversity; but still this fact corroborates our argument, that in proportion as any chord is perfect, it is impatient of the smallest alteration; for this reason, even in temperament, the octave endures no alteration at all, and the fifth as little as possible.

less to do with the metaphysical causes of those pleasing sensations which are impressed on the mind by harmony; causes which are still less discovered, and which, according to all appearances, will remain latent in perpetual obscurity. We are alone concerned to show how the chief and most essential laws of harmony may be deduced from one single experiment; and for which, if we may speak so, preceding artists have been under a necessity of groping in the dark.

With an intention to render this work as generally useful as possible, I have endeavoured to adapt it to the capacity even of those who are absolutely uninstru-cted in music. To accomplish this design, it ap-peared necessary to pursue the following plan.

To begin with a short introduction, in which are defined the technical terms most frequently used in this art; such as chord, harmony, key, third, fifth, octave, &c.

Afterwards to enter into the theory of harmony, which is explained according to M. Rameau, with all possible perspicuity. This is the subject of the First Part; which, as well as the introduction, presupposes no other knowledge of music than that of the names and powers of the syllables, ut, re, mi, fa, sol, la, si, or C, D, E, F, G, A, B, which all the world knows (†).

The theory of harmony requires some arithmetical calculations, which are necessary for comparing sounds one with another. These calculations are very short, extremely simple, and conducted in such a manner as to be feasibly comprehended by every one; they demand no operation but what is clearly explained, and which every school-boy with the slightest attention may perform. Yet, that even the trouble of this may be spared to such as are not disposed to take it, I have not inserted these calculations in the body of the treatise, but transferred them to the notes, which the reader may omit, if he can satisfy himself by taking for granted the propositions contained in the work, which will be found proved in the notes.

These calculations I have not endeavoured to multiply; I could even have wished to suppress them, if it had been possible: so much did it appear to me to be apprehended that my readers might be misled upon this subject, and might either believe themselves, or at least suspect me of believing, all this arithmetic necessary to form an artist. Calculations may indeed facilitate the understanding of certain points in the theory, as of the relations between the different notes in the gammut and of the temperament; but the calculations necessary for treating of these points are so simple, and, to speak more properly, of so little importance, that nothing can require a less minute or

ostentatious display. Do not let us imitate those musicians who, believing themselves geometers, or those geometers who, believing themselves musicians, fill their writings with figures upon figures; imagining, perhaps, that this apparatus is necessary to the art. The propensity of adorning their works with a false air of science, can only impose upon credulity and ignorance, and serve no other purpose but to render their treatises more obscure and less instructive. In the character of a geometer, I think I have some right to protest here (if I may be permitted to express myself in this manner) against such ridiculous abuse of geometry in music.

This I may do with so much more reason, that in Mathematics this subject the foundations of those calculations are in some manner hypothetical, and can never arise to a degree of certainty above hypothesis. The relation of the octave as 1 to 2, that of the fifth as 2 to 3, that of the third major as 4 to 5, &c. are not perhaps the genuine relations established in nature; but only relations which approach them, and such as experience can discover. For are the results of experience any thing more but mere approaches to truth?

But happily these approximated relations are sufficient, though they should not be exactly agreeable to truth, for giving a satisfactory account of those phenomena which depend on the relations of sound; as in the difference between the notes in the gammut, of the alterations necessary in the fifth and third, of the different manner in which instruments are tuned, and other facts of the same kind. If the relations of the octave, of the fifth, and of the third, are not exactly such as we have supposed them, at least no experiments can prove that they are not so; and since these relations are signified by a simple expression, since they are besides sufficient for all the purposes of theory, it would not only be useless, but even contrary to sound philosophy, should any one incline to invent other relations, to form the basis of any system of music less easy and simple than that which we have delineated in this treatise.

The second part contains the most essential rules of composition*, or in other words the practice of harmony. These rules are founded on the principles laid down in the first part; yet those who wish to understand no more than is necessary for practice, without exploring the reasons why such practical rules are necessary, may limit the objects of their study to the introduction and the second part. They who have read the first part, will find at every rule contained in the second, a reference to that passage in the

(†) The names of the seven notes used by the French are here retained, and will indeed be continued through the whole ensuing work; as we imagine, that, if properly associated with the sounds which they denominate, they will tend to impress these sounds more distinctly on the memory of the scholar than the letters C, D, E, F, G, A, B, from which characters, except in sol-fa-ing, the notes in the diatonic series are generally named in Britain. Amongst us, in the progress of intonation, the syllables ut, re, and si, have been omitted, by which means the teachers of church-music have rendered it still more difficult to express by the four remaining denominations the various changes of the semitones in the octave. As these artificially change their places, the seven syllables above mentioned also diversify their powers, and are variously arranged according to the intervals in which the notes they are intended to signify may be placed.

For an account of these variations, see Rousseau's Musical Dictionary, article GAMME. See also the Essay towards a Rational System of Music, by John Holden, part i. chap. 1.

Prelim. the first where the reasons for establishing that rule are given.

94 Some rules, on account of their intricacy, transferred to the notes. That we may not present at once too great a number of objects and precepts, I have transferred to the notes in the second part several rules and observations which are less frequently put in practice, which perhaps it may be proper to omit till the treatise is read a second time, when the reader is well acquainted with the essential and fundamental rules explained in it.

This second part, strictly speaking, presupposes, no more than the first, any habit of singing, nor even any knowledge of music; it only requires that one should know, not even the rules and manner of intonation, but merely the position of the notes in the clef fa or F on the fourth line, and that of sol or G upon the second: and even this knowledge may be acquired from the work itself; for in the beginning of the second part I explain the positions of the clefs and of the notes. Nothing else is necessary but to render it a little familiar to our memory, and we shall have no more difficulty in it.

93 All the rules of composition not to be expected in an elementary essay. It would be wrong to expect here all the rules of composition, and especially those which direct the composition of music in several parts, and which, being less severe and indispensable, may be chiefly acquired by practice, by studying the most approved models, by the assistance of a proper master, but above all by the cultivation of the ear and of the taste. This treatise is properly nothing else, if I may be allowed the expression, but the rudiments of music, intended for explaining to beginners the fundamental principles, not the practical detail of composition. Those who wish to enter more deeply into this detail, will either find it in Mr Rameau's treatise of harmony, or in the code of music which he published more lately (1), or lastly in the explication of the theory and practice of music by M. Bethizi (x): this last book appears to me clear and methodical.

One may look upon it (with respect to a practical detail) as a supplement to my own performance. I do this justice to the author with so much more cheerfulness, as he is entirely unknown to me, and as his animadversions upon my work appear to me less severe than it deserved (u).

94 Nature the essential mistress of musical composition. Is it necessary to add, that, in order to compose music in a proper taste, it is by no means enough to have familiarized with much application the principles explained in this treatise? Here can only be learned the mechanism of the art; it is the province of nature alone to accomplish the rest. Without her assistance, it is no more possible to compose agreeable music by having read these elements, than to write verses in a proper manner with the Dictionary of Richelet. In one word, it is the elements of music alone, and not the principles of genius, that the reader may expect to find in this treatise.

Such was the aim I pursued in its composition, and Definitions such should be the ideas of the reader in its perusal. Once more let me add, that to the discovery of its fundamental principles I have not the remotest claim. The sole end which I proposed was to be useful; to reach that end, I have omitted nothing which appeared necessary, and I should be sorry to find my endeavours unsuccessful.

DEFINITIONS OF SEVERAL TECHNICAL TERMS.

1. What is meant by Melody, by Chord, by Harmony, by Interval.

95 1. Melody is nothing else but a series of sounds Melody, which succeed one to another in a manner agreeable what. to the ear.

96 2. That is called a chord which arises from the Chord and mixture of several sounds heard at the same time; and harmony is properly a series of chords which in their succession one to another delights the ear. A single chord is likewise sometimes called harmony, to signify the consequence of sounds which that chord creates, and the sensation produced in the ear by that consequence. We shall occasionally use the word harmony in this last sense, but in such a manner as never to leave our meaning ambiguous.

3. In melody and harmony, the distance between one sound and another is called an interval; and this is increased or diminished as the sounds between which it intervenes are higher or lower one than the other. See later.

4. That we may learn to distinguish the intervals, and the manner of perceiving them, let us take the ordinary scale ut, re, mi, fa, sol, la, si, UT, which every person whose ear or voice is not extremely false naturally modulates. These are the observations which will occur to us in singing this gammut.

97 The sound re is higher or sharper than the sound ut, the sound mi higher than the sound re, the sound fa higher than the sound mi, &c. and so through the whole octave; so that the interval or the distance from the sound ut to the sound re, is less than the interval or distance between the sound ut and the sound mi, the interval from ut to mi is less than that between ut and fa, &c. and in short that the interval from the first to the second ut is the greatest of all. To distinguish the first from the second ut, I have marked the last with capital letters.

98 5. In general, the interval between two sounds is The proportionally greater, as one of these sounds is higher or lower with relation to the other: but it is necessary to observe, that two sounds may be equally high or low, though unequal in their force. The string of a violin touched with a bow produces always a sound equally high, whether strongly or faintly struck; the sound will only have a greater or lesser degree of strength. It is the same with vocal modulation.

(1) From my general recommendation of this code, I except the reflections on the principles of sound which are at the end, and which I should not advise any one to read.

(x) Printed at Paris by Lambert in the year 1754.

(u) That criticism and my answers may be seen in the Journeaux Economiques of 1752.

Definition. lation; let any one form a sound by gradually impelling or swelling the voice, the sound may be perceived to increase in its energy, whilst it continues always equally low or equally high.

99 Between tonic and semitone intervals.
6. We must likewise observe concerning the scale, that the intervals between ut and re, between re and mi, between fa and sol, between sol and la, between la and si, are equal, or at least nearly equal; and that the intervals between mi and fa, and between si and ut, are likewise equal among themselves, but consist almost only of half the former. This fact is known and recognised by every one: the reason for it shall be given in the sequel; in the mean time every one may ascertain its reality by the assistance of an experiment (A).

7. It is for this reason that they have called the interval from mi to fa, and from si to ut, a semitone; whereas those between ut and re, re and mi, fa and sol, sol and la, la and si, are tones.

* See the figure marked A.
† See Inter-
val.

The tone is likewise called a second major*, and the semitone a second minor†.

8. To descend or rise diatonically, is to descend or rise from one sound to another by the interval of a tone or of a semitone, or in general by seconds, whether major or minor; as from re to ut, or from ut to re, from fa to mi, or from mi to fa.

11. The Terms by which the different Intervals of the Gammut are denominated. Definitions.

9. An interval composed of a tone and a semitone, as from mi to sol, from la to ut, or from re to fa, is nor, what. called a third minor. 100

An interval composed of two full tones, as from ut to mi, from fa to la, or from sol to si, is called a third major. 101

An interval composed of two tones and a semitone, as from ut to fa, or from sol to ut, is called a fourth. 102

An interval consisting of three full tones, as from fa to si, is called a tritone or fourth redundant. 103

An interval consisting of three tones and a semitone, as from ut to sol, from fa to ut, from re to la, or from mi to si, &c. is called a fifth. 104

An interval composed of three tones and two semitones, as from mi to ut, is called a sixth minor. 105

An interval composed of four tones and a semitone, as from ut to la, is called a sixth major. 106

An interval consisting of four tones and two semitones, as from re to ut, is called a seventh minor. 107

An interval composed of five tones and a semitone, as from ut to si, is called a seventh major. 108

(A) This experiment may be easily tried. Let any one sing the scale of ut, re, mi, fa, sol, la, si, UT, it will be immediately observed without difficulty, that the last four notes of the octave sol, la, si, UT, are quite similar to the first ut, re, mi, fa; inasmuch, that if, after having sung this scale, one would choose to repeat it, beginning with ut in the same tone which was occupied by sol in the former scale, the note re of the last scale would have the same sound with the note la in the first, the mi with the si, and the fa with the ut.

From whence it follows, that the interval between ut and re, is the same as between sol and la; between re and mi, as between la and si; and mi and fa, as between si and ut.

It will likewise be found, that from re to mi, from fa to sol, there is the same interval as from ut to re. To be convinced of this, we need only sing the scale once more; then sing it again, beginning with ut, in this last scale, in the same tone which was given to re in the first; and it will be perceived, that the re in the second scale will have the same sound, at least as far as the ear can discover, with the mi in the former scale; from whence it follows, that the difference between re and mi is, at least as far as the ear can perceive, equal to that between ut and re. It will also be found, that the interval between fa and sol is, so far as our sense can determine, the same with that between ut and re.

This experiment may perhaps be tried with some difficulty by those who are not inured to form the notes and change the key; but such may very easily perform it by the assistance of a harpichord, by means of which the performer will be saved the trouble of retaining the sounds in one intonation whilst he performs another. In touching upon this harpichord the keys sol, la, si, ut, and in performing with the voice at the same time ut, re, mi, fa, in such a manner that the same sound may be given to ut in the voice with that of the key sol in the harpichord, it will be found that re in the vocal intonation shall be the same with la upon the harpichord, &c.

It will be found likewise by the same harpichord, that if one should sing the scale beginning with ut in the same tone with mi on the instrument, the re which ought to have followed ut, will be higher by an extremely perceptible degree than the fa which follows mi: thus it may be concluded, that the interval between mi and fa is less than between ut and re; and if one would rise from fa to another sound which is at the same distance from fa as fa from mi, he would find in the same manner, that the interval from mi to this new sound is almost the same as that between ut and re. The interval then from mi to fa is nearly half of that between ut and re.

Since then, in the scale thus divided, ut, re, mi, fa, sol, la, si, UT, the first division is perfectly like the last; and since the intervals between ut and re, between re and mi, and between fa and sol, are equal; it follows, that the intervals between sol and la, and between la and si, are likewise equal to every one of the three intervals between ut and re, between re and mi, and between fa and sol; and that the intervals between mi and fa and between si and ut are also equal, but that they only constitute one half of the others.

Definition. And in short, an interval consisting of five tones and two semitones, as from ut to UT, is called an octave.

¹⁰⁹
Octave,
what. A great many of the intervals which have now been mentioned, are still signified by other names, as may be seen in the beginning of the second part; but those which we have now given are the most common, and the only terms which our present purpose demands.

¹¹⁰
Unison,
what. 10. Two sounds equally high, or equally low, however unequal in their force, are said to be in unison one with the other.

11. If two sounds form between them any interval, whatever it be, we say, that the highest when ascending is in that interval with relation to the lowest; and when descending, we pronounce the lowest in the same interval with relation to the highest. Thus in the third minor mi, sol, where mi is the lowest and sol the highest sound, sol is a third minor from mi ascending, and mi is third minor from sol in descending.

12. In the same manner, if, speaking of two sonorous bodies, we should say, that the one is a fifth above the other in ascending; this infers that the sound given by the one is at the distance of a fifth ascending from the sound given by the other.

III. Of Intervals greater than the Octave.

See fig. B. 13. If, after having sung the scale ut, re, mi, fa, sol, la, si, UT, one would carry this scale still farther in ascent, it would be discovered without difficulty that a new scale would be formed, UT, RE, MI, FA, &c. entirely similar to the former, and of which the sounds will be an octave ascending, each to its correspondent note in the former scale: thus RE, the second note of the second scale, will be an octave in ascent to the re of the first scale; in the same manner MI shall be the octave to mi, &c. and so of the rest.

¹¹¹
Definition. 14. As there are nine notes from the first ut to the second RE, the interval between these two sounds is called a ninth, and this ninth is composed of six full tones and two semitones. For the same reason the interval from ut to FA is called an eleventh, and the interval between ut and SOL, a twelfth, &c.

¹¹²
It is plain that the ninth is the octave of the second, and the eleventh of the fourth, and the twelfth of the fifth, &c.

¹¹³
The octave above the octave of any sound is called a double octave; the octave of the double octave is called a triple octave, and so of the rest.

The double octave is likewise called a fifteenth; and for the same reason the double octave of the third is called a seventeenth, the double octave of the fifth a nineteenth, &c. (n).

IV. What is meant by Sharps and Flats.

15. It is plain that one may imagine the five tones which enter into the scale, as divided each into two semitones; thus one may advance from ut to re, forming in his progress an intermediate sound, which shall be higher by a semitone than ut, and lower in the same degree than re. A sound in the scale is called sharp, when it is raised by a semitone; and it is marked with this character $\backslash sharp$: thus ut $\backslash sharp$ signifies ut sharp, that is to say, ut raised by a semitone above its pitch in the natural scale. A sound in the scale depressed by a semitone is called flat, and is marked thus, $\backslash flat$: thus la $\backslash flat$ signifies la flat, or la depressed by a semitone.

V. What is meant by Consonances and Dissonances.

16. A chord composed of sounds whose union or consonance pleases the ear is called a consonance; and hence, the sounds which form this chord are said to be consonant.

(n) Let us suppose two vocal strings formed of the same matter, of the same thickness, and equal in their tension, but unequal in their length, it will be found by experience.

1^st, That if the shortest is equal to half the longest, the sound which it will produce must be an octave above the sound produced by the longest.

2^dy, That if the shortest constitutes a third part of the longest, the sound which it produces must be a twelfth above the sound produced by the longest.

3^dy, That if it constitutes the fifth part, its sound will be a seventeenth above.

Besides, it is a truth demonstrated and generally admitted, that in proportion as one musical string is less than another, the vibrations of the least will be more frequent (that is to say, its departures and returns through the same space) in the same time; for instance, in an hour, a minute, a second, &c. in such a manner that one string which constitutes a third part of another, forms three vibrations, whilst the largest has only accomplished one. In the same manner, a string which is one half less than another, performs two vibrations, whilst the other only completes one; and a string which is only the fifth part of another, will perform five vibrations in the same time which is occupied by the other in one.

From thence it follows, that the sound of a string is proportionally higher or lower, as the number of its vibrations is greater or smaller in a given time; for instance, in a second.

It is for that reason, that if we represent any sound whatever by 1, one may represent the octave above by 2, that is to say, by the number of vibrations formed by the string which produces the octave, whilst the longest string only vibrates once; in the same manner we may represent the twelfth above the sound 1 by 3, the seventeenth major above 5, &c. But it is very necessary to remark, that by these numerical expressions, we do not pretend to compare sounds as such; for sounds in themselves are nothing but mere sensations, and it cannot be said of any sensation that it is double or triple to another: thus the expressions 1, 2, 3, &c. employed to denominate a sound, its octave above, its twelfth above, &c. signify only, that if a string performs a certain number of vibrations, for instance, in a second, the string which is in the octave above shall double the number in the same time, the string which is in the twelfth above shall triple it, &c.

Thus to compare sounds among themselves is nothing else than to compare among themselves the numbers of vibrations which are formed in a given time by the strings that produce these sounds.

Definition. A sound one with relation to the other. The reason of this denomination is, that a chord is found more perfect, as the sounds which form it coalesce more closely among themselves.

17. The octave of a sound is the most perfect of consonances of which that sound is susceptible; then the fifth, afterwards the third, &c. This is a fact founded on experiment.

18. A number of sounds simultaneously produced whose union is disagreeable to the ear is called a dissonance.

and the sounds which form it are said to be dissonant one with relation to the other. The second, the tritone, and the seventh of a sound, are dissonants with relation to it. Thus the sounds ut re, ut fa, or ut, fa f, &c. simultaneously heard, form a dissonance. The reason which renders dissonance disagreeable, is, that the sounds which compose it, seem by no means coalesce to the ear, and are heard each of them by itself as distinct sounds, though produced at the same time.

PART I. THEORY OF HARMONY.

CHAP. I. Preliminary and Fundamental Experiments.

EXPERIMENT I.

29. WHEN a sonorous body is struck till it gives a sound, the ear, besides the principal sound and its octave, perceives two other sounds very high, of which one is the twelfth above the principal sound, that is to say, the octave to the fifth of that sound;

and the other is the seventeenth major above the same sound, that is to say, the double octave of its third major.

20. This experiment is peculiarly sensible upon the thick strings of the violoncello, of which the sound being extremely low, gives to an ear, though not very much practised, an opportunity of distinguishing with sufficient ease and clearness the twelfth and seventeenth now in question (c).

21. The principal sound is called the generator *; * See Gen. and Mater.

(c) Since the octave above the sound 1 is 2, the octave below that same sound shall be $\backslash frac\{1\}\{2\}$; that is to say, that the string which produces this octave shall have performed half its vibration, whilst the string which produces the sound 1 shall have completed one. To obtain therefore the octave above any sound, the operator must multiply the quantity which expresses the sound by 2; and to obtain the octave below, he must on the contrary divide the same quantity by 2.

The fifth then above the sound 1 being the octave beneath the twelfth, shall be, as we have immediately observed, $\backslash frac\{1\}\{2\}$; which signifies that this string performs $\backslash frac\{1\}\{2\}$ vibrations; that is to say, one vibration and a half during a single vibration of the string which gives the sound 1.

To obtain the fourth above the sound 1, we must take the twelfth below that sound, and the double octave above that twelfth. In effect, the twelfth below ut, for instance, is fa, of which the double octave fa is the fourth above ut. Since then the twelfth below 1 is $\backslash frac\{1\}\{3\}$, it follows that the double octave above this twelfth, that is to say, the fourth from the sound 1 in ascending, will be $\backslash frac\{1\}\{3\}$ multiplied by 4, or $\backslash frac\{4\}\{3\}$.

In short, the third major being nothing else but the double octave beneath the seventeenth, it follows, that the third major above the sound 1 will be 5 divided by 4, or in other words $\backslash frac\{5\}\{4\}$.

The third major of a sound, for instance the third major mi, from the sound ut, and its fifth sol, form between them a third minor mi, sol; now mi is $\backslash frac\{4\}\{3\}$, and sol $\backslash frac\{3\}\{4\}$, by what has been immediately demonstrated: from whence it follows, that the third minor, or the interval between mi and sol, shall be expressed by the relation of the fraction $\backslash frac\{3\}\{4\}$ to the fraction $\backslash frac\{4\}\{3\}$.

To determine this relation, it is necessary to remark, that $\backslash frac\{3\}\{4\}$ are the same thing with $\backslash frac\{12\}\{16\}$, and that $\backslash frac\{4\}\{3\}$ are the same thing with $\backslash frac\{16\}\{12\}$; so that $\backslash frac\{3\}\{4\}$ shall be to $\backslash frac\{4\}\{3\}$ in the same relation as $\backslash frac\{12\}\{16\}$ to $\backslash frac\{16\}\{12\}$; that is to say, in the same relation as 10 to 12, or as 5 to 6. If, then, two sounds form between themselves a third minor, and that the first is represented by 5, the second shall be expressed by 6; or, what is the same thing, if the first is represented by 1, the second shall be expressed by $\backslash frac\{6\}\{5\}$.

Thus

Theory of Harmony. and the two other sounds which it produces, and with which it is accompanied, are, inclusive of its octave, called its harmonics §.

22. There is no person insensible of the resemblance which subsists between any sound and its octave, whether above or below. These two sounds, when heard together, almost entirely coalesce in the organ of sensation. We may besides be convinced (by two facts which are extremely simple) of the facility with which one of these sounds may be taken for the other.

Let it be supposed that any person has an inclination to sing a tune, and having at first begun this air upon a pitch too high or too low for his voice, so that he is obliged, lest he should strain himself too much, to sing the tune in question on a key higher or lower than the first; I affirm, that, without being initiated in the art of music, he will naturally take his new key in the octave below or the octave above the first; and that in order to take this key in any other interval except the octave, he will find it necessary to exert a sensible degree of attention. This is a fact of which we may easily be persuaded by experience.

Another fact. Let any person sing a tune in our presence, and let it be sung in a tone too high or too

low for our voice; if we wish to join in singing this air, we naturally take the octave below or above, and frequently, in taking this octave, we imagine it to be the unison (D).

23. To render our ideas still more precise and permanent, we shall call the tone produced by the sonorous body ut; it is evident, by the first experiment, that this sound is always attended by its 12th and 17th major; that is to say, with the octave of sol, and the double octave of mi.

24. This octave of sol then, and this double octave of mi, produce the most perfect chord which can be joined with ut, since that chord is the work and choice of nature (§).

25. For the same reason, the modulation formed by ut with the octave of sol and the double octave of mi, sung one after the other, would likewise be the most simple and natural of all modulations which do not descend or ascend directly in the diatonic order, if our voices had sufficient compass to form intervals so great without difficulty: but the ease and freedom with which

Thus the third minor, an harmonic sound which is even found in the protracted and coalescent tones of a sonorous body between the sound mi and sol, an harmonic of the principal sound, may be expressed by the fraction $\backslash frac\{3\}\{4\}$.

N. B. One may see by this example, that in order to compare two sounds one with another which are expressed by fractions, it is necessary first to multiply the numerator of the fraction which expresses the first by the denominator of the fraction which expresses the second, which will give a primary number; as here the numerator 5 of the fraction $\backslash frac\{5\}\{4\}$, multiplied by 2 of the fraction $\backslash frac\{1\}\{2\}$, has given 10. Afterwards may be multiplied the numerator of the second fraction by the denominator of the first, which will give a secondary number, as here 12 is the product of 4 multiplied by 3; and the relation between these two numbers (which in the preceding example are 10 and 12), will express the relation between these sounds, or, what is the same thing, the interval which there is between the one and the other; in such a manner, that the farther the relation between these sounds departs from unity, the greater the interval will be.

Such is the manner in which we may compare two sounds one with another whose numerical value is known. We shall now show the manner how the numerical expression of a sound may be obtained, when the relation which it ought to have with another sound is known whose numerical expression is given.

Let us suppose, for example, that the third major of the fifth $\backslash frac\{1\}\{4\}$ is sought. That third major ought to be, by what has been shown above, the $\backslash frac\{1\}\{4\}$ of the fifth; for the third major of any sound whatever is the $\backslash frac\{1\}\{4\}$ of that sound. We must then look for a fraction which expresses the $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{4\}$; which is done by multiplying the numerators and denominators of both fractions one by the other, from whence results the new fraction $\backslash frac\{1\}\{16\}$. It will likewise be found that the fifth of the fifth is $\backslash frac\{1\}\{2\}$, because the fifth of the fifth is the $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$.

Thus far we have only treated of fifths, fourths, thirds major and minor, in ascending; now it is extremely easy to find by the same rules the fifths, fourths, thirds major and minor in descending. For suppose ut equal to 1, we have seen that its fifth, its fourth, its third, its major and minor in ascending, are $\backslash frac\{1\}\{4\}$, $\backslash frac\{1\}\{5\}$, $\backslash frac\{1\}\{6\}$, $\backslash frac\{1\}\{7\}$. To find its fifth, its fourth, its third, its major and minor in descending, nothing more is necessary than to reverse these fractions, which will give $\backslash frac\{4\}\{1\}$, $\backslash frac\{5\}\{1\}$, $\backslash frac\{6\}\{1\}$, $\backslash frac\{7\}\{1\}$.

(D) It is not then imagined that we change the value of a sound in multiplying or dividing it by 2, by 4, or by 8, &c. the number which expresses these sounds, since by these operations we do nothing but take the simple, double, or triple octave, &c. of the sound in question, and that a sound coalesces with its octave.

(E) The chord formed with the twelfth and seventeenth major united with the principal sound, being exactly conformed to that which is produced by nature, is likewise for that reason the most agreeable of all; especially when the composer can proportion the voices and instruments together in a proper manner to give this chord its full effect. M. Rameau has executed this with the greatest success in the opera of Pygmalion, page 34. where Pygmalion sings with the chorus, L'amour triomphe, &c.: in this passage of the chorus, the two parts of the vocal and instrumental basses give the principal sound and its octave; the first part above, or treble, and that of the counter-tenor, produce the seventeenth major, and its octave, in descending; and in short, the second part, or tenor above, gives the twelfth.

Theory of which we can substitute its octave to any sound, when
Harmony. it is more convenient for the voice, afford us the means
of representing this modulation.

119
Mode ma-
jor, what.
26. It is on this account that, after having sung
the tone ut, we naturally modulate the third mi, and
the fifth sol, instead of the double octave of mi, and
the octave of sol; from whence we form, by joining
the octave of the sound ut, this modulation, ut, mi, sol,
ut, which in effect is the simplest and easiest of them all;
and which likewise has its origin even in the protracted
and compounded tones produced by a sonorous body.

See
Mode. See
likewise
Interval.
27. The modulation ut, mi, sol, ut, in which the
chord ut, mi, is a third major, constitutes that kind
of harmony or melody which we call the mode major;
from whence it follows, that this mode results from
the immediate operation of nature.

110
Mode mi-
nor, what.
28. In the modulation ut, mi, sol, of which we
have now been treating, the sounds mi and sol are so
proportioned one to the other, that the principal
sound ut (art. 19.) causes both of them to resound;
but the second tone mi does not cause sol to resound,
which only forms the interval of a third minor.

