M U S I C;

Definition. 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 capacious. 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

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*. 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 rhythmical, 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 melodie, 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 rhythmoscopie, 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 accentuated 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

* See Composition.

nues 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 littlest 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 object 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 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 humanized 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 methodized 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 amulement 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 practiced 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 characterized 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

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 stifled 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 coexistence 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 a 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:

"Farther, when we consider by whom these ancient tunes were composed, and how they were first performed, we shall see that such harmonical succession 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 emphatical note should be a chord 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

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 manœuvre 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 feistive 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 possess a manœuvre and expression peculiar to themselves, which it is impossible to describe, and which can only be exhibited by good performers.

Having thus far pursued the general idea of music, we shall, after the history, give a more particular detail of the science.

HISTORY OF MUSIC.

MUSIC is capable of so infinite a variety, 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 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.

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 artless. 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.

By comparing the accounts of Diodorus Siculus
VOL. XIV. Part II.

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 judgement. 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.

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 calaceione 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

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 calceione 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 so wonderful an improvement in literature.

The Egyptian Hermes the inventor of the lyre.

The Hermes or Mercury of the Egyptians, firnamed 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 entitled 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 animal."

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 single flute of the Egyptians.

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 drefs of a tibicen, 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 expence used on these occasions advanced by degrees to an excessive extent. The number of flute-players in the processions amounted sometimes to several hundreds,

hundreds, and the attendance of the guests continued frequently for 30 days *.

lib. ix. c. 9. 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 a 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.

Grecian music. Cadmus, with 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.

Progress of the Grecian lyre. 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 named hypate and parhypate." It has been already mentioned, that the lyre invented by the Egyptian Mercury had but three strings. By putting these cir-

cumstances 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 of the great system, and first tetrachord invented by the ancients, answering to our A, on the fifth line in the base. If this sound 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 mese, parhypate mese, and mese diatone: The addition, therefore, of mese 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 dilutive, 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 sealds 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 annals 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 (A). During the century which elapsed between the days of Sappho and those of Anacreon, no literary productions are preserved entire.—

3 Q 2 From

(A) 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.

From Anacreon to Pindar there is another chasm of near a century. Subsequent to this time, the works fill extant of the three great tragic poets, Æschylus, Sophocles, and Euripides, together with those of Piato, 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 581. 5s. 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 ourselves. Amobaeus, a harper, was paid an Attic talent, or 1931. 15s. per day for his performance (B). Extravagance of the ancients with respect to music.

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, was a public performer, as well as were many other elevated female spirits, who 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 feels, and of much diversity of opinion.—The founders of the most distinguished feels were Pythagoras and Aristoxenus.

Like every other people, the Romans, from their Roman 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 fruits 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 (Phonaseus) 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

Vociferous music of the Greeks.

(B) Roscius gained 500 sestertis, or 4036. 9s. 2d. sterling.

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 chanting 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 was employed in the church service, first by St Augustine, 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 Copronymus 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 or 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 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 sacred 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, infensibly 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 successes 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 clothes, 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, men-trieurs, 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 embellishments 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 at present speak. A poet of the 14th century, Machau, 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

the viol. 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 viola 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 joculator 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 particularly 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 authorize 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, Banister, 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

dered as the father of that plaintive melody which in Scotch tunes is so pleasing to a taste not vitiated by modern affectation. Besides the testimony of Fordun and Major, 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, plaintive and melancholy, different from all others; in which he has been imitated by Carlo Gesualdo prince of Venosa, 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 and ingenious antiquary † 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 Dunkeld, Ballenden archdeacon of Murray, Dunbar, Henryson, Scott, Montgomery, Sir David Lindsay, and many others, whose fine poems have been preserved in Banatyne's Collection, and of which several have been published by Allan 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: 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 be sufficient for any matter 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 to study all over Europe.

The most eminent musical theorists of Italy, who

flourished in the 16th century, were, Franchinus Gamberius, or Gafforio of Lode, Pietro Aaron of Florence, Lodovico Fogliano, Giov. Spato, Giov. Maria da Terentio Lanfranco, Stefano Uanico, Anton. 16th century, Franciscus Dore, Luigi Dentice, Nicolo Vicentino, and Girolamo Zarlini, the most general, voluminous, and celebrated theorist of that period, Vincentio Galilei, a Florentine nobleman, and father of the great Galileo Galilei, Maria Artusi of Bologna, Orfeo Tegrini, Pietro Pontio, and Lodovico Zacconi.

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

Of the Venetians, Adrian Willaert 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 might also furnish an ample list of eminent musicians during the 16th century, of whom, however, our limits will not admit of a particular enumeration:—The chief of them were, Constanzo Porta, Galfoldi, Biffi, Cima, Vocchi, and Monteverde.

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

Francisco Corteccis, a celebrated organist and composer, and Alessandro Striggio, a lutenist and voluminous composer, were the most eminent Florentines.

The inhabitants of the extensive empire of Germany have long made music a part of general education.—They hold the place, next to 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. Reischius, Michael Roswick, Andreas Ornitoparchus, Paul Hofheimer, Lufpeinius, Henry Loris or Lorit, Faber, Fink, Hofman, and many others whom it would be tedious to mention; and for a particular account of whole treatises and compositions we must refer to more voluminous histories of music.

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

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.

The Netherlands, likewise, during the period of which we have been speaking, produced eminent composers; the Netherlands.

† See Tessani's Dissertation on the Scotch Music, vol. 1, of the Transactions of the Society of Antiquaries in Scotland.

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

of whom we may mention Verletot, Gombert, Arka-
delt, Berchem, Richafort or Ricciafort, Crequilon Le
Cock or Le Coq, Canis, Jacob Clemens Non Papa,
Pierre Manchicourt, Baston, Kerl, Rore, Orlandi di
Lasso, and his sons Ferdinand and Rodolph.

In the 17th century, the musical writers and com-
posers who acquired fame in England, were, Dr Na-
thanael Giles, Thomas Tomkins, and his son of the
same name; Elway Bevin, Orlando Gibbons, Dr Wil-
liam Child, Adrian Batten, Martin Pierfon, William
Lawes, Henry Lawes, Dr John Wilson, John Hil-
ton, John Playford, Captain Henry Cook, Pelham
Humphrey, John Blow, William Turner, Dr Chris-
topher Gibbons, Benjamin Rogers, and Henry Pur-
cell. 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 Hychin.

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 pas-
sion seems to have been excited in England for the
violin, and for pieces expressly composed for it, in
the Italian manner (B). 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 culti-
vated 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 pro-
ductions which chiefly employed the master's study
and the hearer's attention.

So late as the beginning of the 18th century, ac-
cording 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, whom the night before you had seen in the char-
acters 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 nu-

merous. Music seems to have been but little culti-
vated 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 ac-
count of her extraordinary character and romantic ad-
ventures, deserves to be mentioned. She eloped from
her husband with a fencing-master, of whom she learnt
the small sword. She became an excellent fencer. At
Marfelles she entertained a strange attachment to a young
lady, who was seized with a whimsical fondness in re-
turn, on account of which the latter was confined in a
convent. La Maupin obtained admission into the same
convent as a novice. She set fire to the building, and
in the confusion carried off her favourite. At Paris
when she appeared on the stage in 1695, Dumeni a
fencer having affronted her, she put on men's clothes,
and insisted 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 men's clothes; and having behaved im-
pertinently to a lady, three of the lady's friends, sup-
posing La 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
40,000 livres. She threw it at the count's head, tell-
ing him, it was a recompense worthy of such meanness
as he displayed. 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 com-
posers for the church were Clarke, Dr Holden, Dr the church
Creyghton, Tueker, Aldrich, Golwin, Weldon, Dr in England.
Crofts, Dr Greene, 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 furnish-
ed 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-
sical drama. It was afterwards perfected by Metasta-
sio. No musical dramas similar to those afterwards
known

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

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 Giasone was performed. In 1679, the opera of Dou 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'Onofra negl' 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 jackbuts, 6 great flutes, 6 minirets playing on Turkish instruments, 6 others on octave flutes, 6 pages, 3 sergeants, 6 cymbalists. There were 12 huntsmen, 12 grooms, 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, descending 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 has been furnished with composers and performers from that city.

VOL. XIV. Part II.

The word opera seems to have been familiar to French and 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 Circe 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 Arinnoe 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 Crofts, and Mrs Lyndley. The translation of Arinnoe, 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 Chayton 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 Chayton, 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 Cavalier 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, Valentin Urban, and a female singer called The Baroness,¹³

Baronesi, arrived. Margarita de l'Epini, who afterwards married Dr Pepulch, 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.

Arrival of
Handel in
England.

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 an engagement at the Opera, where her salary is said to have been 1000l. 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 at the age of 88, entitled her to be mentioned even in a compend too short for biography.

The conducting the opera having been found to be more expensive than profitable, it was entirely suspended from 1717 till 1720, when a fund of 50,000l. 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 1000l. were 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, than king of Poland. Here Handel engaged Senefino-Berenstadt, Boschi, and the Darantanti.

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 Haufe, 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 50,000l. 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 Anihale Pio Fabri, his wife, Signora Bertoldi, and John Godfrid Reimelschneider.

The sacred musical drama, or oratorio, was invented early in the 12th 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 to England, 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 Carestini, 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. Carestini'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, his manner was articulate and admirable. It was the opinion of Haufe, as well as other eminent professors, that

Progress of
the opera
under his
management.

that whoever had not heard Carestini, 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 part, who at this time arrived. This renowned finger 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 Carestini, 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 800l.

Opera in England given up.
After a fruitless attempt by Heidegger, the conductor of Handel in the conduct of the opera, and patentee 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.

Revived.
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. Calluzzi 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 history of instrumental music of England. His powers on the violin were unequalled. The same year Dr Croza, then manager of the opera, eloped, 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, called Il Filosofo di Campagna, 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, and ladies in full dress, without servants or carriages,

were obliged to walk home, amidst the merriment of the spectators on the streets.

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.

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

1769.
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 sung 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 remember 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 sung 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 Aeolian harp. Most other singers affect a swell, or messa 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.

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 (Lucca 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 characters 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 divisions.

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.

Caterina
Gabrielli.

The season 1775 and 1776 was rendered memorable by the arrival of the celebrated Caterina Gabrielli, styled early in life La Cuochetina, 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 sung 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 Gabrielli's voice, an elegance in the finishing of her musical periods or passages, an accent and precision in her divisions, 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.

Agujari at
the Pan-
theon.

About the time of which we have been treating, the proprietors of the Pantheon ventured to engage Agujari at the enormous salary of 100l. per night, for singing two songs only! Lucresia 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 base to A on the sixth line in the treble, and beyond that in alt she had in early youth more than another octave. She has been heard to ascend to Bb in altissimo. 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.

Anna
Pozzi.

In 1776 arrived Anna Pozzi, as successor to 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. After that time, however, Pozzi, with more study and knowledge, became one of the best and most admired female singers in Italy.

Georgi.

After the departure of Agujari for the second and last time, the managers of the Pantheon engaged Georgi as her successor. Her voice was exquisitely fine, but totally uncultivated. She was thereafter employed as the first woman in the operas of the principal cities of Italy.

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

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 de camera, when confined to the graziosa in a room, left 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 Gaspardo Pacchierotti appeared in London, whether his high reputation had penetrated long before. The natural tone of his voice was interesting, sweet and pathetic. His compass downwards was great, with an ascent up to Bb, and sometimes to C in alt. He possessed 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.

About this time dancing became an important branch of the amusements of the opera house. Mademoiselle Heinel, M. Vestris le Jeune, Mademoiselle Baccelli, had, during some years, delighted the audience at the opera; but on the arrival of M. Vestris l'Aîné, 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. After that time, the most mute and respectful attention was paid to the manly grace of Le Picq, and the light fantastic toe of the younger Vestris; to the Rossis, the Theodoros, the Coaulons, the Hillingburgs; while the lighted fingers were 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 commemoration 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; and in subsequent years to still greater numbers.

Dr Burney published An Account of the Musical Performances in Commemoration of Handel, for the benefit

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 Giardini the greatest performer on the violin now in Europe.

Excellence of Madame Mara. As a compensation for these losses, this memorable year is distinguished by the arrival of Madame 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 ecstacy and rapture.

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

A new dance by N. Noverre. 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 so 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.

Marchesi. This year arrived Signor Luigi Marchesi, a finger whose talents have been the subject of praise and admiration on every great theatre of Europe. Marchesi's style of singing was 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 were wonderful. Many of his graces were elegant and of his own invention.

Discriminated characters of Pacchierotti, Rubinielli, and Marchesi. The three greatest Italian singers of these times were 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 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.

Sovereign princes dilettanti. During the latter part of the 18th century many eminent composers 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 particularized, 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 Princo Lobkowitz, as eminent dilettanti of modern times.

Singers on theatres and in public gardens. Besides the opera singers whom we have mentioned, 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.

Our favourite musicians at this time were, Dubourg, Clegg, Clarke, and Festing, on the violin; Kyte on the hautboy; Jack Festing on the German flute; Baston on the common flute; Karba on the bassoon; Valentine Snow on the trumpet; and on the organ, Rosingrave, 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 Galiard 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.

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

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

In 1749 arrived Giardini, whole 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.

Of near 150 musical pieces brought on our national theatres within 40 years, 38 of them at least were set by Arne. The style of this composer, if analyzed, would perhaps appear to be neither Italian nor English; but an agreeable mixture of both and of Scotch.

The late earl of Kelly, who died some 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.

Charles Frederic Abel was an admirable musician: Abel. 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 judgement so correct and certain as never to permit a single note to escape him without 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.

playing an adagio soon became the model of imitation for all our young performers on bowed instruments. Bartholomew Cervetto, Cramer, and Croftil, were in this respect to 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 viola da gamba, that remnant of the old class of viols which during the 17th 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 viola da gamba in Europe): the instrument seems quite laid aside. It was used longer in Germany than elsewhere; but the place of gambist seems now as much suppressed in the chapels of German princes as that of lutanist. 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.

Mrs Billington, after distinguishing herself in childhood as a neat and expressive performer on the piano-forte, appeared all at once in 1786 as a sweet and captivating singer. In emulation of Mara and other great bravura singers, she at first too frequently attempted passages of difficulty; afterward, however, so greatly was she improved, that no song seemed too high or too rapid for her execution. Now, at the distance of 20 years, she retains her high reputation. 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.

The Catch-club at the Thatched House, instituted in 1762 by the 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.

Two female performers have lately appeared of distinguished eminence.

Madame Graffini had exhibited her vocal powers in Paris with extraordinary applause, and arrived in London in 1805, where she excited uncommon admiration. She appeared in Zaira, where the display of her powers not only pleased, but the astonished, when it was considered that the compass of her voice did not exceed eight or ten notes.

The year following Madame Catalani divided the public attention with Graffini.—This eminent performer is a native of Sinigaglia in Italy, where her father was a finger of the comic order.

She was educated in a convent. The virtuous im-

pressions she there received, have continued ever since invariably to influence her conduct.

Her father soon discovered the excellence and the value of her vocal powers, which were first exhibited on the provincial theatres of Italy.—He soon carried her to Spain, where she attained very high celebrity. It was there her husband, M. de Valabregue, first paid his addresses to her; and it was not till after a perseverance of seven months that he at last obtained her consent, to unite her fortunes with his. Her hesitation proceeded from the reluctance of her father, at once to be deprived of his daughter, and of the very great emolument which she brought him. M. de Valabregue had been an officer in the French army under General Moreau.

From Spain Madame Catalani (for she has retained her father's name), proceeded to Portugal, where she accepted an engagement to come to London. She travelled through France, and at Paris appeared at an occasional concert, where her fame was so great, that the usual price of admission was trebled. She particularly attracted the attention of the singular man who now holds the imperial sceptre of the continent of Europe. He ordered her a pension (its value is about 30l. per annum); and it was with much difficulty, and only through the interference of the British ambassador (the earl of Lauderdale) then at Paris, that she was permitted to leave that capital, and proceed on her journey.

In the dramatic music of the opera, this finger is far superior to any performer ever heard in this country. Her merit in Semiramide, in particular, presents almost the idea of perfection. Her voice is equal to the most difficult execution, while her countenance is interesting, her gestures graceful, and her person elegant. It has been reported that she does not sing in tune; but it is an undeniable fact, vouched by the first musicians, that she possesses a most accurate ear. Every vocal performer occasionally emits a false sound in consequence of some temporary organic cause.

Catalani's easy and clear articulation are particularly striking. Her tones are full and liquid. Her cadences are appropriate and masterly. She has a practice of rapidly descending in half notes, which has excited admiration chiefly by its entire novelty. The clearness and rapidity displayed by her in chromatic passages excite astonishment; and she combines mellowness with distinctness, a high qualification which Mara first taught us to appreciate. In the course of summer 1807, Madame Catalani visited the provincial theatres of England, and appeared likewise in Dublin, Edinburgh, and Glasgow. Her total receipts for that year are said to have exceeded 15,000l.

We have been somewhat particular in our account of musical affairs in our own country during the 18th 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 will have recourse to 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 (D) 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 man: 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 probably may 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 of music 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 accessions 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 (E); 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

(C) 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 a former edition of this work, it ought to have all the merit of an original. We have given a translation of it; and in the notes, we have added, from the works of succeeding authors, and from our own observation, such explanations as appeared necessary, to adapt the work to the present day.

(D) 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 terminate 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 shew 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.

(E) 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, 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,

Preliminary 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 practise 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 origin of arts often accidental, and their progress gradual. 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 evolution of its powers, and the progress of its attainments.

Delineations of the laws of harmony recent and imperfect. 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 compass by which the artist could direct and regulate his course.

Preliminary Discourse. M. Rameau was the first who began to transmute 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 not deducible which we receive from it. His principle he 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 adepts 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 present treatise; in which we claim no other merit than that of having developed, elucidated, and perhaps in some respects improved, the ideas of another (*).

The first edition of this essay, published 1752, having been favourably received, we have endeavoured to render this more perfect. The detail which is meant to be given 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 delightful 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 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 as major as minor; the two tetrachords employed in ancient music; the formation of our diatonic scale; the different values which the same sound may have in that scale, according to the turn which is given to the bass; 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 pronounced. See System. See Chord. See Tetrachords. See Diatonic. See Values. See Bass. See Alterations. See Mode. See Intonation. See Tones.

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.

(*) See M. Rameau's letter upon this subject, Merc. de Mai, 1752.

Preliminary discourse 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 elucidate, but to simplify the discoveries of M. Rameau.—For instance, besides the fundamental experiment mentioned above, that celebrated musician, to facilitate the explication of certain phenomena, had recourse to another experiment; 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 account for some other rules established in harmony; but 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 questions foreign to it.

In some other points also, (as, the origin of the chord of the sub-dominant*, and the explication of the seventh in certain cases) it is imagined that we have simplified, and perhaps in some measure extended, the principles of the celebrated artist.

We have likewise banished every consideration of geometrical, arithmetical, and harmonical proportions and progressions, which have been fought 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 either 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 our readers against misapprehension either of the nature of our subject or of the purpose of our endeavours.

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 vain to expect what is called demonstration: it is much to have reduced the principal facts to a consistent and connected system; to have de-

duced them from one simple experiment; and to have established upon this foundation the most common and essential rules of the musical art. But if the intimate and unalterable conviction which can only be produced by the strongest evidence is not here to be required, we must also doubt whether a clearer elucidation of our subject be possible.

After this declaration, it will not excite surprise, that, amongst the facts deduced from our fundamental experiment, some should immediately appear to depend upon that experiment, and others to result 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 than those which arise from analogy or congruity, it is natural that the analogy should be sometimes more and sometimes less sensible; and we will venture to pronounce that mind very unphilosophical, 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 of the minor mode in descending, the formation of the chord commonly termed the sixth redundant† or superfluous, 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 of music appear to be deducible in a simple and easy manner from the protracted tone of sonorous bodies, it ought not perhaps with too much temerity to be affirmed as yet, that this mixed and protracted tone is demonstratively the only original principle of harmony. 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 yet account for 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

Preliminary 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; of having made the practice of it more simple and easy; and of having 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 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 (G). If at once two different sounds are produced from two instruments of the same kind, these two

sounds generate a third different from both the others. We have inserted in the Encyclopédie, under the article Fundamental, a detail of this experiment according to M. Martini; and we owe to the public information, of which in composing this article we were ignorant: M. Romieu, 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

Tartini's experiment.

(G) 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, or 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 connexion 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, Malcolm'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 Signor 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 found 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 minor (whose highest note forms an octave with the lowest in the third formerly mentioned) will be produced a found 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 found only lower by double the quantity of a greater third than the highest; from the second major, a found lower by a double octave than the lowest; from a second minor, a found lower by triple the quantity of a third major than the highest; from the interval of a diatonic or greater semitone, a found lower by a triple octave than the highest; from that of a minor or chromatic semitone, a found 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.

Preliminary which he has not communicated with sufficient perspicuity, and from whence the art might perhaps derive considerable advantage if they were placed in a proper light. Of this we are 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 caution them against mistaking 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, that they can reach the end to which they so ardently aspire, the important end of establishing a theory of music, at once great, complete and luminous. The enlightened philosopher will not attempt the explanation of facts, because he knows how little such explanations are to be relied on. To estimate them according to their proper value, it is only necessary to consider 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. Some 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, 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? Others pretend that there are particles in the air, which, by their different degrees of tension, being naturally susceptible of different oscillations, produce the multiplicity of sound in question. But what do we know of all this? 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 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 it should be granted, would it not follow, 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 judgements? 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, the octave, cannot suffer the most inconsiderable change? Let us in sincerity confess our ignorance concerning the genuine causes of these effects (H). The metaphysical

3 S 2

(H) 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 recognizing 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

Preliminary
Discourse.

Metaphysical conjectures concerning the acoustical 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 err, when they engage in subjects of which they are ignorant.

The rules which we have attempted to establish concerning the track to be followed 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 here (we repeat it), nothing to do with the mechanical principles of protracted and harmonic tones produced by sonorous bodies; principles which have hitherto been and perhaps may yet be long explored in vain: we have less to do with the metaphysical causes of the sensations 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 principal laws of har-

mony may be deduced from one single experiment; Preliminary
Discourse.

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, we have endeavoured to adapt it to the capacity even of those who are absolutely uninstructed in music. To accomplish this design, it appeared necessary to pursue the following plan.

To begin with a short introduction, in which are Plan of the
defined the technical terms most frequently used in this treatise.
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 of the notes, C, D, E, F, G, A, B, which all the world knows (1).

The theory of harmony requires some arithmetical calculations, necessary for comparing sounds one with another. These calculations are short, simple, and may be comprehended by every one; they demand no operation but what is explained, and which every school-boy may perform. Yet, that even the trouble of this may be spared to such as are not disposed to take it, these calculations are not inserted in the text, but in the notes, which the reader may omit, if he can take for granted the propositions contained in the text which will be found proved in the notes.

These calculations we have not endeavoured to multiply; we could even have wished to suppress them, if it had been possible: so much did it appear to us to be apprehended that our readers might be misled upon this subject, and might either believe, or suspect us of believing,

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 coalesce, 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.

(1) In our former editions, the French syllabic names of the notes ut, re, mi, fa, sol, la, si, were retained, as being thought to convey the idea of the relative sounds more distinctly than the seven letters used in Britain. It is no doubt true, that by constantly using the syllables, and considering each as representing one certain sound in the scale, a finger will in time associate the idea of each sound with its proper syllable, so that he will habitually give ut the sound of the first or fundamental note, re that of a second, mi of a third, &c. but this requires a long time, and much application: and is, besides, useless in modulation or changes of the key, and in all instrumental music. Teachers of sol-faing as it is called, or singing by the syllables, in Britain, have long discarded, (if they ever used) the syllables ut, re, and si: and the prevalent, and we think, the sounder opinion is now, that a scholar will, by attending to the sounds themselves rather than to their names, soon learn their distinct characters and relations to the key, and to each other, and be able of course to assign to each its proper degree in the scale which he employs for the time, by whatever name the note representing that degree may be generally known. See Holden's Essay towards a Rational System of Music, Part I. chap. i. § 32, 33.

We have therefore, in our present edition, preferred to the French syllables the British nomenclature by the letters C, D, E, F, G, A, B, as being more simple, more familiar to British musicians, and equally applicable to instrumental as to vocal music.

Preliminary believing, all this arithmetic necessary to form an artist. Discourse. 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 of so little importance, that nothing can require a less ostentatious display. Let us not 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 ignorance, and render their treatises more obscure and less instructive.

Mathematical conclusions not transferable to sensible objects without agitation. This abuse of geometry in music may be condemned with so much more reason, that in 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 be useless, and contrary to sound philosophy, to invent other relations in order to form the basis of any system of music less easy and simple than that which we have delineated in this treatise.

* See Composition. 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 first where the reasons for establishing that rule are given.

That we may not present at once too great a num-

ber of objects and precepts, we have transferred to the Preliminary Discourse. 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 of their the essential and fundamental rules explained in it.

This second part 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 intonation, but merely the position of the notes in the clef F on the fourth line, and that of G upon the second; and even this knowledge may be acquired from the work itself; for in the beginning of the second part we explain the position of the clefs and of the notes. Nothing is necessary but to render it a little familiar, and any difficulty in it will disappear.

It would be wrong to expect here all the rules of All the composition, and especially those which direct the rules of 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, in an elementary 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 the expression may be allowed, 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 M. Rameau's treatise of harmony, or in the code of music which he published more lately (K), or lastly in the exlication of the theory and practice of music by M. Bethizi (L); this last book appears to us clear and methodical (M).

Is it necessary to add, that, in order to compose Nature the music in a proper taste, it is by no means enough to essential have familiarized with much application the principles of musical composition. 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.

DEFINITIONS.

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

1. Melody is a series of sounds which succeed one to another in a manner agreeable to the ear. Melody, what.
2. A Chord is a combination of several sounds heard together; and Harmony is properly a series of chords of which the succession pleases the ear. Chord and harmony, what.
A single chord

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

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

(M) In addition to the works mentioned in the text, we recommend to our readers, Holden's Essay, Glasgow 1770, Edin. 1805; Kollmann's Essay on Musical Harmony, 1796; his Essay on Musical Composition, fol. 1799; Shield's Introduction, 1809; and Dr. Calcott's Musical Grammar, 1806.

Definitions. is likewise sometimes called harmony, to signify the coalescence of the sounds which form the chord, and the sensation produced in the ear by that coalescence. We shall occasionally use the word harmony in this last sense, but in such a manner as never to leave our meaning ambiguous.

See Interval. 3. An Interval, in melody and harmony, is the distance, or difference in pitch, between one sound, and another higher or lower than it.

4. That we may learn to distinguish the intervals, and the manner of perceiving them, let us take the ordinary scale C, D, E, F, G, A, B, c, which every person whole ear or voice is not extremely false naturally modulates. The following observations will occur to us in singing this scale.

Account of the simple intervals. The sound D is higher or sharper than the sound C, the sound E higher than the sound D, the sound F higher than the sound E, &c. and so through the whole octave; so that the interval, or the distance from the sound C to the sound D, is less than the interval or distance between the sound C and the sound E, the interval from C to F is less than that between C and G, &c. and in short that the interval from the first to the second C is the greatest of all.—

To distinguish the first from the second C, we have marked the last with a small letter (c).

5. In general, the interval between two sounds is The dis- proportionably greater, as one of these sounds is high- function between or lower with relation to the other: but it is neces- strong and sary to observe, that two sounds may be equally high faint, or or low, though unequal in their force. The string of acute and a violin touched with a bow produces always a sound grave. 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; let any one form a sound by gradually swelling the voice, the sound may be perceived to increase in force, whilst it continues always equally low or equally high.

6. We must likewise observe concerning the scale, Between that the intervals between C and D, between D and E, between F and G, between G and A, between A and B, are equal, or at least nearly equal; and that the intervals between E and F, and between B and C, are likewise equal among themselves, but consist almost only of half the former. This fact is known and recognized 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 (o).

7. It

(N) We shall afterwards find that three different series of the seven letters are used, which we have distinguished by capitals, small Roman, and Italic characters. When the notes represented by small Roman characters occur in this treatise we shall, merely to distinguish them from the typography of the text, place them in inverted commas, thus 'c', 'd', &c.

(o) This experiment may be easily tried. Let any one sing the scale C, D, E, F, G, A, B, 'c', it will be immediately observed without difficulty, that the last four notes of the octave G, A, B, 'c', are quite similar to the first C, D, E, F; inasmuch, that if, after having sung this scale, one would choose to repeat it, beginning with C in the same tone which was occupied by G in the former scale, the note D of the last scale would have the same sound with the note A in the first, the E with the B, and the F with the 'c'.

Whence it follows, that the interval between C and D, is the same as between G and A; between D and F, as between A and B, and E and F, as between B and 'c'.

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

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 harpsichord, 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 harpsichord the keys G, A, B, 'f', and in performing with the voice at the same time C, D, E, F, in such a manner that the same sound may be given to C in the voice with that of the key G in the harpsichord, it will be found that D in the vocal intonation shall be the same with A upon the harpsichord, &c.