29. Let us then imagine, that, instead of this
sound mi, one should substitute between the sounds ut
and sol another note which (as well as the sound ut) has
the power of causing sol to resound, and which is,
however, different from the sound ut; the sound which
we explore ought to be such, by art. 19. that it may
have for its 17th major sol, or one of the octaves of
sol; of consequence the sound which we seek ought
to be a 17th major below sol, or, what is the same
thing, a third major below the same sol. Now the
sound mi being a third minor beneath sol, and the
third major being (art. 9.) greater by a semitone than
the third minor, it follows, that the sound of which we
are in search shall be a semitone beneath the natural
mi, and of consequence mi b.

30. This new arrangement, ut, mi b, sol, in which
the sounds ut and mi b have both the power of causing
sol to resound, though ut does not cause mi b to re-
sound, is not indeed equally perfect with the first ar-
rangement ut, mi, sol; because in this the two sounds
mi and sol are both the one and the other generated
by the principal sound ut; whereas, in the other, the
sound mi b is not generated by the sound ut; but this
arrangement ut, mi b, sol, is likewise dictated by na-
ture (art. 19.), though less immediately than the for-
mer.
N° 233.

mer; and accordingly experience evinces that the ear
accommodates itself almost as well to the latter as to
the former.

121
31. In this modulation or chord ut, mi b, sol, ut, Origin of
it is evident that the third from ut to mi b is minor; mode mi-
and such is the origin of that mode which we call minor (x).
See
Mode. See
also Inter-
val.

122
32. The most perfect chords then are, 1. All chords
related one to another, as ut, mi, sol, ut, consisting of
any sound of its third major, of its fifth, and of its
octave. 2. All chords related one to another, as ut
mi b, sol, ut, consisting of any sound, of its third
minor, of its fifth, and of its octave. In effect, these
two kinds of chords are exhibited by nature; but the
first more immediately than the second. The first are
called perfect chords major, the second perfect chords
minor.

CHAP. III. Of the Series which the Fifth re-
quires, and of the Laws which it observes.

123
33. SINCE the sound ut causes the sound sol to be
heard, and is itself heard in the sound fa, which
sounds sol and fa are its two-twelfths, we may ima-
gine a modulation composed of that sound ut and its
two-twelfths, or, which is the same thing (art. 22.),
of its two-fifths, fa and sol, the one below, the other
above; which gives the modulation or series of fifths
fa, ut, sol, which I call the fundamental base of ut by
fifths.

We shall find in the sequel (Chap. XVIII.), that
there may be some fundamental bases by thirds, de-
duced from the two seventeenths, of which the one is
an attendant of the principal sound, and of which the
other includes that sound. But we must advance step
by step, and satisfy ourselves at present to consider im-
mediately the fundamental base by fifths.

34. Thus, from the sound ut, one may make a
transition indifferently to the sound sol, or to the
sound fa.

35. One may, for the same reason, continue this
kind of fifths in ascending, and in descending, from ut,
in this manner:

mi b, fi b, fa, ut, sol, re, la, &c.

And from this series of fifths one may pass to any
sound which immediately precedes or follows it.

36. But it is not allowed in the same manner to
pass

(x) The origin which we have here given of the mode minor, is the most simple and natural that can
possibly be given. In the first edition of this treatise, I had followed Mr. Rameau in deducing it from the fol-
lowing experiment.—If you put in vibration a musical string AB, and if there are at the same time contiguous
to this two other strings CF, LM, of which the first shall be a twelfth below the string AB, and the second
LM a seventeenth major below the same AB, the strings CF, LM, will vibrate without being struck as soon
as the string AB shall give a sound, and divide themselves by a kind of undulation, the first into three, the last
into five equal parts; in such a manner, that, in the vibration of the string CF, you may easily distinguish two
points at rest D, E, and in the tremulous motion of the string LM four acquiescent points N, O, P, Q, all
placed at equal distances from each other, and dividing the strings into three or five equal parts. In this
experiment, says M. Rameau, if we represent by ut the tone of the string AB, the two other strings will
represent the sounds fa and la b; and from thence M. Rameau deduces the modulation fa, la b, ut, and of
consequence the mode minor. The origin which we have assigned to the minor mode in this new edition,
appears to me more direct and more simple, because it presupposes no other experiment than that of art. 19.
and because also the fundamental sound ut is still retained in both the modes, without being obliged, as
M. Rameau found himself, to change it into fa.

Theory of Harmony. 124 Exception to the rule. 125 Two perfect chords in succession proved.

pals from one found to another which is not immediately contiguous to it; for instance, from ut to re, or from re to ut: for this very simple reason, that the found re is not contained in the found ut, nor the found ut in that of re; and thus these sounds have not any alliance the one with the other, which may authorise the transition from one to the other.

37. And as these sounds ut and re, by the first experiment, naturally bring along with them the perfect chords consisting of greater intervals ut, mi, sol, ut, re, fa, la, re; hence may be deduced this rule, That two perfect chords, especially if they are major (G), cannot succeed one another diatonically in a fundamental bass; we mean, that in a fundamental bass two sounds cannot be diatonically placed in succession, each of which, with its harmonics, forms a perfect chord, especially if this perfect chord be major in both.

CHAP. IV. Of Modes in general.

126 Mode in general, what. 127 Modes, how represented by the series of fifths.

38. A mode, in music, is nothing else but the order of sounds prescribed, as well in harmony as melody, by the series of fifths. Thus the three sounds fa, ut, sol, and the harmonics of each of these three sounds, that is to say, their thirds major and their fifths, compose all the major modes which are proper to ut.

39. The series of fifths then, or the fundamental bass fa, ut, sol, of which ut holds the middle space, may be regarded as representing the mode of ut. One may likewise take the series of fifths, or fundamental bass, ut, sol, re, as representing the mode of sol; in the same manner si, fa, ut, will represent the mode of fa.

By this we may see, that the mode of sol, or rather the fundamental bass of that mode, has two sounds in common with the fundamental bass of the mode of ut. It is the same with the fundamental bass of the mode fa.

128 Principal mode, and adjuncts, what. See Ad. jant. 129 Modes related in proportion as their sounds are common.

40. The mode of ut (fa, ut, sol) is called the principal mode with respect to the modes of these two fifths, which are called its two adjuncts.

41. It is then, in some measure, indifferent to the ear whether a transition be made to the one or to the other of these adjuncts, since each of them has equally two sounds in common with the principal mode. Yet the mode of sol seems a little more eligible: for sol is heard amongst the harmonics of ut, and of consequence is implied and signified by ut; whereas ut does not cause fa to be heard, though ut is included in the same found fa. It is hence that the ear, affected by the

VOL. XII. Part II.

mode of ut, is a little more prepossessed for the mode of sol than for that of fa. Nothing likewise is more frequent, nor more natural, than to pass from the mode of ut to that of sol.

42. It is for this reason, as well as to distinguish the two fifths one from the other, that we call sol the fifth above the generator the dominant sound, and the fifth fa beneath the generator the subdominant.

43. It remains to add, as we have seen in the preceding chapter, that, in the series of fifths, we may indifferently pass from one found to that which is contiguous: In the same manner, and for the same reason, one may pass from the mode of sol to the mode of re, after having made a transition from the mode of ut to the mode of sol, as from the mode of fa to the mode of si. But it is necessary, however, to observe, that the ear which has been immediately affected with the principal mode feels always a strong propensity to return to it. Thus the further the mode to which we make a transition is removed from the principal mode, the less time we ought to dwell upon it; or rather, to speak in the terms of the art, the less ought the phrase (faa) of that mode to be protracted.

CHAP. V. Of the Formation of the Diatonic Scale as used by the Greeks.

44. FROM this rule, that two sounds which are contiguous may be placed in immediate succession in the series of fifths, fa, ut, sol, it follows, that one may form this modulation, or this fundamental bass, by fifths, sol, ut, sol, ut, fa, ut, fa.

45. Each of the sounds which forms this modulation brings necessarily along with itself its third major, its fifth, and its octave; in such a way that he who, for instance, sings the note sol, may be reckoned to sing at the same time the notes sol, si, re, sol: in the same manner the found ut in the fundamental bass brings along with it this modulation, ut, mi, sol, ut; and, in short, the same found fa brings along with it fa, la, ut, fa. This modulation then, or this fundamental bass,

sol, ut, sol, ut, fa, ut, fa,
si, ut, re, mi, fa, sol, la;

gives the following diatonic series, which is precisely the diatonic scale of the Greeks. We are ignorant upon what principles they had formed this scale; but it may be sensibly perceived, that that series arises from the bass sol, ut, sol, ut, fa, ut, fa; and that of consequence this bass is justly called fundamental, as being the real primitive modulation, that which

3 T

conducts

(G) I say especially if they are major; for in the major chord re, fa, la, re, besides that the sounds ut and re have no common harmonical relation, and are even dissonant between themselves (Art. 18.), it will likewise be found, that fa forms a dissonance with ut. The minor chord re, fa, la, re, would be more tolerable, because the natural fa which occurs in this chord carries along with it its fifth ut, or rather the octave of that fifth: It has likewise been sometimes the practice of composers, though rather by a licence indulged them than strictly agreeable to their art, to place a minor in diatonic succession to a major chord.

(faa) As the mere English reader, unacquainted with the technical phraseology of music, may be surprised at the use of the word phrase when transferred from language to that art, we have thought proper to insert the definition of Rousseau.

A phrase, according to him, is in melody a series of modulations, or in harmony a succession of chords, which form without interruption a sense more or less complete, and which terminate in a repose by a cadence more or less perfect.

conducts the ear, and which it feels to be implied in the diatonic modulation, fi, ut, re, mi, fa, sol, la. (8).

46. We shall be still more convinced of this truth by the following remarks.

In the modulation fi, ut, re, mi, fa, sol, la, the sounds re and fa form between themselves a third minor, which is not so perfectly true as that between mi and sol (1). Nevertheless, this alteration in the third minor between re and fa gives the ear no pain, because that re and that fa, which do not form between themselves a true third minor, form, each in particular, consonances perfectly just with the sounds in the fundamental bass which correspond with them: for re in the scale is the true fifth of sol, which answers to it in the fundamental bass; and fa in the scale is the true octave of fa, which answers to it in the same bass.

47. If, therefore, these sounds in the scale form consonances perfectly true with the notes which correspond to them in the fundamental bass, the ear gives itself little trouble to investigate the alterations which there may be in the intervals which these sounds in the scale form between themselves. This is a new proof that the fundamental bass is the genuine guide of the ear, and the true origin of the diatonic scale.

48. Moreover, this diatonic scale includes only seven sounds, and goes no higher than fi, which would be the octave of the first: a new singularity, for which

a reason may be given by the principles above established. In reality, in order that the sound fi may succeed immediately in the scale to the sound la, it is necessary that the note sol, which is the only one from whence fi as a harmonic may be deduced, should immediately succeed to the sound fa, in the fundamental bass, which is the only one from whence la can be harmonically deduced. Now, the diatonic succession from fa to sol cannot be admitted in the fundamental bass, according to what we have remarked (art. 36.). The sounds la and fi, then, cannot immediately succeed one another in the scale: we shall see in the sequel why this is not the case in the series ut, re, mi, fa, sol, la, fi, UT, which begins upon ut; whereas the scale in question here begins upon fi.

49. The Greeks likewise, to form an entire octave, added below the first fi the note la, which they distinguished and separated from the rest of the scale, and which for that reason they called prostantambano. See Prostantambano, scale, and put before fi to form the entire octave.

50. The diatonic scale fi, ut, re, mi, fa, sol, la, is composed of two tetrachords, that is to say, of two composed diatonic scales, each consisting of four sounds, fi, ut, re, mi, and mi, fa, sol, la. These two tetrachords are exactly similar; for from mi to fa there is the same interval as from fi to ut, from fa to sol the same as from ut to re, from sol to la the same as from re to mi.

(8) Nothing is easier than to find in this scale the value or proportions of each sound with relation to the sound ut, which we call 1; for the two sounds sol and fa in the bass are $\backslash frac\{1\}\{4\}$ and $\backslash frac\{2\}\{3\}$; from whence it follows,

1. 1. That ut in the scale is the octave of ut in the bass; that is to say, 2.
2. 2. That fi is the third major of sol; that is to say $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{4\}$ (note c), and of consequence $\backslash frac\{1\}\{16\}$.
3. 3. That re is the fifth of sol; that is to say $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{4\}$, and of consequence $\backslash frac\{1\}\{16\}$.
4. 4. That mi is the third major of the octave of ut, and of consequence the double of $\backslash frac\{1\}\{4\}$; that is to say, $\backslash frac\{1\}\{2\}$.
5. 5. That fa is the double octave of fa of the bass, and consequently $\backslash frac\{1\}\{2\}$.
6. 6. That sol of the scale is the octave of sol of the bass, and consequently 3.
7. 7. In short, that la in the scale is the third major of fa of the scale; that is to say, $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{4\}$, or $\backslash frac\{1\}\{16\}$.

Hence then will result the following table, in which each sound has its numerical value above or below it.

And if, for the convenience of calculation, we choose to call the sound ut, of the scale 1; in this case there is nothing to do but to divide each of the numbers by 2, which represent the diatonic scale, and we shall have

(1) In order to compare re with fa, we need only compare $\backslash frac\{2\}\{3\}$ with $\backslash frac\{1\}\{4\}$; the relation between these fractions will be (Note c) that of 9 times 3 to 8 times 4; that is to say, of 27 to 32: the third minor, then, from re to fa, is not true; because the proportion of 27 to 32 is not the same with that of 5 to 6, these two proportions being between themselves as 27 times 6 is to 32 times 5, that is to say, as 162 to 160, or as the halves of these two numbers, that is to say, as 81 to 80.

M. Rameau, when he published, in 1726, his New theoretical and practical System of Music, had not as yet found the true reason of the alteration in the consonance which is between re and fa, and of the little attention which the ear pays to it. For he pretends, in the work now quoted, that there are two thirds minor, one in the proportion of 5 to 6, the other in the proportion of 27 to 32. But the opinion which he has afterwards adopted, seems much preferable. In reality, the genuine third minor, is that which is produced by nature between mi and sol, in the continued tone of those sonorous bodies of which mi and sol are the two harmonics; and that third minor, which is in the proportion of 5 to 6, is likewise that which takes place in the minor mode, and not that third minor which is false and different, being in the proportion of 27 to 32.

Theory of mi (L): this is the reason why the Greeks distinguished these two tetrachords; yet they joined them by the note mi, which is common to both, and which gave them the name of conjunctive tetrachords.

137 Intervals in both tetrachords equal. 51. Moreover, the intervals between any two sounds, taken in each tetrachord in particular, are precisely true: thus, in the first tetrachord, the intervals of ut mi, and si re, are thirds, the one major and the other minor, exactly true, as well as the fourth si mi (M); it is the same thing with the tetrachord mi, fa, sol, la, since this tetrachord is exactly like the former.

138 Intervals between the notes of different tetrachords dissimilar. 52. But the case is not the same when we compare two sounds taken each from a different tetrachord; for we have already seen, that the note re in the first tetrachord forms with the note fa in the second a third minor, which is not true. In like manner it will be found, that the fifth from re to la is not exactly true, which is evident; for the third major from fa to la is true, and the third minor from re to fa is not so: now, in order to form a true fifth, a third major and a third minor, which are both exactly true, are necessary.

139 Another reason for distinguishing the scale into two tetrachords. 53. From thence it follows, that every consonance is absolutely perfect in each tetrachord taken by itself; but that there is some alteration in passing from one tetrachord to the other. This is a new reason for distinguishing the scale into these two tetrachords.

140 The source of tones major and minor investigated. 54. It may be ascertained by calculation, that in the tetrachord si, ut, re, mi, the interval, or the tone from re to mi, is a little less than the interval or tone from ut to re (N). In the same manner, in the second tetrachord mi, fa, sol, la, which is, as we have proved, perfectly similar to the first, the note from sol to

la is a little less than the note from fa to sol. It is for this reason that they distinguish two kinds of tones; the greater tone*, as from ut to re, from fa to sol, &c. &c.; and the lesser †, as from re to mi, from sol to la, &c.

CHAP. VI. The formation of the Diatonic Scale among the Moderns, or the ordinary Gammut.

55. We have just shown in the preceding chapter, how the scale of the Greeks is formed, si, ut, re, mi, fa, sol, la, by means of a fundamental bass composed of three sounds only, fa, ut, sol: but to form the scale ut, re, mi, fa, sol, la, si, UT, which we use at present, we must necessarily add to the fundamental bass the note re, and form, with these four sounds fa, ut, sol, re, the following fundamental bass:

ut, sol, ut, fa, ut, sol, re, sol, ut;

from whence we deduce the modulation or scale

ut, re, mi, fa, sol, la, si, UT.

In effect (O), ut in the scale belongs to the harmony of ut which corresponds with it in the bass; re, which is the second note in the gammut, is included in the harmony of sol, the second note of the bass; mi, the third note of the gammut, is a natural harmonic of ut, which is the third sound in the bass, &c.

56. From thence it follows, that the diatonic scale of the Greeks is, at least in some respects, more simple than ours; since the scale of the Greeks (chap. v.) may be formed alone from the mode proper to ut; whereas ours is originally and primitively formed, not only from the mode of ut (fa, ut, sol), but likewise from the mode of sol, (ut, sol, re).

It will likewise appear, that this last scale consists of two parts; of which the one, ut, re, mi, fa, sol, is in the

(L) The proportion of si to ut is as $\backslash frac\{1\}\{2\}$ to 1, that is to say as 15 to 16; that between mi and fa is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$, that is to say (note c), as 5 times 3 to 4 times 4, or as 15 to 16: these two proportions then are equal. In the same manner, the proportion of ut to re is as 1 to $\backslash frac\{9\}\{8\}$, or as 8 to 9; that between fa and sol is as $\backslash frac\{3\}\{4\}$ to $\backslash frac\{1\}\{2\}$; that is to say (note c), as 8 to 9. The proportion of mi to ut is as $\backslash frac\{1\}\{2\}$ to 1, or as 5 to 4; that between fa and la is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$, or as 5 to 4: the proportions here then are likewise equal.

(M) The proportion of mi to ut is as $\backslash frac\{1\}\{2\}$ to 1, or as 5 to 4, which is a true third major; that from re to si is as $\backslash frac\{2\}\{3\}$ to $\backslash frac\{1\}\{2\}$; that is to say, as 9 times 16 to 15 times 8, or as 9 times 2 to 15, or as 6 to 5. In like manner, we shall find, that the proportion of mi to si is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{1\}\{2\}$; that is to say, as 5 times 16 to 15 times 4, or as 4 to 3, which is a true fourth.

(N) The proportion of re to ut is as $\backslash frac\{2\}\{3\}$ to 1, or as 9 to 8; that of mi to re is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{2\}\{3\}$, that is to say, as 40 to 36, or as 10 to 9: now $\backslash frac\{1\}\{9\}$ is less removed from unity than $\backslash frac\{2\}\{9\}$; the interval then from re to mi is a little less than that from ut to re.

If any one would wish to know the proportion which $\backslash frac\{1\}\{9\}$ bear to $\backslash frac\{2\}\{9\}$, he will find (note c) that it is as 8 times 10 to 9 times 9, that is to say, as 80 to 81. Thus the proportion of a lesser to a greater tone is as 80 to 81; this difference between the greater and lesser tone is what the Greeks called a comma.

We may remark, that this difference of a comma is found between the third minor when true and harmonical, and the same chord when it suffers alteration re fa, of which we have taken notice in the scale (note 1); for we have seen, that this third minor thus altered is in the proportion of 80 to 81 with the true third minor.

(O) The values or estimates of the notes shall be the same in this as in the former scale, excepting only the tone la; for re being represented by $\backslash frac\{2\}\{3\}$, its fifth will be expressed by $\backslash frac\{1\}\{2\}$; so that the scale will be numerically signified thus:

$\backslash frac\{1\}\{2\}$ $\backslash frac\{2\}\{3\}$ $\backslash frac\{1\}\{2\}$ $\backslash frac\{1\}\{2\}$ $\backslash frac\{1\}\{2\}$ $\backslash frac\{1\}\{2\}$ $\backslash frac\{1\}\{2\}$ $\backslash frac\{1\}\{2\}$
ut, re, mi, fa, sol, la, si, UT.

Where you may see, that the note la of this scale is different from that in the scale of the Greeks; and that the la in the modern series stands in proportion to that of the Greeks as $\backslash frac\{3\}\{8\}$ to $\backslash frac\{1\}\{2\}$, that is to say, as 81 to 80; these two la's then likewise differ by a comma.

57. It is for this reason that the note sol is found to be twice repeated in immediate succession in this scale; once as the fifth of ut, which corresponds with it in the fundamental bass; and again, as the octave of sol, which immediately follows ut in the same bass. As to what remains, these two consecutive sol's are otherwise in perfect union. It is for this reason that we are satisfied with singing only one of them when one modulates the scale ut, re, mi, fa, sol, la, si, UT; but this does not prevent us from employing a pause or repose, expressed or understood, after the sound fa. There is no person who does not perceive this whilst he himself sings the scale.

58. The scale of the moderns, then, may be considered as consisting of two tetrachords, disjunctive indeed, but perfectly similar one to the other, ut, re, mi, fa, and sol, la, si, ut, one in the mode of ut, the other in that of sol. For what remains, we shall see in the sequel by what artifice one may cause the scale ut, re, mi, fa, sol, la, si, UT, to be regarded as belonging to the mode of ut alone. For this purpose it is necessary to make some changes in the fundamental bass, which we have already alligned: but this shall be explained at large in chap. xiii.

59. The introduction of the mode proper to sol in the fundamental bass has this happy effect, that the notes fa, sol, la, si, may immediately succeed each other in ascending the scale, which cannot take place (art. 43.) in the diatonic series of the Greeks, because that series is formed from the mode of ut alone. From whence it follows:

1. 1. That we change the mode at every time when we modulate three notes in succession.
2. 2. That if these three notes are sung in succession in the scale ut, re, mi, fa, sol, la, si, UT, this cannot be done but by the assistance of a pause expressed or understood after the note fa; inasmuch, that the three tones fa, sol, la, si, (thrice only because the note sol which is repeated is not enumerated) are supposed to belong to two different tetrachords.

60. It ought not then any longer to surprise us, that we feel some difficulty whilst we ascend the scale in singing three tones in succession, because this is impracticable without changing the mode; and if one pause in the same mode, the fourth found above the mode the first note will never be higher than a semitone above the one that immediately precedes it; as may be seen by singing ut, re, mi, fa, and by sol, la, si, ut, where there is no more than a semitone between mi and fa, and between si and ut.

61. We may likewise observe in the scale ut, re, mi, fa, that the third minor from re to fa is not true, for the reasons which have been already given (art. 49.). though all it is the same case with the third minor from la to ut, and with the third major from fa to la: but each of these sounds form otherwise consonances perfectly true, with their correspondent sounds in the fundamental bass.

62. The thirds la ut, fa la, which were true in the former scale, are false in this; because in the former scale la was the third of fa, and here it is the fifth of re, which corresponds with it in the fundamental bass.

63. Thus it appears, that the scale of the Greeks contains fewer consonances that are altered than ours (P); and this likewise happens from the introduction of the mode of sol into the fundamental bass (Q).

We see likewise that the value of la in the diatonic scale, a value which authors have been divided in ascertaining, solely depends upon the fundamental bass, and that it must be different according as the note la has fa or re for its bass. See the note (O).

CHAP. VII. Of Temperament.

64. THE alterations which we have observed in the intervals between particular sounds of the diatonic scale, naturally lead us to speak of temperament. To give why a clear idea of this, and to render the necessity of it palpable, let us suppose that we have before us an instrument with keys, a harpichord, for instance, consisting of several octaves or scales, of which each includes its twelve semitones.

(P) In the scale of the Greeks, the note la being a third from fa, there is an altered fifth between la and re; but in ours, la being a fifth to re, produces two altered thirds, fa la, and la ut; and likewise a fifth altered, la mi, as we shall see in the following chapter. Thus there are in our scale two intervals more than in the scale of the Greeks which suffer alteration.

(Q) But here it may be with some colour objected: The scale of the Greeks, it may be said, has a fundamental bass more simple than ours; and besides, in it there are fewer chords which will not be found exactly true: why then, notwithstanding this, does ours appear more easy to be sung than that of the Greeks? The Grecian scale begins with a semitone, whereas the intonation prompted by nature seems to impel us to rise by a full tone at once. This objection may be thus answered. The scale of the Greeks is indeed better disposed than ours for the simplicity of the bass, but the arrangement of ours is more suitable to natural intonation. Our scale commences by the fundamental sound ut, and it is in reality from that sound that we ought to begin; it is from this that all the others naturally arise, and upon this that they depend; nay, if I may speak so, in this they are included: on the contrary, neither the scale of the Greeks, nor its fundamental bass, commences with ut; but it is from this ut that we must depart, in order to regulate our intonation, whether in rising or descending: now, in ascending from ut, the intonation, even of the Greek scale, gives the series ut, re, mi, fa, sol, la; and so true is it that the fundamental sound ut is here the genuine guide of the ear, that if, before we modulate the sound ut, we should attempt to rise to it by that note in the scale which is most immediately contiguous, we cannot reach it but by the note si, and by the semitone from si to ut. Now to make a transition from si to ut, by this semitone, the ear must of necessity be predisposed for that modulation, and consequently preoccupied with the mode of ut: if this were not the case, we should naturally rise from si to ut, and by this operation pass into another mode.

Theory of Harmony. Let us choose in that harpichord one of the strings which will found the note UT, and let us tune the string SOL to a perfect fifth with UT in ascending; let us afterwards tune to a perfect fifth with this SOL the RE which is above it; we shall evidently perceive that this RE will be in the scale above that from which we set out; but it is also evident that this RE must have in the scale a re which corresponds with it, and which must be tuned a true octave below RE; and between this and SOL there should be the interval of a fifth; so that the re in the first scale will be a true fourth below the SOL of the same scale. We may afterwards tune the note LA of the first scale to a just fifth with this last re; then the note MI in the highest scale to a true fifth with this new LA, and of consequence the mi in the first scale to a true fourth beneath this same LA: Having finished this operation, it will be found that the last mi, thus tuned, will by no means form a just third major from the found UT (r); that is to say, that it is impossible for mi to constitute at the same time the third major of UT and the true fifth of LA; or, what is the same thing, the true fourth of LA in descending.

65. What is still more, if, after having successively and alternately tuned the strings UT, SOL, re, LA, mi, in perfect fifths and fourths one from the other, we continue to tune successively by true fifths and fourths the strings mi, fa, fa, mi, sol, re, mi, fa; we shall find, that, though fa, being a semitone higher than the natural note, should be equivalent to UT natural, it will by no means form a just octave to the first ut in the scale, but be considerably higher (s); yet this fa upon the harpichord ought not to be different from the octave above UT; for every fa and every UT is the same sound, since the octave or the scale only consists of twelve semitones.

66. From thence it necessarily follows, 1. That it is impossible that all the octaves and all the fifths should be just at the same time, particularly in instruments which have keys, where no intervals less than a semitone are admitted. 2. That, of consequence, if the fifths are justly tuned, some alteration must be made in the octaves; now the sympathy or found which subsists between any note and its octave, does not permit us to make such an alteration: this perfect coalescence of sound is the cause why the octave should

(r) The LA considered as the fifth of re is $\backslash frac\{1\}\{2\}$, and the fourth beneath this LA will constitute $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, that is to say, $\backslash frac\{1\}\{4\}$; $\backslash frac\{1\}\{4\}$ then shall be the value of mi, considered as a true fourth from LA in descending: now mi, considered as the third major of the found UT, is $\backslash frac\{1\}\{3\}$, or $\backslash frac\{1\}\{3\}$: these two mi's then are between themselves in the proportion of 81 to 80; thus it is impossible that mi should be at the same time a perfect third major from UT, and a true fourth beneath LA.

(s) In effect, if you thus alternately tune the fifth above, and the fourth below, in the same octave, you may here see what will be the process of your operation.

UT, SOL, a fifth; re a fourth; LA a fifth; mi a fourth; fa a fifth; fa a fourth; mi a fifth; sol a fourth; RE a fifth; lo a fourth; MI or FA a fifth; fa a fourth: now it will be found, by a very easy computation, that the first UT being represented by 1, SOL shall be $\backslash frac\{1\}\{2\}$, re $\backslash frac\{2\}\{3\}$, LA $\backslash frac\{1\}\{2\}$, mi $\backslash frac\{1\}\{4\}$, &c. and so of the rest till you arrive at fa, which will be found $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$. This fraction is evidently greater than the number 2, which expresses the perfect octave ut to its correspondent UT; and the octave below fa would be one half of the same fraction, that is to say $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$, which is evidently greater than UT represented by unity. This last fraction $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$ is composed of two numbers; the numerator of the fraction is nothing else but the number 2 multiplied 11 times in succession by itself, and the denominator is the number 2 multiplied 18 times in succession by itself. Now it is evident, that this fraction, which expresses the value of fa, is not equal to the unity which expresses the value of the found UT; though, upon the harpichord, fa and UT are identical. This fraction rises above unity by $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$, that is to say, by about $\backslash frac\{1\}\{16\}$; and this difference was called the comma of Pythagoras. It is palpable that this comma is much more considerable than that which we have already mentioned (note N), and which is only $\backslash frac\{1\}\{128\}$.