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

Since then, in the scale thus divided, C, D, E, F, G, A, B, 'c', the first division is perfectly like the last; and since the intervals between C and D, between D and E, and between F and G, are equal; it follows, that the intervals between G and A, and between A and B, are likewise equal to every one of the three intervals between C and D, between D and E, and between F and G; and that the intervals between E and F and between B and 'c' are also equal, but that they only constitute one half of the others.

Definitions. 7. It is for this reason that they have called the interval from E to F, and from B to C, a semitone; whereas those between C and D, D and E, F and G, G and A, A and B, are tones.

* Plate CG. XXIII. fig. 1. The tone is likewise called a second major*, and the semitone a second minor†.

† See Inter- val. 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 D to C, or from C to D, from F to E, or from E to F.

II. The Terms by which the different Intervals of the Scale are denominated.

Third minor, what. 9. An interval composed of a tone and a semitone, as from E to G, from A to C, or from D to F, is called a third minor.

Third major, what. An interval composed of two full tones, as from C to E, from F to A, or from G to B, is called a third major.

Fourth, what. An interval composed of two tones and a semitone, as from C to F, or from G to C, is called a fourth.

Triton, what. An interval consisting of three full tones, as from F to B, is called a tritone or fourth redundant.

Fifth, what. An interval consisting of three tones and a semitone, as from C to G, from F to C, from D to A, or from E to B, &c. is called a fifth.

Sixth minor, what. An interval composed of three tones and two semitones, as from E to C, is called a sixth minor.

Sixth major, what. An interval composed of four tones and a semitone, as from C to A, is called a sixth major.

Seventh minor, what. An interval consisting of four tones and two semitones, as from D to C, is called a seventh minor.

Seventh major, what. An interval composed of five tones and a semitone, as from C to B, is called a seventh major.

Octave, what. And in short, an interval consisting of five tones and two semitones, as from C to 'c' is called an octave.

Several of the intervals now mentioned, are distinguished by other names, as may be seen in the beginning of the second part; but those now given are the most common, and the only terms which our present purpose demands.

Unison, what. 10. Two sounds equally high, or equally low, how-

ever unequal in their force, are said to be in unison one Definitions.

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, E, G, where E is the lowest and G the highest sound, G is a third minor from E ascending, and E is third minor from G 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.

13. If, after having sung the scale C, D, E, F, G, Fig. 28 A, B, c, one would carry this scale still farther in ascent, it would be discovered without difficulty that a new scale would be formed, 'c, d, e, f', &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 'd', the second note of the second scale, will be an octave in ascent to the D of the first scale; in the same manner 'e' shall be the octave to E, &c. and so of the rest.

14. As there are nine notes from the first C to the Ninth, second 'd', 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 C to 'f' is called an eleventh, and the interval between C and 'g' a twelfth, &c.

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

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. * See Inter- val and.

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

IV.

(P) 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 seven-

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 C to D, forming in his progress an intermediate sound, which shall be higher by a semitone than C, and lower in the same degree than D. 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 $C\; \backslash sharp$ signifies C sharp, that is to say, C 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 $A\; \backslash flat$ signifies A flat, or A depressed by a semitone.

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

nant 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 Dissonance, whose union is displeasing 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 CD, CB, or FB, &c. simultaneously heard, form a dissonance. The reason which renders dissonance disagreeable, is, that the sounds which compose it, seem by no means coalescent to the ear, and are heard each of them by itself as distinct sounds, though produced at the same time.

19. 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 about 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 practiced, an opportunity of distinguishing with judicious ease and clearness the twelfth and seventeenth now in question (Q).

teenth 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.

(Q) 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.

21. The principal found is called the generator *; and the two other founds 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 found and its octave, whether above or below. These two founds, 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 founds 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

VOL. XIV. Part II.

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; he will naturally, without being initiated in the art of music, take his new key in the octave below or the octave above the first; and 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 (Q*).

served, $\backslash frac\{1\}\{2\}$; 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 found 1.

To obtain the fourth above the found 1, we must take the twelfth below that found, and the double octave above that twelfth. In effect, the twelfth below C, for instance, is F, of which the double octave f is the fourth above c. Since then the twelfth below 1 is $\backslash frac\{1\}\{2\}$, it follows that the double octave above this twelfth, that is to say, the fourth from the found 1 in ascending, will be $\backslash frac\{1\}\{2\}$ multiplied by 4, or $\backslash frac\{1\}\{2\}$.

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

The third major of a found, for instance the third major E, from the found C, and its fifth G, form between them a third minor E, G; now E is $\backslash frac\{1\}\{2\}$, and G $\backslash frac\{1\}\{2\}$, by what has been immediately demonstrated: from whence it follows, that the third minor, or the interval between E and G, shall be expressed by the relation of the fraction $\backslash frac\{1\}\{2\}$ to the fraction $\backslash frac\{1\}\{2\}$.

To determine this relation, it is necessary to remark, that $\backslash frac\{1\}\{2\}$ are the same thing with $\backslash frac\{1\}\{2\}$, and that $\backslash frac\{1\}\{2\}$ are the same thing with $\backslash frac\{1\}\{2\}$: so that $\backslash frac\{1\}\{2\}$ shall be to $\backslash frac\{1\}\{2\}$ in the same relation as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{1\}\{2\}$; that is to say, in the same relation as 10 to 12, or as 5 to 6. If, then, two founds 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 the third minor, an harmonic found which is even found in the protracted and coalescent tones of a sonorous body between the found E and G, an harmonic of the principal found, may be expressed by the fraction $\backslash frac\{6\}\{5\}$.

N. B. One may see by this example, that in order to compare two founds 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 founds, 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 founds departs from unity, the greater the interval will be.

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

Let us suppose, for example, that the third major of the fifth $\backslash frac\{1\}\{5\}$ is sought. That third major ought to be, by what has been shown above, the $\backslash frac\{1\}\{2\}$ of the fifth; for the third major of any found whatever is the $\backslash frac\{1\}\{2\}$ of that found. We must then look for a fraction which expresses the $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{5\}$; which is done by multiplying the numerators and denominators of both fractions one by the other, from whence results the new fraction $\backslash frac\{1\}\{10\}$. It will likewise be found that the fifth of the fifth is $\backslash frac\{1\}\{5\}$, because the fifth of the fifth is the $\backslash frac\{1\}\{5\}$ of $\backslash frac\{1\}\{5\}$.

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 C equal to 1, we have seen that its fifth, its fourth, its third, its major and minor in ascending, are $\backslash frac\{1\}\{2\}$, $\backslash frac\{1\}\{3\}$, $\backslash frac\{1\}\{4\}$, $\backslash frac\{1\}\{5\}$. 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 $\backslash frac\{2\}\{1\}$, $\backslash frac\{3\}\{1\}$, $\backslash frac\{4\}\{1\}$, $\backslash frac\{5\}\{1\}$.

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

23. To render our ideas still more precise and permanent, we shall call the tone produced by the sonorous body C: 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 G, and the double octave of E.

24. This octave of G then, and this double octave of E, produce the most perfect chord which can be joined with C, since that chord is the work and choice of nature (8).

25. For the same reason, the modulation formed by C with the octave of G, and the double octave of E, 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 we can substitute its octave to any sound, when it is more convenient for the voice, afford us the means of representing this modulation.

26. It is on this account that, after having sung the tone C, we naturally modulate the third E, and the fifth G, instead of the double octave of E, and the octave of G; from whence we form, by joining the octave of the sound G, this modulation, C, E, G, 'c', 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.

27. The modulation C, E, G, 'c', in which the chord C, E, 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.

28. In the modulation C, E, G, of which we have now been treating, the sounds E and G are so propor-

tioned one to the other, that the principal sound C (art. 19.) causes both of them to resound; but the second tone E does not cause G to resound, which only forms the interval of a third minor.

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

30. This new arrangement, C, E b, G, in which the sounds C and E b have both the power of causing G to resound, though C does not cause E b to resound, is not indeed equally perfect with the first arrangement C, E, G; because in this the two sounds E and G are both the one and the other generated by the principal sound C; whereas, in the other, the sound E b, is not generated by the sound C; but this arrangement C, E b, G, is likewise dictated by nature (art. 19.), though less immediately than the former; and accordingly experience evinces that the ear accommodates itself almost as well to the latter as to the former.

31. In this modulation or chord C, E b, G, C, Origin of it is evident that the third from C to E b is minor; and such is the origin of that mode which we call mode minor (8). See Mode. See also Interval.

32. The most perfect chords then are, 1. All chords related one to another, as C, E, G, 'c', consisting of any found, of its third major, of its fifth, and of its octave. 2. All chords related one to another, as E b, G, 'c', consisting of any found, of its third minor,

(R) 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 the second part, or tenor above gives the twelfth.

(S) The origin which we have here given of the mode minor, is the most simple and natural that can possibly be given. M. Rameau deduces it, more artificially, from the following experiment.—If you put in vibration a musical string HI, and if there are at the same time contiguous to this two other strings KN, RW, of which the first shall be a twelfth, and the second a seventeenth major below the string HI, the strings KN, RW will vibrate without being struck as soon as the string HI 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 KN, you may easily distinguish two points at rest LM, and in the tremulous motion of the string RW, four quiescent points S, T, U, V, 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 the note C the tone of the string HI, the two other strings will represent the sounds E and A b; and from thence M. Rameau deduces the modulation F, A b, C, and of consequence the mode minor. The origin which we have assigned to the minor mode, appears more direct and more simple, because it presupposes no other experiment than that of art. 19. and because also the fundamental sound C is still retained in both the modes, without being obliged, as M. Rameau found himself, to change it into F.

Theory of Harmony. 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 Succession by Fifths, and of the Law which it observes.

Fundamental bass, what. 33. SINCE the sound C causes the sound G to be heard, and is itself heard in the sound F, which sounds G and F are its two twelfths, we may imagine a modulation composed of that sound C and its two twelfths, or, which is the same thing (art. 22.), of its two fifths, F and G, the one below, the other above; which gives the modulation or series of fifths F, C, G, which we call the fundamental bass of C by fifths.

We shall find in the sequel (Chap. XVIII.), that there may be some fundamental basses by thirds, deduced 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 immediately the fundamental basses by fifths.

34. Thus, from the sound C, one may make a transition indifferently to the sound G, or to the sound F.

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

E♭, B♭, F, C, G, D, A, &c.

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

Exception to the rule. 36. But it is not allowed in the same manner to pass from one sound to another which is not immediately contiguous to it; for instance, from C to D, or from D to C: for this very simple reason, that the sound D is not contained in the sound C, nor the sound C in that of D; and thus these sounds have not any alliance the one with the other, which may authorise the transition from one to the other.

Two perfect chords in succession prescribed. 37. And as these sounds C and D, by the first experiment, naturally bring along with them the perfect chords consisting of greater intervals C, E, G, 'c', and D, F♯, A, 'd'; hence may be deduced this rule, That two perfect chords, especially if they are major (T), 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.

Mode in general, what. 38. A mode, in music, is, the order of sounds prescribed, as well in harmony as melody, by the series of

fifths. Thus the three sounds F, C, G, 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 C.

39. The series of fifths then, or the fundamental bass Modes, F, C, G, of which C holds the middle space, may be how represented by regarded as representing the mode of C. One may likewise take the series of fifths, or fundamental bass, fifths, C, G, D, as representing the mode of G; in the same manner B♭, F, C, will represent the mode of F.

Thus the mode of G, or rather the fundamental bass of that mode, has two sounds in common with the fundamental bass of the mode of C. It is the same with the fundamental bass of the mode F.

40. The mode of C (F, C, G) 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 Modes related in the mode of G seems a little more eligible: for G is heard amongst the harmonics of C, and of consequence sounds are implied and signified by C; whereas C does not common cause F to be heard, though C is included in the same sound F. It is hence that the ear, affected by the mode of C, is a little more prepossessed for the mode of G than for that of F. Nothing likewise is more frequent, nor more natural, than to pass from the mode of C to that of G.

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

43. As in the series of fifths, we may indifferently pass from one sound to that which is contiguous: so, having passed from the mode of C to that of G, one may from thence proceed to the mode of D. And on the other hand, having passed from the mode of C to that of F we may then pass to the mode of B♭. 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 (u) 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, F, C, G, it follows, that one may form

(T) We say especially if they are major; for in the major chord D, F♯, A, 'd', besides that the sounds C and D have no common harmonical relation, and are even dissonant between themselves (art. 13.), it will likewise be found, that F♯ forms a dissonance with C. The minor chord D, F, A, 'd', would be more tolerable, because the natural F, which occurs in this chord carries along with it its fifth C, 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.

(u) As the mere English reader, unacquainted with the technical phraseology of music, may be surprised at the

Theory of Harmony. form this modulation, or this fundamental bass, by fifths, G, C, G, C, F, C, F.

See fig. 4. Formation of the Greek diatonic scale by the fundamental bass. 45. Each of the sounds which forms this modulation brings necessarily along with itself its third major, its fifth, and its octave; inasmuch that he who, for instance, sings the note G, may be reckoned to sing at the same time the notes G, B, 'd', g': in the same manner the sound C in the fundamental bass brings along with it this modulation, C, E, G, C: and, in short, the sound F brings along with it F, A, C, 'f'. This modulation then, or this fundamental bass,

See fig. 4. 46. We shall be still more convinced of this truth by the following remarks. 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.

Theory of Harmony. In the modulation B, 'c, d, e, f, g, a', the sounds 'd' and 'f' form between themselves a third minor, which is not so perfectly true as that between 'c' and 'g' (x). Nevertheless, this alteration in the third minor between 'd' and 'f' gives the ear no pain, because that 'd' and that 'f' 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 'd' in the scale is the true fifth of G, which answers to it in the fundamental bass; and 'f' in the scale is the true octave of F, which answers to it in the same bass.

Altered intervals, no objection. 48. Moreover, this diatonic scale includes only seven sounds, and goes no higher than 'b', which would be the octave of the first: a new singularity, for which a reason may be given by the principles above established.

Reasons why this scale includes only seven sounds.

the use of the word phrase when transferred from language to that art, we have though 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.

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

1. 1. That 'c' in the scale is the octave of C in the bass; that is to say, 2.
2. 2. That 'b' is the third major of G; that is to say $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$ (note 2), and of consequence $\backslash frac\{1\}\{4\}$.
3. 3. That 'd' is the fifth of G; that is to say $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, and of consequence $\backslash frac\{1\}\{4\}$.
4. 4. That 'e' is the third major of the octave of C, and of consequence the double of $\backslash frac\{1\}\{2\}$; that is to say, $\backslash frac\{1\}\{2\}$.
5. 5. That 'f' is the double octave of F of the bass, and consequently $\backslash frac\{1\}\{2\}$.
6. 6. That 'g' of the scale is the octave of G of the bass, and consequently 3.
7. 7. That 'a' in the scale is the third major of 'f' of the scale; that is to say, $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$.

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 C of the scale 1; in this case we have only to divide each of the numbers by 2, which represent the diatonic scale, and we shall have

(x) In order to compare 'd' with 'f', we need only compare $\backslash frac\{3\}\{2\}$ with $\backslash frac\{5\}\{4\}$; 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 'd' to 'f', 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 'd' and 'f', 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 'c' and 'g', in the continued tone of those sonorous bodies of which 'c' and 'g' 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.

ed. In reality, in order that the found 'b' may succeed immediately in the scale to the found 'a', it is necessary that the note 'g', which is the only one from whence 'b' as a harmonic may be deduced, should immediately succeed to the found 'f', in the fundamental bass, which is the only one from whence 'a' can be harmonically deduced. Now, the diatonic succession from F to G cannot be admitted in the fundamental bass, according to what we have remarked (art. 36.). The sounds 'a' and 'b', then, cannot immediately succeed one another in the scale: we shall see in the sequel why this is not the case in the series 'c, d, e, f, g, a, b', c, which begins upon C; whereas the scale in question here begins upon B.

49. The Greeks likewise, to form an entire octave, added below the first B the note A, which they distinguished and separated from the rest of the scale, which for that reason they called prostanomene, that is to say, a string or note subadded to the scale, and put before B to form the entire octave.

50. The diatonic scale B, 'c, d, e, f, g, a', is composed of two tetrachords, that is to say, of two diatonic scales, each consisting of four sounds, B, 'c, d, e, and 'e, f, g, a'. These two tetrachords are exactly similar; for from 'e' to 'f' there is the same interval as from B to 'c', from 'f' to 'g' the same as from 'e' to 'd', from 'g' to 'a' the same as from 'd' to 'e' (z): this is the reason why the Greeks distinguished these two tetrachords; yet they joined them by the note 'a' which is common to both, and which gave them the name of conjunctive tetrachords.

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 C'e', and B'd', are thirds, the one major and the other minor, exactly true, as well as the fourth B'e' (AA); it is the same thing with the tetrachord 'e, f, g, a', since this tetrachord is exactly like the former.

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 'd' in the first tetrachord forms with the note 'f' in the second a third minor, which is not true. In like manner it will be

found, that the fifth from 'd' to 'a' is not exactly true, which is evident; for the third major from 'f' to 'a' is true, and the third minor from 'd' to 'f' 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.

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.

54. It may be ascertained by calculation, that in the tetrachord B, 'c, d, e', the interval, or the tone from 'd' to 'e', is a little less than the interval or tone from 'c' to 'd' (BB). In the same manner, in the second tetrachord 'e, f, g, a', which is, as we have proved, perfectly similar to the first, the note from 'g' to 'a' is a little less than the note from 'f' to 'g'. It is for this reason that they distinguish two kinds of tones; the greater tone, as from 'c' to 'd', from 'f' to 'g', &c.; and the lesser tone, as from 'd' to 'e', from 'g' to 'a', &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, B, 'c, d, e, f, g, a', by means of a fundamental bass composed of three sounds only, F, C, G; but to form the scale 'c, d, e, f, g, a, b', c', which we use at present, we must necessarily add to the fundamental bass the note D, and form, with these four sounds F, C, G, D, the following fundamental bass:

C, G, C, F, C, G, D, G, C;

from whence we deduce the modulation or scale

'c, d, e, f, g, a, b', c'.

In effect (cc), 'c' in the scale belongs to the harmony of C which corresponds with it in the bass; 'd', which is the second note in the gammut, is included in the harmony of G, the second note of the bass; 'e', the third note of the gammut, is a natural harmonic of C, which is the third sound in the bass, &c.

(z) The proportion of B to 'c' is as $\backslash frac\{1\}\{2\}$ to 1, that is to say as 15 to 16; that between 'e' and 'f' is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$, that is to say (note q), 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 'c' to 'd' is as 1 to $\backslash frac\{3\}\{2\}$, or as 8 to 9; that between 'f' and 'g' is as $\backslash frac\{1\}\{2\}$ to 1; that is to say (note q), as 8 to 9. The proportion of 'e' to 'a' is as $\backslash frac\{1\}\{2\}$ to 1, or as 5 to 4; that between 'f' and 'a' is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$, or as 5 to 4: the proportions here then are likewise equal.

(AA) The proportion of 'e' to 'c' is as $\backslash frac\{1\}\{2\}$ to 1, or as 5 to 4, which is a true third major; that from 'd' to 'b' is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$; 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 'c' to 'b' is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$; that is to say, as 5 times 16 to 15 times 4, or as 4 to 3, which is a true fourth.

(BB) The proportion of 'd' to 'c' is as $\backslash frac\{2\}\{3\}$ to 1, or as 9 to 8; that of 'e' to 'd' is as $\backslash frac\{1\}\{2\}$ to $\backslash frac\{3\}\{4\}$, that is to say, as 40 to 36, or as 10 to 9: now $\backslash frac\{1\}\{2\}$ is less removed from unity than $\backslash frac\{2\}\{3\}$; the interval then from 'd' to 'e' is a little less than that from 'c' to 'd'.

If any one would wish to know the proportion which $\backslash frac\{1\}\{2\}$ bear to $\backslash frac\{2\}\{3\}$, he will find (note q) 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 harmonic, and the same chord when it suffers alteration 'd', 'f', of which we have taken notice in the scale (note y); for we have seen, that this third minor thus altered is in the proportion of 80 to 81 with the true third minor.

(cc) The values or estimates of the notes shall be the same in this as in the former scale, excepting only the tone

36. Hence 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 C; whereas ours is originally and primitively formed, not only from the mode of C (F, C, G), but likewise from the mode of G, (C, G, D).

It will likewise appear, that this last scale consists of two parts; of which the one, 'c, d, e, f, g,' is in the mode of C; and the other, 'g, a, b,' c, in that of G.

37. For this reason the note 'g' is twice repeated in immediate succession in this scale; once as the fifth of the diatonic C, which corresponds with it in the fundamental bass; and again, as the octave of G, which immediately follows G in the same bass. These two consecutive 'g's are otherwise in perfect unison. For this reason we sing only one of them when we modulate the scale 'c, d, e, f, g, a, b,' c; but this does not prevent us from employing a pause or repose, expressed or understood, after the found 'f'. There is no person who does not perceive this whilst he himself sings the scale.

38. The scale of the moderns, then, may be considered as consisting of two tetrachords, disjunctive indeed, but perfectly similar one to the other, 'c, d, e, f,' and 'g, a, b, c,' one in the mode of C, the other in that of G. We shall see in the sequel, by what artifice one may cause the scale 'c, d, e, f, g, a, b, c,' to be regarded as belonging to the mode of C alone. For this purpose it is necessary to make some changes in the fundamental bass, which we have already assigned: but this shall be explained at large in chap. xiii.

39. The introduction of the mode proper to G in the fundamental bass has this happy effect, that the notes 'f, g, a, b,' may immediately succeed each other in ascending the scale, which cannot take place (art. 48.) in the diatonic series of the Greeks, because that series is formed from the mode of C alone. Whence it follows:

1. That we change the mode at every time when we modulate three whole tones in succession.

2. That if these three tones are sung in succession in the scale 'c, d, e, f, g, a, b,' c, this cannot be done but by the assistance of a pause expressed or understood after the note 'f'; inasmuch, that the three tones 'f, g, a,' 'a, b,' 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 singing pause in the same mode, the fourth found above the three consecutive notes will never be higher than a semitone above that which immediately precedes it; as may be seen by 'c, d, e, f,' and by 'g, a, b,' c, where there is no more than a semitone between 'c' and 'f', and between 'b' and 'c'.

61. We may likewise observe in the scale 'c, d, e, f,' intervals, that the third minor from 'd' to 'f', is not true, for the reasons which have been already given (art. 49.). It is the same case with the third minor from 'a' to 'c,' and with the third major from 'f' to 'a'; but each of these consonances founds forms otherwise consonances perfectly true, with their correspondent founds in the fundamental bass.

62. The thirds 'a'c, 'fa', which were true in the former scale, are false in this; because in the former scale 'a' was the third of 'f', and here it is the fifth of D, 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 (DD); and this likewise happens from the introduction of the mode of G into the fundamental bass (EE).

We see likewise that the value of 'a' in the diatonic scale, a value which authors have been divided in ascertaining, solely depends upon the fundamental bass, and that

tone 'a'; for 'd' being represented by $\backslash frac\{3\}\{4\}$, its fifth will be expressed by $\backslash frac\{15\}\{4\}$; so that the scale will be numerically signified thus:

Where you may see, that the note 'a' of this scale is different from that in the scale of the Greeks; and that the 'a' in the modern series stands in proportion to that of the Greeks as $\backslash frac\{15\}\{4\}$ to $\backslash frac\{5\}\{4\}$, that is to say, as 8 to 2; these two 'a's then likewise differ by a comma.

(DD) In the scale of the Greeks, the note 'a' being a third from 'f', there is an altered fifth between 'a' and 'd'; but in ours, 'a' being a fifth to 'd', produces two altered thirds, 'fa' and 'a'c; and likewise a fifth altered, 'a'e, 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.

(EE) 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 found c, and it is in reality from that found that we ought to begin; it is from this that all the others naturally arise, and upon this that they depend; nay, if we may speak so, in this they are included: on the contrary, neither the scale of the Greeks, nor its fundamental bass, commences with C; but it is from this C that we must depart, in order to regulate our intonation, whether in rising or descending; now, in ascending from 'c', the intonation, even of the Greek scale, gives the series 'c, d, e, f, g, a': and so true is it that the fundamental found C is here the genuine guide of the ear, that if, before we modulate the found 'c', we

Theory of Harmony. that it must be different according as the note 'a' has 'f' or 'd' for its base. See the note (CC).

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 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.

Let us choose in that harpichord one of the strings which will found the note C, and let us tune the string G to a perfect fifth with C in ascending; let us afterwards tune to a perfect fifth with this G the 'd' which is above it; we shall evidently perceive that this 'd' will be in the scale above that from which we set out: but it is also evident that this 'd' must have in the scale a D which corresponds with it, and which must be tuned a true octave below 'd'; and between 'd' and G there

should be the interval of a fifth; so that the D in the first scale will be a true fourth below the G of the same scale. We may afterwards tune the note A of the first scale to a just fifth with this last D; then the note 'e' in the highest scale to a true fifth with this new A, and of consequence the E in the first scale to a true fourth beneath this same A: Having finished this operation, it will be found that the last E, thus tuned, will by no means form a just third major from the sound C (FF): that is to say, that it is impossible for E to constitute at the same time the third major of C and the true fifth of A; or, what is the same thing, the true fourth of A in descending.

65. If, after having successively and alternately tuned the strings C, G, 'd', A, E, in perfect fifths and fourths one from the other, we continue to tune successively by true fifths and fourths the strings E, B, F#, C#, G#, 'd#', E#, B#; we shall find, that, though B#, being a semitone higher than the natural note, should be equivalent to 'c' natural, it will by no means form a just octave to the first C in the scale, but be considerably higher (GG); yet this B# upon the harpichord ought not

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 B, and by the semitone from B to 'c'. Now to make a transition from B to 'c', by this semitone, the ear must of necessity be predisposed for that modulation, and consequently preoccupied with the mode of C: if this were not the case, we should naturally rise from B to 'c#', and by this operation pass into another mode.

(FF) The A considered as the fifth of D is $\backslash frac\{4\}\{3\}$, and the fourth beneath this A will constitute $\backslash frac\{1\}\{2\}$ of $\backslash frac\{4\}\{3\}$, that is to say, $\backslash frac\{2\}\{3\}$; $\backslash frac\{2\}\{3\}$ then shall be the value of E, considered as a true fourth from A in descending: now E, considered as the third major of the sound C, is $\backslash frac\{4\}\{3\}$, or $\backslash frac\{12\}\{9\}$: these two E's then are between themselves in the proportion of 8 to 9; thus it is impossible that E should be at the same time a perfect third major from C, and a true fourth beneath A.

(GG) 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.

C, G, a fifth; D a fourth; A a fifth; E a fourth; B a fifth; F# a fourth; C# a fifth; G# a fourth; 'd#' a fifth; A# a fourth; 'e#' or 'f#' a fifth; B# a fourth: now it will be found, by a very easy computation, that the first C being represented by 1, G shall be $\backslash frac\{4\}\{3\}$, D $\backslash frac\{3\}\{2\}$, A $\backslash frac\{4\}\{3\}$, E $\backslash frac\{3\}\{2\}$, &c. and so of the rest, till you arrive at B#, which will be found $\backslash frac\{12\}\{7\}$. This fraction is evidently greater than the number 2, which expresses the perfect octave c to its correspondent C; and the octave below B# would be one half of the same fraction, that is to say $\backslash frac\{6\}\{7\}$, which is evidently greater than C represented by unity. This last fraction $\backslash frac\{6\}\{7\}$ is composed of two numbers; the numerator of the fraction is nothing else but the number 3 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 B#, is not equal to the unity which expresses the value of the found C, though, upon the harpichord, B# and C are identical. This fraction rises above unity by $\backslash frac\{1\}\{7\}$, that is to say, by about $\backslash frac\{1\}\{7\}$; 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 BB), and which is only $\backslash frac\{1\}\{12\}$.

We have already proved that the series of fifths produces a 'c' different from B#, the series of thirds major gives another still more different. For, let us suppose this series of thirds, C, E, G#, B#, we shall have E equal to $\backslash frac\{4\}\{3\}$, G# to $\backslash frac\{5\}\{3\}$, and B to $\backslash frac\{6\}\{5\}$, whose octave below is $\backslash frac\{12\}\{5\}$; from whence it appears, that this last B is less than unity (that is to say than C), by $\backslash frac\{1\}\{5\}$, or by $\backslash frac\{1\}\{10\}$, or near it: A new comma, much greater than the preceding, and which the Greeks have called apotome major.

It may be observed, that this B#, deduced from the series of thirds, is to the B# deduced from the series of fifths, as $\backslash frac\{12\}\{5\}$ is to $\backslash frac\{12\}\{7\}$; 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 B'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 $\backslash frac\{1\}\{12\}$.

Moreover, if, after having found the G# equal to $\backslash frac\{5\}\{3\}$, we then tune by fifths and by fourths, G#, 'd#', A#, C# B#, as we have done with respect to the first series of fifths, we find that the B# must be $\backslash frac\{12\}\{7\}$; its difference, then, from unity, or, in other words, from C, is $\backslash frac\{6\}\{7\}$, that is to say, about $\backslash frac\{1\}\{7\}$; a comma still less than any of the preceding, and which the Greeks have called apotome minor.