We have already proved that the series of fifths produces an ut different from fa, the series of thirds major gives another still more different. For, let us suppose this series of thirds, ut, mi, sol, fa, we shall have mi equal to $\backslash frac\{1\}\{3\}$, sol to $\backslash frac\{1\}\{3\}$, and fa to $\backslash frac\{1\}\{3\}$, whose octave below is $\backslash frac\{1\}\{6\}$; from whence it appears, that this last fa is less than unity (that is to say, than ut), by $\backslash frac\{1\}\{12\}$, or by $\backslash frac\{1\}\{24\}$, or near it: A new comma, much greater than the preceding, and which the Greeks have called apstone major.

It may be observed, that this fa, deduced from the series of thirds, is to the fa deduced from the series of fifths, as $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$ is to $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$; that is to say, in multiplying by 524288, as 125 multiplied by 4096 is to 531441, or as 51200 to 531441, that is to say, nearly as 26 is to 27: from whence it may be seen, that these two fa's are very considerably different one from the other, and even sufficiently different to make the ear sensible of it; because the difference consists almost of a minor semitone, whose value, as will afterwards be seen (art. 139.), is $\backslash frac\{1\}\{128\}$.

Moreover, if, after having found the sol equal to $\backslash frac\{1\}\{3\}$, we then tune by fifths and by fourths, sol, re, sol, mi, fa, as we have done with respect to the first series of fifths, we find that the fa must be $\backslash frac\{1\}\{3\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$; its difference, then, from unity, or, in other words, from UT, is $\backslash frac\{1\}\{3\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$, that is to say, about $\backslash frac\{1\}\{12\}$; a comma still less than any of the preceding, and which the Greeks have called apstone minor.

In a word, if, after having found mi equal to $\backslash frac\{1\}\{3\}$ in the progression of thirds, we then tune by fifths and fourths mi, fa, fa, mi, &c. we shall arrive at a new fa, which shall be $\backslash frac\{1\}\{3\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$, and which will not differ from unity but by about $\backslash frac\{1\}\{128\}$, which is the last and smallest of all the commas; but it must be observed, that, in this case, the thirds major from mi to sol, from sol to fa, or ut, &c. are extremely false, and greatly altered.

should serve as limits to the other intervals, and that all the notes which rise above or fall below the ordinary scale, are no more than repetitions, i. e. repetitions, of all that have gone before them. For this reason, if the octave were altered, there could be no longer any fixed point either in harmony or melody. It is then absolutely necessary to tune the ut or fa in a just octave with the first; from whence it follows, that, in the progression of fifths, or what is the same thing, in the alternate series of fifths and fourths, UT, SOL, re, LA, mi, fa, fa, ut, sol, re, la, mi, fa, it is necessary that all the fifths should be altered, or at least some of them. Now, since there is no reason why one should rather be altered than another, it follows, that we ought to alter them all equally. By these means, as the alteration is made to influence all the fifths, it will be in each of them almost imperceptible; and thus the fifth, which, after the octave, is the most perfect of all consonances, and which we are under the necessity of altering, must only be altered in the least degree possible.

67. It is true, that the thirds will be a little harsh; but as the interval of sounds which constitutes the third, produces a less perfect coalescence than that of the fifth, it is necessary, says M. Rameau, to sacrifice the justice of that chord to the perfection of the fifth; for the more perfect a chord is in its own nature, the more displeasing to the ear is any alteration which can be made in it. In the octave the least alteration is insupportable.

68. This change in the intervals of instruments

which have, or even which have not, keys, is that which we call temperament.

69. It results then from all that we have now said, that the theory of temperament may be reduced to this question.—The alternate succession of fifths and fourths having been given, UT, SOL, re, LA, mi, fa, fa, ut, sol, re, la, mi, fa, in which fa or ut is not the true octave of the first UT, it is proposed to alter all the fifths equally, in such a manner that the two ut's may be in a perfect octave the one to the other.

70. For a solution of this question, we must begin with tuning the two ut's in a perfect octave the one to the other; in consequence of which, we will render all the semitones which compose the octave as equal as possible. By this means ($\backslash tau$) the alteration made in each fifth will be very considerable, but equal in all of them.

71. In this, then, the theory of temperament con-¹⁵⁴ Rameau's
fils; but as it would be difficult in practice to tune a method of
harpsichord or organ by thus rendering all the semi-tempera-
tones equal, M. Rameau, in his Generation Harmonique, has furnished us with the following method, to
alter all the fifths as equally as possible.

72. Take any key of the harpsichord which you please; but let it be towards the middle of the instrument; for instance, UT: then tune the note SOL a fifth above it, at first with as much accuracy as possible; this you may imperceptibly diminish: tune afterwards the fifth to this with equal accuracy, and diminish it in the same manner; and thus proceed from one fifth to another

($\backslash tau$) All the semitones being equal in the temperament proposed by M. Rameau, it follows, that the twelve semitones ut, ut, re, re, mi, mi, &c. shall form a continued geometrical progression; that is to say, a series in which ut shall be to ut in the same proportion as ut to re, as re to re, &c. and so of the rest.

These twelve semitones are formed by a series of thirteen sounds, of which UT and its octave ut are the first and last. Thus to find by computation the value of each sound in the temperament, which is the present object of our speculations, our scrutiny is limited to the investigation of eleven other numbers between 1 and 2 which may form with the 1 and the 2 a continued geometrical progression.

However little any one is practised in calculation, he will easily find each of these numbers, or at least a number approaching to its value. These are the characters by which they may be expressed, which mathematicians will easily understand, and which others may neglect.

It is obvious, that in this temperament all the fifths are equally altered. One may likewise prove, that the alteration of each in particular is very inconsiderable; for it will be found, for instance, that the fifth from ut to sol, which should be $\backslash frac\{1\}\{2\}$, ought to be diminished by about $\backslash frac\{1\}\{12\}$ of $\backslash frac\{1\}\{2\}$; that is to say, by $\backslash frac\{1\}\{24\}$, a quantity almost inconceivably small.

It is true, that the thirds major will be a little more altered; for the third major from ut to mi, for instance, shall be increased in its interval by about $\backslash frac\{1\}\{12\}$: but it is better, according to M. Rameau, that the alteration should fall upon the third than upon the fifth, which after the octave is the most perfect chord, and from the perfection of which we ought never to degenerate but as little as possible.

Besides, it has appeared from the series of thirds major ut, mi, sol, fa, that this last fa is very different from ut (note 3); from whence it follows, that if we would tune this fa in unison with the octave of ut, and alter at the same time each of the thirds major by a degree as small as possible, they must all be equally altered. This is what occurred in the temperament which we propose; and if in it the third be more altered than the fifth, it is a consequence of the difference which we find between the degrees of perfection in these intervals; a difference with which, if we may speak so, the temperament proposed conforms itself. Thus this diversity of alteration is rather advantageous than inconvenient.

Theory of Harmony. another in ascent: and as the ear does not appreciate so exactly sounds that are extremely sharp, it is necessary, when by fifths you have risen to notes extremely high, that you should tune in the most perfect manner the octave below the last fifth which you had immediately formed; then you may continue always in the same manner; till in this process you arrive at the last fifth from mi to fa, which should of themselves be in tune; that is to say, they ought to be in such a state, that fa, the highest note of the two which compose the fifth, may be identical with the sound UT, with which you began, or at least the octave of that sound

perfectly just: it will be necessary then to try if this UT, or its octave, forms a just fifth with the last found mi or fa which has been already tuned. If this be the case, we may be certain that the harpichord is properly tuned. But if this last fifth be not true, in this case it will be too sharp, and it is an indication that the other fifths have been too much diminished, or at least some of them; or it will be too flat, and consequently discover that they have not been sufficiently diminished. We must then begin and proceed as formerly, till we find the last fifth in tune of itself, and without our immediate interposition (U).

By

(U) All that remains, is to acknowledge, with M. Rameau, that this temperament is far remote from that which is now in practice: you may here see in what this last temperament consists as applied to the organ or harpichord. They begin with UT in the middle of the keys, and they flatten the four first fifths sol, re, la, mi, till they form a true third major from mi to ut; afterwards, setting out from this mi, they tune the fifths fa, fa, ut, sol, but flattening them still less than the former, so that sol may almost form a true third major with mi. When they have arrived at sol, they stop; they resume the first ut, and tune to it the fifth fa in descending, then the fifth fa, &c. and they heighten a little all the fifths till they have arrived at la, which ought to be the same with the sol already tuned.

If, in the temperament commonly practised, some thirds are found to be less altered than in that prescribed by M. Rameau, in return, the fifths in the first temperament are much more false, and many thirds are likewise so; inasmuch, that upon a harpichord tuned according to the temperament in common use, there are five or six modes which the ear cannot endure, and in which it is impossible to execute any thing. On the contrary, in the temperament suggested by M. Rameau, all the modes are equally perfect; which is a new argument in its favour, since the temperament is peculiarly necessary in passing from one mode to another, without shocking the ear; for instance, from the mode of ut to that of sol, from the mode of sol to that of re, &c. It is true, that this uniformity of modulation will to the greatest number of musicians appear a defect: for they imagine, that, by tuning the semitones of the scale unequal, they give each of the modes a peculiar character; so that, according to them, the scale of ut,

ut, re, mi, fa, sol, la, si, UT,

is not perfectly similar to the gammut or diatonic scale of the mode of mi

mi, fa, sol, la, si, ut, re, mi,

which, in their judgment, renders the modes of ut and mi proper for different manners of expression. But after all that we have said in this treatise on the formation of diatonic intervals, every one should be convinced, that, according to the intention of nature, the diatonic scale ought to be perfectly the same in all its modes: The contrary opinion, says M. Rameau, is a mere prejudice of musicians. The character of an air arises chiefly from the intermixture of the modes; from the greater or lesser degrees of vivacity in the movement; from the tones, more or less grave, or more or less acute, which are assigned to the generator of the mode; and from the chords more or less beautiful, as they are more or less deep, more or less flat, more or less sharp, which are found in it.

In short, the last advantage of this temperament is, that it will be found conformed, or at least very little different from that which they practise upon instruments without keys; as the bass-viol, the violin, in which true fifths and fourths are preferred to thirds and sixths tuned with equal accuracy; a temperament which appears incompatible with that commonly used in tuning the harpichord.

Yet we must not suffer our readers to be ignorant, that M. Rameau, in his New System of Music, printed in 1726, had adopted the ordinary temperament. In that work, (as may be seen CHAP. XXIV.), he pretends that the alteration of the fifths is much more supportable than that of the thirds major; and that this last interval can hardly suffer a greater alteration than the octave, which, as we know, cannot suffer the slightest alteration. He says, that if three strings are tuned, one by an octave, the other by a fifth, and the next by a third major to a fourth string, and if a sound be produced from the last, the strings tuned by a fifth will vibrate, though a little less true than it ought to have been; but that the octave and the third major, if altered in the least degree, will not vibrate: and he adds, that the temperament which is now practised, is founded upon that principle. M. Rameau goes still farther; and as, in the ordinary temperament, there is a necessity for altering the last thirds major, and to make them a little more sharp, that they may naturally return to the octave of the principal sound, he pretends that this alteration is tolerable, not only because it is almost insensible, but because it is found in modulations not much in use, unless the composer should choose it on purpose to render the expression stronger. "For it is proper to remark (says he), that we receive different impressions from the intervals in proportion to their different alterations: for instance, the third major, which naturally elevates us to joy, in proportion as we feel it, heightens our feelings even to a kind of fury, when it is tuned too sharp; and the third minor, which naturally inspires us with tenderness and serenity, depresses us to melancholy when it is too flat." All this strain, as you may see, is immensely different from that which this celebrated musician afterwards.

By this method all the twelve sounds which compose one of the scales shall be tuned: nothing is necessary but to tune with the greatest possible exactness their octaves in the other scales, and the harpsichord shall be well tuned.

We have given this rule for temperament from M. Rameau; and it belongs only to disinterested artists to judge of it. However this question be determined, and whatever kind of temperament may be received, the alterations which it produces in harmony will be but very small, or not perceptible to the ear, whose attention is entirely engrossed in attuning itself with the fundamental basis, and which suffers, without uneasiness, these alterations, or rather takes no notice of them, because it supplies from itself what may be wanting to the truth and perfection of the intervals.

Simple and daily experiments confirm what we now advance. Listen to a voice which is accompanied, in singing, by different instruments; though the temperament of the voice, and the temperament of each of the instruments, are all different one from another, yet you will not be in the least affected with the kind of cacophony which ought to result from these diversities, because the ear supposes these intervals true of which it does not appreciate differences.

We may give another experiment. Strike upon an organ the three keys mi, sol, si, you will hear nothing but the minor perfect chord; though mi, by the construction of that instrument, must cause sol likewise to be heard; though sol should have the same effect upon re, and si upon fa; inasmuch, that the ear is at once affected with all these sounds, re, mi, fa, sol, sol, si: how many dissonances perceived at the same time, and what a jarring multitude of discordant sensations, would result from thence to the ear, if the perfect chord with which it is preoccupied had not power entirely to abstract its attention from such sounds as might offend!

CHAP. VIII. Of Reposes or Cadences (†).

73. In a fundamental basis whose procedure is by fifths, there always is, or always may be, a repose, or crisis, in which the mind acquiesces in its transition
N° 233

from one sound to another: but a repose may be more or less distinctly signified, and of consequence more or less perfect. If one should rise by fifths; if, for instance, we pass from ut to sol; it is the generator which passes to one of these fifths, and this fifth was already pre-existent in its generator: but the generator exists no longer in this fifth; and the ear, as this generator is the principle of all harmony and of all melody, feels a desire to return to it. Thus the transition from a sound to its fifth in ascent, is termed an imperfect repose, or imperfect cadence; but the transition from any sound to its fifth in descent, is denominated a perfect cadence, or an absolute repose: it is the offspring which returns to its generator, and as it were recovers its existence once more in that generator itself, with which when sounding it resounds (chap. i.)

74. Amongst absolute repouses, there are some, if
we may be allowed the expression, more absolute, that is to say, more perfect, than others. Thus in the fundamental basis

ut, sol, ut, fa, ut, sol, re, sol, ut,

which forms, as we have seen, the diatonic scale of the moderns, there is an absolute repose from re to sol, as from sol to ut: yet this last absolute repose is more perfect than the preceding, because the ear, prepossessed with the mode of ut by the multiplied impression of the sound ut which it has already heard thrice before, feels a desire to return to the generator ut; and it accordingly does so by the absolute repose sol, ut.

75. We may still add, that what is commonly called cadence in melody, ought not to be confounded with what we name cadence in harmony.

In the first case, this word only signifies an agreeable and rapid alteration between two contiguous sounds, called likewise a trill or shake; in the second, it signifies a repose or close. It is however true, that this shake implies, or at least frequently enough prefaces, a repose, either present or impending, in the fundamental basis (x).

76. Since there is a repose in passing from one sound to another in the fundamental basis, there is also a repose in passing from one note to another in the diatonic scale, which is formed from it, and which this basis represents: and as the absolute repose sol, ut, is scale, and of which the most perfect.

terwards exhibited in his Generation Harmonique, and in the performances which followed it. From this we can only conclude, that the reasons which, after him, we have urged for the new temperament, must without doubt have appeared to him very strong, because in his mind they had superseded those which he had formerly adduced in favour of the ordinary temperament.

We do not pretend to give any decision for either the one or the other of these methods of temperament, each of which appears to us to have its particular advantages. We shall only remark, that the choice of the one or the other must be left absolutely to the taste and inclination of the reader; without, however, admitting this choice to have any influence upon the principles of the system of music, which we have followed even till this period, and which must always subsist, whatever temperament we adopt.

(†) That the reader may have a clear idea of the term before he enters upon the subject of this chapter, it may be necessary to caution him against a mistake into which he may be too easily led by the ordinary signification of the word repose. In music, therefore, it is far from being synonymous with the word rest. It is, on the contrary, the termination of a musical phrase which ends in a cadence more or less emphatic, as the sentiment implied in the phrase is more or less complete. Thus a repose in music answers the same purpose as punctuation in language. See Repos in Rousseau's Musical Dictionary.

(x) M. Rousseau, in his letter on French music, has called this alternate undulation of different sounds a trill, from the Italian word trillo, which signifies the same thing; and some French musicians already appear to have adopted this expression.

Theory of all others the most perfect in the fundamental bass, Harmony. the repose from fa to ut, which answers to it in the scale, and which is likewise terminated by the generator, is for that reason the most perfect of all others in the diatonic scale ascending.

160 Definition and use of a sensible note.
See Sensible Note.
77. It is then a law dictated by nature itself, that if you would ascend diatonically to the generator of a mode, you can only do this by means of the third major from the fifth of that very generator. This third major, which with the generator forms a semitone, has for that reason been called the sensible note, as introducing the generator, and preparing us for the most perfect repose.

We have already proved, that the fundamental bass is the principle of melody. We shall besides make it appear in the sequel, that the effect of a repose in melody arises solely from the fundamental bass.

CHAP. IX. Of the Minor Mode and its Diatonic Series.

161 The diatonic series of 29. 30. 31. and 32.) by what means, and upon what the minor principle, the minor chord ut, mi, sol, ut, may be formed, which is the characteristical chord of the minor mode. Now what we have there said, taking ut for the principal and fundamental sound, we might likewise have said of any other note in the scale, assumed in the same manner as the principal and fundamental sound: but as in the minor chord ut, mi, sol, ut, there occurs a mi which is not found in the ordinary diatonic scale, we shall immediately substitute, for greater ease and convenience, another chord, which is likewise minor and exactly similar to the former, of which all the notes are found in the scale.

79. The scale affords us three chords of this kind, viz. re, fa, la, re; la, ut, mi, la; and mi, sol, fa, mi. Amongst these three we shall choose la, ut, mi, la: because this chord, without including any sharp or flat, has two sounds in common with the major chord ut, mi, sol, ut; and besides, one of these two sounds is the very same ut: so that this chord appears to have the most immediate, and at the same time the most simple, relation with the chord ut, mi, sol, ut. Concerning this we need only add, that this preference of the chord la, ut, mi, la, to every other minor chord, is by no means in itself necessary for what we have to say in this chapter upon the diatonic scale of the minor mode. We might in the same manner have chosen any other minor chord; and it is only, as we have said, for greater ease and convenience that we fix upon this.

80. Let us now remark, that in every mode, whether major or minor, the principal sound which implies the perfect chord, whether major or minor, may be called the tonic note or key; thus ut is the key in its proper mode, la in the mode of la, &c. Having said down this principle,

163 The formation of the sol, which constitute (art. 38.) the mode of ut, of which scale pursue the first fa and the last sol are the two-fifths of ut, one descending the other rising, produce the scale fa, ut, re, mi, fa, sol, la, of the major mode, by means of the fundamental bass sol, ut, sol, ut, fa, ut, fa: let us in the

same manner take the three sounds re, la, mi, which constitute the mode of la, for the same reason that the sounds fa, ut, sol, constitute the mode of ut; and of them let us form this fundamental bass, perfectly like the preceding, mi, la, mi, la, re, la, re: let us afterwards place below each of these sounds one of their harmonics, as we have done (chap. v.) for the first scale of the major mode; with this difference, that we must suppose re and la as implying their thirds minor in the fundamental bass to characterise the minor mode; and we shall have the diatonic scale of that mode,

sol, la, fa, ut, re, mi, fa.

82. The sol, which corresponds with mi in the fundamental bass, forms a third major with that mi, though the mode be minor; for the same reason that a third from the fifth of the fundamental sound ought to be major (art. 77.) when that third rises to the fundamental sound la.

83. It is true, that, in causing mi to imply its third major sol, one might also rise to la by a diatonic progress. But that manner of rising to la would be less perfect than the preceding; for this reason (art. 76.), that the absolute repose or perfect cadence, mi, la, which is found in the fundamental bass, ought to be represented in the most perfect manner in the two notes of the diatonic scale which answer to it, especially when one of these two notes is la, the key itself upon which the repose is made. From whence it follows, that the preceding note sol ought rather to be sharp than natural; because sol, being included in mi (art. 19.), much more perfectly represents the note mi in the bass, than the natural sol could do, which is not included in mi.

84. We may remark this first difference between the scale sol, la, fa, ut, re, mi, fa, and the scale which corresponds with it in the major mode fa, ut, re, mi, fa, sol, la,

that from mi to fa, which are the two last notes of the former scale, there is only a semitone; whereas from sol to la, which are the two last sounds of the latter series, there is the interval of a complete tone: but this is not the only discrimination which may be found between the scales of the two modes.

85. To investigate these differences, and to discover the reason for which they happen, we shall begin by forming a new diatonic scale of the minor mode, similar to the second scale of the major mode,

ut, re, mi, fa, sol, sol, la, fa, ut.

That last series, as we have seen, was formed by means of the fundamental bass fa, ut, sol, re, disposed in this manner,

ut, sol, ut, fa, ut, sol, re, sol, ut.

Let us take in the same manner the fundamental bass re, la, mi, fa, and arrange it in the following order,

la, mi, la, re, la, mi, fa, mi, la,

and it will produce the scale immediately subjoined, la, fa, ut, re, mi, mi, fa, sol, la, in which ut forms a third minor with la, which in the fundamental bass corresponds with it, which denominates the minor mode; and, on the contrary, sol forms a third major with mi in the fundamental bass, because sol rises towards la, (art. 82. and 83.)

86. We see besides a fa, which does not occur in the former,

sol, la, fi, ut, re, mi, fa,

where fa is natural. It is because, in the first scale, fa is a third minor from re in the bass; and in the second, fa is the fifth from fi in the bass.

87. Thus the two scales of the minor mode are still between them this respect more different one from the other than two scales of the major mode; for we do not remark this difference of a semitone between the two scales of the major mode. We have only observed (art. 63.) some difference in the value of a as it stands in each of these scales, but this amounts to much less than a semitone.

88. From thence it may be seen why fa and sol are sharp in the sharp when ascending in the minor mode; nay, besides, the fa is only natural in the first scale sol, la, fi, ut, re, mi, fa, because this fa cannot rise to sol, (art. 48.)

89. It is not the same case in descending. For mi, the fifth of the generator, ought not to imply the third major sol, but in the case when that mi descends to the generator la to form a perfect repose (art. 77. and 83.); and in this case the third major sol rises to the generator la: but the fundamental bass la mi may, in descending, give the scale la sol natural, provided sol does not rise towards la.

90. It is much more difficult to explain how the fa, which ought to follow this sol in descending, is natural and not sharp; for the fundamental bass

la, mi, fi, mi, la, re, la, mi, la,

produces in descending,

la, sol, fa, mi, mi, re, ut, fi, la.

And it is plain that the fa cannot be otherwise than sharp, since fa is the fifth of the note fi of the fundamental bass. In the mean time, experience evinces that the fa is natural in descending in the diatonic scale of the major mode of la, especially when the preceding sol is natural: and it must be acknowledged, that here the fundamental bass appears in some measure defective.

M. Rameau has invented the following means for obtaining a solution of this difficulty. According to him, in the diatonic scale of the minor mode in descending, la, sol, fa, mi, re, ut, fi, la, sol, may be regarded simply as a note of passage, merely added to give sweetness to the modulation, and as a diatonic gradation by which we may descend to fa natural.

It is easily perceived, according to M. Rameau, by this fundamental bass,

la, re, la, re, la, mi, la,

which produces

la, fa, mi, re, ut, fi, la;

which may be regarded, as he says, as the real scale of the minor mode in descending; to which is added sol natural between la and fa, to preserve the diatonic order.

This answer appears the only one which can be given to the difficulty above proposed: but I know not whether it will fully satisfy the reader; whether he will not see with regret, that the fundamental bass does not produce, to speak properly, the diatonic scale of the minor mode in descent, when at the same time this same bass so happily produces the diatonic scale of that identical mode in ascending, and the diatonic scale of the major mode whether in rising or descending (y).

CHAP. X. Of Relative Modes.

91. Two modes which are of such a nature that we can pass from the one to the other, are called relative modes. Thus we have already seen, that the major mode of ut is relative to the major mode of fa and to the mode of sol. It may likewise appear from what goes before, how many intimate connections there are between the species (†) or major mode of ut, and the species or minor mode of la. For, 1. The perfect chords, one major ut mi sol ut, the other minor la ut mi la, which characterise each of those two kinds of modulation* or harmony, have two sounds in common, ut or mi. 2. The diatonic scale of the minor mode of la in descent, absolutely contains the same sounds with the gammut or diatonic scale of the major mode of ut.

It is for this reason that the transition is so natural and easy from the major mode of ut to the minor mode of la, or from the minor mode of la to the major mode of ut, as experience proves.

92. In the minor mode of mi, the minor perfect chord mi sol fi mi, which characterises it, has likewise two sounds, mi, sol, in common with the perfect chord major ut mi sol ut, which characterises the major mode of ut. But the minor mode of mi is not so closely related nor allied to the major mode of ut as to the minor mode of la; because the diatonic scale of the minor mode of mi in descent, has not, like the series of the

(y) For what remains, when sol is said to be natural in descending the diatonic scale of the minor mode of la, this only signifies, that this sol is not necessarily sharp in descending as it is in rising; for this sol, besides, may be sharp in descending to the minor mode of la, as may be proved by numberless examples, of which all musical compositions are full. It is true, that when the sound sol is found sharp in descending to the minor mode of la, still we are not sure that the mode is minor till the fa or ut natural is found; both of which impress a peculiar character on the minor mode, viz. ut natural, in rising and in descending, and the fa natural in descending.

(†) Species was the only word which occurred to the translator in English by which he could render the French word genre. It is, according to Rousseau, intended to express the different divisions and dispositions of the intervals which formed the two tetrachords in the ancient diatonic scale; and as the gammut of the moderns consists likewise of two tetrachords, though diversified from the former, as our author has shown at large, the genre or species, as the translator has been obliged to express it, must consist in the various dispositions and divisions of the different intervals between the notes or semitones which compose the modern scale.

Theory of the minor mode of la, all these sounds in common with Harmony. the scale of ut. In reality, this scale is mi re ut si la sol fa# mi, where there occurs a fa sharp which is not in the scale of ut. We may add, that though the minor mode of mi is less relative to the major mode of ut than that of la; yet the artist does not hesitate sometimes to pass immediately from the one to the other.

Of this may be seen one instance (among many others) in the prologue des Amours des Dieux, at this passage, Ovide est l'objet de la fete, which is in the minor mode of mi, though what immediately precedes it is in the major mode of ut.

We may see besides, that when we pass from one mode to another by the interval of a third, whether in descending or rising, as from ut to la, or from la to ut, from ut to mi, or from mi to ut, the major mode becomes minor, or the minor mode becomes major.

93. There is still another minor mode, into which an immediate transition may be made in issuing from the major mode of ut. It is the minor mode of ut itself in which the perfect minor chord ut mi sol ut has two sounds, ut and sol, in common with the perfect major chord ut mi sol ut. Nor is there any thing more common than a transition from the major mode of ut to the minor mode, or from the minor to the major (z).

CHAP. XI. Of Dissonance.

94. We have already observed, that the mode of ut (fa, ut, sol), has two sounds in common with the mode of sol (ut, sol, re); and two sounds in common with the mode of fa (si, fa, ut); of consequence, this procedure of the bass ut sol may belong to the mode of ut, or to the mode of sol, as the procedure of the bass fa ut, or ut fa, may belong to the mode of ut or the mode of fa. When any one therefore passes from ut to fa or to sol in a fundamental bass, he is still ignorant even to that crisis what mode he is in. It would be, however, advantageous to know it, and to be able by some means to distinguish the generator from its fifths.

95. This advantage may be obtained by uniting at the same time the sounds sol and fa in the same harmony, that is to say, by joining to the harmony sol si re of the fifth sol, the other fifth fa in this manner, sol, si, re, fa; this fa which is added, forms a dissonance with sol (art. 18.) It is for that reason that the chord sol si re fa, is called a dissonant chord, or a chord of the seventh. It serves to distinguish the fifth sol

from the generator ut, which always implies, without Theory of Harmony. mixture or alteration, the perfect chord ut, mi, sol, ut, resulting from nature itself (art. 32.) By this we may see, that when we pass from ut to sol, one passes at the same time from ut to fa, because fa is found to be comprehended in the chord of sol; and the mode of ut by these means plainly appears to be determined, because there is none but that mode to which the sounds fa and sol at once belong.