Theory of
Harmony.
Reasons
and rules
for temper-
ament.

not to be different from the octave above C; for every B♭ and every 'c' 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 sound 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 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 replications, 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 'c' or B♭ 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, C, G, D, A, E, B, F♭, C♭, G♭, 'd♭', A♭, 'c♭', B♭, 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, (art. 66.), in which B♭ or C is not the true octave of the first C; it is proposed to alter all the fifths equally, in such a manner that the two C'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 C'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 (III) the alteration made in each

In a word, if, after having found E equal to $\backslash frac\{1\}\{2\}$ in the progression of thirds, we then tune by fifths and fourths E, B, F♭, C♭, &c. we shall arrive at a new B♭, which shall be $\backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}\; \backslash cdot\; \backslash frac\{1\}\{2\}$, 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 E to G♭, from G♭ to B♭ or C, &c. are extremely false, and greatly altered.

(III) All the semitones being equal in the temperament proposed by M. Rameau, it follows, that the twelve semitones C, C♭, D, D♭, E, E♭, &c. shall form a continued geometrical progression; that is to say, a series in which C shall be to C♭ in the same proportion as C♭ to D, as D to D♭, &c. and so of the rest.

These twelve semitones are formed by a series of thirteen sounds, of which C and its octave 'c' 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 C to G, which should be $\backslash frac\{1\}\{2\}$, ought to be diminished by about $\backslash frac\{1\}\{128\}$ of $\backslash frac\{1\}\{2\}$; that is to say, by $\backslash frac\{1\}\{256\}$, a quantity almost inconsiderably small.

It is true, that the thirds major will be a little more altered; for the third major from C to E, for instance, shall be increased in its interval by about $\backslash frac\{1\}\{128\}$: 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 C, E, G♭, B♭, that this last B♭ is very different from 'c' (note GG); from whence it follows, that if we would tune this B♭ in unison with the octave of C, 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 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. each fifth will be very considerable, but equal in all of them.

Rameau's method of temperament proposed. 71. In this, then, the theory of temperament consists: but as it would be difficult in practice to tune a harpichord or organ by thus rendering all the semitones 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 harpichord which you please; but let it be towards the middle of the instrument; for instance, C: then tune the note G 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 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

VOL. XIV. Part II.

formed; then you may continue always in the same manner; till in this process you arrive at the last fifth from E♯ to B♯, which should of themselves be in tune; that is to say, they ought to be in such a state, that B♯, the highest note of the two which compose the fifth, may be identical with the found C, with which you began, or at least the octave of that found perfectly just: it will be necessary then to try if this C, or its octave, forms a just fifth with the last found E♯ or F, 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 interpolation (11).

3 U

By

(11) We have only to acknowledge, with M. Rameau, that this temperament is far remote from that which is now in practice: it may here be seen in what this last temperament consists as applied to the organ or harpichord. They begin with C in the middle of the keys, and they flatten the four first fifths G, D, A, E, till they form a true third major from E to C; afterwards, setting out from this E, they tune the fifths B, F♯, C♯, G♯, but flattening them still less than the former, so that G♯ may almost form a true third major with E. When they have arrived at G♯, they stop; they resume the first C, and tune to it the fifth F in descending, then the fifth B♯, &c. and they heighten a little all the fifths till they have arrived at A♯, which ought to be the same with the G♯ 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 C to that of G, from the mode of G to that of D, &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 C,

C, D, E, F, G, A, B, C,

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

E, F♯, G♯, A♯, B, C♯, D♯, e,

which, in their judgement, renders the modes of C and E 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 with, or at least very little different from that which is practised 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 M. Rameau, in his New System of Music, printed in 1726, 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,

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 harpichord 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 alteration 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 bass, 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. Let the three keys E, G, B be struck upon an organ, and the minor perfect chord only will be heard; though E, by the construction of that instrument, must cause G likewise to be heard; though G should have the same effect upon D, and B upon F; inasmuch that the ear is at once affected with all these sounds, D, E, F, G, G, B; 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!

73. In a fundamental bass whose procedure is by fifths, there always is, & always may be, a repose, or cadence, in which the mind acquiesces in its transition 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 C to G; 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 reposes, there are some, if we may be allowed the expression, more absolute, that is to say, more perfect, than others. Thus in the fundamental bass

C, G, C, F, C, G, D, G, C.

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

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.

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 is very different from what this celebrated musician afterwards 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.

(KK) 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.

Theory of 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 bass (L.L.).

Cadences in the fundamental bass necessary in the diatonic scale, and which the most perfect. 76. Since there is a repose in passing from one sound to another in the fundamental bass, there is also a repose in passing from one note to another in the diatonic scale, which is formed from it, and which this bass represents: and as the absolute repose G C is of all others the most perfect in the fundamental bass, the repose from B to 'c', 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.

Definition and use of a 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 or leading note, as introducing the generator, and preparing us for the most perfect repose.

See Sensible Note. 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.

The diatonic series of the minor mode affected by different examples. 78. In the second chapter, we have explained (art. 20. 30. 31. and 32.) by what means, and upon what principle, the minor chord C, Eb, G, 'c', may be formed, which is the characteristical chord of the minor mode. Now what we have there said, taking C 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, C, Eb, G, 'c', there occurs an Eb which is not found in the ordinary diatonic scale, we shall immediately substitute, for greater ease and conveniency, 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. D, F, A, 'd'; A, 'c, e, a'; and E, G, B, 'e'. Among these three we shall choose A, 'c, e, a'; because this chord, without including any sharp or flat, has two sounds in common with the major chord C, E, G, 'c'; and besides, one of these two sounds is the very same 'c': so that this chord appears to have the most immediate, and at the same time the most simple, relation with the chord C, E, G, 'c'. Concerning this we need only add, that this preference of the chord A, 'c, e, a', to every other minor chord, is by no means in itself necessary for what we have to say in this chapter upon the dia-

tonic 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 conveniency that we fix upon this.

80. In every mode, whether major or minor, the principal sound which implies the perfect chord, whether major or minor, is called the tonic note or key; thus what C is the key in its proper mode, A in the mode of A, &c. Having laid down this principle, See Principal.

81. We have shown how the three sounds, F, C, G, which constitute (art. 38.) the mode of C, of which the first, F, and the last, G, are the two fifths of C, one scale pur-descending, the other rising, produce the scale, B, 'c, d, e, f, g, a', of the major mode, by means of the fundamental bass G, C, G, C, F, C, F; let us in the same manner take the three sounds D, A, E, which constitute the mode of A, for the same reason that the sounds F, C, G, constitute the mode of C; and of them let us form this fundamental bass, perfectly like the preceding E, A, F, A, D, A, D; 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 D and A as implying their thirds minor in the fundamental bass to characterize the minor mode; and we shall have the diatonic scale of that mode, See fig. 7.

G♯, A, B, 'c, d, e, f'. 82. The G♯, which corresponds with E in the fundamental bass, forms a third major with that E, 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 A. See fig. 7.

83. It is true, that, in causing E to imply its third minor G, one might also rise to A by a diatonic progress. But that manner of rising to A would be less perfect than the preceding; for this reason (art. 76.), that the absolute repose or perfect cadence E, A, 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 A, the key itself upon which the repose is made. From whence it follows, that the preceding note G ought rather to be sharp than natural; because G♯, being included in E (art. 19.), much more perfectly represents the note E in the bass, than the natural G could do, which is not included in E. See Imply or Carry.

84. We may remark this first difference between the scales Diversities in the scales of the major and minor mode.

G♯, A, B, 'c, d, e, f', and the scale which corresponds with it in the major mode

B, 'c, d, e, f, g, a', that from 'c' to 'f', which are the two last notes of the former scale, there is only a semitone; whereas from 'g' to 'a', 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.

(L.L.) 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.

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,

'c, d, e, f, g, g, a, b', c.

That last series, as we have seen, was formed by means of the fundamental bass F, C, G, D, disposed in this manner,

C, G, C, F, C, G, D, G, C.

Let us take in the same manner the fundamental bass D, A, E, B, and arrange it in the following order, A, E, A, D, A, E, B, E, A,

See fig. 8. and it will produce the scale immediately subjoined,

A, B, 'c, d, e, f, g, g, a',

in which 'c' forms a third minor with A, which in the fundamental bass corresponds with it, which denominates the minor mode; and, on the contrary, 'g' forms a third major with E in the fundamental bass, because 'g' rises towards 'a' (art. 82. 83.)

86. We see besides an 'f', which does not occur in the former,

G, A, B, 'c, d, e, f',

where 'f' is natural. It is because, in the first scale, 'f' is a third minor from D in the bass; and in the second, 'f' is the fifth from B in the bass (MM).

87. Thus the two scales of the minor mode are still in this respect more different one from the other than the 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.

'f' and 'g' sharp in the minor mode, and why. The case different in descending and why.

88. From thence it may be seen why 'f' and 'g' are sharp when ascending in the minor mode; besides the the 'f' is only natural in the first scale G, A, B, 'c', d, e, f', because this 'f' cannot rise to 'g', (art. 48.)

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

Explanation of the descending scale in the minor mode from a fundamental bass difficult.

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

A, E, B, E, A, D, A, E, A,

produces in descending,

'a, g, g, e, e, d, c', B, A.

And it is plain that the 'f' cannot be otherwise than

sharp, since 'f' is the fifth of the note B of the fundamental bass. Experience, however, evinces that the 'f' is natural in descending in the diatonic scale of the major mode of A, especially when the preceding 'g' is natural: and it must be acknowledged, that here the fundamental bass appears defective.

M. Rameau has attempted the following solution of this difficulty. In the diatonic scale of the minor mode is descending, ('a, g, f, e, d, c', B, A,) 'g' may be regarded simply as a note of passage, merely added to give sweetness to the modulation, and as a diatonic factor, gradation by which we may descend to 'f' natural. This is easily perceived, according to M. Rameau, by the fundamental bass,

A, D, A, D, A, E, A,

which produces

'a, f, e, d, c', B, A;

which may be regarded, as he says, as the real scale of the minor mode in descending; to which is added 'g' natural between 'a' and 'f', to preserve the diatonic order.

This appears the only possible answer to the difficulty above proposed: but we 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 (NN).

CHAP. X. Of Relative Modes.

91. Two modes of such a nature that we can pass from the one to the other, are called relative modes. Thus the major mode of C is relative to the major mode of F and to that of G. It has also been seen how many intimate connexions there are between the major mode of C, and the minor mode of A. For, 1. The perfect chords, one major, C, E, G, 'c', the other minor, A, 'c', e, a', which characterize each of those two kinds of modulation * or harmony, have two sounds in common, 'c' and 'e'. 2. The scale of the minor mode of A in descent, absolutely contains the same sounds with the scale of the major mode of C.

Hence the transition is so natural and easy from the major mode of C to the minor mode of A, or from the minor mode of A to the major mode of C, as experience proves.

92. In the minor mode of E, the minor perfect chord E, G, B, 'c', which characterizes it, has likewise two sounds, E, G, in common with the perfect chord major C, E, G, 'c', which characterizes the major mode of

(MM) Besides, without appealing to the proof of the fundamental bass, 'f' obviously presents itself as the sixth note of this scale; because the seventh note being necessarily 'g' (art. 77.) if the sixth were not 'f', but 'f', there would be an interval of three semitones between the sixth and the seventh, consequently the scale would not be diatonic, (art. 8.)

(NN) When 'g' is said to be natural in descending the diatonic scale of the minor mode of A, it is only meant that this 'g' is not necessarily sharp in descending as it is in rising; for it may be sharp, as may be proved by numberless examples, of which all musical compositions are full. It is true, that when 'g' is found sharp in descending to the minor mode of A, we are not sure that the mode is minor till the 'f' or 'c' natural is found; both of which impress a peculiar character on the minor mode, viz. 'c' natural, in rising and in descending, and the 'f' natural in descending.

Theory of Harmony. But the minor mode of E is not so closely related nor allied to the major mode of C as the minor mode of A; because the diatonic scale of the minor mode of E in descent, has not, like the series of the minor mode of A, all these sounds in common with the scale of C. In reality, this scale is 'c, d, c', B, A, G, F♯, E, where there occurs an 'f' sharp which is not in the scale of C. Though the minor mode of E is thus less relative to the major mode of C than that of A; yet the artist does not hesitate sometimes to pass immediately from the one to the other.

When we pass from one mode to another by the interval of a third, whether in descending or rising, as from C to A, or from A to C, from C to E, or from E to C, 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 C. It is the minor mode of C itself in which the perfect minor chord C, Eb, G, 'c', has two sounds, C and G, in common with the perfect major chord C, E, G, 'c'. Nor is there any thing more common than a transition from the major mode of C to the minor mode, or from the minor to the major (00).

CHAP. XI. Of Dissonance.

Cases in which the mode is uncertain. 94. WE have already observed, that the mode of C (F, C, G,) has two sounds in common with the mode of G (C, G, D); and two sounds in common with the mode of F (Bb, F, C); of consequence, this procedure of the bass C G may belong to the mode of C, or to the mode of G, as the procedure of the bass F C, or C F, may belong to the mode of C or the mode of F.

When one therefore passes from C to F or to G in a fundamental bass, he is still ignorant 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.

How we may investigate the generator and its fifths, and by that means determine the mode. 95. This advantage may be obtained by uniting at the same time the sounds G and F in the same harmony, that is to say, by joining to the harmony G, B, 'd' of the fifth G, the other fifth F in this manner, G, B, 'd', f'; this 'f' which is added, forms a dissonance with G (art. 18.) Hence the chord G, B, 'd', f', is called a dissonant chord, or a chord of the seventh. It serves to distinguish the fifth G from the generator C, which always implies, without mixture or alteration,

the perfect chord C, E, G, 'c', resulting from nature itself (art. 32.) By this we may see, that when we pass from C to G, one passes at the same time from C to F, because 'f' is found to be comprehended in the chord of G; and the mode of C by these means plainly appears to be determined, because there is none but that mode to which the sounds F and G at once belong.

96. Let us now see what may be added to the harmony F, A, C, of the fifth F 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 G, so that the generator C, in passing to F, may at the same time pass to G, and that by this the mode should be determined: but this introduction of G, in the chord F, A, C, would produce two dissonances whose union would prove extremely harsh to the ear; an inconvenience to be avoided. For if, to distinguish the mode, we should alter the harmony of the fifth F in the fundamental bass, it must only be altered in the least degree possible.