96. Let us now see what may be added to the harmony fa, la, ut, of the fifth fa below the generator, to distinguish this harmony from that of the generator. It seems probable at first, that we should add to it the other fifth sol, so that the generator ut, in passing to fa, may at the same time pass to sol, and that by this the mode should be determined: but this introduction of sol, in the chord fa, la, ut, would produce two seconds in succession fa, sol, sol, la, that is to say, two dissonances whose union would prove extremely harsh to the ear; an inconvenience which ought carefully to be avoided. For if, to distinguish the mode, we should alter the harmony of the fifth fa in the fundamental bass, it must only be altered in the least degree possible.

97. For this reason, instead of sol, we shall take its fifth re, which is the sound that approaches it the nearest; and we shall have, instead of the fifth fa, the chord fa, la, ut, re, which is called a chord of the great sixth.

One may here remark the analogy there is observed between the harmony of the fifth sol and that of the fifth fa.

98. The fifth sol, in rising above the generator, gives a chord entirely consisting of thirds ascending from sol, si, re, fa; now the fifth fa being below the generator ut in descending, we shall find, as we go lower by thirds from ut towards fa, the same sounds ut, la, fa, re, which form the chord fa, la, ut, re, given to the fifth fa.

99. It appears besides, that the alteration of the harmony in the two fifths consists only in the third minor re, fa, which was reciprocally added to the harmony of these two fifths.

CHAP. XII. Of the Double Use or Employment of Dissonance.

100. It is evident by the resemblance of sounds to their octaves, that the chord fa, la, ut, re, is in effect the same as the chord re, fa, la, ut, taken inversely *; that the inverse of the chord ut, la, fa, re, has been found

3 U 2

(z) There are likewise other minor modes, into which we may pass in our egress from the mode major of ut; as that of fa minor, in which the perfect minor chord fa, la, ut, includes the sound ut, and whose scale in ascent fa, sol, la, si, ut, re, mi, fa, only includes the two sounds la, si, which do not occur in the scale of ut. We find an example of this transition from the mode major of ut to that of fa minor, in the opera of Pegmalion by M. Rameau, where the saratondo is in the minor mode of fa, and the rigadoon in the mode major of ut. This kind of transition, however, is not frequent.

The minor mode of re has only in its scale ascending re, mi, fa, sol, la, si, ut#, re, one ut sharp which is not found in the scale of ut. For this reason a transition may likewise be made, without grating the ear, from the mode of ut major to the mode of re minor; but this passage is less immediate than the former, because the chords ut, mi, sol, ut, re, fa, la, re, not having a single sound in common, one cannot (art. 37.) pass immediately from the one to the other.

Theory of found (art. 93.) in descending by thirds from the generator ut (AA).

101. The chord re, fa, la, ut, is a chord of the seventh like the chord sol, fa, re, fa: with this only difference, that in this the third sol, fa, is major: whereas in the second, the third re, fa, is minor. If the fa were sharp, the chord re, fa, la, ut, would be a genuine chord of the dominant, like the chord sol, fa, re, fa; and as the dominant sol may descend to ut in the fundamental bass, the dominant re implying or carrying with it the third major fa might in the same manner descend to sol.

102. Now I say, that if the fa should be changed into fa natural, re, the fundamental tone of this chord re, fa, la, ut, might still descend to sol; for the change from fa to fa natural, will have no other effect, than to preserve the impression of the mode of ut, instead of that of the mode of sol, which the fa would have here introduced. For what remains, the note re will always preserve its character as the dominant, on account of the mode of ut, which forms a seventh. Thus in the chord of which we treat, re, fa, la, ut, re, may be considered as an imperfect dominant: I call it imperfect, because it carries with it the third minor fa, instead of the third major fa. It is for this reason that in the sequel I shall call it simply the dominant, to distinguish it from the dominant sol, which shall be named the tonic dominant†.

103. Thus the sounds fa and sol, which cannot succeed each other (art. 36.) in a diatonic bass, when they only carry with them the perfect chords fa, la, ut, sol, fa, re, may succeed one another if you join re to the harmony of the first, and fa to the harmony of the second; and if you invert the first chord, that is to say, if you give to the two chords this form, re, fa, la, ut, sol, fa, re, fa.

104. Besides, the chord fa, la, ut, re, being allowed to succeed the perfect chord ut, mi, sol, ut, it follows for the same reasons, that the chord ut, mi, sol, ut, may be succeeded by re, fa, la, ut; which is not contradictory to what we have above said (art. 37.), that the sounds ut and re cannot succeed one another in the fundamental bass: for in the passage quoted, we had supposed that both ut and re carried with them a

perfect chord major; whereas, in the present case, re carries the third minor fa, and likewise the sound ut, by which the chord re, fa, la, ut is connected with that which precedes it ut, mi, sol, ut; and in which the sound ut is found. Besides, this chord, re, fa, la, ut, is properly nothing else but the chord fa, la, ut, re inverted, and, if we may speak so, disguised.

105. This manner of presenting the chord of the Double sub-dominant under two different forms, and of employing it under these two different forms, has been called by M. Rameau its double office or employment†. This is the source of one of the finest varieties in harmony; and we shall see in the following chapter the advantages which result from it.

We may add, that as this double employment is a kind of licence, it ought not to be practised without some precaution. We have lately seen that the chord re, fa, la, ut, considered as the inverse of fa, la, ut, re, may succeed to ut, mi, sol, ut, but this liberty is not reciprocal: and though the chord fa, la, ut, re may be followed by the chord ut, mi, sol, ut, we have no right to conclude from thence that the chord re, fa, la, ut, considered as the inverse of fa, la, ut, re, may be followed by the chord ut, mi, sol, ut. For this the reason shall be given CHAP. XVI.

CHAP. XIII. Concerning the Use of this Double Employment, and its Rules.

106. We have shown (chap. vi.) how the diatonic scale, or ordinary gammut, may be formed from the fundamental bass fa, ut, sol, re, by twice repeating the word sol in that series; so that this gammut is primitively and originally composed of two similar tetra-chords, one in the mode of ut, the other in that of sol. Now it is possible, by means of this double employment, to preserve the impression of the mode of ut through the whole extent of the scale, without twice repeating the note sol, or even without supposing this repetition. For this effect we have nothing to do but form the following fundamental bass,

ut, sol, ut, fa, ut, re, sol, ut:
in which ut is understood to carry with it the perfect chord ut, mi, sol, ut; sol, the chord sol, fa, re, fa; fa, the chord

(AA) "M. Rameau, in several passages of his works (for instance, in p. 110, 111, 112, and 113, of the Generation Harmonique), appears to consider the chord re, fa, la, ut, as the primary chord and generator of the chord fa, la, ut, re, which is nothing but that chord itself reversed; in other passages (particularly in p. 116, of the same performance), he seems to consider the first of these chords as nothing else but the reverse of the second. It would seem that this great artist has neither expressed himself upon this subject with so much uniformity nor with so much precision as is required. For my own part, I think there is some foundation for considering the chord fa, la, ut, re, as primitive: 1. Because in this chord, the fundamental and principal note is the sub-dominant fa, which ought in effect to be the fundamental and principal sound in the chord of the sub-dominant. 2. Because that without having recourse, with M. Rameau, to harmonical and arithmetical progressions, of which the consideration appears to us quite foreign to the question, we have found a probable and even a satisfactory reason for adding the note re to the harmony of the fifth fa (art. 96. and 97.) The origin thus assigned for the chord of the sub-dominant appears to us the most natural, though M. Rameau does not appear to have felt its full value; for scarcely has it been slightly insinuated by him."

Thus far our author. We do not enter with him into the controversy concerning the origin of the chord in question; but only propose to add to his definition of the sub-dominant Rousseau's idea of the same note. It is a name, says he, given by M. Rameau to the fourth note in any modulation relative to a given key, which of consequence is in the same interval from the key in descending as the dominant in rising; from which circumstance it takes its name.

Theory of Harmony. chord fa la ut re; and re, the chord re fa la ut. It is plain from what has been said in the preceding chapter, that in this case ut may ascend to re in the fundamental bass, and re descend to sol, and that the impression of the mode of ut is preserved by the fa natural, which forms the third minor re fa, instead of the third major which re ought naturally to imply.

107. This fundamental bass will give, as it is evident, the ordinary diatonic scale,

ut, re, mi, fa, sol, la, si, UT,

which of consequence will be in the mode of ut alone; and if one should choose to have the second tetrachord in the mode of sol, it will be necessary to substitute fa instead of fa natural in the harmony of re (en).

108. Thus the generator ut may be followed according to pleasure in ascending diatonically either by a tonic dominant (re fa la ut), or by a simple dominant (re fa la ut).

109. In the minor mode of la, the tonic dominant mi ought always to imply its third major mi sol, when this dominant mi descends to the generator la (art. 83.); and the chord of this dominant shall be mi sol si re, entirely similar to sol si re fa. With respect to the sub-dominant re, it will immediately imply the third minor fa, to denominate the minor mode; and we may add si above its chord re fa la, in this manner re fa la si, a chord similar to that of fa la ut re; and as we have deduced from the chord fa la ut re that of re fa la ut, we may in the same manner deduce from the chord re fa la si a new chord of the seventh si re fa la, which will exhibit the double employment of dissonances in the minor mode.

110. One may employ this chord si re fa la, to preserve the impression of the mode of la in the diatonic scale of the minor mode, and to prevent the necessity of twice repeating the found mi; but in this case, the fa must be rendered sharp, and change this chord to si re fa la, the fifth of si is fa, as we have seen above; this chord is then the inverse of re fa la si, where the sub-dominant implies the third major, which ought not to surprise us. For in the minor mode of la, the second tetrachord mi fa sol la is exactly the same as it would be in the major mode of la; now, in the major mode of la, the sub-dominant re ought to imply the third major fa.

111. From thence we may see that the minor mode is susceptible of a much greater number of varieties than the major: likewise the major mode is the pro-

duct of nature alone; whereas the minor is, in some measure, the product of art. But in return, the major mode has received from nature, to which it owes its immediate formation, a force and energy which the minor cannot boast.

CHAP. XIV. Of the Different Kinds of Chords of the Seventh.

112. The dissonance added to the chord of the dominant and of the sub-dominant, though in some measure insinuated by nature (chap. xi.), is nevertheless a work of art; but as it produces great beauties in consequence of harmony by the variety which it introduces into it, let some successful advances, art may not still be carried farther.

113. We have already three different kinds of chords of the seventh, viz.

1. The chord sol si re fa, composed of a third major followed by two thirds minor.

2. The chord re fa la ut, or si re fa la, composed of a third major between two minors.

3. The chord si re fa la, composed of two thirds minor followed by a major.

114. There are still two other kinds of chords of the seventh which are employed in harmony; one is composed of a third minor between two thirds major, ut mi sol si, or fa la ut mi; the other is wholly composed of thirds minor sol si re fa. These two chords, which at first appear as if they ought not to enter into harmony if we rigorously keep to the preceding rules, are nevertheless frequently practiced with success in the fundamental bass. The reason is this:

115. According to what has been said above, if we would add a seventh to the chord ut mi sol, to make a dominant of ut, one can add nothing but si; and in this case ut mi sol si would be the chord of why the tonic dominant in the mode of fa, as sol si re fa is the chord of the tonic dominant in the mode of ut; but if you would preserve the impression of the mode of ut in the harmony, you then change this si into si natural, and the chord ut mi sol si becomes ut mi sol si. It is the same case with the chord fa la ut mi, which is nothing else but the chord fa la ut mi; in which one may substitute for mi, mi natural, to preserve the impression of the mode of ut, or of that of fa.

Besides, in such chords as ut mi sol si, fa la ut mi, the sounds si and mi, though they form a dissonance with

(en) We need only add, that it is easy to see, that this fundamental bass ut sol, ut fa, ut re, sol ut, which formed the ascending scale ut, re, mi, fa, sol, la, si, UT, cannot by inverting it, and taking it inversely in this manner si, ut, sol, re, ut, fa, ut, sol, UT, form the diatonic scale UT, si, la, sol, fa, mi, re, ut, in descent. In reality, from the chord sol, si, re, fa, we cannot pass to the chord re, fa, la, ut, nor from thence to ut, mi, sol, ut. It is for this reason that in order to have the fundamental bass of the scale, UT, si, la, sol, fa, mi, re, ut, in descent, we must either determine to invert the fundamental bass mentioned in art. 55. in this manner, ut, sol, re, sol, ut, fa, ut, sol, ut, in which the second sol and the second ut answer to the sol alone in the scale; or otherwise we must form the fundamental bass ut, sol, re, sol, ut, sol, ut, in which all the notes imply perfect chords major, except the second sol, which implies the chord of the seventh sol, si, re, fa, and which answers to the two notes of the scale sol, fa, both comprehended in the chord sol, si, re, fa.

Whichever of these two basses we shall choose, it is obvious that neither the one nor the other shall be wholly in the mode of ut, but in the mode of ut and in that of sol. From whence it follows, that the double employment which gives to the scale a fundamental bass all in the same mode when ascending, cannot do the same in descending; and that the fundamental bass of the scale in descending will be necessarily in two different modes.

with ut in the first case, and with fa in the second, are nevertheless supportable to the ear, because these sounds si and mi (art. 19.) are already contained and understood, the first in the note mi of the chord ut mi sol fa, as likewise in the note sol of the same chord; the second in the note la of the chord fa la ut mi, as likewise in the note ut of the same chord. All together then seem to allow the artist to introduce the note si and mi into these two chords (cc).

186. With respect to the chord of the seventh sol fa si re fa, wholly composed of thirds minor, it may be regarded as formed from the union of the two chords of the dominant and of the sub-dominant in the minor mode. In effect, in the minor mode of la, for instance, these two chords are mi sol fa si re, and re fa la si, whose union produces mi sol fa si re fa la. Now, if we should suffer this chord to remain thus, it would be disagreeable to the ear, by its multiplicity of dissonances, re mi, mi la, la sol fa, la si, re sol fa, (art. 18.); so that, to avoid this inconvenience, the generator la is immediately expurgated, which (art. 19.) is as it were understood in re, and the fifth or dominant mi whose place the sensible note sol fa is supposed to hold; thus there remains no more than the chord sol fa si re fa, wholly composed of thirds minor, and in which the dominant mi is considered as understood; in such a manner that the chord sol fa si re fa represents the chord of the tonic dominant mi sol fa si re, to which we have joined the chord of the sub-dominant re fa la si, but in which the dominant mi is always reckoned the principal note (dd).

187. Since, then, from the chord mi sol fa si re, we may pass to the perfect la ut mi la, and vice versa, we may in like manner pass from the chord sol fa si re fa to the chord la ut mi la, and from this last to the chord sol fa si re fa: this remark will be very useful to us in the sequel.

CHAP. XV. Of the Preparation of Dissonances.

188. In every chord of the seventh, the highest note, that is to say, the seventh above the fundamental, is called a dissonance or discord; thus fa is the dissonance of the chord sol fa si re fa, ut in the chord re fa la ut, &c.

189. When the chord sol fa si re fa follows the chord ut mi sol ut, as this may happen, and in reality often happens, it is obvious that we do not find the dissonance fa in the preceding chord ut mi sol ut. Nor ought it indeed to be found in that chord; for this

dissonance is nothing else but the sub-dominant added to the harmony of the dominant to determine the mode: now, the sub-dominant is not found in the harmony of the generator.

190. For the same reason, when the chord of the sub-dominant fa la ut re follows the chord ut mi sol ut, the note re, which forms a dissonance with ut, is not found in the preceding chord.

It is not so when the chord re fa la ut follows the chord ut mi sol ut; for ut, which forms a dissonance in the second chord, stands as a consonance in the preceding.

189. In general, dissonance being the production of art (chap. xi.), especially in such chords as are not only to be of the tonic dominant nor sub-dominant; the only means to prevent its displeasing the ear by appearing too heterogeneous to the chord, is, that it may be, if we may speak so, announced to the ear by being found in the preceding chord, and by that means serve to connect the two chords. From whence follows this rule:

190. In every chord of the seventh, which is not the chord of the tonic dominant, that is to say, (art. 102.) which is not composed of a third major followed by two thirds minor, the dissonance which this chord forms ought to stand as a consonance in the chord which precedes it.

This is what we call a prepared dissonance. 190. From thence it follows, that in order to prepare a dissonance, it is absolutely necessary that the fundamental bass should ascend by the interval of a second, as

UT mi sol ut, RE fa la ut;

or descend by a third, as

UT mi sol ut, LA ut mi sol;

or descend by a fifth, as

UT mi sol ut, FA la ut mi:

in every other case the dissonance cannot be prepared. This is what may be easily ascertained. If, for instance, the fundamental bass rises by a third, as ut mi sol ut, mi sol fa re, the dissonance re is not found in the chord ut mi sol ut. The same might be said of ut mi sol ut, sol fa re fa, and ut mi sol ut, si re fa la, in which the fundamental bass rises by a fifth or descends by a second.

191. It may only be added, that when a tonic, that is to say, a note which carries with it a perfect chord, is followed by a dominant in the interval of a fifth or third, this procedure may be regarded as a process from that same tonic to another, which has been

(cc) On the contrary, a chord such as ut mi sol fa, in which mi would be flat, could not be admitted in harmony, because in this chord the si is not included and understood in mi. It is the same case with several other chords, such as si re fa la, si re fa la, &c. It is true, that in the last of these chords, la is included in fa, but it is not contained in re; and this re likewise forms with fa and with la a double dissonance, which, joined with the dissonance si fa, would necessarily render this chord not very pleasing to the ear; we shall yet, however, see in the second part, that this chord is sometimes used.

(dd) We have seen (art. 109.) that the chord si re fa la, in the minor mode of la, may be regarded as the inverse of the chord re fa la si; it would likewise seem, that, in certain cases, this chord si re fa la may be considered as composed of the two chords sol fa si re fa, fa la ut re, of the dominant and of the sub-dominant of the major mode of ut; which chords may be joined together, after having excluded from them, r. The dominant sol, represented by its third major si, which is presumed to retain its place. 2. The note ut which is understood in fa, which will form this chord si re fa la. The chord si re fa la, considered in this point of view, may be understood as belonging to the major mode of ut upon certain occasions.

Theory of Harmony. been rendered a dominant by the addition of the dissonance.

Moreover, we have seen (art. 119 and 120.) that a dissonance does not stand in need of preparation in the chords of the tonic dominant and of the sub-dominant: from whence it follows, that every tonic carrying with it a perfect chord may be changed into a tonic dominant (if the perfect chord be major), or into a subdominant (whether the chord be major or minor) by adding the dissonance all at once.

CHAP. XVI. Of the Rules for resolving Dissonances.

125. We have seen (chap. v. and vi.) how the diatonic scale, so natural to the voice, is formed by the harmonies of fundamental sounds; from whence it follows, that the most natural succession of harmonical sounds is to be diatonic. To give a dissonance then, in some measure, as much the character of an harmonic found as may be possible, it is necessary that this dissonance, in that part of the modulation where it is found, should descend or rise diatonically upon another note, which may be one of the consonances of the subsequent chord.

126. Now in the chord of the tonic dominant it ought rather to descend than to rise; for this reason. Let us take, for instance, the chord sol si re fa followed by the chord ut mi sol ut; the part which formed the dissonance fa ought to descend to mi rather than rise to sol, though both the sounds mi and sol are found in the subsequent chord ut mi sol ut; because it is more natural and more conformed to the connection which ought to be found in every part of the music, that sol should be found in the same part where sol has already been sounded, whilst the other part was sounding fa, as may be here seen (parts first and fourth.)

127. For the same reason, in the chord of the simple dominant re fa la ut, followed by sol si re fa, dissonance ut ought rather to descend to si than rise to re.

128. In short, for the same reason, we shall find, that in the chord of the sub-dominant fa la ut re, the dissonance re ought to rise to mi of the following chord ut mi sol ut, rather than descend to ut; whence may be deduced the following rules.

129. 1°. In every chord of the dominant, whether tonic or simple, the note which constitutes the seventh, that is to say the dissonance, ought diatonically to descend upon one of the notes which form a consonance in the subsequent chord.

2°. In every chord of the subdominant, the dissonance ought to rise diatonically upon the third of the subsequent chord.

130. A dissonance which descends or rises diatonically according to these two rules, is called a dissonance resolved.

From these rules it is a necessary result, that the chord of the seventh re fa la ut, though one should even consider it as the inverse of fa la ut re, cannot be succeeded by the chord ut mi sol ut, since there is

not in this last chord of si any note upon which the dissonance ut of the chord re fa la ut can descend.

One may besides find another reason for this rule, in examining the nature of the double employment of dissonances. In effect, in order to pass from re fa la ut, to ut mi sol ut, it is necessary that re fa la ut should in this case be understood as the inverse of fa la ut re. Now the chord re fa la ut can only be conceived as the inverse of fa la ut re, when this chord re fa la ut precedes or immediately follows the ut mi sol ut; in every other case the chord re fa la ut is a primitive chord, formed from the perfect minor chord re fa la, to which the dissonance ut was added, to take from re the character of a tonic. Thus the chord re fa la ut, could not be followed by the chord ut mi sol ut, but after having been preceded by the same chord. Now, in this case, the double employment would be entirely a futile expedient, without producing any agreeable effect; because, instead of this succession of chords, ut mi sol ut, re fa la ut, ut mi sol ut, it would be much more easy and natural to substitute this other, which furnishes this natural process, ut mi sol ut, fa la ut re, ut mi sol ut. The proper use of the double employment is, that, by means of inverting the chord of the sub-dominant, it may be able to pass from that chord thus inverted to any other chord except that of the tonic, to which it naturally leads.

CHAP. XVII. Of the Broken or Interrupted Cadence.

131. Is a fundamental bass which moves by fifths; there is always, as we have formerly observed (chap. viii.), a repose more or less perfect from one sound to another; and of consequence there must likewise be a repose more or less perfect from one sound to another in the diatonic scale, which results from that bass. It may be demonstrated by a very simple experiment, that the cause of a repose in melody is solely in the fundamental bass expressed or understood. Let any person sing these three notes ut re ut, performing on the re a shake, which is commonly called a cadence; the modulation will appear to him to be finished after the second ut, in such a manner that the ear will neither expect nor wish any thing to follow. The case will be the same if we accompany this modulation with its natural fundamental bass ut sol ut; but if, instead of this bass, we should give it the following, ut sol la; in this case the modulation ut re ut would not appear to be finished, and the ear would still expect and desire something more. This experiment may easily be made.

132. This passage sol la, when the dominant sol diatonically ascends upon the note la, instead of descending by a fifth upon the generator ut, as it ought naturally to do, is called a broken cadence; because the perfect cadence sol ut, which the ear expected after the dominant sol, is, if we may speak so, broken and suspended by the transition from sol to la.

133. From thence it follows, that if the modulation ut re ut appeared finished when we supposed no bass to it at all, it is because its natural fundamental bass ut sol ut is supposed to be implied; because the ear desires something to follow this modulation, as soon as it is reduced to the necessity of hearing another bass.

134. The interrupted cadence may, as it seems to me, be considered as having its origin in the double employment of dissonances; since this cadence, like the double employment, only consists in a diatonic process of the bass ascending (chap. xii.) In effect, nothing hinders us to descend from the chord sol si re fa to the chord ut mi sol la, by converting the tonic ut into a sub-dominant, that is to say, by passing all at once from the mode of ut to the mode of sol: now to descend from sol si re fa to ut mi sol la is the same thing as to rise from the chord sol si re fa to the chord la ut mi sol, in changing the chord of the sub-dominant ut mi sol la for the imperfect chord of the dominant, according to the laws of the double employment.

135. In this kind of cadence, the dissonance of the first chord is resolved by descending diatonically upon the fifth of the subsequent chord. For instance, in the broken cadence sol si re fa, la ut mi sol, the dissonance fa is resolved by descending diatonically upon the fifth mi.

136. There is still another kind of cadence called an interrupted cadence, where the dominant descends by a third to another dominant, instead of descending by a fifth upon the tonic, as in this process of the bass, sol si re fa, mi sol si re; in the case of an interrupted cadence, the dissonance of the former chord is resolved by descending diatonically upon the octave of the fundamental note of the subsequent chord, as may be here seen, where fa is resolved upon the octave of mi.

137. This kind of interrupted cadence, as it seems to me, has likewise its origin in the double employment of dissonances. For let us suppose these two chords in succession, sol si re fa, sol si re mi, where the note sol is successively a tonic dominant and sub-dominant; that is to say, in which we pass from the mode of ut to the mode of re; if we should change the second of these chords into the chord of the dominant, according to the laws of the double employment, we shall have the interrupted cadence sol si re fa, mi sol si re.

CHAP. XVIII. Of the Chromatic Species.

138. THE series of fundamental bass by thirds proportion 234.

(EE) In reality, ut being supposed 1, as we have always supposed it, mi is $\backslash frac\{2\}\{3\}$, and sol $\backslash frac\{2\}\{3\}\; \backslash times\; \backslash frac\{2\}\{3\}$: now sol being $\backslash frac\{2\}\{3\}$, sol then shall be to sol as $\backslash frac\{2\}\{3\}$ to 1; that is to say, as 25 times 2 to 3 times 16: the proportion then of sol to sol is as 25 to 24, an interval much less than that of 16 to 15, which constitutes the semitone from ut to si, or from fa to mi (note 2.)

(FF) It may be observed, that a minor joined to a major semitone will form a minor tone; that is to say, if one rises, for instance, from mi to fa, by the interval of a semitone major, and afterwards from fa to fa by the interval of a minor semitone, the interval from mi to fa will be a minor tone. For let us suppose mi to be 1, fa will be $\backslash frac\{2\}\{3\}$, and fa will be $\backslash frac\{2\}\{3\}$ of $\backslash frac\{2\}\{3\}$; that is to say, 25 times 16 divided by 24 times 15, or $\backslash frac\{1\}\{3\}$; mi then is to fa as 1 is to $\backslash frac\{1\}\{3\}$, the interval which constitutes the minor tone (note 2.)

With respect to the tone major, it cannot be exactly formed by two semitones: for, 1. Two major semitones in immediate succession would produce more than a tone major. In effect, $\backslash frac\{2\}\{3\}$ multiplied by $\backslash frac\{2\}\{3\}$ gives $\backslash frac\{4\}\{9\}$, which is greater than $\backslash frac\{1\}\{2\}$, the interval which constitutes (note 2) the major tone. 2. A semitone minor and a semitone major would give less than a major tone, since they amount only to a true minor. 3. And, a fortiori, two minor semitones would give still less.

(GG) In effect, mi being $\backslash frac\{2\}\{3\}$, sol will be $\backslash frac\{2\}\{3\}$ of $\backslash frac\{2\}\{3\}$; that is to say, (note 2) $\backslash frac\{2\}\{3\}$: now the proportion of $\backslash frac\{1\}\{2\}$ to $\backslash frac\{2\}\{3\}$ (note 2) is that of 3 times 25 to 2 times 36; that is to say, as 25 to 24.

duces the diatonic species in common use (chap. vi.): now the third major being one of the harmonics of a fundamental found as well as the fifth, it follows, that we may form fundamental basses by thirds major, as we have already formed fundamental basses by fifths.

139. If then we should form this bass ut, mi, sol, A chromatic interval or minor semitone, which how found. See fig. K. is between this sol and this sol: now the semitone which is between this sol and this sol is an interval much less than the semitone which is found in the diatonic scale between mi and fa, or between si and ut. This may be ascertained by calculation (22): it is for this reason that the semitone from mi to fa is called major, and the other minor (22).

140. If the fundamental bass should proceed by thirds minor in this manner, ut, mi, a succession which is allowed when we have investigated the origin of the minor mode (chap. ix.), we shall find this modulation sol, sol, which would likewise give a minor semitone (22).

141. The minor semitone is hit by young practitioners in intonation with more difficulty than the semitone major. For which this reason may be assigned: The semitone major which is found in the diatonic scale, as from mi to fa, results from a fundamental bass by fifths ut fa, that is to say, by a succession which is most natural, and for this reason the easiest to the ear. On the contrary, the minor semitone arises from a succession by thirds, which is still less natural than the former. Hence, that scholars may truly hit the minor semitone, the following artifice is employed. Let us suppose, for instance, that they intend to rise from sol to sol; they rise at first from sol to la, then descend from la to sol by the interval of a semitone major; for this sol sharp, which is a semitone major below la, proves a semitone minor above sol. [See the notes (22) and (22).]

142. Every procedure of the fundamental bass by thirds, whether major or minor, rising or descending, gives the minor semitone. This we have already seen from the succession of thirds in ascending. The series of thirds minor in descending, ut, la, gives ut, ut the fundamental bass by thirds.

Theory of (RR) and the series of thirds major in descending, ut, lab, gives ut, utb, (11).

143. The minor semitone constitutes the species called chromatic; and with the species which moves by diatonic intervals, resulting from the succession of fifths (chap. v. and vi.), it comprehends the whole of melody.

CHAP. XIX. Of the Enharmonic Species.

144. THE two extremes, or highest and lowest notes, ut sol, of the fundamental bass by thirds major, ut mi sol, give this modulation ut fi; and these two sounds ut, fi, differ between themselves by a small interval which is called the disse, or enharmonic fourth of a tone (LL), which is the difference between a semitone major and a semitone minor (MM). This quarter tone is inapprehensible by the ear, and impracticable upon several of our instruments. Yet have means been found to put it in practice in the following manner, or rather to perform what will have the same effect upon the ear.

145. We have explained (art. 116.) in what manner the chord sol fi re fa may be introduced into the minor mode, entirely consisting of thirds minor perfectly true, or at least supposed such. This chord supplying the place of the cord of the dominant (art. 116.) from thence we may pass to that of the tonic or generator la (art. 117.). But we must remark,

1. That this chord sol fi re fa, entirely consisting of thirds minor, may be inverted or modified according to the three following arrangements, fi re fa sol, re fa sol fi, fa sol fi re; and that in all these three

VOL. XII. Part II.

different states, it will still remain composed of thirds minor; or at least there will only be wanting the enharmonic fourth of a tone to render the third minor between fa and sol entirely just; for a true third minor, as that from mi to sol in the diatonic scale, is composed of a semitone and a tone both major. Now from fa to sol there is a tone major, and from sol to sol there is only a minor semitone. There is then wanting (art. 144.) the enharmonic fourth of a tone, to render the third fa sol exactly true.

2. But as this division of a tone cannot be found in the gradations of any scale practicable upon most of our instruments, nor be appreciated by the ear, the ear takes the different chords,

which are absolutely the same, for chords composed every one of thirds minor exactly just.

Now the chord sol fi re fa, belonging to the minor mode of la, where sol is the sensible note; the chord fi re fa sol, or fi re fa lab, will, for the same reason, belong to the minor mode of ut, where fi is the sensible note. In like manner, the chord re fa sol fi, or fi re fa lab utb, will belong to the minor mode of mi, and the chord fa sol fi re, or fa lab utb utb, to the minor mode of sol.

After having passed then by the mode of la to the chord sol fi re fa (art. 117.), one may by means of this last chord, and by merely satisfying ourselves to invert it, afterwards pass all at once to the modes of ut minor, of mi minor, or of sol minor; that is to say, into the modes which have nothing, or almost nothing,

3 X

nothing,

(RR) La being $\backslash frac\{1\}\{2\}$, ut is $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{2\}$; that is to say $\backslash frac\{1\}\{4\}$, and ut is 1: the proportion then between ut and ut is that of 1 to $\backslash frac\{1\}\{4\}$, or of 24 to 25.

(11) Lab being the third major below ut, will be $\backslash frac\{4\}\{3\}$ (note c): utb, then, is $\backslash frac\{1\}\{3\}$ of $\backslash frac\{4\}\{3\}$; that is to say $\backslash frac\{4\}\{9\}$. The proportion, then, between ut and utb, is as 25 to 24.

(LL) Sol being $\backslash frac\{3\}\{2\}$ and fi being $\backslash frac\{1\}\{2\}$ of $\backslash frac\{3\}\{2\}$, we shall have fi equal (note c) to $\backslash frac\{3\}\{4\}$, and its octave below shall be $\backslash frac\{3\}\{8\}$; an interval less than unity by about $\backslash frac\{1\}\{16\}$ or $\backslash frac\{1\}\{17\}$. It is plain then from this fraction, that the fi in question must be considerably lower than ut.

This interval has been called the fourth of a tone, and this denomination is founded on reason. In effect, we may distinguish in music four kinds of quarter tones.

1. The fourth of a tone major: now, a tone major being $\backslash frac\{2\}\{1\}$, and its difference from unity being $\backslash frac\{1\}\{2\}$, the difference of this quarter tone from unity will be almost the fourth of $\backslash frac\{1\}\{2\}$; that is to say, $\backslash frac\{1\}\{8\}$.

2. The fourth of a tone minor; and as a tone minor, which is $\backslash frac\{3\}\{2\}$, differs from unity by $\backslash frac\{1\}\{2\}$, the fourth of a minor tone will differ from unity about $\backslash frac\{1\}\{16\}$.

3. One half of a tone major; and as this semitone differs from unity by $\backslash frac\{1\}\{2\}$, one half of it will differ from unity about $\backslash frac\{1\}\{16\}$.

4. Finally, one half of a semitone minor, which differs from unity by $\backslash frac\{1\}\{4\}$: its half then will be $\backslash frac\{1\}\{8\}$.

The interval, then, which forms the enharmonic fourth of a tone, as it does not differ from unity but by $\backslash frac\{1\}\{16\}$, may justly be called the fourth of a tone, since it is less different from unity than the largest interval of a quarter tone, and more than the least.

We shall add, that since the enharmonic fourth of a tone is the difference between a semitone major and a semitone minor; and since the tone minor is formed (note RR) of two semitones, one major and the other minor; it follows, that two semitones major in succession form an interval larger than that of a tone by the enharmonic fourth of a tone; and that two minor semitones in succession form an interval less than a tone by the same fourth of a tone.

(MM) That is to say, that if you rise from mi to fa, for instance, by the interval of a semitone major, and afterwards, returning to mi, you should rise by the interval of a semitone minor to another sound which is not in the scale, and which I shall mark thus, fa+, the two sounds fa+ and fa will form the enharmonic fourth of a tone: for mi being 1, fa will be $\backslash frac\{4\}\{3\}$; and fa+ $\backslash frac\{11\}\{9\}$: the proportion then between fa+ and fa is that of $\backslash frac\{11\}\{9\}$ to $\backslash frac\{4\}\{3\}$ (note c); that is to say, as 25 times 15 to 16 times 1; or otherwise, as 25 times 15 to 16 times 8, or as 125 to 128. No: this proportion is the same which is found, in the beginning of the preceding note, to express the enharmonic fourth of a tone.

nothing, in common with the minor mode of la, and which are entirely foreign to it (†).

146. It must, however, be acknowledged, that a transition so abrupt, and so little expected, cannot deceive nor elude the ear; it is struck with a sensation so unlooked-for without being able to account for the passage to itself. And this account has its foundation in the enharmonic fourth of a tone; which is overlooked as nothing, because it is inapprehensible by the ear; but of which, though its value is not ascertained, the whole harshness is sensibly perceived. The instant of surprise, however, immediately vanishes; and that astonishment is turned into admiration, when one feels himself transported as it were all at once, and almost imperceptibly, from one mode to another, which is by no means relative to it, and to which he never could have immediately passed by the ordinary series of fundamental notes.

CHAP. XX. Of the Diatonic Enharmonic Species.

147. If we form a fundamental bass, which rises alternately by fifths and thirds, as fa, ut, mi, fa, this bass will give the following modulation, fa, mi, mi, re♯; in which the semitones from fa to mi, and from mi to re♯, are equal and major (88).

This species of modulation or of harmony, in which all the semitones are major, is called the enharmonic diatonic species. The major semitones peculiar to this species give it the name of diatonic, because major semitones belong to the diatonic species; and the tones which are greater than major by the excess of a fourth, resulting from a succession of major semitones, give it the name of enharmonic (note 11).

CHAP. XXI. Of the Chromatic Enharmonic Species.

148. If we pass alternately from a third minor in descending to a third major in rising, as ut, ut, la, ut♯, ut♯, we shall form this modulation mi♯, mi, mi, mi, mi♯, in which all the semitones are minor (90).

This species is called the chromatic enharmonic species: the minor semitones peculiar to this kind give it the name of chromatic, because minor semitones belong to the chromatic species; and the semitones which are lesser by the diminution of a fourth resulting from a succession of minor semitones, give it the name of enharmonic (note 11).

149. These new species confirm what we have all along said, that the whole effects of harmony and melody reside in the fundamental bass.

150. The diatonic species is the most agreeable, because the fundamental bass which produces it is formed from a succession of fifths alone, which is the most agreeable, and why.

151. The chromatic being formed from a succession of thirds, is the most natural after the preceding.

152. Finally, the enharmonic is the least agreeable of all, because the fundamental bass which gives it is not immediately indicated by nature. The fourth of a tone which constitutes this species, and which is itself inapprehensible to the ear, neither produces nor can produce its effect, but in proportion as imagination suggests the fundamental bass from whence it results; a bass whose procedure is not agreeable to nature, since it is formed of two sounds which are not contiguous one to the other in the series of thirds (art. 144.)

CHAP. XXII. Showing that Melody is the Offspring of Harmony.

153. All that we have hitherto said, as it seems to me, is more than sufficient to convince us, that melody has its original principle in harmony; and that it is in harmony, expressed or understood, that we ought to look for the effects of melody.

154. If this should still appear doubtful, nothing more is necessary than to pay due attention to the first experiment (art. 19.), where it may be seen that the principal sound is always the lowest, and that the sharper sounds which it generates are with relation to it what the treble of an air is to its bass.

155. Yet more, we have proved, in treating of broken cadence (chap. xvii.), that the diversification of basses

(†) As this method for obtaining or supplying enharmonic gradations cannot be practised on every occasion when the composer or practitioner would wish to find them, especially upon instruments where the scale is fixed and invariable, except by a total alteration of their economy, and re-tuning the strings, Dr Smith in his Harmonies has proposed an expedient for redressing or qualifying this defect, by the addition of a greater number of keys or strings, which may divide the tone or semitone into as many appreciable or sensible intervals as may be necessary. For this, as well as for the other advantageous improvements which he proposes in the structure of instruments, we cannot with too much warmth recommend the perusal of his learned and ingenious book to such of our readers as aspire to the character of genuine adepts in the theory of music.

(88) It is obvious, that if fa in the bass be supposed 1, fa of the scale will be 2, ut of the bass $\backslash frac\{1\}\{2\}$, and mi of the scale $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, that is, $\backslash frac\{1\}\{4\}$; the proportion of fa to mi is as 2 to $\backslash frac\{1\}\{4\}$, or as 1 to $\backslash frac\{1\}\{8\}$. Now mi of the bass being likewise $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$; fa of the bass is $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, and its third major re♯ $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$; this third major, approximated as much as possible to mi in the scale by means of octaves, will be $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$: mi then of the scale will be to re♯ which follows it, as $\backslash frac\{1\}\{2\}$ is to $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, that is to say, as 1 to $\backslash frac\{1\}\{4\}$. The semitones then from fa to mi, and from mi to re♯, are both major.

(90) It is evident that mi♯ is $\backslash frac\{5\}\{6\}$ (note c), and that mi is $\backslash frac\{1\}\{2\}$: these two mi's, then, are between themselves as $\backslash frac\{5\}\{6\}$ to $\backslash frac\{1\}\{2\}$, that is to say, as 6 times 4 to 5 times 5, or as 24 to 25, the interval which constitutes the minor semitone. Moreover, the la of the bass is $\backslash frac\{1\}\{2\}$, and ut♯ $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$: ut♯ then is $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, the mi in the scale is likewise to the mi♯ which follows it, as 24 to 25. All the semitones therefore in this scale are minor.

Theory of Harmony. basses produces effects totally different in a modulation which, in other respects, remains the same.

156. Can it be still necessary to adduce more convincing proofs? We have nothing to do but examine the different basses which may be given to this very simple modulation sol, ut; of which it will be found susceptible of a great many, and each of these basses will give a different character to the modulation sol ut, though in itself it remains always the same; in such a manner that we may change the whole nature and effects of a modulation, without any other alteration except that of changing its fundamental bass.

M. Rameau has shown, in his New System of Music, printed at Paris 1726, p. 44. that this modulation sol ut, is susceptible of 20 different fundamental basses. Now the same fundamental bass, as may be seen in our second part, will afford several continued or thorough basses. How many means, of consequence, may be practised to vary the expression of the same modulation?

217 Consequences deducible from this principle. 157. From these different observations it may be concluded, 1. That an agreeable melody, naturally implies a bass extremely sweet and adapted for singing; and that reciprocally, as musicians express it, a bass of this kind generally prognosticates an agreeable melody (pp).

2. That the character of a just harmony is only to form in some measure one system with the modulation, so that from the whole taken together the ear may only

receive, if we may speak so, one simple and indivisible Theory of impression.

3. That the character of the same modulation may be diversified, according to the character of the bass which is joined with it.

But notwithstanding the dependency of melody upon harmony, and the sensible influence which the latter may exert upon the former; we must not however from thence conclude, with some celebrated musicians, that the effects of harmony are preferable to those of melody. Experience proves the contrary. [See, on this account, what is written on the licence of music, printed in tom. iv. of D'Alembert's Melanges de Littérature, p. 448.]

THE diatonic scale or gammut being composed of twelve semitones, it is clear that each of these semitones taken by itself may be the generator of a mode; and that thus there must be twenty-four modes in all, twelve major and twelve minor. We have assumed the major mode of ut, to represent all the major modes in general, and the minor mode of la to represent the modes minor, to avoid the difficulties arising from sharps and flats, of which we must have encountered either a greater or lesser number in the other modes. But the rules we have given for each mode are general, whatever note of the gammut be taken for the generator of a mode.

218 Composition in harmony, what. See Composition. 158. COMPOSITION, which is likewise called counterpoint, is not only the art of composing an agreeable air, but also that of composing a great many airs in such a manner that when heard at the same time, they may unite in producing an effect agreeable and delightful to the ear; this is what we call composing music in several parts.

The highest of these parts is called the treble, the lowest is termed the bass; the other parts, when there are any, are termed middle parts; and each in particular is signified by a different name.

219 Particular intervals signified by different names, and why. 159. In the introduction (art. 9.), which is at the front of this treatise, we have seen a detail of the most common names which are given to the different intervals. But there are particular intervals which have obtained different names, according to particular circumstances; which it is proper to explain.

220 Second redundant, what. 160. An interval composed of a tone and a semitone, which is commonly called a third minor, is likewise sometimes called a second redundant; such is the

interval from ut to re in ascending, or that of la to sol descending.

This interval is so termed, because one of the sounds 222 Why is it always either sharp or flat, and that, called. if you deduce that sharp or that flat, the interval will be that of a second.

161. An interval composed of two tones and two 223 false fifth, what. semitones, as that from fa to fa, is called a false fifth. This interval is the same with the tritone (art. 9.), since two tones and two semitones are equivalent to three tones. There are, however, some reasons for distinguishing them, as will appear below.

162. As the interval from ut to re in ascending 224 has been called a second redundant, they likewise call the interval from ut to sol in ascending a fifth redundant, or from fa to mi in descending, each of which intervals are composed of four tones.

This interval is, in the main, the same with that of 225 the sixth minor (art. 6.); but in the fifth redundant there is always a sharp or a flat; inasmuch, that if this sharp or flat were deduced, the interval would become a true fifth.

163. For the same reason, an interval composed of seven 226 three tones and three semitones, as from sol to fa in ascending, what.

(pp) There are likewise several eminent musicians, who in their compositions, if we can depend on what has been affirmed, begin with determining and writing the bass. This method, however, appears in general more proper to produce a learned and harmonious music, than a strain prompted by genius and animated by enthusiasm.

Principles of Composition. Principles ascending, is called a seventh diminished; because, if you deduce the sharp from sol, the interval from sol to fa will become that of an ordinary seventh. The interval of a seventh diminished is in other respects the same with that of the sixth major (art. 9.)

226 Seventh major and redundant coincident. 164. The major seventh is likewise sometimes called a seventh redundant (QQ.)

CHAP. II. Comparison of the Different Intervals.

227 Notes in different octaves or scales replication of the other. 165. If we sing ut fa in descending by a second, and afterwards ut fa in ascending by a seventh, these two fa's shall be octaves one to the other; or, as we cations each commonly expresses it, they will be replications one of the other.

228 Hence to descend to one replication, and rise to another, has the same effect. 166. On account then of the resemblance between every found and its octave (art. 22.), it follows, that to rise by a seventh, or descend by a second, amount to one and the same thing.

229 Detail of replication. 167. In like manner, it is evident that the sixth is nothing but a replication of the third, nor the fourth but a replication of the fifth.

230 Examples of this. 168. The following expressions either are or ought to be regarded as synonymous.

169. Thus, therefore, we shall employ them indif-

ferently the one for the other; so that when we say, for instance, to rise by a third, it may be said with equal propriety to descend by a sixth, &c.

CHAP. III. Of the different Clefs; of the Value or Quantity; of the Rhythm; and of Syncopation.

170. THERE are three clefs* in music; the clef of fa ; the clef of ut ; and the clef of sol .

But, in Britain, the following characters are used: The F, or bass-clef ; the C, or tenor clef ; and the G, or treble clef .

The clef of fa is placed on the fourth line, or on the third; and the line upon which this clef is placed gives the name of fa or F, to all the notes which are upon that line.

The clef of ut is placed upon the fourth, the third, the second, or the first line; and in these different positions all the notes upon that line where the clef is placed take the name of ut, or C.

Lastly, the clef of sol is placed upon the second or first line; and all the notes upon that line where the clef is placed take the name of sol, or G.

171. As the notes are placed on the lines, and in the spaces between the lines, any one, when he sees the clef, may easily find the name of any note whatever. Thus he may see, that, in the first clef of fa, the note which is placed on the lowest line ought to be sol; that the note which occupies the space between the two first lines should be la; and that the note which is on the second line is a fa, &c. (RR.)

(QQ.) The chief use of these different denominations is to distinguish chords: for instance, the chord of the redundant fifth and that of the diminished seventh are different from the chord of the sixth; the chord of the seventh redundant, from that of the seventh major. This will be explained in the following chapters.

(RR.) It is on account of the different compasses of voices and instruments that these clefs have been invented.

The masculine voice, which is the lowest, may at its greatest depth, without straining, descend to sol, which is in the last line of the first clef of fa; and the female voice, which is the sharpest, may at its highest pitch rise to a sol, which is a triple octave above the former.

The lowest of masculine voices is adapted to a part which may be called a mean bass, and its clef is that of fa on the fourth line; this clef is likewise that of the violoncello and of the deepest instruments. A mean bass extremely deep is called a baritonus or counter-bass.

The masculine voice which is next in depth to what we have called the mean bass may be termed the concordant bass. Its clef is that of fa on the third line.

The masculine voice which follows the concordant bass may be denominated a tenor; a voice of this pitch is the most common, yet seldom extremely agreeable. Its clef is that of ut on the fourth line. This clef is also that of the bassoon or bass-hautboy.

The highest masculine voice of all may be called counter tenor. Its clef is that of ut on the third line. It is likewise the clef of tenor violins, &c.

The deepest female voice immediately follows the counter tenor, and may be called bass in alt. Its clef is that of ut upon the first line. The clef of ut upon the second line is not in frequent use.

The sharpest female voice is called treble; its clef is that of sol on the second line.

This last clef, as well as that of sol on the first line, is likewise the clef of the sharpest instruments, such as the violin, the flute, the trumpet, the hautboy, the flageolet, &c.

The ut which may be seen in the clefs of fa and in the clefs of ut is a fifth above the fa which is on the line of the clef of fa; and the sol which is on the two clefs of sol is a fifth above ut; inasmuch that sol which

172. A note before which there is a sharp (marked thus ♯) ought to be raised by a semitone; and if, on the contrary, there is a ♭ before it, it ought to be depressed by a semitone, (♭ being the mark of a flat).

The natural (marked thus ♮) restores to its natural value a note which had been raised or depressed by a semitone.

173. When you place at the cleft a sharp or a flat, all the notes upon the line on which this sharp or flat is marked are sharp or flat. Thus let us take, for instance, the cleft of ut upon the first line, and let us place a sharp in the space between the second and third line, which is the place of fa; all the notes which shall be marked in that space will be fa♯; and if you would restore them to their original value of fa natural, you must place a ♭ or a ♮ before them.

In the same manner, if a flat be marked at the cleft, and if you would restore the note to its natural state, you must place a ♯ or a ♮ before it.

174. Every piece of music is divided into different equal times, which they call measures or bars; and each bar is likewise divided into different times.

There are properly two kinds of measures or modes of time (See T): the measure of two times, or of common time, which is marked by the figure 2 placed at the beginning of the tune; and the measure of

three times, or of triple time, which is marked by the figure 3 placed in the same manner. (See V.)

The different bars are distinguished by perpendicular lines.

In a bar we distinguish between the perfect and imperfect time; the perfect time is that which we beat, the imperfect that in which we lift up the hand or foot. A bar consisting of four times ought to be regarded as compounded of two bars, each consisting of two times: thus there are in this bar two perfect and two imperfect times. In general, by the words perfect and imperfect, even the parts of the same time are distinguished: thus the first note of each time is reckoned as belonging to the perfect part, and the others as belonging to the imperfect.

175. The longest of all notes is a semibreve. A minim is half its value; that is to say, in singing, we only employ the same duration in performing two minims which was occupied in one semibreve. A minim in the same manner is equivalent to two crotchets, the crotchet to two quavers, &c.

176. A note which is divided into two parts by a syncopation, that is to say, which begins at the end of a time, and terminates in the time following, is called (ss) a syncopated note. (See Z; where the notes si, fa, and la, are each of them syncopated.) (†)

is on the lowest line of the first cleft of fa, is lower by two whole octaves than the sol which is on the lowest line of the second cleft of sol.

[Thus far the translator has followed his original as accurately as possible; but this was by no means an easy task. Among all the writers on music which he has found in English, there is no such thing as different names for each particular part which is employed to constitute full or complete harmony. He was therefore under a necessity of substituting by analogy such names as appeared most expressive of his author's meaning. To facilitate this attempt, he examined in Rousseau's musical dictionary the terms by which the different parts were denominated in D'Alembert; but even Rousseau, with all his depth of thought and extent of erudition, instead of expressing himself with that precision which the subject required, frequently applies the same names indiscriminately to different parts, without assigning any reason for this promiscuous and licentious use of words. The English reader therefore will be best able to form an accurate idea of the different parts, by the nature and situation of the clefs with which they are marked; and if he should find any impropriety in the names which are given them, he may adopt and associate others more agreeable to his ideas.]

(ss) Syncopation consists in a note which is protracted in two different times belonging partly to the one and partly to the other, or in two different bars; yet not so as entirely to occupy or fill up the two times, or the two bars. A note, for instance, which begins in the imperfect time of a bar, and which ends in the perfect time of the following, or which in the same bar begins in the imperfect part of one time and ends in the perfect of the following, is syncopated. A note which of itself occupies one or two bars, whether the measure consists of two or three times, is not considered as syncopated: this is a consequence of the preceding definition. This note is said to be continued or protracted. In the end of the example Z, the ut of the first bar consisting of three times is not syncopated, because it occupies two whole times. It is the same case with mi of the second bar, and with the ut of the fourth and fifth. These therefore are continued or protracted notes.

(†) Times and bars in music answer the very same end as punctuation in language. They determine the different periods of the movement, or the various degree of completion, which the sentiment, expressed by that movement, has attained. Let us suppose, for instance, a composer in music intending to express grief or joy, in all its various gradations, from its first and faintest sensation, to its acme or highest possible degree. We do not say that such a progress of any passion either has been or can be delineated in practice, yet it may serve to illustrate what we mean to explain. Upon this hypothesis, therefore, the degrees of the sentiment will pass from less to more sensible, as it rises to its most intense degree. The first of these gradations may be called a time, which is likewise the most convenient division of a bar or measure into its elementary or aliquot parts, and may be deemed equivalent to a comma in a sentence; a bar denotes a degree still more sensible, and may be considered as having the force of a semicolon; a strain brings the sentiment to a tolerable degree of perfection, and may be reckoned equal to a colon: the full period is the end of the imitative piece. It must have been remarked by observers of measure in melody or harmony, that the notes of which a bar or measure consists, are not diversified by their different durations alone, but likewise by greater or lesser degrees of em-
phasis.

177. A note followed by a point or dot is increased half its value. The si, for instance, in the fifth bar of the example Y, followed by a point, has the value (*) or duration of a minim and of a crotchet at the same time.

CHAP. IV. Containing a Definition of the principal Chords.

178. THE chord composed of a third, a fifth, and an octave, as ut mi sol ut, is called a perfect chord (art. 32.)

If the third be major, as in ut mi sol ut, the perfect chord is denominated major; if the third be minor, as in la ut mi la, the perfect chord is minor. The perfect chord major constitutes what we call the major mode; and the perfect chord minor, what we term the minor mode (art. 31).

179. A chord composed of a third, a fifth, and a seventh, as sol fa re fa, or re fa la ut, &c. is called a chord of the seventh. It is obvious that such a chord is wholly composed of thirds in ascending.

All chords of the seventh are practiced in harmony, save that which might carry the third minor and the seventh major, as ut mi sol fa; and that which might carry a false fifth and a seventh major, as fa re fa la ut, (chap. xiv. Part I.)

180. As thirds are either major or minor, and as they may be differently arranged, it is clear that there are different kinds of chords of the seventh; there is even one, fa re fa la, which is composed of a third, a false fifth, and a seventh.

181. A chord composed of a third, a fifth, and a sixth, as fa la ut re, re fa la fa, is called a chord of the greater sixth.

182. Every note which carries a perfect chord is

called a tonic, and a perfect chord is marked by an 8, by a 3, or by a 5, which is written above the note; but frequently these numbers are suppressed. Thus in the example I. the two ut's equally carry a perfect chord.

183. Every note which carries a chord of the seventh is called a dominant (art. 102); and this chord is marked by a 7 written above the note. Thus in the example II. re carries the chord re fa la ut, and sol the chord sol fa re fa.

It is necessary to remark, that among the chords of the seventh we do not reckon the chord of the seventh diminished, which is only improperly called a chord of the seventh; and of which we shall say more below.

184. Every note which carries the chord of the great sixth, is called a subdominant, (art. 97, and 42.) and is marked with a 6. Thus in the example III. fa carries the chord of fa la ut re. You ought to remark that the sixth should always be major, (art. 97, and 109).

185. In every chord, whether perfect, or a chord of the seventh, or of the great sixth, the note which carries this chord, and which is the flattest or lowest, is called the fundamental note. Thus ut in the example I. re and sol in the example II. and fa in the example III. are fundamental notes.

186. In every chord of the seventh, and of the great sixth, the note which forms the seventh or sixth of a chord, above the fundamental, that is to say, the highest note of the chord, is called a dissonance. Thus in the chords of the seventh sol fa re fa, re fa la ut, fa and ut are the dissonances, viz. fa with relation to sol in the first chord, and ut with relation to re in the second. In the chord of the great sixth fa la ut re, re is the dissonance (art. 120.); but that re is only, properly

phasis. The most emphatic parts of a bar are called the accented parts; those which require less energy in expression are called the unaccented. The same observation holds with regard to times as bars. The stroke, therefore, of the hand or foot in beating marks the accented part of the bar, the elevation or preparation for the stroke marks the unaccented part. Let us once more resume our composition intended to express the different periods in the progress of grief or joy. There are some revolutions in each of these so rapid as not to be marked by any sensible transition whether diatonic or consonant. In this case, the most expressive tone may be continued from one part of a time or measure to another, and end before the period of that time or measure in which it begins. Here therefore is a natural principle upon which the practice of syncopation may be founded even in melody: but when music is composed in different parts to be simultaneously heard, the continuance of one note not divided by regular times and measures, nor beginning and ending with either of them, whilst the other parts either ascend or descend according to the regular divisions of the movement, has not only a sensible effect in rendering the imitation more perfect, but even gives the happiest opportunities of diversifying the harmony, which of itself is a most delightful perception.

For the various dispositions of accent in times and measures, according to the movement of any piece, see a Treatise on Music by Alexander Malcolm.

For the opportunity of diversifying harmony afforded by syncopation, see Rameau's Principles of Composition.

(*) To prevent ambiguity or confusion of ideas, it is necessary to inform our readers, that we have followed M. D'Alembert in his double sense of the word value, though we could have wished he had distinguished the different meanings by different words. A sound may be either estimated by its different degrees of intensity, or by its different quantities of duration.

To signify both those ideas the word value is employed by D'Alembert. The reader, therefore, will find it of importance to distinguish the value of a note in height from its value in duration. This he may easily do, by considering whether the notes are treated as parts of the diatonic scale, or as continued for a greater or lesser duration.

Principles of Composition. properly speaking, a dissonance with relation to ut from which it is a second, and not with respect to fa from which it is a sixth major (art. 17, and 18).

²⁴⁷ 187. When a chord of the seventh is composed of Tonic and a third major followed by two thirds minor, the fundamental note of this chord is called the tonic dominant. In every other chord of the seventh the fundamental is called the simple dominant (art. 102.). Thus in the chord sol si re fa, the fundamental sol is the tonic dominant; but in the other chords of the seventh, as ut mi sol si, re fa la ut, &c. the fundamentals ut and re are simple dominants.