97. For this reason, instead of G, we shall take its chord of fifth 'd', the sound that approaches it the nearest; and the great sixth, we shall have, instead of the fifth F, the chord F, A, 'c', d', which is called a chord of the great sixth.

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

98. The fifth G, in rising above the generator, gives a chord entirely consisting of thirds ascending from G, C, B, 'd', f'; now the fifth F being below the generator C in descending, we shall find, as we go lower by thirds from 'c' towards E, the same sounds 'c', A, F, D, which form the chord F, A, 'c', d', given to the fifth F.

99. It appears besides, that the alteration of the harmony in the two fifths consists only in the third minor D, F, 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 F, A, 'c', d', is in effect the same as the chord D, F, A, 'c', taken inversely; that the inverse of the chord C, A, F, D, has been found (art. 98.) in descending by thirds, from the generator C (ff).

101. The

(00) There are likewise other minor modes, into which we may pass in our egress from the mode major of C; as that of F minor, in which the perfect minor chord F, Ab, 'c', includes the sound 'c', and whole scale in ascent F, G, Ab, Bb, 'c', d, e, f', only includes the two sounds Ab, Bb, which do not occur in the scale of C. This transition, however, is not frequent.

The minor mode of D has only in its scale ascending D, E, F, G, A, B, 'c', d', one 'c' sharp which is not found in the scale of C. For this reason a transition may likewise be made, without grating the ear, from the mode of C major to the mode of D minor; but this passage is less immediate than the former, because the chords C, E, G, 'c', and D, F, A, 'd', not having a single sound in common, one cannot (art. 37.) pass immediately from the one to the other.

(ff) 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 D, F, A, C, as the primary chord and generator of the chord E, A, 'c', d', which is that chord 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

this.

101. The chord D, F, A, 'c', is a chord of the seventh like the chord G, B, 'd', 'f'; with this only difference, that the latter in the third G, B, is major: whereas in the former, the third D, F, is minor. If the F were sharp, the chord D, F#, A, 'c', would be a genuine chord of the dominant, like the chord G, B, D, 'f'; and as the dominant G may descend to C in the fundamental bass, the dominant D implying or carrying with it the third major F# might in the same manner descend to G.

102. Now if the F# should be changed into F natural, D, the fundamental tone of this chord D, F, A, 'c', might still descend to G; for the change from F# to F natural will have no other effect, than to preserve the impression of the mode of C, instead of that of the mode of G, which the F# would have here introduced. The note D will, however, preserve its character as a dominant, on account of the mode of C, which forms a seventh. Thus in the chord of which we treat, (D, F, A, 'c'), D may be considered as an imperfect dominant: we call it imperfect, because it carries with it the third minor F, instead of the third major F#. It is for this reason that in the sequel we shall call it simply the dominant, to distinguish it from the dominant G, which shall be named the tonic dominant †.

103. Thus the sounds F and G, which cannot succeed each other (art. 36.) in a diatonic bass, when they only carry with them the perfect chords F A C, G B d, may succeed one another, if 'd' be added to the harmony of the first, and 'f' to the harmony of the second; and if the first chord be inverted, that is to say, if the two chords take this form, D, F, A, C, G, B, d, a.

104. Besides, the chord F, A, 'c', d', being allowed to succeed the perfect chord C, E, G, 'c', it follows for the same reasons, that the chord C, E, G, C may be succeeded by D, F, A, 'c'; which is not contradictory to what we have above said (art. 37.), that the sounds C and D cannot succeed one another in the fundamental bass: for in the passage quoted, we had supposed that both C and D carried with them a perfect chord major; whereas, in the present case, D carries the third minor E, and likewise the sound 'c', by which the chord D F A 'c' is connected with that which precedes it C E G 'c'; and in which the sound 'c' is found. Besides, this chord, D F A 'c', is properly nothing else but the chord F A 'c' d' inverted, and if we may speak so, disguised.

105. This manner of presenting the chord of the

subdominant 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 what, and which result from it.

We may add, that as this double employment is a kind of license, it ought not to be practised without some precaution. We have lately seen that the chords D F A 'c', considered as the inverse of F A 'c' d', may succeed to C E G 'c', but this liberty is not reciprocal: and though the chord F A 'c' d', may be followed by the chord C E G 'c', we have no right to conclude from thence that the chord D F A 'c', considered as the inverse of F A 'c' d', may be followed by the chord C E G 'c'. For this the reason shall be given in chap. xvi.

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

106. We have shown (chap. xvi.) how the diatonic scale, or ordinary gammut, may be formed from the fundamental bass F, C, G, D, by twice repeating the note G in that series; so that this gammut is primitively composed of two similar tetrachords, one in the mode of C, the other in that of G. Now it is possible, by means of this double employment, to preserve the impression of the mode of C through the whole extent of the scale, without twice repeating the note C, or even without supposing this repetition. For this effect we form the following fundamental bass,

C, G, C, F, C, D, G, C;

in which C is understood to carry with it the perfect chord C E G 'c'; G, the chord G B 'd' f'; F the chord F A 'c' d'; and D, the chord D F A 'c'. It is plain from what has been said in the preceding chapter, that in this case C may ascend to D in the fundamental bass, and D descend to G, and that the impression of the mode of C is preserved by the 'f' natural, which forms the third minor 'd' f', instead of the third major which D ought naturally to imply.

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

'c, d, e, f, g, a, b', c,

which of consequence will be in the mode of C alone; and if one should choose to have the second tetrachord in the mode of G, it will be necessary to substitute 'f# instead of 'f' in the harmony of D (qq).

108. Thus the generator C may be followed according

this great artist has neither expressed himself upon this subject with so much uniformity nor with so much precision as is required. We think that there is some foundation for considering the chord F, A, 'c', d', as primitive: 1. Because in this chord, the fundamental and principal note is the subdominant F, which ought in effect to be the fundamental and principal found 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 'd' to the harmony of the fifth F (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.

(qq) It is obvious that this fundamental bass C, G, C, F, C, D, G, C, which formed the ascending scale 'c, d, e, f, g, a, b', c, cannot by inverting it, and taking it inversely in this manner, C, G, D, C, F, C, G, C, form the diatonic scale 'c, 'b, a, g, f, e, d, 'c', in descent. In reality, from the chord G, B, 'd', 'f', we cannot pass to the chord D, F, A, 'c', nor from thence to C, E, G 'c'. For this reason, in order to have the fundamental

Theory of ing to pleasure in ascending distonically either by a tonic dominant (D F A C), or by a simple dominant (D F A C).

109. In the minor mode of A, the tonic dominant E ought always to imply its third major E G, when this dominant E descends to the generator A (art. 83.); and the chord of this dominant shall be E G B d', entirely similar to G B d' f'. With respect to the sub-dominant D, it will immediately imply the third minor F, to denominate the minor mode; and we may add B above its chord D F A, in this manner D F A B, a chord similar to that of F A 'c d'; and as we have deduced from the chord F A 'c d' that of D F A 'c', we may in the same manner deduce from the chord D F A B 'a' a new chord of the seventh B d' f', which will exhibit the double employment of dissonances in the minor mode.

110. One may employ this chord B d' f', to preserve the impression of the mode of A in the diatonic scale of the minor mode, and to prevent the necessity of twice repeating the sound E; but in this case, the F must be rendered sharp, and the chord changed to B d' f' a', the fifth of B being 'f', as we have seen above. This chord is then the inverse of D F A B, the sub-dominant implying the third major, which ought not to surprise us; for in the minor mode of A, the second tetrachord E F G A is exactly the same as it would be in the major mode of A: Now, in the major mode of A the subdominant D ought to imply the third major F.

Diversities in the minor mode more numerous than in the major. 111. Hence the minor mode is susceptible of a much greater number of varieties than the major: the major mode is founded in 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.

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

discover whether, in consequence of this first advance, art may not still be carried farther.

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

1. The chord G B d' f', composed of a third major followed by two thirds minor.

2. The chord D F A 'c', or B d' f' a', a third major between two minors.

3. The chord B d' f' a', 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, C E G B, or F A 'c e'; the other is wholly composed of thirds minor G B d' f'. 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 practised 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 C E G, to make a dominant of C, one can add nothing but B; and in this case C E G B would be the chord of the tonic dominant in the mode of F, as G B d' f' is the chord of the tonic dominant in the mode of C; but if we would preserve the impression of the mode of C in the harmony, we change this B into B natural, and the chord C E G B becomes C E G B. It is the same case with the chord F A 'c e', which is nothing else but the chord F A 'c e'; in which one may substitute for 'e', 'e' natural, to preserve the impression of the mode of C, or of that of F.

Besides, in such chords as C E G B, F A 'c e', the sounds B and 'e', though they form a dissonance with C in the first case, and with F in the second, are nevertheless supportable to the ear, because these sounds B and 'e' (art. 19.) are already contained and understood, the first in the note E of the chord C E G B, as likewise in the note G of the same chord; the second in the note A of the chord F A 'c e', as likewise in the note 'c' of the same chord. All together then seem to allow the artist to introduce the note B and 'e' into these two chords (RR).

116. With respect to the chord of the seventh G B d' f', wholly composed of thirds minor, it may be regarded as formed from the union of the two chords of

bass of the scale, c, b, a, g, f, e, d, c', in descent, we must either determine to invert the fundamental bass mentioned in art. 55. in this manner, C, G, D, G, C, F, C, G, C, in which the second G and the second C answer to the G alone in the scale; or otherwise we must form the fundamental bass C, G, D, G, C, G, C, in which all the notes imply perfect chords major, except the second G, which implies the chord of the seventh G, B, d, f', and which answers to the two notes of the scale G, F, both comprehended in the chord G, B, d, f'.

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 C, but in the mode of C and in that of G. 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.

(RR) On the contrary, a chord such as C E G B, in which E would be flat, could not be admitted in harmony, because in this chord the B is not included and understood in E. It is the same case with several other chords, such as B D F A, B D F A, &c. It is true, that in the last of these chords, A is included in F, but it is not contained in D; and this D likewise forms with F and with A a double dissonance, which, joined with the dissonance B F, 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.

the dominant and of the sub-dominant in the minor mode. In effect, in the minor mode of A, for instance, these two chords are E G♯ B♭ d♭, and D E A B, whose union produces E G♯ B♭ d♭, B♭ d♭, a♭. Now, if we should suffer this chord to remain thus, it would be disagreeable to the ear, by its multiplicity of dissonances, D E, E F, F G♯, A B, D G♯, (art. 18.); so that, to avoid this inconveniency, the generator A is immediately expunged, which, (art. 19.) is as it were understood in D, and the fifth or dominant E, whose place the sensible note G♯ is supposed to hold: thus there remains only the chord G♯ B♭ d♭, wholly composed of thirds minor, and in which the dominant E is considered as understood; in such a manner that the chord G♯ B♭ d♭ represents the chord of the tonic dominant E G♯ B♭ d♭, to which we have joined the chord of the sub-dominant D F A B, but in which the dominant E is always reckoned the principal note (38).

117. Since, then, from the chord E G♯ B♭ d♭, we may pass to the perfect A C♭ e♭, and vice versa, we may in like manner pass from the chord G♯ B♭ d♭ to the chord A C♭ e♭, and from this last to the chord G♯ B♭ d♭: this remark will be very useful to us in the sequel.

CHAP. XV. Of the Preparation of Dissonances.

118. 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 'f' is the dissonance of the chord G♭ B♭ d♭; 'c' in the chord D F, A♭ c♭, &c.

119. When the chord G♭ B♭ d♭ follows the chord C E G♭ c♭, as often happens, it is obvious that we do not find the dissonance 'f' in the preceding chord C E G♭ c♭. 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.

120. For the same reason, when the chord of the sub-dominant F A♭ c♭ d♭ follows the chord C E G♭ c♭, the note 'd', which forms a dissonance with 'c', is not found in the preceding chord.

It is not so when the chord D F A♭ c♭ follows the chord C E G♭ c♭; for 'c', which forms a dissonance in the second chord, stands as a consonance in the preceding.

121. In general, dissonance being the production of art (chap. xi.), especially in such chords as are not 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 connect the two chords. Hence follows this rule:

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

This is what we call a prepared dissonance. See Preparation. 123. Hence, in order to prepare a dissonance, the fundamental bass must necessarily ascend by the interval of a second, as

C E G♭ c♭, D F A♭ c♭;
or descend by a third, as
C E G♭ c♭, A C E G♭;
or descend by a fifth, as
C E G♭ c♭, F A C E.

in every other case the dissonance cannot be prepared. This may be easily ascertained. If, for instance, the fundamental bass rises by a third, as C E G♭ c♭, E G♭ B♭ d♭, the dissonance 'd' is not found in the chord C E G♭ c♭. The same might be said of C E G♭ c♭, G♭ B♭ d♭, and C E G♭ c♭, B♭ D♭ f♭, in which the fundamental bass rises by a fifth or descends by a second.

124. 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 succession may be regarded as a process from that same tonic to another, which has been rendered a dominant by the addition of the dissonance.

Moreover, we have seen (art. 119. and 120.) that a dissonance does not require preparation in the chords of the tonic dominant and of the sub-dominant: 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 sub-dominant (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 consonances to be 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, and made 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 to be resolved, the dissonance

(38) We have seen (art. 109.) that the chord B♭ d♭ f♭, in the minor mode of A, may be regarded as the inverse of the chord D F A B; it would likewise seem, that, in certain cases, this chord B♭ d♭ f♭ may be considered as composed of the two chords G♭ B♭ d♭, F A♭ c♭ d♭ of the dominant and of the sub-dominant of the major mode of C; which chords may be joined together after having excluded from them, 1. The dominant G, represented by its third major B, which is presumed to retain its place. 2. The note C which is understood in F, which will form with this chord B♭ d♭ f♭. The chord B♭ d♭ f♭, considered in this point of view, may be understood as belonging to the major mode of C upon certain occasions.

ought rather to descend than to rise; for this reason. Let us take, for instance, the chord G B d f followed by the chord C E G c; the part which formed the dissonance f ought to descend to c rather than rise to g, though both the sounds E and G are found in the subsequent chord C E G c; because it is more natural and more conformed to the connexion which ought to be found in every part of the music, that G should be found in the same part where G has already been sounded, whilst the other part was sounding f, as may be here seen (Parts First and Fourth).

127. So, in the chord of the simple dominant D F A c, followed by G B d f, the dissonance c ought rather to descend to B than rise to d.

128. And, for the same reason, in the chord of the sub-dominant F A c d, the dissonance d ought to rise to e of the following chord C E G c, rather than descend to c; whence may be deduced the following rules.