²⁴⁸ Major chords, how rendered minor, and vice versa. 188. In every chord, whether perfect, or of the seventh, or of the sixth, if you have a mind that the third above the fundamental note should be major, though it is naturally minor, you must place a sharp above the fundamental note. For example, if I would mark the perfect major chord re fa la re, as the third fa above re is naturally minor, I place above re a sharp, as you may see in example IV. In the same manner the chord of the seventh re fa la ut, and the chord of the great sixth re fa la si, is marked with a ♯ above re, and above the ♯ a 7 or a 6 (see V. and VI.).

On the contrary, when the third is naturally major, and if you should incline to render it minor, you must place above the fundamental note a ♭. Thus the examples VII. VIII. IX. show the chords sol si re sol, sol si re fa, sol si re mi (TT).

CHAP. V. Of the Fundamental Bases.

²⁴⁹ Fundamental bases, how formed. 189. INVENT a modulation at your pleasure; and under this modulation let there be set a base composed of different notes, of which some may carry a perfect chord, others that of the seventh, and others that of the great sixth, in such a manner that each note of the modulation which answers to each of the bases, may be one of those which enters into the chord of that note in the bases; this base being composed according

to the rules which shall be immediately given, will be the fundamental base of the modulation proposed. See Part I. where the nature and principles of the fundamental bases are explained.

Thus (Exam. XVIII.) you will find that this modulation, ut re mi fa sol la si ut, has or may admit for its fundamental bases, ut sol ut fa ut re sol ut.

In reality, the first note ut in the upper part is found in the chord of the first note ut in the base, which chord is ut mi sol ut; the second note re in the treble is found in the chord sol si re fa, which is the chord of the second note in the base, &c. and the base is composed only of notes which carry a perfect chord, or that of the seventh, or that of the great sixth. Moreover, it is formed according to the rules which we are now about to give.

CHAP. VI. Rules for the Fundamental Bases.

²⁵⁰ 190. ALL the notes of the fundamental bases being only capable of carrying a perfect chord, or the chord of the seventh, or that of the great sixth, are either tonics, or dominants, or sub-dominants; and the dominants may be either simple or tonic.

The fundamental bases ought always to begin with a tonic, as much as it is practicable. And now follow the rules for all the succeeding chords; rules which are evidently derived from the principles established in the First Part of this treatise. To be convinced of this, we shall find it only necessary to review the articles 34, 91, 122, 124, 126, 127.

RULE I.

191. In every chord of the tonic, or of the tonic dominant, it is necessary that at least one of the notes which form that chord should be found in the chord that precedes it.

RULE II.

192. In every chord of the simple dominant, it is necessary

(TT) We may only add, that there is no occasion for marking these sharps or flats when they are originally placed at the cleff. For instance, if the sharp be upon the cleff of fa (see Exam. X.), one may satisfy himself with simply writing re, without a sharp to mark the perfect chord major of re, re fa la re. In the same manner, in the Example XI. where the flat is at the cleff upon si, one may satisfy himself with simply writing sol, to mark the perfect chord minor of sol si re sol.

But if a case occurs where there is a sharp or a flat at the cleff, if any one should wish to render the chord minor which is major, or vice versa, he must place above the fundamental note a ♯ or a ♭. Thus the Example XII. marks the minor chord re fa la re, and Example XIII. the major chord sol si re sol. Frequently, in lieu of a natural, a flat is used to signify the minor chord, and a sharp to signify the major. Thus Example XIV. marks the minor chord re fa la re, and Example XV. the major chord sol si re sol.

When in a chord of the great sixth, the dissonance, that is to say, the sixth, ought to be sharp, and when the sharp is not found at the cleff, they write before or after the 6 a ♯; and if this sixth should be flat according to the cleff, they write a ♭.

In the same manner, if in a chord of the seventh of the tonic dominant, the dissonance, that is to say, the seventh, ought to be flat or natural, they write by the side of the seventh a ♭ or a ♮. Many musicians, when a seventh from the simple dominant ought to be altered by a sharp or a natural, have likewise written by the side of the seventh a ♯ or a ♭; but M. Rameau suppresses these characters. The reason shall be given below, when we speak of chords by supposition.

If there be a sharp on the cleff of fa, and if I should incline to mark the chord sol si re fa, or the chord ut mi fa, I would place before the seventh or the sixth a ♯ or a ♭.

In the same manner, if there be a flat on the cleff at si, and if I should incline to mark the chord ut mi sol si, I would place before the seventh a ♭ or a ♮; and so of the rest.

Principles of Composition. necessary that the note which constitutes the seventh, or dissonance, should likewise be found in the preceding chord.

Principles of Composition. the three following, which are nothing but consequences from them, and which you may pass unnoticed if you think it proper.

193. In every chord of the sub-dominant, at least one of its consonances must be found in the preceding chord. Thus, in the chord of the sub-dominant fa la ut re, it is necessary that fa, la, or ut, which are the consonances of the chord, should be found in the chord preceding. The dissonance re may either be found in it or not.

194. Every simple or tonic dominant ought to descend by a fifth. In the first case, that is to say, when the dominant is simple, the note which follows can only be a dominant; in the second it may be any one you choose; or, in other words, it may either be a tonic, a tonic dominant, a simple dominant, or a sub-dominant. It is necessary, however, that the conditions prescribed in the second rule should be observed, if it be a simple dominant.

This last reflection is necessary as you will presently see. For let us assume the succession of the two chords a ut mi sol re fa la ut (see Exam. XIX.), this succession is by no means legitimate, though in it the first dominant descends by a fifth; because the ut which forms the dissonance in the second chord, and which belongs to a simple dominant, is not in the preceding chord. But the succession will be admissible, if, without meddling with the second chord, one should take away the sharp carried by the ut in the first; or if, without meddling with the first chord, one should render ut or fa sharp in the second (uu); or in short, if one should simply render the re of the second chord a tonic dominant, in causing it to carry fa instead of fa natural (119. & 122.).

It is likewise by the same rule that we ought to reject the succession of the two following chords,

re fa la ut, sol si re fa;

(see Exam. XX.).

195. Every sub-dominant ought to rise by a fifth; and the note which follows it may, at your pleasure, be either a tonic, a tonic dominant, or a sub-dominant.

257 Other rules given, instead of the three first, one may substitute substituted. N^o 234.

If a note of the fundamental bass be a tonic, and rise by a fifth or a third to another note, that second note may be either a tonic (34. & 91.), see Examples XXI. and XXII. (xx); a tonic dominant (124.), see XXIII. and XXIV.; or a sub-dominant (124.), see XXV. and XXVI.; or, to express the rule more simply, that second note may be any one you please, except a simple dominant.

If a note of the fundamental bass be a tonic, and descend by a fifth or a third upon another note, this second note may be either a tonic (34. & 91.), see Exam. XXVII. and XXVIII.; or a tonic dominant, or a simple dominant, yet in such a manner that the rule of art. 192. may be observed (124.), see XXIX. XXX. XXXI. XXXII.; or a sub-dominant (124.), see XXXIII. and XXXIV.

The procedure of the bass ut mi sol ut, fa la ut mi, from the tonic ut to the dominant fa (Ex. XXXV.), is excluded by art. 192.

If a note in the fundamental bass be a tonic, and rise by a second to another note, that note ought to be a tonic dominant, or a simple dominant (101. & 102.). See XXXVI. and XXXVII. (vv).

We must here advertise our readers, that the examples XXXVIII. XXXIX. XL. XLI. belong to the fourth rule above, art. 194.; and the examples XLII. XLIII. XLIV. to the fifth rule above, art. 195. See the articles 34, 35, 121, 123, 124.

196. The transition from a tonic dominant to a Perfect and tonic is called an absolute repose, or a perfect cadence (73.); and the transition from a sub-dominant to a tonic is called an imperfect or irregular cadence (73.); how em- the cadences are formed at the distance of four bars played. one from another, whilst the tonic then falls within the first time of the bar. See XLV. and XLVI.

197. We must avoid, as much as we can, syncopa- 253 Syncopa- tions in the fundamental bass; that, within the first tion only time of which a bar is constituted, the ear may be en- admissible tained with a harmony different from that which it in the fun- had had fundamental bass by li- cence.

(uu) In this chord it is necessary that the ut and fa should be sharp at the same time; for the chord re fa la ut, in which ut would be sharp without the fa, is excluded by art. 179.

(xx) When the bass rises or descends from one tonic to another by the interval of a third, the mode is commonly changed; that is to say, from a major it becomes a minor. For instance, if I ascend from the tonic ut to the tonic mi, the major mode of ut, ut mi sol ut, will be changed into the minor mode of mi, mi sol si mi. For what remains, we must never ascend from one tonic to another, when there is no found common to both their modes: for example, you cannot rise to the mode of ut, ut mi sol ut, from the minor mode of mi, mi sol si mi (91.).

(yy) By this we may see, that all the intervals, viz. the third, the fifth, and second, may be admitted in the fundamental bass, except that of a second in descending. For what remains, it is very proper to remark, that the rules immediately given for the fundamental bass are not without exception, as approved compositions in music will certainly discover; but these exceptions being in reality licences, and for the most part in opposition to the great principle of connection, which prescribes that there should be at least one note in common between a preceding and a subsequent chord, it does not seem necessary to entertain initiates with a minute detail of these licences in an elementary work, where the first and most essential rules of the art alone ought to be expected.

Principles of Composition. had before perceived in the last time of the preceding bar. Nevertheless, syncopation may be sometimes admitted in the fundamental bass, but it is by a licence (22).

for the same reason, answer to several notes in the bass. For instance, sol alone may answer to these three notes in the bass, ut sol ut (AAA).

RULE I. for the TREBLE.

200. If the note which forms the seventh in a chord of the simple dominant is found in the treble, the note which precedes it must be the very same. This is what we call a discord prepared (122). For instance, let us suppose that the note of the fundamental bass shall be re, bearing the chord of the simple dominant re fa la ut; and that this ut, which (art. 18. and 118.) is the dissonance, should be found in the treble; it is necessary that the note which goes before it in the treble should likewise be an ut.

201. And it is requisite to observe, that, according to the rules which we have given for the fundamental bass, ut will always be found in the chord of that note in the fundamental bass which precedes the simple dominant re. See XLVIII. XLIX. L. In the first example the dissonance is ut, in the second sol, and in the third mi; and these notes are already in the preceding chord (222).

RULE II.

202. If a note of the fundamental bass be a tonic dominant, or a simple dominant, and if the dissonance be found in the treble, this dissonance in the same treble ought to descend diatonically. But if the note

3 Y of

CHAP. VII. Of the Rules which ought to be observed in the Treble with relation to the Fundamental Bass.

254. Definition of treble. 198. THE treble is nothing else but a modulation above the fundamental bass, and whose notes are found in the chords of that bass which corresponds with it (189.). Thus in Ex. XVIII. the scale ut re mi fa sol la si ut, is a treble with respect to the fundamental bass ut sol ut fa ut re sol ut.

255. One note in the treble or bass may answer to several of its correspondent parts, and why. 199. We are just about to give the rules for the treble; but first we think it necessary to make the two following remarks.

1. It is obvious, that many notes of the treble may answer to one and the same note in the fundamental bass, when these notes belong to the chord of the same note in the fundamental bass. For example, this modulation ut mi sol mi ut, may have for its fundamental bass the note ut alone, because the chord of that note comprehends the sounds ut, mi, sol, which are found in the treble.

2. In like manner, a single note in the treble may, VOL. XII. Part II.

(22) There are notes which may be found several times in the fundamental bass in succession with a different harmony. For instance, the tonic ut, after having carried the chord ut mi sol ut, may be followed by another ut which carries the chord of the seventh, provided that this chord be the chord of the tonic dominant ut mi sol si. See LXXII. In the same manner, the tonic ut may be followed by the same tonic ut, which may be rendered a sub-dominant, by causing it to carry the chord ut mi sol la. See LXXIII.

A dominant, whether tonic or simple, sometimes descends or rises upon one another by the interval of a tritone or false fifth. For example, the dominant fa, carrying the chord fa la ut mi, may be followed by another dominant si, carrying the chord si re fa la. This is a licence in which the musician indulges himself, that he may not be obliged to depart from the scale in which he is; for instance, from the scale of ut to which fa and si belong. If one should descend from fa to si by the interval of a just fifth, he would then depart from that scale, because si is no part of it.

(AAA) There are often in the treble several notes which may, if we choose, carry no chord, and be regarded merely as notes of passage, serving only to connect between themselves the notes that do carry chords, and to form a more agreeable modulation. These notes of passage are commonly quavers. See Exam. XLVII. in which this modulation ut re mi fa sol, may be regarded as equivalent to this other, ut mi sol, as re and fa are no more than notes of passage. So that the bass of this modulation may be simply ut sol.

When the notes are of equal duration, and arranged in a diatonic order, the notes which occupy the perfect part of each time, or those which are accented, ought each of them to carry chords. Those which occupy the imperfect part, or which are unaccented, are no more than mere notes of passage. Sometimes, however, the note which occupies the imperfect part may be made to carry harmony; but the value of this note is then commonly increased by a point which is placed after it, which proportionably diminishes the continuance of the note that occupies the perfect time, and makes it pass more swiftly.

When the notes do not move diatonically, they ought generally all of them to enter into the chord which is placed in the lower part correspondent with these notes.

(222) There is, however, one case in which the seventh of a simple dominant may be found in a modulation without being prepared. It is when, having already employed that dominant in the fundamental bass, its seventh is afterwards heard in the modulation, as long as this dominant may be retained. For instance, let us imagine this modulation,

ut | re ut si ut | re si
and this fundamental bass, ut | re sol ut | sol

(see Example LI.); the re of the fundamental bass answers to the two notes re ut of the treble. The dissonance ut has no need of preparation, because the note re of the fundamental bass having already been employed for the re which precedes ut, the dissonance ut is afterwards presented, below which the chord re may be preserved, or re fa la ut.

Principles of Composition. of the bass be a sub-dominant, it ought to rise diatonically. This dissonance, which rises or descends diatonically, is what we have called a dissonance faced or reflected (129, 130). See LII. LIII. LIV.

202. One may likewise observe here, that, according to the rules for the fundamental bass which we have given, the note upon which the dissonance ought to descend or rise will always be found in the subsequent chord (ccc).

CHAP. VIII. Of the Continued Bass, and its Rules.

204. A CONTINUED * or thorough bass, is nothing else but a fundamental bass whose chords are inverted.

We invert a chord when we change the order of the notes which compose it. For example, if instead of the chord sol si re fa, I should say si re fa sol, or re fa sol si, &c. the chord is inverted. Let us see then, in the first place, all the possible ways in which a chord may be inverted.

The ways in which a PERFECT CHORD may be INVERTED.

205. The perfect chord ut mi sol ut may be inverted in two different ways.

1. Mi sol ut mi, which we call a chord of the sixth, composed of a third, a sixth, and an octave, and in this case the note mi is marked with a 6. (See LV.)

2. Sol ut mi sol, which we call a chord of the sixth and fourth, composed of a fourth, a sixth, and an octave; and it is marked with a $\backslash frac\{3\}\{4\}$. (See LVII.)

The perfect minor chord is inverted in the same manner.

The ways in which the CHORD of the SEVENTH may be INVERTED.

206. In the chord of the tonic dominant, as sol si re fa, the third major si above the fundamental note sol is called a sensible note (77.); and the inverted

Principles of Composition. chord si re fa sol, composed of a third, a false fifth, and sixth, is called the chord of the false fifth, and is marked with an 8 or a 5 (see LVIII. and LIX.)

The chord re fa sol si, composed of a third, a fourth, and a sixth, is called the chord of the sensible sixth, and marked with a 6 or a 6. In this chord thus figured, the third is minor, and the sixth major, as it is easy to be perceived. (See LX.)

The chord fa sol si re, composed of a second, a tritone, and a sixth, is called the chord of the tritone, and is marked thus 4+, thus x4, or thus 4. (See LXI.)

207. In the chord of the simple dominant re fa la ut, we find,

1. Fa la ut re, a chord of the great sixth, which is composed of a third, a fifth, and a sixth, and which is figured with a 5. See LXIII. (DDD).

2. La ut re fa, a chord of the lesser sixth, which is figured with a 6. See LXIV. (EEE).

3. Ut re fa la, a chord of the second, composed of a second, a fourth, and a sixth, and which is marked with a 2. See LXII. (EEE).

The ways in which the CHORD of the sub-DOMINANT may be inverted.

208. The chord of the sub-dominant, as fa la ut re, may be inverted in three different manners; but the method of inverting it which is most in practice is the chord of the lesser sixth la ut re fa, which is marked with a 6, and the chord of the seventh re fa la ut. See LXIV.

Rules for the CONTINUED BASS.

209. The continued bass is a fundamental bass, whose chords are only inverted in order to render it more in the taste of singing, and suitable to the voice. See LXV. in which the fundamental bass which in itself is monotonic and little suited for singing, ut sol ut sol ut sol ut, produces, by inverting its chords, this continued

(ccc) When the treble syncopates in descending diatonically, it is common enough to make the second part of the syncopate carry a discord, and the first a concord. See Example LV. where the first part of the syncopated note sol is in concord with the notes ut mi sol ut, which answer to it in the fundamental bass, and where the second part is a dissonance in the subsequent chord la ut mi sol. In the same manner, the first part of the syncopated note fa is in concord with the notes re fa la ut, which answer to it; and the second part is a dissonance in the subsequent chord sol si re fa, which answer to it, &c.

(DDD) We are obliged to mark likewise, in the continued bass, the chord of the sub-dominant with a 5, which in the fundamental bass is figured with a 6 alone; and this to distinguish it from the chords of the sixth and of the lesser sixth. (See Examples LVI. and LXIV.) For what remains, the chord of the great sixth in the fundamental bass carries always the sixth major, whereas in the continued bass it may carry the sixth minor. For instance, the chord of the seventh ut mi sol si, gives the chord of the great sixth mi sol si ut, thus improperly called, since the sixth from mi to ut is minor.

(EEE) M. Rameau has justly observed, that we ought rather to figure this lesser sixth with a $\backslash frac\{3\}\{4\}$, to distinguish it from the sensible sixth which arises from the chord of the tonic dominant, and from the sixth which arises from the perfect chord. In the mean time he figures in his works with a 6 alone, the lesser sixths which do not arise from the tonic dominant; that is to say, he figures them as those which arise from the perfect chord; and we have followed him in that, though we thought with him, that it would be better to mark this chord by a particular figure.

(FFF) The chord of the seventh si re fa la gives, when inverted, the chord fa la si re, composed of a third, a tritone, and a sixth. This chord is commonly marked with a 6, as if the tritone were a just fourth. It is his business who performs the accompaniment, to know whether the fourth above fa be a tritone or a fourth redundant. One may, as to what remains, figure this chord thus $\backslash frac\{6\}\{3\}$.

Principles of Composition. continued bass highly proper to be sung, ut si ut re mi fa mi, &c. (GGG.)

The continued bass then is properly nothing else but a treble with respect to the fundamental bass. Its rules immediately follow, which are properly no other than those already given for the treble.

210. Every note which carries the chord of the false fifth, and which of consequence must be what we have called a sensible note, ought (77) to rise diatonically upon the note which follows it. Thus in example LXV. the note si, carrying the chord of the false fifth marked with an 8, rises diatonically upon ut (HHH).

211. Every note carrying the chord of the tritone should descend diatonically upon the subsequent note. Thus in the same example LXV. fa, which carries the chord of the tritone figured with a 4$\backslash times$, descends diatonically upon mi. (Art. 202.)

212. The chord of the second is commonly put in practice upon notes which are syncopated in descending, because these notes are dissonances which ought to be prepared and resolved (200, 202.) See the example LXVI. where the second ut, which is syncopated, and which descends afterwards upon si, carries the chord of the second (III).

(GGG) The continued bass is proportionably better adapted to singing, as the sounds which form it more scrupulously observe the diatonic order, because this order is the most agreeable of all. We must therefore endeavour to preserve it as much as possible. It is for this reason that the continued bass in Example LXV. is much more in the taste of singing, and more agreeable, than the fundamental bass which answers to it.

(HHH) The continued bass being a kind of treble with relation to the fundamental bass, it ought to observe the same rules with respect to that bass as the treble. Thus a note, for instance re, carrying a chord of the seventh re fa la ut, to which the chord of the sub-dominant fa la ut re corresponds in the fundamental bass, ought to rise diatonically upon mi. (Art. 129, n^o 2. and art. 202.)

(III) When there is a rep^res in the treble, the note of the continued bass ought to be the same with that of the fundamental bass. (see example LXVII.) In the closes which are found in the treble at si and ut (bars third and fourth), the notes in the fundamental and continued bass are the same, viz. sol for the first cadence, and ut for the second. This rule ought above all to be observed in final cadences which terminate a piece or a modulation.

It is necessary, as much as possible, to prevent coincidences of the same notes in the treble and continued bass, unless the motion of the continued bass should be contrary to that of the treble. For example, in the second note of the second bar in example LXVII. mi is found at the same time in the continued bass and in the treble; but the treble descends from fa to mi, whilst the bass rises from re to mi.

Two octaves, or two fifths, in succession, must likewise be shunned. For instance, in the treble sounds sol mi, the bass must be prevented from sounding sol mi, ut la, or re si, because in the first case there are two octaves in succession, sol against sol, and mi against mi; and because in the second case there are two fifths in succession, ut against sol, and la against mi, or re against sol, and si against mi. This rule, as well as the preceding, is founded upon this principle, that the continued bass ought not to be a copy of the treble, but to form a different melody.

Every time that several notes of the continued bass answer to one note alone of the fundamental, the composer satisfies himself with figuring the first of them. Nay he does not even figure it if it be a tonic; and he draws above the others a line, continued from the note upon which the chord is formed. See example LXXIII. where the fundamental bass ut gives the continued bass ut mi sol mi; the two mi's ought in this bass to carry the chord 6, and sol the chord 2; but as these chords are comprehended in the perfect chord ut mi sol ut, which is the first of the continued bass, we place nothing above ut, only we draw a line over ut mi sol mi.

In like manner, in the second bar of the same example, the notes fa and re of the continued bass, rising from the note sol alone of the fundamental bass which carries the chord sol si re fa, we think it sufficient to figure fa with the number of the tritone 4$\backslash times$, and to draw a line above fa and re.

It should be remarked, that this fa ought naturally to descend to mi; but this note is considered as substituting so long as the chord subsists; and when the chord changes, we ought necessarily to find the mi, as may be seen by that example.

In general, whilst the same chord subsists in passing through different notes, the chord is reckoned the same as if the first note of the chord had subsisted; in such a manner, that, if the first note of the chord is, for instance, the sensible note, we ought to find the tonic when the chord changes. See example LXXIX. or this continued bass, ut si sol si re ut, is reckoned the same with this ut si ut. (Example LXX.)

If a single note of the continued bass answers to several notes of the fundamental bass, it is figured with the different chords which agree to it. For example, the note sol in a continued bass may answer to this fundamental bass ut sol ut. (see example LXXI.); in this case, we may regard the note sol as divided into three parts, of which the first carries the chord 2, the second the chord 7, and the third the chord 2.

We shall repeat here, with respect to the rules of the continued bass, what we have formerly said concerning the rules of the fundamental bass in the note upon the third rule, art. 193. The rules of the continued bass have exceptions, which practice and the perusal of good authors will teach. There are likewise several other rules which might require a considerable detail, and which will be found in the Treatise of Harmony by M. Rameau, and elsewhere. These rules, which are proper for a complete dissertation, did not appear to me indispensably necessary in an elementary essay upon music, such as the present. The books which we have quoted at the end of our preliminary discourse will more particularly instruct the reader concerning this practical detail.

Principles of Composition. art. 219. In this state the chord is simply composed of a third, fifth, and ninth, and is marked with a 9. See LXXIX. (PPP)

218. What is more, in the chord of the simple dominant, as re fa la ut, when the fifth sol is added, they frequently obliterate the sounds fa and la, that too great a number of dissonances may be avoided, which reduces the chord to sol ut re. This last is composed only of the fourth and the fifth. It is called a chord of the fourth, and it is figured with a 4. (See LXXX.)

219. Sometimes they only remove the note la, and then the chord ought to be figured with $\backslash frac\{4\}\{4\}$ or $\backslash frac\{4\}\{4\}$ (QQQ).

220. Finally, in the minor mode, for example, in that of la, where the chord of the tonic dominant (109,) is mi sol fi re; if we add to this chord the third ut below, we shall have ut mi sol fi re, called the chord of the fifth redundant, and composed of a third, a fifth redundant, a seventh, and a ninth. It is figured with a 5, or a +5. See LXXXI. (RRR.)

§ 3. Of the CHORD of the DIMINISHED SEVENTH.

221. In the minor mode, for instance, in that of la, mi a fifth from la is the tonic dominant (109), and carries the chord mi sol fi re, in which sol is the sensible note. For this chord they sometimes substitute

that other sol fi re fa, (116), all composed of minor thirds; and which has for its fundamental sound the sensible note sol. This chord is called a chord of the flat, or diminished seventh, and is figured with a 7 in the fundamental bass, (see LXXXII.): but it is always considered as representing the chord of the tonic dominant.

222. This chord in the fundamental bass produces in the continued bass the following chords:

1. The chord fi re fa sol fi, composed of a third, false fifth, and sixth major. They call it the chord of the what, and sixth sensible and false fifth; and it is figured thus $\backslash frac\{5\}\{6\}$, or +5. (See LXXXIII.)

2. The chord re fa sol fi, composed of a third, a tritone, and a sixth, they call it the chord of the tritone and third minor; and they mark it thus $\backslash frac\{4\}\{5\}$. (See LXXXIV.)

3. The chord fa sol fi re, composed of a second redundant, a tritone, and a sixth. They call it the chord of the second redundant, and they figure it thus $\backslash frac\{2\}\{2\}$, or +2. See LXXXV. (SSS.)

223. Besides, since the chord sol fi re fa represents the chord mi sol fi re, it follows, that if we operate by supposition upon the first of these chords, it must be performed as one would perform it upon

dissonance between mi and re which was in the original chord, we have two new dissonances, ut fi, and ut re; that is to say, the seventh and the ninth. These dissonances, like the others, ought to be prepared and resolved. They are prepared by being syncopated, and resolved by descending diatonically upon one of the consonances of the subsequent chord. The sensible note alone can be resolved in ascending; but it is even necessary that this sensible note should be in the chord of the tonic dominant. As to the dissonances which are found in the primitive chord, they should always follow the common rules. (See art. 202.)

(PPP) Several musicians call this last chord the chord of the ninth; and that which, with M. Rameau, we have simply called a chord of the ninth, they term a chord of the ninth and seventh. This last chord they mark with a 9; but the denomination and figure used by M. Rameau are more simple, and can lead to no error; because the chord of the ninth always includes the seventh, except in the cases of which we have already spoken.

(QQQ) They often remove some dissonances from chords of supposition, either to soften the harshness of the chord, or to remove discords which can neither be prepared nor resolved. For instance, let us suppose, that in the continued bass the note ut is preceded by the sensible note fi, carrying the chord of the false fifth, and that we should choose to form upon this note ut the chord ut mi sol fi re, we must obliterate the seventh fi, because in retaining it we should destroy the effect of the sensible note fi, which ought to rise to ut.

In the same manner, if to the harmony of a tonic dominant sol fi re fa, one should add the note by supposition ut, it is usual to retrench from this chord the sensible note fi; because, as the re ought to descend diatonically to ut, and the fi to rise to it, the effect of the one would destroy that of the other. This above all takes place in the suspence, concerning which we shall presently treat.

(RRR) Supposition produces what we call suspence; and which is almost the same thing. Suspence consists in retaining as many as possible of the sounds in a preceding chord, that they may be heard in the chord which

succeeds. For instance, if this fundamental bass be given ut sol ut, and this continued bass above it ut ut ut,

it is a supposition; but if we have this fundamental bass ut sol sol ut, and this continued bass above it ut sol ut ut, it is a suspence; because the perfect chord of ut, which we naturally expect after sol in the continued bass, is

suspended and retarded by the chord ut, which is formed by retaining the sounds sol fi re fa of the preceding

chord to join them to the note ut in this manner, ut sol fi re fa; but this chord ut does nothing in this case but suspend for a moment the perfect chord ut mi sol ut, which ought to follow it.

(SSS) The chord of the diminished seventh, such as sol fi re fa, and the three derived from it, are termed chords of substitution. They are in general harsh, and proper for imitating melancholy objects.

mi sol fa si re fa; that is to say, that it will be necessary to add to the chord sol fa si re fa, the notes ut or la, which are the third or fifth below mi, and which will produce,

1. By adding ut, the chord ut sol fa si re fa, composed of a fifth redundant, a seventh, a ninth, and eleventh, which is the octave of the fourth. It is called a chord of the fifth redundant and fourth, and thus marked $\backslash frac\{5\}\{4\}$, or $\backslash frac\{8\}\{4\}$. (See LXXXVI.)