129. 1^o. 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^o. In every chord of the sub-dominant, 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 D F A c, though it should even be considered as the inverse of F A c d, cannot be succeeded by the chord C E G c, since there is not in this last chord the note B, upon which the dissonance c of the chord D F A c 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 D F A c, to C E G c, it is necessary that D F A c should in this case be understood as the inverse of F A c d. Now the chord D F A c can only be conceived as the inverse of F A c d, when this chord D F A c precedes or immediately follows the C E G c; in every other case the chord D F A c is a primitive chord, formed from the perfect minor chord D F A, to which the dissonance c was added, to take from D the character of a tonic. Thus the chord D F A c, could not be followed by the chord C E G c, 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, C E G c, D F A c, C E G c, it would be much more easy and natural to substitute this other, which furnishes this natural succession C E G c, F A c d, C E G c. 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

VOL. XIV. Part II.

to any other chord except that of the tonic, to which it naturally leads.

CHAP. XVII. Of the Broken or Interrupted Cadence.

131. In 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 found to another; and of consequence there must likewise be a repose more or less perfect from one found 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 c d g, performing on the d a shake, which is commonly called a cadence; the modulation will appear to him to be finished after the second c, 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 C G C: but if, instead of this bass, we should give it the following, C G A: in this case the modulation c d c 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 G A, when the dominant G diatonically ascends upon the note A instead of descending by a fifth upon the generator C, as it ought naturally to do, is called a broken cadence; because the perfect cadence G C, which the ear expected after the dominant G, is, if we may speak so, broken and suspended by the transition from G to A.

133. Hence it follows, that if the modulation c d c appeared finished when we supposed no bass to it at all, it is because its natural fundamental bass C G C is implied; for the ear desires something to follow this modulation, as soon as it is reduced to the necessity of hearing another bass.

134. The broken cadence may be considered as having its origin in the double employment of dissonances; broken since this cadence, like the double employment, only consists in a diatonic procedure of the bass ascending (chap. xii.) In effect, nothing hinders us to descend from the chord G B d f to the chord C E G A by converting the tonic C into a sub-dominant, that is to say, by passing all at once from the mode of C to the mode of G: now to descend from G B d f to C E G A is the same thing as to rise from the chord G B d f to the chord A c e g, in changing the chord of the sub-dominant C E G A 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 G B d f, A c e g, the dissonance f is resolved by descending diatonically upon the fifth c.

136. There is 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 succession of the bass

G B d f', E G B d'; 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 'f' is resolved upon the octave of E.

137. This kind of interrupted cadence has likewise its origin in the double employment of dissonances. For let us suppose these two chords in succession, G B d f', G B d e', where G is successively a tonic dominant and sub-dominant; that is to say, in which we pass from the mode of C to the mode of D; 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 G B d f', E G B d'.

CHAP. XVIII. Of the Chromatic Species.

138. THE series or fundamental bass by fifths produces 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 C, E, G♯, the two first found carrying each along with it their thirds major and fifths, it is evident that C will give G, and that E will give G♯: now the semitone which is between this G and this G♯ is an interval much less than the semitone which is found in the diatonic scale between E and F, or between B and 'c'. This may be ascertained by calculation (TT): and for this reason the semitone from E to F is called major, and the other minor (UU).

140. If the fundamental bass should proceed by thirds minor in this manner, C, Eb, a succession which is allowed when we have investigated the origin of the minor mode (chap. ix.), we shall find this mo-

duction G, Gb, which would likewise give a minor semitone (XX).

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 E to F, results from a fundamental bass by fifths C F, 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 G to G♯; they rise at first from G to A, then descend from A to G♯ by the interval of a semitone major: for this G sharp, which is a semitone major below A, proves a semitone minor above G. [See the notes (TT) and (UU).]

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 be found in every procedure of the fundamental bass by thirds. The series of thirds minor in descending, C A, gives, C, C♯ (YY); and the series of thirds major in descending, C, Ab, gives C, Cb, (ZZ).

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, C G♯, of the fundamental bass by thirds major C E G♯, give this modulation 'c' B♯; and these two founds 'c' B♯, differ between themselves by a small interval which is called the disjunct, or enharmonic fourth * of a tone (3A), which

(TT) In reality, C being supposed 1, as we have always supposed it, E is $\backslash frac\{4\}\{3\}$, and G♯ $\backslash frac\{5\}\{3\}$: now G being $\backslash frac\{3\}\{2\}$, G♯ then shall be to G as $\backslash frac\{5\}\{3\}$ to $\backslash frac\{3\}\{2\}$; that is to say, as 25 times 2 to 3 times 16: the proportion then of G♯ to G is as 25 to 24, an interval much less than that of 16 to 15, which constitutes the semitone from 'c' to B, or from F to E (note Z).

(UU) A minor joined to a major semitone will form a minor tone; that is to say, if one rises, for instance, from E to F, by the interval of a semitone major, and afterwards from F to F♯ by the interval of a minor semitone, the interval from E to F♯ will be a minor tone. For let us suppose E to be 1, F will be $\backslash frac\{4\}\{3\}$, and F♯ will be $\backslash frac\{5\}\{3\}$; that is to say, 25 times 16 divided by 24 times 15, or $\backslash frac\{5\}\{3\}$; E then is to F♯ as 1 is to $\backslash frac\{5\}\{3\}$, the interval which constitutes the minor tone (note BB).

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, $\backslash frac\{4\}\{3\}$ multiplied by $\backslash frac\{4\}\{3\}$ gives $\backslash frac\{16\}\{9\}$, which is greater than $\backslash frac\{3\}\{2\}$, the interval which constitutes (note BB) 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 still give less.

(XX) In effect, Eb being $\backslash frac\{5\}\{3\}$, Gb will be $\backslash frac\{6\}\{5\}$ of $\backslash frac\{5\}\{3\}$; that is to say, (note Q) $\backslash frac\{15\}\{5\}$: now the proportion of $\backslash frac\{1\}\{2\}$ to $\backslash frac\{15\}\{5\}$ (note Q) is that of 3 times 25 to 2 times 36; that is to say, as 25 to 24.

(YY) A being $\backslash frac\{3\}\{2\}$, C♯ is $\backslash frac\{4\}\{3\}$ of $\backslash frac\{3\}\{2\}$; that is to say $\backslash frac\{12\}\{5\}$, and C is 1: the proportion then between C and C♯ is that of 1 to $\backslash frac\{12\}\{5\}$, or of 24 to 25.

(ZZ) Ab being the third major below C, will be $\backslash frac\{4\}\{3\}$ (note Q): Cb, then, is $\backslash frac\{3\}\{2\}$ of $\backslash frac\{4\}\{3\}$; that is to say $\backslash frac\{6\}\{5\}$. The proportion, then, between C and Cb, is as 25 to 24.

(3A) G♯ being $\backslash frac\{5\}\{3\}$ and B♯ being $\backslash frac\{4\}\{3\}$ of $\backslash frac\{5\}\{3\}$, we shall have B♯ equal (note Q) to $\backslash frac\{20\}\{9\}$, and its octave below shall be $\backslash frac\{10\}\{9\}$; an interval less than unity by about $\backslash frac\{1\}\{25\}$ or $\backslash frac\{1\}\{27\}$. It is plain then from this fraction, that the B♯ in question must be considerably lower than C.

Theory of Harmony. which is the difference between a semitone major and a semitone minor (3 B). This quarter tone is inapplicable 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.

Manner of seemingly introducing this interval upon instruments of fixed scales. 145. We have explained (art. 116.) in what manner the chord G♯ B♯ d♯ f♯ 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 chord of the dominant (art. 116.) from thence we may pass to that of the tonic or generator A (art. 117.). But we must remark,

1. That this chord G♯ B♯ d♯ f♯, entirely consisting of thirds minor, may be inverted or modified according to the three following arrangements, B♯ d♯ f♯ g♯♯, D F G♯ B, F G♯ B d♯; and that in all these three 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 F and G♯ entirely just; for a true third minor, as that from E to G in the diatonic scale, is composed of a semitone and a tone both major. Now from F to G there is a tone major, and from G to G♯ there is only a minor semitone. There is then wanting (art. 144.) the enharmonic fourth of a tone, to render the third F G♯ 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 G♯ B♯ d♯ f♯, belonging to the minor mode of A, where G♯ is the sensible note; the chord B♯ d♯ f♯ g♯♯, or B♯ d♯ f♯ a♯, will, for the same reason, belong to the minor mode of C, where B is the sensible note. In like manner, the chord D F G♯ B, or D F A♯ c♯, will belong to the minor mode of Eb, and the chord F G♯ B d♯, or F A♯ c♯ eb♯, to the minor mode of G♯.

After having passed then by the mode of A to the chord G♯ B♯ d♯ f♯ (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 C minor, of Eb minor, or of G♯ minor; that is to say, into the modes which have nothing, or almost nothing, in common with the minor mode of A, and which are entirely foreign to it (3 c).

146. It must, however, be acknowledged, that a The alteration so abrupt, and so little expected, cannot de-ceive nor elude the ear; it is struck with a sensation which it is so unlooked-for, without being able to account for the effectuated passage to itself. And this account has its foundation abrupt and in the enharmonic fourth of a tone; which is overlook-
feasible.

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 $\backslash frac\{1\}\{8\}$.

3. One half of a semitone major; and as this semitone differs from unity by $\backslash frac\{1\}\{2\}$, one half of it will differ from unity about $\backslash frac\{1\}\{8\}$.

4. Finally, one half of a semitone minor, which differs from unity by $\backslash frac\{1\}\{2\}$: 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 $\backslash frac\{1\}\{8\}$, 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 uv) 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.

(3 B) That is to say, that if you rise from E to F, for instance, by the interval of a semitone major, and afterwards, returning to E, 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, F+, the two sounds F+ and F will form the enharmonic fourth of a tone: for E being 1, F will be $\backslash frac\{1\}\{2\}$; and F+ $\backslash frac\{1\}\{2\}$: the proportion then between F+ and F is that of $\backslash frac\{1\}\{2\}$ to $\backslash frac\{1\}\{4\}$ (note q); that is to say, as 25 times 15 to 16 times 24; or otherwise, as 25 times 5 to 16 times 8, or as 125 to 128. Now this proportion is the same which is found, in the beginning of the preceding note, to express the enharmonic fourth of a tone.

(3 c) 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 Harmonics 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.

ed 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 F, C, E, B, this bass will give the following modulation, 'f, e, c, d$\backslash sharp$;', in which the semitones from 'f' to 'e', and from 'e' to 'd$\backslash sharp$', are equal and major (3 D).

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 3 A).

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 C, C, A, C$\backslash sharp$, C$\backslash flat$, we shall form this modulation 'c$\backslash flat$, e, c, e$\backslash sharp$;', in which all the semitones are minor (3 E).

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 3 F).

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 natural of all others.

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 the broken cadence (chap. xvii.), that the diversification of 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 but to examine the different basses which may be given to this very simple modulation GC. It will be found susceptible of many, and each will give a different character to the modulation GC, though in itself it remains always the same. We may thus change the whole nature and effects of a modulation, without any other alteration than that of its fundamental bass.

M. Rameau has shown, in his New System of Music, printed at Paris 1726, p. 44. that this modulation GC, 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 practiced to vary the expression of the same modulation?

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 (3 F).

2. That the character of a just harmony is only to form in some measure one system with the modulation, so

(3 D) It is obvious, that if F in the bass be supposed 1, 'f' of the scale will be 2, C of the bass $\backslash frac\{1\}\{2\}$ and 'e' of the scale $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, that is, $\backslash frac\{1\}\{4\}$; the proportion of 'f' to 'e' is as 2 to $\backslash frac\{1\}\{4\}$, or as 1 to $\backslash frac\{1\}\{8\}$. Now E of the bass being likewise $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$; B of the bass is $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$, and its third major D$\backslash sharp$ $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$ of $\backslash frac\{1\}\{4\}$, or $\backslash frac\{1\}\{16\}$; of $\backslash frac\{1\}\{4\}$; this third major, approximated as much as possible to 'e' in the scale by means of octaves, will be $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$; 'e' then of the scale will be to 'd$\backslash sharp$' which follows it, as $\backslash frac\{1\}\{4\}$ is to $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$, that is to say, as 1 to $\backslash frac\{1\}\{8\}$. The semitones then from 'f' to 'e', and from 'e' to 'd$\backslash sharp$', are both major.

(3 E) It is evident that 'e$\backslash flat$' is $\backslash frac\{1\}\{2\}$ (note Q), and that 'e' is $\backslash frac\{1\}\{2\}$: these two 'e's, then, are between themselves as $\backslash frac\{1\}\{2\}$ 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 A of the bass is $\backslash frac\{1\}\{2\}$, and C$\backslash sharp$ $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{2\}$, or $\backslash frac\{1\}\{4\}$: 'e$\backslash sharp$' then is $\backslash frac\{1\}\{2\}$ of $\backslash frac\{1\}\{4\}$, the 'e' in the scale is likewise to the 'e$\backslash sharp$' which follows it, as 24 to 25. All the semitones therefore in this scale are minor.

(3 F) Many composers begin with determining and writing the bass; a method, however, which appears in general

Principles of Composition. so that from the whole taken together, the ear may only receive, if we may speak so, one simple and indivisible 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 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 license 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 C, to represent all the major modes in general, and the minor mode of A 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.

Composition in harmony, what. See Composition. 158. COMPOSITION, called also counterpoint, is not only the art of composing an agreeable air, but also that of composing several 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.

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

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 C to D♯ in ascending, or that of A to G♭ descending.

Why so called. 161. This interval is so termed, because one of the sounds which form it is always either sharp or flat, and that, if that sharp or flat be taken away, the interval will be that of a second (3 C).

False fifth, what. 162. An interval composed of two tones and two semitones, as that from B to F♯, 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, reasons for distinguishing them, as will appear below.

162. As the interval from C to D♯ in ascending Fifth redundant, or from B to E♭ in descending, each of which intervals are composed of four tones (3 H).

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

163. For the same reason, an interval composed of Seventh diminished, three tones and three semitones, as from G♯ to F♯ in ascending, is called a seventh diminished; because, if we remove the sharp from G, the interval from G to F♯ 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.) (3 I).

164. The major seventh is likewise sometimes called a seventh redundant (3 K).

165. If we sing 'c' B in descending by a second, and afterwards C B in ascending by a seventh, these two B's shall be octaves one to the other; or, as we commonly express it, they will be replications one of the other.

166. On account then of the resemblance between every

general more proper to produce a learned and harmonious music, than a strain prompted by genius and animated by enthusiasm.

(3 G) For the same reason, this interval is frequently termed by English musicians an extreme sharp-second.

(3 H) This interval is usually termed by English theorists a sharp fifth.

(3 I) The material difference between the diminished seventh and the major sixth is, that the former always implies a division of the interval into three minor thirds, whereas a division into a fourth and third major, or into a second and major and minor third, is usually supposed in the latter.