2. By adding la, we shall have the chord la sol fa si re fa, composed of a seventh redundant, a ninth, an eleventh, and a thirteenth minor, which is the octave of the sixth minor. It is called the chord of the seventh redundant and sixth minor, and marked $\backslash frac\{7\}\{6\}$, or $\backslash frac\{8\}\{6\}$. (See LXXXVII.) It is of all chords the most harsh, and the most rarely practiced (rrr).

In the Treatise of Harmony by M. Rameau, and elsewhere, may be seen a much longer detail of the chords by supposition: But here we delineate the elements alone.

CHAP. X. Of some Licences used in the Treble and Continued Bass.

224. SOMETIMES in a treble, the dissonance which ought to have been resolved by descending diatonically upon the succeeding note, instead of descending, on the contrary rises diatonically: but in that case, the note upon which it ought to have descended must be found in some of the other parts. This licence ought to be rarely practiced.

In like manner, in a continued bass, the dissonance in a chord of the sub-dominant inverted, as la in the chord la ut mi sol, inverted from ut mi sol la, may sometimes descend diatonically instead of rising as it ought to do, art. 129. n. 2; but in that case the note ought to be repeated in another part, that the dissonance may be there resolved in ascending.

225. SOMETIMES likewise, to render a continued bass more agreeable by causing it to proceed diatonically, they place between two sounds of that bass a note

which belongs to the chord of neither. See example XCIV, in which the fundamental bass sol ut produces the continued bass sol la si sol ut, where la is added on account of the diatonic modulation. This la has a line drawn above it to show its resolution by passing under the chord sol si re fa.

In the same manner, (see XCV), this fundamental bass ut fa may produce the continued bass ut re mi fa, where the note re which is added passes under the chord ut mi sol ut.

CHAP. XI. Containing the Method of finding the Fundamental Bass when the Continued Bass is figured.

226. To exercise yourself with greater ease in finding the fundamental bass, and to render it more familiar to you, it is necessary to observe how eminent matters, and above all how M. Rameau has put the rules in practice. Now, as they never place any thing but the continued bass in their works, it becomes then necessary to know how to find the fundamental bass when the continued bass is figured. This problem may be easily solved by the following rules.

227. 1. Every note which has no figure in the continued bass, ought to be the same, and without a figure in the fundamental bass; it either is a tonic, or reckoned such. (vvv).

2. Every note which in the continued bass carries a 6, ought in the fundamental bass to give its third below not figured *, or its fifth below marked with a 7. * See Fig. We shall distinguish these two cases below. (See LVI. red. and LXIV, and the note xxx).

3. Every note carrying $\backslash frac\{5\}\{4\}$ gives in the fundamental bass its fifth below not figured. (See LVII.)

4. Every note figured with a 7 or a $\backslash frac\{7\}\{4\}$, is the same in both basses, and with the same figure (xxx).

5. Every note figured with a 2 gives in the fundamental bass the diatonic note above figured with a 7. See LXII. (yyy).

6. Every note marked with a 4 gives in the fundamental

(rrr) As the chord of the diminished seventh sol fa si re fa, and the chord of the tonic dominant mi sol fa si re, only differ one from the other by the notes mi and fa; one may form a diatonic modulation of these two notes, and then the fundamental bass does nothing but pass from the tonic dominant to the sensible note, and from that note to the tonic dominant, till it arrives at the tonic. (See XCII.)

For the same reason, as the chord of the diminished seventh sol fa si re fa, and the chord si re fa la, which carries the fifth si of the tonic dominant mi, only differs by the sensible note sol, and the tonic la; one may sometimes, while the treble modulates sol la sol la sol la, ascend in the fundamental bass, from the bass note to the third above, provided one descend at last from thence to the tonic dominant, and from thence to the tonic; (see XCIII.) As to what remains, this and the preceding examples are licences.

(vvv) I say a tonic, or reckoned such, because it may perhaps be a dominant from which the dissonance has been removed. But in that case one may know that it is a real dominant by the note which precedes it. For instance, if the note sol, carrying a perfect chord, is preceded by re a simple dominant, carrying the chord re fa la ut, that note sol is not a real tonic; because, in order to this, it would have been necessary that re should have been a tonic dominant, and should have carried the chord re fa la ut; and that a simple dominant, as re, carrying the chord re fa la ut, should only naturally descend to a dominant, (art. 194.)

(xxx) SOMETIMES a note which carries a 7 in the continued bass, gives in the fundamental bass its third above, figured with a 6. For example, this continued bass la si ut gives this fundamental bass ut sol ut; but in this case it is necessary that the note figured with a 6 should rise by a fifth, as we see here ut rise to sol.

(yyy) A note figured with a 2, gives likewise sometimes in the fundamental bass its fourth above, figured with

Principle of Composition. mental bass the diatonic note above, figured with a 7. (See LXI.)

7. Every note figured with an 8 gives its third below figured with a 7. (See LVIII.)

8. Every note marked with a ♪ gives the fifth below marked with a 7; (see LX.) and it is plain by art. 187, that in the chord of the seventh, of which we treat in these three last articles, the third ought to be major, and the seventh minor, this chord of the seventh being the chord of the tonic dominant. (See art. 102.)

9. Every note marked with a ♪ gives its third above figured with a 7. (See LXXVII and LXXIX.)

10. Every note marked with a ♪ gives the fifth above figured with a 7. (See LXXVIII.)

11. Every note marked with a ♪, or with a +5, gives the third above figured with a ♪. (See LXXXI.)

12. Every note marked with a ♪7 gives a fifth above figured with a 7, or with a ♪. (See LXXVI.) It is the same case with the notes marked ♪, ♪, or ♪: which shows a retrenchment, either in the complete chord of the eleventh, or in that of the seventh redundant.

13. Every note marked with a 4 gives a fifth above figured with a 7, or a ♪. (See LXXX.)

14. Every note marked with a ♪ gives the third minor below, figured with a ♪. (See LXXXIII.)

15. Every note marked with a ♪ gives the tritone above figured with a 7. (See LXXXIV.)

16. Every note marked with a +2 gives the second redundant above, figured with a ♪. (See LXXXV.)

17. Every note marked with a ♪ gives the fifth redundant above, figured with a ♪. (See LXXXVI.)

18. Every note marked with a ♪7 gives the seventh redundant above, figured with a ♪. See LXXXVII. (zzz.)

228. We have omitted two cases, which may cause some uncertainty. 270

The first is that where the note of the continued bass is figured with a 6. We now present the reason of the difficulty.

Suppose we should have the dominant re in the fundamental bass, the note which answers to it in the continued bass may be la carrying the figure 6 (see LXIV.); that is to say, the chord la ut re fa: now if we should have the sub-dominant fa in the fundamental bass.

with a 6; but it is necessary in that case that the note figured with a 6, may even here rise to a fifth. (See note xxx.)

These variations in the fundamental bass, as well in the chord concerning which we now treat, as in the chord figured with a 7, and in two others which shall afterwards be mentioned (art. 228 and 229), are caused by a deficiency in the signs proper for the chord of the sub-dominant, and for the different arrangements by which it is inverted.

M. l'Abbe Roussier, to redress this deficiency, had invented a new manner of figuring the continued bass. His method is most simple for those who know the fundamental bass. It consists in expressing each chord by only signifying the fundamental found with that letter of the scale by which it is denominated, to which is joined a 7 or ♪, or a 6, in order to mark all the discords. Thus the fundamental chord of the seventh re fa la ut is expressed by a $\backslash overset\{7\}\{D\}$; and the same chord, when it is inverted from that of the sub-dominant fa la ut re, is characterized by $\backslash overset\{6\}\{F\}$; the chord of the second ut re fa la, inverted from the dominant re fa la ut, is likewise represented by $\backslash overset\{7\}\{D\}$; and the same chord ut re fa la inverted from that of the sub-dominant fa la ut re is signified by $\backslash overset\{6\}\{F\}$; the case is the same when the chords are differently inverted. By this means it would be impossible to mistake either with respect to the fundamental bass of a chord, or with respect to the note which forms its dissonance, or with respect to the nature and species of that discord.

(zzz) We may only add, that here and in the preceding articles, we suppose, that the continued bass is figured in the manner of M. Rameau. For it is proper to observe, that there are not, perhaps, two musicians who characterize their chords with the same figures: which produces a great inconvenience to the person who plays the accompaniments: but here we do not treat of accompaniments. For every reason, then, we should advise initiates to prefer the continued basses of M. Rameau to all the others, as by them they will most successfully study the fundamental bass.

It is even necessary to advertise the reader, and I have already done it (note EEE), that M. Rameau only marks the lesser sixth by a 6 without a line, when this lesser sixth does not result from the chord of the tonic dominant; in such a manner that the 6 renders it uncertain whether in the fundamental bass we ought to choose the third or the fifth below: but it will be easy to see whether the third or the fifth is signified by that figure. This may be distinguished, 1. In observing which of the two notes is excluded by the rules of the fundamental bass. 2. If the two notes may with equal propriety be placed in the fundamental bass, the preference must be determined by the tone or mode of the treble in that particular passage. In the following chapter we shall give rules for determining the mode.

There is a chord of which we have not spoken in this enumeration, and which is called the chord of the sixth redundant. This chord is composed of a note, of its third major, of its redundant fourth or tritone, and its redundant sixth, as fa la si re ♪. It is marked with a 6 ♪. It appears difficult to find a fundamental bass for this chord; nor is it indeed much in use amongst us. (See the note upon the art. 115.)

mental bass, this sub-dominant might produce in the continued bass the same note la figured with a 6. When therefore one finds in the continued bass a note marked with a 6, it appears at first uncertain whether we should place in the fundamental bass the fifth below marked with a 7, or the third below marked with a 6.

229. The second case is that in which the continued bass is figured with a 7. For instance, if there

should be found fa in the continued bass, one may be ignorant whether he ought to insert in the fundamental bass fa marked with a 6, or re figured with a 7.

230. You may easily extricate yourself from this little difficulty, in leaving for an instant this uncertain note in suspense, and in examining what is the succeeding note of the fundamental bass: for if that note be in the present case a fifth above fa, that is to say, if it is ut, in this case, and in this alone, he may place fa in the fundamental bass. It is a consequence of this rule, that in the fundamental bass every sub-dominant ought to rise by a fifth (195).

CHAP. XII. What is meant by being in a Mode or Tone.

231. In the first part of this treatise (chap. vi), we have explained, how by the means of the note ut, and of its two fifths sol and fa, one in ascending, which is called a tonic dominant, the other in descending, which is called a sub-dominant, the scale ut re mi fa sol la si ut may be found: the different sounds which form this scale compose what we call the major mode of ut, because the third mi above ut is major. If therefore we would have a modulation in the major mode of ut, no other sounds must enter into it than those which compose this scale: in such a manner that if, for instance, I should find fa in this modulation, this fa discovers to me that I am not in the mode of ut, or at least that, if I have been in it, I am no longer so.

232. In the same manner, if I form this scale in ascending la si ut re mi fa sol la si ut, which is exactly similar to the scale ut re mi fa sol la si ut of the major N^o 234.

mode of ut, this scale, in which the third from la to ut is major, shall be in the major mode of la; and if I incline to be in the minor mode of la, I have nothing to do but to substitute for ut sharp ut natural; so that the major third la ut may become minor la ut; I shall have then

la si ut re mi fa sol la,

which is (85) the scale of the minor mode of la in ascending; and the scale of the minor mode of la in descending shall be (90)

la sol fa mi ut re si la,

in which the sol and fa are no longer sharp. For it is a singularity peculiar to the minor mode, that its scale is not the same in rising as in descending (89).

233. This is the reason why, when we wish to begin a piece in the major mode of la, we place three sharps at the clef upon fa, ut, and sol; and on the contrary, in the minor mode of la, we place none, because the minor mode of la, in descending, has neither sharps nor flats.

234. As the scale contains twelve sounds, each distant from the other by the interval of a semitone, it is obvious that each of these sounds can produce both a major and a minor mode, which constitute 24 modes upon the whole. Of these we shall immediately give a table, which may be very useful to discover the mode in which we are.

A TABLE of the DIFFERENT MODES.

Major Modes.

(AAAA) The major mode of fa, of w or re, and of sol or la, are not much practised. In the opera of Pyramus and Thisbe, p. 267, there is a passage in the scene, of which one part is in the major mode of fa, and the other in the major mode of w, and there are six sharps at the clef.

When a piece begins upon w, there ought to be seven sharps placed at the clef: but it is more convenient only to place five flats, and to suppose the key re, which is almost the same thing with w. It is for this reason that we substitute here the mode of re for that of w.

It is still much more necessary to substitute the mode of la for that of sol; for the scale of the major mode of sol is sol la si ut re mi fa sol la si ut, in which you may see that there are at the same time both a sol natural and a sol sharp: it would then be necessary, even at the same time, that upon sol there should and should not be a sharp at the clef; which is shocking and inconsistent. It is true that this inconvenience may be avoided by placing a sharp upon sol at the clef, and by marking the note sol with a natural through the course of the music wherever it ought to be natural; but this would become troublesome, above all if there should be occasion to transpose. In the article 236, we shall give an account of transposition. One might likewise in this series, instead of sol natural, which is the note immediately before the last, substitute fa, that is to say, fa twice sharp: which, however, is not absolutely the same sound with sol natural, especially upon instruments whose scales are fixed, or whose intervals are invariable. But in that case two sharps may be placed at the clef upon fa, which would produce another inconvenience. But by substituting la for sol, the trouble is eluded.

In descending. la sol fa mi re ut fi la.
In rising. la fi ut re mi fa sol la.

In descending. mi re ut fi la sol fa mi.
In rising. mi fa sol la fi ut re mi.

In descending. fi la sol fa mi re ut fi.
In rising. fi ut re mi fa sol la fi.

In descending. sa mi re ut fi la sol fa.
In rising. sa sol la fi ut re mi fa.

In descending. ut fi la sol fa mi re ut fi.
In rising. ut re mi fa sol la fi ut.

In descending. sol fa mi re ut fi la sol fa.
In rising. la fi ut re mi fa sol la.

In descending. wi re ut fi la sol fa mi.
In rising. mi fa sol la fi ut re mi.

In descending. fi la sol fa mi re ut fi.
In rising. fi ut re mi fa sol la.

In descending. sa mi re ut fi la sol fa.
In rising. sa sol la fi ut re mi.

In descending. ut fi la sol fa mi re ut.
In rising. ut re mi fa sol la fi ut.

In descending. sol fa mi re ut fi la sol.
In rising. sol la fi ut re mi fa.

In descending. re ut fi la sol fa mi re.
In rising. re mi fa sol la fi ut re.

235. These then are all the modes, as well major as minor. Those which are crowded with sharps and flats are little practised, as being extremely difficult in execution.

1. That when there are neither sharps nor flats at the cleff, it is a token that the piece begins in the major mode of ut, or in the minor mode of la.

2. That when there is one single sharp, it will always be placed upon fa, and that the piece begins in the major mode of sol, or the minor of mi, in such a manner that it may be sung as if there were no sharp, by singing fi instead of fa, and in singing the tune as if it had been in another cleff. For instance, let there be a sharp upon fa in the cleff of sol upon the first line; one may then sing the tune as if there were no sharp: And instead of the cleff of sol upon the first line, let there be the cleff of ut; for the fa, when changed into fi, will require that the cleff of sol should be changed to the cleff of ut, as may be easily seen. This is what we call transposition (‡).

237. It is evident, that when fa is changed into fi, sol must be changed into ut, and mi into la. Thus by transposition, the air has the same melody as if it were in the major mode of ut, or in the minor mode of la.

(BEEB) We have already seen, that in each mode, the principal note is called a tonic; that the fifth above that note is called a tonic dominant, or the dominant of the mode, or simply a dominant; that the fifth beneath the tonic, or, what is the same thing, the fourth above that tonic, is called a sub-dominant; and in short, that the note which forms a semitone beneath the tonic, and which is a third major from the dominant, is called a senfible note. The other notes have likewise in every mode particular names which it is advantageous to know. Thus a note which is a tone immediately above the tonic, as re in the mode of ut, and fi in that of la, is termed a sub-tonic; the following note, which is a third major or minor from the tonic, according as the chord is major or minor, such as mi in the major mode of ut, and ut in the minor mode of la, is called a mediant; in short, the note which is a tone above the dominant, such as la in the mode of ut, and sa in that of la, is called a sub-dominant.

‡ Though our author's account of this delicate operation in music will be found extremely just and compendious; though it proceeds upon simple principles, and comprehends every possible contingency; yet as the manner of thinking upon which it depends may be less familiar to English readers, if not profoundly skilled in music, it has been thought proper to give a more familiar, though less comprehensive, explanation of the manner in which transposition may be executed.

It will easily occur to every reader, that if each of the intervals through the whole diatonic series were equal, in a mathematical sense, it would be absolutely indifferent upon what note any air were begun, if within the compass of the gammut; because the same equal intervals must always have the same effects. But since, besides the natural semitones, there is another distinction of diatonic intervals into greater and lesser tones; and since these vary their positions in the series of an octave, according as the note from whence you begin is placed, that note is consequently the best key for any tune whose natural series is most exactly correspondent with the intervals which that melody or harmony requires. But in instruments whose scales are fixed, notwithstanding the temperament and other expedients of the same kind, such a series is far from being easily found, and is indeed in common practice almost totally neglected. All that can frequently be done is, to take care that the ear may not be sensibly shocked. This, however, would be the case, if, in transposing any tune, the situation of the semitones, whether natural or artificial, were not exactly correspondent in the series to which your air must be transposed, with their positions in the scale from which you transpose it. Suppose

of la. The major mode then of sol, and the minor of mi, are by transposition reduced to those of ut major, and of la minor. It is the same case with all the other modes, as any one may easily be convinced (cccc).

CHAP. XIII. To find the Fundamental Bafs of a given Modulation.

238. As we have reduced to a very small number

the rules of the fundamental bafs, and those which in the treble ought to be observed with relation to this bafs, it should no longer be difficult to find the fundamental bafs of a given modulation, nay, frequently to find several; for every fundamental bafs will be legitimate, when it is formed according to the rules which we have given (Chap. VI.); and that, besides this, the dissonances which the modulation may form with this bafs, are not difficult, and why.

for instance, your air should begin upon ut or C, requiring the natural diatonic series through the whole gammut, in which the distance between mi and fa, or E and F, as also that between fi and ut, or B and C, is only a semitone. Again, suppose it necessary for your voice, or the instrument on which you play, that the same air should be transposed to sol or G, a fifth above its former key; then because in the first series the intervals between the third and the fourth, seventh and eighth notes, are no more than semitones, the same intervals must take the same place in the octave to which you transpose. Now, from sol or G, the note with which you propose to begin, the three tones immediately succeeding are full; but the fourth, ut or C, is only a semitone; it may therefore be kept in its place. But from fa or F, the seventh note above, to sol or G, the eighth, the interval is a full tone, which must consequently be redressed by raising your fa a semitone higher. Thus the situations of the semitone intervals in both octaves will be correspondent; and thus, by conforming the positions of the semitones in the octave to which you transpose, with those in the octave in which the original key of the tune is contained, you will perform your operation with as much success as the nature of fixed scales can admit: But the order in which you must proceed, and the intervals required in every mode, are minutely and ingeniously delineated by our author.

(cccc) Two sharps, fa and ut, indicate the major mode of re, or the minor of fi; and then, by transposition, the ut is changed into fi, and of consequence, re into ut and fi into la.

Three sharps, fa ut sol, indicate the major mode of la, or the minor of fa; and it is then sol, which must be changed into fi, and of consequence la into ut, and fa into la.

Four sharps, fa ut sol re, indicate the major mode of mi, or the minor of ut; then the re is changed into fi, and of consequence mi into ut, and ut into la.

Five sharps, fa ut sol re la, indicate the major mode of fi, or the minor of sol; la then is changed into fi, and of consequence fi into ut, and sol into la.

Six sharps, fa ut sol re la mi, indicate the major mode of fa; mi then is changed into fi, and of consequence fa into ut.

Six flats, fi mi la re sol ut, indicate the minor mode of mi; ut is changed into fa, and of consequence mi into la.

Five flats, fi mi la re sol, indicate the major mode of re, or the minor mode of fi; then the fi is changed into fa, and of consequence the re into ut, and the fi into la.

Four flats, fi mi la re, indicate the major mode of la, or the minor mode of fa; re then is changed into fa, and of consequence la into ut, and fa into la.

Three flats, fi mi la, indicate the major mode of mi, or the minor of ut; the la then is changed into fa, and of consequence mi into ut, and the sol into la.

Two flats, fi mi, indicate the major mode of fi, or the minor of sol; mi then is changed into fa, and of consequence fi into ut, and the fa into la.

One flat, fi, indicates the major mode of fa, or the minor mode of re, and fi is changed into fa; of consequence the fa is changed into ut, and the re into la.

All the major modes then may be reduced to that of ut, and the modes minor to that of la minor.

It only remains to remark, that many musicians, and amongst others the ancient musicians of France, as Lulli, Campra, &c. place one flat less in the minor mode: so that in the minor mode of re, they place neither sharp nor flat at the cleff; in the minor mode of sol, one flat only; in the minor mode of ut, two flats, &c.

This practice in itself is sufficiently indifferent, and scarcely merits the trouble of a dispute. Yet the method which we have here described, according to M. Rameau, has the advantage of reducing all the modes to two; and besides it is founded upon this simple and very general rule, That in the major mode, we must place as many sharps or flats at the cleff, as are contained in the diatonic scale of that mode in ascending; and in the minor mode, as many as are contained in that same scale in descending.

However this be, I here present you with a rule for transposition, which appears to me more simple than the rule in common use.

For the Sharps.

Suppose sol, re, la, mi, fi, fa, and change sol into ut if there is one sharp at the cleff, re into ut if there are two sharps, la into ut if there are three, &c.

For the Flats.

Suppose fa, fi, mi, la, re, sol, and change fa into ut if there is only one flat at the cleff, fi into ut if there are two flats, mi into ut if there are three, &c.

Principles of Composition. this bass, will both be prepared, if it is necessary that they should be so, and always resolved (dnd).

280 239. It is of the greatest utility in searching for the fundamental bass, to know what is the tone or mode of the melody to which bass should correspond.

assigning general rules for ascertaining in which nothing may be left that appears indifferent to one mode or another; because sometimes we seem to have the free choice of referring a particular melody either to one mode or another. For example, this melody sol ut may belong to all the modes, as well major as minor, in which sol and ut are found together; and each of these two sounds may even be considered as belonging to a different mode.

281 Reasons why one may proceed without the knowledge of the mode, and how he may be preserved from deviating in composition. 240. For what remains, one may sometimes, as it should seem, operate without the knowledge of the mode, for two reasons: 1. Because, since the same sounds belong to several different modes, the mode is sometimes considerably undetermined; above all, in the middle of a piece, and during the time of one or two bars. 2. Without giving ourselves much trouble about the mode, it is often sufficient to preserve us from deviating in composition, if we observe in the simplest manner the rules above prescribed (ch. VI.) for the procedure of the fundamental bass.

232 Knowledge of the mode in beginning a piece indispensable, and why. 241. In the mean time, it is above all things necessary to know in what mode we operate at the beginning of the piece, because it is indispensable that

the fundamental bass should begin in the same mode, and that the treble and bass should likewise end in it; nay, that they should even terminate in its fundamental note, which in the mode of ut is ut, and la in that of la, &c. Besides, in those passages of the modulation where there is a cadence, it is generally necessary that the mode of the fundamental bass should be the same with that of the part to which it corresponds.

242. To know upon what mode or in what key a piece commences, our inquiry may be entirely reduced to distinguish the major mode of ut from the minor of la. For we have already seen (art. 236 and 237.), that all the modes may be reduced to these two, at least in the beginning of the piece. We shall now therefore give a detail of the different means by which these two modes may be distinguished.

1. From the principal and characteristical sounds of the mode, which are ut mi sol in the one, and la ut mi in the other; so that if a piece should, for instance, begin thus, la ut mi la, it may be almost constantly concluded, that the tone or mode is in la minor, although the notes la ut mi belong to the mode of ut.

2. From the sensible note, which is si in the one, and sol in the other; so that if sol appears in the first bars of a piece, one may be certain that he is in the mode of la.

3. From the adjuncts of the mode, that is to say, the modes of its two fifths, which for ut are fa and sol, and re and mi for la. For example, if after having be-

3 Z 2

gun

(dnd) We often say, that we are upon a particular key, instead of saying that we are in a particular mode. The following expressions therefore are synonymous; such a piece is in ut major, or in the mode of ut major, or in the key of ut major.

We have seen that the diatonic scale or gammut of the Greeks was la si ut re mi fa sol la (art. 49.) A method has likewise been invented of representing each of the sounds in this scale by a letter of the alphabet; la by A, si by B, ut by C, &c. It is from hence that these forms of speaking proceed: Such a piece is upon A, with mi, la, and its third minor; or, simply, it is upon A, with mi, la, and its minor; such another piece upon C, with sol, ut, and its third major; or, simply, upon C, with sol, ut, and its major; to signify that the one is the mode of la minor, or that the other is in that of ut major; this last manner of speaking is more concise, and on this account it begins to become general.

They likewise call the cleff of ut fa F, the cleff of re sol G, &c. to denominate the cleff of fa, the cleff of sol, &c.

They say likewise to take the A mi la, to give the A mi la; that is to say, to take the unison of a certain note called la in the harpichord, which la is the same that occupies the fifth line, or the highest line in the first cleff of fa. This la divides in the middle the two octaves which subfit (note xx) between the sol which occupies the first line in the cleff of sol upon that same line, and that sol which occupies the first line in the cleff of fa upon the fourth; and as it possesses (if we may speak so) the middle station between the sharpest and lowest sounds, it has been chosen to be the sound with relation to which all the voices and instruments ought to be tuned in a concert (§).

(§) Thus far our author: and though the note is no more than an illustration of the technical phraseology in his native language, we did not think it consistent with the fidelity of a translation to omit it. We have little reason to envy, and still less to follow, the French in their abbreviations of speech; the native energy of our tongue supercedes this necessity in a manner so effectual, that, in proportion as we endeavour to become succinct, our style, without the smallest sacrifice of perspicuity, becomes more agreeable to the genius of our language; whereas, in French, laconic diction is equally ambiguous and disagreeable. Of this we cannot give a more flagrant instance than the note upon which these observations are made, in its original. We must, however, follow the author's example, in reciting a few technical phrases upon the same subject, which occur in our language, and which, if we are not mistaken, will be found equally concise, at the same time that they are more natural and intelligible. When we mean to express the fundamental note of that series within the diatonic octave which any piece of music demands, we call that note the key. When we intend to signify its mode, whether major or minor, we denominate the harmony sharp or flat. When in a concert we mean to try how instruments are in tune by that note upon which, according to the genius of each particular instrument, they may best agree in unison, we desire the musicians who join us to sound A.

gun a melody by some of the notes which are common to the modes of ut and of la (as mi re mi fa mi re ut si ut), I should afterwards find the mode of sol, which I ascertain by the fa, or that of sa which I ascertain by the sy or mi; I may conclude that I have begun in the mode of ut; but if I find the mode of re, or that of mi, which I ascertain by sy, mi, or re, &c. I conclude from thence that I have begun in the mode of la.

4. A mode is not for ordinary deserted, especially in the beginning of a piece, but that we may pass into one or other of these modes which are most relative to it, which are the mode of its fifth above, and that of its third below, if the original mode be major, or of its third above if it be minor. Thus, for instance, the modes which are most intimately relative to the major mode of ut, are the major mode of sol, and that of la minor. From the mode of ut we commonly pass either into the one or the other of these modes; so that we may sometimes judge of the principal mode in which we are, by the relative mode which follows it, or which goes before it, when these relative modes are decisively marked. For what remains, besides these two relative modes, there are likewise two others into which the principal mode may pass, but less frequently, viz. the mode of its fifth below, and that of its third above, as sa and mi for the mode of ut (XXXX).

5. The modes may still be likewise distinguished by the cadences of the melody. These cadences ought to occur at the end of every two, or at most of every four bars, as in the fundamental bass: now the note of the fundamental bass which is most suitable to these closes*, is always easy to be found. For the sounds which occur in the treble may be consulted M. Rameau, p. 54. of his Nouveau Systeme de Musique theorique et pratique (XXXX).

When a person is once able to ascertain the mode, and can render himself sure of it by the different means which we have pointed out, the fundamental bass will cost little pains. For in each mode there are three fundamental sounds.

1. The tonic of the mode, or its principal sound,

which carries always the perfect chord major or minor, according as the mode itself is major or minor.

Major mode of UT. ut mi sol ut.

Minor mode of LA. la ut mi la.

2. The tonic dominant, which is a fifth above the tonic, and which, whether in the major or minor mode, always carries a chord of the seventh, composed of a third major followed by two thirds minor.

Tonic dominant.

Major mode of UT. sol si re fa.

Tonic dominant.

Minor mode of LA. mi sol si re.

3. The sub-dominant, which is a fifth below the tonic, and which carries a chord composed of a third, fifth, and sixth major, the third being either greater or lesser, according as the mode is major or minor.

Sub-dominant.

Major mode of UT. fa la ut re.

Minor mode of LA. re fa la si.

These three sounds, the tonic, the tonic dominant, and the sub-dominant, contain in their chords all the notes which enter into the scale of the mode: so that when a melody is given, it may almost always be found which of these three sounds should be placed in the fundamental bass, under any particular note of the upper part. Yet it sometimes happens that not one of these notes can be used. For example, let it be supposed that we are in the mode of ut, and that we find in the melody these two notes la si in succession; if we confine ourselves to place in the fundamental bass one of the three sounds ut sol fa, we shall find nothing for the sounds la and si but this fundamental bass fa sol; now such a succession as fa to sol is prohibited by the fifth rule for the fundamental bass, according to which every sub-dominant, as fa, should rise by a fifth; so that fa can only be followed by ut in the fundamental bass, and not by sol.

To remedy this, the chord of the sub-dominant fa la ut re must be inverted into a fundamental chord of the seventh, in this manner, re fa la ut, which has been called the double employment (art. 105.) because it is a secondary manner of employing the chord of the sub-

* See Ge-
nere.

285
Having as-
certained
the mode,
the funda-
mental bass
not diffi-
cult.

(XXXX) It is certain that the minor mode of mi has an extremely natural connection with the mode of ut, as has been proven (art. 92.) both by arguments and by examples. It has likewise appeared in the note upon the art. 93. that the minor mode of re may be joined to the major mode of ut: and thus in a particular sense, this mode may be considered as relative to the mode of ut, but it is still less so than the major modes of sol and fa, or than those of la and mi minor; because we cannot immediately, and without licence, pass in a fundamental bass from the perfect minor chord of ut to the perfect minor chord of re; and if you pass immediately from the major mode of ut to the minor mode of re in a fundamental bass, it is by passing, for instance, from the tonic ut, or from mi sol ut, to the tonic dominant of re, carrying the chord la ut mi sol, in which there are two sounds, mi sol, which are found in the preceding chord; or otherwise from ut mi sol ut to sol sy re mi, a chord of the sub-dominant in the minor mode of re, which chord has likewise two sounds, sol and mi, in common with that which went immediately before it.

(XXXX) All these different manners of distinguishing the modes ought, if we may speak so, to give mutual light and assistance one to the other. But it often happens, that one of these signs alone is not sufficient to determine the mode, and may even lead to error. For example, if a piece of music begins with these three notes, mi ut sol, we must not with too much precipitation conclude from thence that we are in the major mode of ut, although these three sounds, mi ut sol, be the principal and characteristic sounds in the major mode of ut: we may be in the minor mode of mi, especially if the note mi should be long. You may see an example in the fourth act of Zoroaster, where the first air sung by the priests of Arimanes begins thus with two times sol mi sy, each of these notes being a crotchet. The air is in the minor mode of sol, and not in the major mode of mi, as one would at first be tempted to believe it. Now we may be sensible that it is in sol minor, by the relative modes which follow, and by the notes where the cadences fall.

Principles of Composition. By these means we give to the modulation la fi, this fundamental bass re fol, which procedure is agreeable to rules.

Here then are four chords, ut mi sol ut. sol fi re fa. fa la ut re. re fa la ut, which may be employed in the major mode of ut. We shall find in like manner, for the minor mode of la, four chords,

la ut mi la. mi sol fi re. re fa la fi. fi re fa la.

And in this mode we sometimes change the last of these chords into fi re fa la, substituting the fa for fa. For instance, if we have this melody in the minor mode of la mi fa sol la, we would cause the first note mi to carry the perfect chord la ut mi la, the second note fa to carry the chord of the seventh fi re fa la, the third note sol the chord of the tonic dominant mi sol fi re, and in short, the last the perfect chord la ut mi la.

On the contrary, if this melody is given always in the minor mode la la sol la, the second la being syncopated, it might have the same bass as the modulation mi fa sol la, with this difference alone, that fa might be substituted for fa in the chord fi re fa la, the better to mark out the minor mode.

Besides these chords which we have just mentioned, and which may be regarded as the principal chords of the mode, there are still a great many others; for example, the series of dominants,

ut la re sol ut fa fi mi la re sol ut.

which are terminated equally in the tonic ut, either entirely belong, or at least may be reckoned as belonging (gggg) to the mode of ut; because none of these dominants are tonic dominants, except sol, which is the tonic dominant of the mode of ut; and besides, because the chord of each of these dominants forms no other sounds than such as belong to the scale of ut.

But if I were to form this fundamental bass,

ut la re sol ut.

considering the last ut as a tonic dominant in this manner, ut mi sol fi; the mode would then be changed at the second ut, and we should enter into the mode of fa, because the chord ut mi sol fi indicates the tonic dominant of the mode of fa; besides, it is evident that the mode is changed, because fi does not belong to the scale of ut.

In the same manner, were I to form this fundamental bass

ut la re sol ut.

considering the last ut as a tonic dominant in this manner, ut mi sol fa; this last ut would indicate the mode of sol, of which ut is the sub-dominant.

In like manner, still, if in the first series of dominants, I caused the first re to carry the third major, in this manner, re fa la ut; this re having become a tonic dominant, would signify to me the major mode of sol, and the sol which should follow it, carrying the chord fi re fa, would relapse into the mode of ut, from whence we had departed.

Finally, in the same manner, if in this series of dominants, one should cause fi to carry fa in this manner, fi re fa la, this fa would show that we had departed from the mode ut, to enter into that of sol.

From hence it is easy to form this rule for discovering the changes of mode in the fundamental bass.

1. When we find a tonic in the fundamental bass, we are in the mode of that tonic; and the mode is major or minor, according as the perfect chord is major or minor, according as the perfect chord is major or minor, according as the perfect chord is major or minor.

2. When we find a sub-dominant, we are in the mode of the fifth above that sub-dominant; and the mode is major or minor, according as the third in the chord of the sub-dominant is major or minor.

3. When we find a tonic dominant, we are in the mode of the fifth below that tonic dominant. As the tonic dominant carries always the third major, one cannot be secure by the assistance of this dominant alone, whether the mode be major or minor: but it is only necessary for the composer to cast his eye upon the following note, which must be the tonic of the mode in which he is; by the third of this tonic he will discover whether the mode be major or minor.

243. Every change of the mode supposes a cadence; and when the mode changes in the fundamental bass, it is almost always either after the tonic of the mode in which we have been, or after the tonic dominant of that mode, considered then as a tonic by favour of a close which ought necessarily to be found in that place: Whence it happens that cadences in a melody for the most part preface a change of mode which ought to follow them.

244. All these rules, joined with the table of modes which we have given (art. 234.), will serve to discover in what mode we are in the middle of a piece, especially in the most essential passages, as cadences (HHHH).

I here subjoin the soliloquy of Armida, with the continued and fundamental basses. The changes of the mode will be easily distinguished in the fundamental bass,

(gggg) I have said, that they may be reckoned as belonging to this mode, for two reasons: 1. Because, properly speaking, there are only three chords which essentially and primitively belong to the mode of ut, viz. ut carrying the perfect chord, fa carrying that of the sub-dominant, and sol that of the tonic dominant, to which we may join the chord of the seventh, re fa la ut (art. 105.): but we here regard as extended the series of dominants in question, as belonging to the mode of ut, because it preserves in the ear the impression of that mode. 2. In a series of dominants, there are a great many of them which likewise belong to other modes; for instance, the simple dominant la belongs naturally to the mode of sol, the simple dominant fi to that of la, &c. Thus it is only improperly, and by way of extension, as I have already said, that we regard here these dominants as belonging to the mode of ut.

(HHHH) Two modes are so much more intimately relative as they contain a greater number of sounds common to both; for example, the minor mode of ut and the major of sol, or the major mode of ut and the minor

bass, by the rules which we have just given at the end of the article 242. This folioquy will serve for a lesson to beginners. M. Rameau quotes it in his New System of Music, as an example of modulation highly just and extremely simple. (See Plate VI. and the following (1111).)

CHAP. XIV. Of the Chromatic and Enharmonic.

245. We call that melody chromatic which is composed of several notes in succession, whether rising or descending by semitones. (See LXXXVIII. and LXXXIX.)

246. When an air is chromatic in descending, the most natural and ordinary fundamental bass is a concatenated series of tonic dominants; all of which follow one another in descending by a fifth, or which is the same thing, in rising by a fourth. See LXXXVIII (LLLL).

247. When the air is chromatic in ascending, one may form a fundamental bass by a series of tonics and of tonic dominants, which succeed one another alternately by the interval of a third in descending, and of a fourth in ascending, (see LXXXIX). There are many other ways of forming a chromatic air, whether in rising or descending; but these details in an elementary essay are by no means necessary.

248. With respect to the enharmonic, it is very rarely put in practice; and we have explained its formation in the first book, to which we refer our readers. We shall content ourselves with saying, that,

in the beautiful folioquy of the fourth act of Dardanus, at the words lieux funestes, &c. "fatal places, &c." we find an example of the enharmonic; an example of the diatonic enharmonic in the trio of the Fatal Sisters, in Hippolitus and Aricia, at the words, On cours-tu malheureux, "Whither, unhappy, dost thou run;" and that there are no examples of the chromatic enharmonic, at least in our French operas. M. Rameau had imitated an earthquake by this species of music, in the second act of the Gallant Indians; but he informs us, that in 1735 he could not cause it to be executed by the band. The trio of the Fatal Sisters in Hippolitus has never been sung in the opera as it is composed. But M. Rameau asserts, (and we have heard it elsewhere by people of taste, before whom the piece was performed), that the trial had succeeded when made by able hands that were not mercenary, and that its effect was astonishing.

CHAP. XV. Of Design, Imitation, and Fugue. See Design.

249. In music, the name of design, or subject, is generally given to a particular air or melody, which the composer intends should prevail through the piece; whether it is intended to express the meaning of words to which it may be set, or merely inspired by the impulse of taste and fancy. In this last case, design is distinguished into imitation and fugue.

250. Imitation consists in causing to be repeated the melody of one or of several bars in one single part, or in the whole harmony, and in any of the various modes

of la: on the contrary, two modes are less intimately relative as the number of sounds which they contain as common to both is smaller; for instance, the major mode of ut and the minor of si, &c.

When you find yourself led away by the current of the modulation, that is to say, by the manner in which the fundamental bass is constituted, into a mode remote from that in which the piece was begun, you must continue in it but for a short time, because the ear is always impatient to return to the former mode.

(1111) It is extremely proper to remark, that we have given the fundamental, the continued bass, and in general the modulation of this folioquy, merely as a lesson in composition extremely suitable to beginners; not that we recommend the folioquy in itself as a model of expression. Upon this last object what we have said may be seen in what we have written concerning the liberties to be taken in music, Vol. IV. p. 435, of our Literary Miscellany. It is precisely because this folioquy is a proper lesson for initiates, that it would be a bad one for the mature and ingenious artist. The novice should learn tenaciously to observe his rules; the man of art and genius ought to know on what occasions and in what manner they may be violated when this expedient becomes necessary.

(LLLL) We may likewise give to a chromatic melody in descending, a fundamental bass, into which may enter chords of the seventh and of the diminished seventh, which may succeed one another by the intervals of a false fifth and a fifth redundant: thus in the Example XC. where the continued bass descends chromatically, it may easily be seen that the fundamental bass carries successively the chords of the seventh and of the diminished seventh, and that in this bass there is a false fifth from re to sol, and a fifth redundant from sol to ut.

The reason of this licence is, as it appears to me, because the chord of the diminished seventh may be considered as representing (art. 221.) the chord of the tonic dominant; in such a manner that this fundamental bass

7 # 7 7 7 #
la re sol ut fa # si mi la

(see Example XCI.) may be considered as representing (art. 116.) that which is written below,

7 # 7 7 7 #
la re mi ut fa # si mi la

Now this last fundamental bass is formed according to the common rules, unless that there is a broken cadence from re to mi, and an interrupted cadence from mi to ut, which are licences (art. 213 and 214.)

Principles of Composition.
* See Air, Canon, Fugue.
293
Principal rules for composing in several parts.

that may be chosen. When all the parts absolutely repeat the same air, or melody, and beginning one after the other, this is called a canon. Fugue consists in alternately repeating that air in the treble, and in the bass, or even in all the parts, if there are more than two.

251. Imitation and fugue are sometimes conducted by rules merely deducible from taste, which may be seen in the 332d and following pages of M. Rameau's Treatise on Harmony; where will likewise be found a detail of the rules for composition in several parts. The chief rules for composition in several parts are, that the dissonance should be found, as much as possible, prepared and resolved in the same part; that a discord should not be heard at the same time in several parts, because its harshness would disgust the ear; and that in no particular part there should be found two octaves or two fifths in succession (M M M M) with respect to the bass. Musicians, however, do not hesitate sometimes to violate this precept, when taste or occasion require. In music, as in all the other fine arts, it is the business of the artist to assign and to observe rules; the province of men who are adorned with taste and genius is to find the exceptions.

CHAP. XVI. Definitions of the Different Airs.

252. We shall finish this treatise by giving in a few words the characteristic distinctions of the different airs to which names have been given, as chacoon, minuet, rigadoon, &c.

The chacoon is a long piece of music, containing three times in each bar, of which the movement is regular, and the bars sensibly distinguished. It consists of several couplets, which are varied as much as possible. Formerly the bass of the chacoon was a constrained bass, or regulated by a rhythmus terminating in 4 bars, and proceeding again by the same number; at present composers of this species no longer confine themselves to that practice. The chacoon begins, for the most part, not with the perfect time, which is struck by the hand or foot, but with the imperfect, which passes while the hand or foot is elevated.

The villanelle is a chacoon a little more lively, with its movement somewhat more brisk than the ordinary chacoon.

The passacaille only differs from a chacoon as it is more slow, more tender, and beginning for ordinary with a perfect time.

The minuet is an air in triple time, whose movement is regular, and neither extremely brisk nor slow, consisting of two parts or strains, which are each of them repeated; and for which reason they are called by the French reprises: each strain of the minuet begins with a time which is struck, and ought to consist of 4, of 8, or of 12 bars; so that the cadences may be easily distinguished, and recur at the end of each 4 bars.

The sarabando is properly a slow minuet; and the

courant a very slow sarabando: this last is no longer in use. The passopied is properly a very brisk minuet, which does not begin like the common minuet, with a stroke of the foot or hand; but in which each strain begins in the last of the three times of which the bar consists.

The loure is an air whose movement is slow, whose time is marked with $\backslash frac\{3\}\{4\}$, and where two of the times in which the bar consists are beaten; it generally begins with that in which the foot is raised. For ordinary the note in the middle of each time is shortened, and the first note of the same time pointed.

The jig is properly nothing else but a loure very brisk, and whose movement is extremely quick.

The forlana is a moderate movement, and in a mediocrity between the loure and the jig.

The rigadoon has two times in a bar, is composed of two strains, each to be repeated, and each consisting of 4, of 8, or of 12 bars: its movement is lively; each strain begins, not with a stroke of the foot, but at the last note of the second time.

The bowce is almost the same thing with the rigadoon.

The gavotte has two times in each bar, is composed of two strains, each to be repeated, and each consisting of 4, of 8, or of 12 bars: the movement is sometimes slow, sometimes brisk; but never extremely quick, nor very slow.

The tambourin has two strains, each to be repeated, and each consisting of 4, of 8, or of 12 bars, &c. Two of the times that make up each bar are beaten, and are very lively; and each strain generally begins in the second time.

The musette consists of two or three times in each bar; its movement is neither very quick nor very slow; and for its bass it has often no more than a single note, which may be continued through the whole piece.

A P P E N D I X.

THE treatise of D'Alembert, of which we have given a translation, is well entitled to the merit of accuracy; but perhaps a person who has not particularly studied the subject, may find difficulty in following the scientific deductions of that author.—We subjoin, therefore, a few general observations on the philosophy of musical sound, commonly called harmonics, which may perhaps convey the full portion of knowledge of the theory of music, with which one in search only of general information, and not a professed student of this particular science, would choose to rest satisfied.

The theory of musical sound, which only in the beginning of the present century was ultimately established by mathematical demonstration, is no other than that which distinguished the ancient musical sect

who

(M M M M) Yet there may be two fifths in succession, provided the parts move in contrary directions, or, in other words, if the progress of one part be ascending, and the other descending; but in this case they are not properly two fifths, they are a fifth and a twelfth; for example, if one of the parts in descending should sound fa re, and the other ut la in rising, ut is the fifth of fa, and la the twelfth of re.

who followed the opinions of Pythagoras on that subject.

No part of natural philosophy has been more fruitful of hypothesis than that of which musical sound is the object. The musical speculators of Greece arranged themselves into a great number of different sects, the chief of whom were the Pythagoreans and the Aristoxenians.

Pythagoras supposed the air to be the vehicle of sound; and the agitation of that element, occasioned by a similar agitation in the parts of the sounding body, to be the cause of it. The vibrations of a string or other sonorous body, being communicated to the air, affected the auditory nerves with the sensation of sound; and this sound, he argued, was acute or grave in proportion as the vibrations were quick or slow.— He discovered by experiment, that of two strings equal in every thing but length, the shorter made the quicker vibrations, and emitted the acuter sound:— in other words, that the number of vibrations made in the same time, by two strings of different lengths, was inversely as those lengths; that is, the greater the length the smaller the number of vibrations in any given time. Thus sound, considered in the vibrations that cause it, and the dimensions of the vibrating body, came to be reduced to quantity, and as such was the subject of calculation, and expressible by numbers.— For instance, the two sounds that form an octave could be expressed by the numbers 1 and 2, which would represent either the number of vibrations in a given time, or the length of the strings; and would mean, that the acuter sound vibrates twice, while the graver vibrates once; or that the string producing the lower sound is twice the length of that which gives the higher. If the vibrations were considered, the higher sound was as 2, the lower as 1; the reverse, if the length was alluded to. In the same manner, in the same sense, the 5th would be expressed by the ratio of 2 to 3, and the 4th by that of 3 to 4.

Aristoxenus, in opposition to the calculations of Pythagoras, held the ear to be the sole standard of musical proportions. That sense he accounted sufficiently accurate for musical, though not for mathematical, purposes; and it was in his opinion absurd to aim at an artificial accuracy in gratifying the ear beyond its own power of distinction. He, therefore, rejected the velocities, vibrations, and proportions of Pythagoras as foreign to the subject, in so far as they substituted abstract causes in the room of experience, and made music the object of intellect rather than of sense.

Of late, however, as has been already mentioned, General observations on Harmonics, have been confirmed by absolute demonstration; and the following propositions, in relation to musical sound, have passed from conjecture to certainty.

Sound is generated by the vibrations of elastic bodies, which communicate the like vibrations to the air, and these again the like to our organs of hearing. This is evident, because sounding bodies communicate tremors to other bodies at a distance from them. The vibrating motion, for instance, of a musical string, excites motion in others, whose tension and quantity of matter dispose their vibrations to keep time with the undulations of air propagated from it (the string first set in motion.)

If the vibrations be isochronous, and the sound musical, continuing at the same pitch, it is said to be acuter, sharper, or higher, than any other sound whose vibrations are slower; and graver, flatter, or lower, than any other whose vibrations are quicker.— For while a musical string vibrates, its vibrations become quicker by increasing its tension or diminishing its length; its sound at the same time will be more acute: and, on the contrary, by diminishing its tension or increasing its length, the vibrations will become slower and the sound graver. The like alteration of the pitch of the sound will follow, by applying, by means of a weight, an equal degree of tension to a thicker or heavier and to a smaller or lighter string, both of the same length, as in the smaller string the mass of matter to be moved by the same force is less.

If several strings, however, different in length, density, and tension, vibrate altogether in equal times, their sounds will have all one and the same pitch, however they may differ in loudness or other qualities.— They are called unisons. The vibrations of unisons are isochronous.

The vibrations of a musical string, whether wider or narrower, are nearly isochronous. Otherwise, while the vibrations decrease in breadth till they cease, the pitch of the sound could not continue the same (which we perceive by experience it does), unless where the first vibrations are made very violently; in which case, the sound is a little acuter at the beginning than afterwards.

Lastly, the word vibration is understood to mean the time which passes between the departure of the vibrating body from any assigned place and its return to the same.

Gloss-Music. See HARMONICA.

MUSIMON, in natural history, the name of an animal esteemed a species of sheep, described by the ancients as common in Corsica, Sardinia, Barbary, and the north-east parts of Asia. It has been doubted whether the animal described under this name is now any where to be found in the world; and whether it was not, probably, a spurious breed between two animals of different species, perhaps the sheep and goat,

N° 234.

which, like the mule, not being able to propagate its species, the production of them may have been discontinued.

Buffon supposes it to be the sheep in a wild state; and it is described as such by Mr Pennant. These animals live in the mountains, and run with great swiftness among the rocks. Those of Kamtschatka are so strong, that 10 men can scarcely hold one; and the horns are so large as sometimes to weigh 30 pounds, and

tone tone semitone tone tone tone semitone

A ut re mi fa sol la si vt

B ut re mi fa sol la si vt re mi fa sol &

Scale first. Scale Second.

The Chromatic Species Scale.

The diatonic Scale of the Greeks.

D Si ut Re Mi Fa Sol La

Scale first.

The Fundamental bass.

Scale.

K Sol Sol &c

ut Mi Sol*

The Fundamental bass.

E ut Re Mi Fa Sol Sol La Si ut

ut Sol ut Fa ut Sol Re Sol ut

The Fundamental bass.

Scale.

L ut Mi Si*

ut Mi Sol*

The Fundamental bass.

F vt, vt*, re, re*, mi, mi*, fa*, sol, sol*, la, la*, si, si*, ut, ut*, re, re*, mi, mi*.

Scale first. Scale Second.

The first Scale of the minor mode.

G Sol La Si ut Re Mi Fa

Mi La Mi La Re La Re

The Fundamental bass.

Scale.

N Mi Mi Mi Mi Mi*

ut ut La ut ut

The Fundamental bass.

The second Scale of the minor mode.

H La Si ut Re Mi mi fa* sol* La

La Mi La Re La Mi Si Mi La

The Fundamental bass.

Scale.

M Fa Mi Mi Re

Fa ut Mi Si

The Fundamental bass.

Scale.

I ut Re Mi Fa Sol La si ut

ut Sol ut Fa ut Re Sol ut

Musical staff showing vocal parts with lyrics: "ut", "O", "ut", "P", "Sol", "Sol".

Musical staff with rhythmic notation and time signatures: "R", "S", "1st Measure", "T", "2nd Measure", "1st Time", "2nd T.", "3rd T.", "with two Times".

Musical staff with rhythmic notation and time signatures: "Semibreve", "Minims", "Crotchets", "Quavers", "Pointed Note", "X", "Y", "Bar 1st", "B. 2d", "B. 3d", "B. 4th", "B. 5th".

Musical staff with rhythmic notation and time signatures: "Z", "Barr 1st", "2d", "3d", "4th", "5th", "6th", "7th".

Musical staff with rhythmic notation and time signatures: "I.", "II.", "III.", "IV.", "V.", "VI.", "VII.", "VIII.", "IX.", "X.", "8", "7", "6", "#", "7", "6", "b", "7", "b".

Musical staff with rhythmic notation and time signatures: "XI.", "XII.", "XIII.", "XIV.", "XV.", "XVI.", "XVII.", "b", "b", "b", "#", "7", "7", "#6".

Musical staff with rhythmic notation and time signatures: "XVIII.", "XIX.", "XX.", "XXI.", "XXII.", "XXIII.", "XXIV.", "7", "7", "7", "7", "7", "7", "7".

Musical staff with rhythmic notation and time signatures: "Treble Part", "Fundamental Bass", "XXV.", "XXVI.", "XXVII.", "XXVIII.", "#6", "6", "to defend by thirds", "to defend or rif. by 5ths or 4ths".

MUSIC.

XXIX. XXX. XXXI. XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII.
XXXVIII. XXXIX. XL. XLI. XLII. XLIII. XLIV. XLV. XLVI.

Perfect Cadence imperfect Cad:

XLVII. XLVIII. XLIX. L. LI.

Treble part Treble Treble Treble Treble

Fundamental Bafs Fund. Bafs Fund. Bafs

LII. LIII. LIV. LV. LVI. LVII. LVIII.

Treble Treble Treble Treble

Fundamental B. Fund. B. Fund. B. Fund. B. F. B. F. B.

LIX. LX. LXI. LXII. LXIII. LXIV. LXV. LXVI.

Th. B. T. B. T. B. T. B. T. B. T. B. Thorough Bafs T. B.

F. B. F. B. F. B. F. B. F. B. Fundamental Bafs F. B.

Treble. Treble.

Thorough. Bass Th. B.

Fundamental Bass Fund. B.

The Key T.B. or tonic The Sensible Note Key T.B. Sen. N. Key Th. B.

Fund. B. Fund. B.

F.B. F.B. F.B. Broken Cadence F.B. Interrupted Cadence

T.B. T.B. T.B. T.B. T.B. T.B. T.B. T.B. T.B. T.B.

Fund. B. F.B. F.B. F.B. F.B. F.B. F.B. F.B. F.B.

Cromatic modulation descending. Cromatic modulation ascending.

T.B. T.B. The Treble The Treble

F.B. F.B. Fund.B. Fund.B.

Treble Fund.B.

T.B. Fund.B.

F.B. Fund.B.

Treble.

Fund.B.

Treble Th. B. F.B.

Fund. B. F.B.

En fin, il est en ma puis-fance, Ce fatal enne mi, Ce superbe vain-

Th.B.

F.B.

-queur, Le charme du som meil le livre à ma ven- geance, Je vais per-

T.B.

F.B.

-cer son in-vin-ci-ble cœur; Par luy, tous mes Captifs sont fortis d'escla-

T.B.

F.B.

vage; Qu'il eprouve toute ma rage Quel trouble me faisit! Qui me fait hési-

Th.B.

F.B.

-ter? Questce qu'en sa fa - veur la pilié me veut di re? Frapons, Ciel! qui peut m'arrê-

Th.B.

F.B.

ter? Achevons je fremis! Vengeons nous je foû pire! Est-ce ainsi que je

Th.B.

F.B.

doit me venger aujour d'huy! Ma co-le-re fé teint Quand j'approche de luy
Th.B.
F.B.

Plus je le vois! plus ma vengeance est vaine; Mon bras tremblant se re-
Th.B.
F.B.

fufe à ma haine: Ah! quelle cruauté de luy ravir le jour! A ce jeune He-
Th.B.
F.B.

ros, tout cé-de sur la terre: Qui croiroit qu'il fût ne seulement pour la guerre, Il

Th.B.

F.B.

femble être fait pour l'A_mour. Ne puis-je me venger à moins qu'il ne pe-

Th.B.

F.B.

riffe? Hé! ne suffi-t-il pas que l'Amour le pu nisse? Puisqu'il n'a pu trou-

Th.B.

F.B.

ver mes yeux as fez charmants; Qu'il m'aime au moins par mes enchante-

T.B.

F.B.

-ments; Que l'il se peut, je le ha-is se.

T.B.

F.B.

Translation. Intended to give such Readers as do not understand French, an idea of the Song.

At length the victim in my power I see,
This fatal year resigns him to my rage;
Subdued by sleep he lies, and leaves me free,
With chastning hand my fury to aswage.
That mighty heart invincible and fierce,
Which all my captives freed from servile chains;
That mighty heart, my vengeful hand shall pierce;
My rage inventive wanton in his pains.
Ha! in my soul what perturbation reigns!
What would compassion in his favour plead?
Strike, hand, O heaven! what charm thy force restrains?
Obey my wrath. I sigh; yet let it bleed.
And is it thus my just revenge improves
The fair occasion to chastize my foe?
As I approach, a softer passion moves,
And all my boasting fury melts in wo.
Trembling, relax'd, and faithless to my hate,
The dreadful task this coward arm declines.

How cruel thus to urge his instant fate,
Depriv'd of life amid his great designs!
In youth how blooming! what a heavenly grace,
Thro' all his form, resistless power displays!
How sweet the smile that dwells upon his face,
Relentless rage disarming whilst I gaze!
Tho' to the prowess of his conquering arms
Earth stood with all her hosts oppos'd in vain;
Yet is he form'd to spread more mild alarms,
And bind all nature in a softer chain.
Can then his blood, his precious blood, alone
Extinguish all the vengeance in my heart?
Tho' still surviving, might he not atone.
For all the wrongs I feel, by gentler smart?
Since all my charms, unfeeling, he defies,
Let Magic force his stubborn soul subdue;
Whilst I, inflexible to tears and sighs,
With hate (if I can hate) his peace pursue.