(3 K) The chief use of these different denominations is therefore 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.

every sound and its octave (art. 22.), it follows, that to rise by a seventh, or descend by a second, amount to the same thing.

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

168. The following expressions either are or ought to be regarded as synonymous.

To rise by a second.—To descend by a seventh.

To descend by a second.—To rise by a seventh.

To rise by a third.—To descend by a sixth.

To descend by a third.—To rise by a sixth.

To rise by a fourth.—To descend by a fifth.

To descend by a fourth.—To rise by a fifth.

169. Thus, therefore, we shall employ them indifferently 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 Clefs; of the Value or Quantity; of the Rhythm; and of Synception.

170. THERE are three clefs* in music; the F clef, the C clef, and the G clef.

The F clef is placed on the fourth line (3. L.) or on the third; and the line on which this clef is placed gives the name of F to all the notes on that line.

The C clef is placed on the fourth, the third, the second, or the first line: and in these different positions the name of C is given to all the notes on that line.

(3. L.) Our author has treated this part of his subject with somewhat less perspicuity than usual. He has neither described the staves or systems of lines on which the clefs are placed, nor explained their relation to each other. We have therefore attempted to supply the deficiency.

Musical sounds, like language, are represented by written characters, by which their graveness or acuteness, their duration, and the other qualities intended to be assigned to them, are accurately distinguished.

The characters which denote the graveness or acuteness, or, as it is termed, the pitch of sounds, are intended to represent the ordinary limits of the human voice, in the exercise of which, or the employment of instruments of nearly the same compass with it, all practical music consists.

From the lowest distinct note, without straining, of the masculine voice, to the highest note generally produced by the female voice, there is an interval of three octaves, or twenty-two diatonic notes.

These notes are represented by characters described alternately on eleven parallel lines, and the spaces between them, forming what we shall here term the general system.

The characters representing the notes are differently formed according to their duration, but with this we have at present no concern. We shall employ the simplest, a small circle or ellipse.

The whole extent of the human voice, then, if described upon the general system, would be represented as at Plate CCCLV. fig. 1.

The masculine voice, rising from the lowest note of the general system, will, generally speaking, reach the note on the central line; and an ordinary female voice will reach the same note, descending from the highest. Male voices more acute, and female voices graver than usual, will consequently execute this note with greater facility.

This central note then, being producible by every species of voice, has been assumed as a fundamental or key note, by which all the others are regulated (art. 4.). And to it is assigned the name of C, by which, in the theory of harmony, (as we have seen), the fundamental sound of the diatonic scale is distinguished.

The other notes take their denominations accordingly. The note below it is B, that above it 'd', &c.; and to distinguish this central C from its octaves, it is called the middle or tenor C.

As no human voice can execute the whole twenty-two notes, the general system is divided into portions of five lines, each portion representing the compass of an ordinary voice; and different portions are made use of, according to the graveness or acuteness of different voices.

The five lines in this state form what is called a staff. Each staff is subdivided into lines and spaces. On the lines, and in the spaces, the heads of the notes are placed. The lines and spaces are counted upwards, from the lowest to the highest; the lowest line is termed the first line; the space between it and the second line is denominated the first space, and so on. Both lines and spaces have the common name of degrees; the staff thus contains nine degrees, viz. five lines and four spaces.

To ascertain what part of the general system is formed by a staff, one of the clefs mentioned in the text is placed at the beginning of the staff, on one or other of the lines of it.

The C or tenor clef always denotes the line on which it is placed to be that which carries the tenor C. The G or treble clef distinguishes the line carrying 'g', the perfect fifth above the tenor C. And the F or bass clef ascertains the line which represents F the perfect fifth below the tenor C.

The figures of the clefs, (which are characters gradually corrupted from the Gothic C, G, and F), and their places in the general system, appear on Plate CCCLV. Fig. 2.

By this disposition of the clefs, we see that the staff, which includes the line bearing the treble clef, is formed by the five highest lines of the general system; and that the staff which comprehends the bass clef consists of the five lowest.

The central line, which carries the tenor C, belongs neither to the treble nor the bass staves. But as that note frequently occurs in composition written on these staves, a small portion of the tenor line is occasionally introduced below the treble clef and above that of the bass (fig. 3.)

Principles of Composition. all the notes on the same line with the cleff take the name of C.

Fig. 7. 3. The G cleff is placed on the second or first line; and all the notes on the line of the cleff take the name of G.

Names of the notes to the spaces between the lines, the name of any note may be discovered from the position of the cleff. Thus, in the F cleff, the note on the lowest line is G; the note on the space between the two first lines A; the note on the second line B, &c.

Marks and power of sharps, flats, and naturals. 172. A note before which there is a sharp (marked thus ♯) must be raised by a semitone; and if there be a flat (marked ♭) before it, it must be depressed by a semitone.

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

173. When a sharp or a flat is placed at the cleff, Fig. 8. all the notes upon the line or space on which this sharp or flat is marked, are sharp or flat. For instance, if in the cleff of G a sharp be placed on the highest line, which is the place of 'F', all the notes on that line will be 'F♯'—to restore them to their original value of 'F' natural, a ♮ must be placed before them.

Fig. 9. In the same manner, if a flat be marked at the cleff, all the notes on the same line or space with the flat will be flat; to restore them to their natural state, a ♮ must be placed before them (3 M).

174. Every piece of music is divided into different Bars and Times, what, equal

As notes still more remote from the staff in use are sometimes introduced, small portions of the lines to which these lines belong are employed in the same manner. Thus, if in writing in the bass staff we want the note properly placed on the lowest line of the treble staff, we draw two short lines above the bass staff, one representing the tenor line, and the other the lowest line of the treble staff, and on this last short line we place the note in question, (fig. 4.)

On the other hand, if, in writing on the treble staff, we would employ a note properly belonging to the bass staff, we place it below the treble staff, and insert the requisite short lines, representing the corresponding lines of the general system (fig. 5.)

The occasional short lines thus employed are termed leger lines.

The same expedient is used to represent notes beyond the limits of the general system. Thus, we write the F which is one degree lower than the lowest G of the bass staff, on the space below that G; the E immediately lower, or on a leger line below the bass staff, and so on. Notes in this position are termed double; thus, the F just mentioned is double F, or FF; the E, double E, or EE, &c.

Again, the 'a' above the highest 'g' of the treble staff is placed on a leger line above that staff. The 'b' is placed on the space above the leger line: The next note 'c' is set on a second leger line, and so on. These high notes are, in compositions for some instruments, carried more than an octave above the general system. Those in the first octave are said to be in alt; those beyond it, to be in altissimo.

The tenor or C cleff is employed to form different intermediate staves between the treble and bass, according to the compass of the voice or instrument for which the staff is wanted.

Compositions for the gravest masculine voices and instruments are written on the bass cleff, and those for female voices and instruments highest in tone, on the treble staff*.

For masculine voices next in depth to the bass and for the higher octave of the violoncello and bassoon, a staff, called the tenor staff, is formed by adding to the tenor line the three highest lines of the bass staff and the lowest line of the treble (fig. 6. 1.)

For the highest masculine voices, which are called counter tenor, and for the tenor violin, a staff is formed by the tenor line, the two highest lines of the bass, and the two lowest of the treble staff (fig. 6. 2.).

For the gravest female voices, which are called mezzo soprano, the tenor line and four lowest lines of the treble form a staff (fig. 6. 3.).

The relation of all the staves to the general system, and to each other, will appear from fig. 6.

The bass cleff on the third line, the tenor cleff on the second, and the treble cleff on the first, rarely occur, except in old French music.

The tenor cleff, and the staves distinguished by it, are now less frequently used than the treble and bass cleffs. Those who cultivate music only as an amusement find it irksome to learn so many modes of notation. The tenor staves are accordingly banished from compositions for keyed instruments. Secular compositions for voices are likewise now written in the treble and bass staves only, although in this there is some inaccuracy, as the tenor parts now written in the treble staff, must often be sung an octave below that in which they appear. The chief use of the tenor cleff is in choral music and compositions for the bassoon and tenor violin; and its principal advantage, the facility of reading ancient music, which is almost exclusively written in this cleff, has seldom been deemed an insufficient recompense for the labour of acquiring it.

(3 M) The disposition of sharps or flats at the cleff, which is termed the signature, depends upon the mode, or tone assumed in the composition as a fundamental or key note, and will be afterwards explained.

The sharps or flats of the signature affect not only the notes placed on the same degree with themselves, as mentioned in the text, but also all the notes of the same letter, in every octave throughout the movement.

The sharps or flats of the signature determine the scale in which the movement is composed, and are therefore said to be essential; those which occur in the course of the piece on an occasional change of the scale, are termed accidental.

* Compositions for French horns are written in the treble staff, although the tone of the instrument be very grave; but this is because the horn is borrowed from and has the same natural intervals with the Trumpet, which is an acute instrument.

equal times, called measures; and each measure is likewise divided into different times.

There are properly two kinds of measures or modes of time; the measure of two times, or common time, marked by the figure 2 at the beginning of the time (fig. 10.); and the measure of three times, or triple time, marked by the figure 3 placed in the same manner (fig. 11.).

The different measures are distinguished by perpendicular lines (3 N), called bars.

In a measure, we distinguish between the strong and the weak time: the strong time is that which is beat; the weak, that in which the hand or foot is raised. A measure consisting of four times ought to be considered as compounded of two measures, each consisting of two times: thus there are in this measure two strong and two weak times. In general by the words strong

and weak even the parts of the same time are distinguished; thus, the first note of each time is considered as strong, and the others as weak.

175. The longest of all notes is a sembreve. A minim is half its value; that is to say, two minims are to be performed in the time occupied by one sembreve. A minim in the same manner is equivalent to two crotchets, the crotchet to two quavers (3 O).

176. A note which is divided into two parts by a bar, that is, which begins at the end of a measure, and terminates in the measure following, is called a syncopated note (3 P).

179. A note followed by a point or dot is increased half its value. Thus a dotted semibreve is equivalent to a sembreve and a minim, a dotted minim, to a minim and a crotchet, &c. (Fig. 17.) (3 Q).

(3 N) All the notes, therefore, contained between two bars constitute one measure; although in common language the word bar is improperly used for measure.

(3 O) The notes, in their figure, consist of a head and a stem, except the sembreve, which has a head only. The place of the note in the staff is determined by the head, which must be placed on the line, or in the space, assigned to the note. The stem may be turned either up or down.

The quaver is equivalent to two semiquavers, and the semiquaver to two demi-semiquavers. In modern music the demi-semiquaver is also subdivided.

The quaver and the notes of shorter duration may be grouped together, by two, three, or four, &c. and joined by as many black lines across the ends of the stem as there are hooks in the single note (fig. 12.) This arrangement is convenient in writing, and assists the eye in performance.

When quavers, or the shorter notes, are to be repeated in the same degree for a time equal to the duration of a longer note, the iterations are, by a sort of musical short-hand, represented by writing the long note only, and placing over or under it, as many short lines as the short note has hooks (fig. 13.) And the repetition of a series of short notes is represented by merely writing for each repetition as many short lines as there are hooks to the short notes of which the series is composed (fig. 14.).

(3 P) A note in the middle of a measure is also said to be syncopated when it begins on a strong, and ends on a weak part of the measure, (see fig. 15.) where D, C, and B are each of them syncopated.

A note which of itself occupies one, two, or more measures, is not said to be syncopated, but continued or protracted. See fig. 16.

(3 Q) Notes have sometimes in modern music a double dot after them, which makes them longer by three-fourths. Thus a minim twice dotted is equal to three crotchets and a half, or seven quavers, &c.

Our author, in this chapter, has omitted the explanation of rests, and of the particular modifications of time. Rests are characters indicating the temporary suspension of musical sounds. There are as many different rests as there are notes. Thus the sembreve rest indicates a pause of the duration of a sembreve; the minim rest, of a minim, &c. (fig. 18.)

The sembreve rest also denotes the silence of one entire measure, in triple as well as common time. The silence of several measures is marked as in fig. 18.; but where the silence exceeds three bars, the number is usually marked over the rests.

Common time is either of a sembreve, or of a minim to the measure. Common time of a sembreve is indicated by the letter C at the clef, fig. 1. of Plate CCCLVI. When it is meant to be somewhat quicker than usual, a perpendicular line is drawn through the C, (fig. 2.)

Common time of a minim to the measure, which is called half time, is indicated by the fraction $\backslash frac\{1\}\{2\}$, that is, two-fourths of a sembreve, or two crotchets equal to a minim, (fig. 3.)

In triple time the measure consist of three minims, three crotchets or three quavers, six crotchets or six quavers, nine quavers or twelve quavers.

Triple time of three minims is marked at the clef $\backslash frac\{1\}\{3\}$, that is, three halves of a sembreve, (fig. 4.)

Triple time of three crotchets is indicated by the fraction $\backslash frac\{1\}\{3\}$, (three-fourths of a sembreve) (fig. 5.) and that of three quavers by $\backslash frac\{1\}\{3\}$ (three-eighths of a sembreve), (fig. 6.)

In the last three examples the measure is divided into three times, of which the first is strong, and the two others weak.

The measure of six crotchets is marked $\backslash frac\{2\}\{4\}$, (fig. 7.); and that of six quavers, $\backslash frac\{2\}\{4\}$, (fig. 8.) In both there are two times, of which the first is strong, and the second weak.

The measure of nine quavers is marked $\backslash frac\{3\}\{4\}$, (fig. 9.); and is divided into one strong and two weak times. That of twelve quavers is marked $\backslash frac\{3\}\{4\}$, (fig. 10.); and is accented as if it were two measures of six quavers.

The measures of $\backslash frac\{2\}\{4\}$ and $\backslash frac\{3\}\{4\}$ rarely occur. Three notes are often performed in the time of two of the same name, and are then termed triplets, (fig. 11.) where

178. (3 R) THE chord composed of a third, a fifth, and an octave, as C, E, G, C, is called a perfect chord (art. 32.).

If the third be major, as in C, E, G, C, the perfect chord is denominated major; if the third be minor, as in A, C, E, A, the perfect chord is minor. The perfect chord major constitutes the major mode; and the perfect chord minor, the minor mode (art. 31.).

179. A chord composed of a third, a fifth, and a seventh, as G, B, D, F, or D, F, A, C, &c. is called a chord of the seventh. 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 C E♭ G B; and that which might carry a false fifth and a seventh major, B D F A♯, (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, B D F A, 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 F A C D, D F A B, 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 1. the two C'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 11. D carries the chord D F A C, and G the chord G B D F.

It is necessary to remark, that among the chords
VOL. XIV. Part II.

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 subdominant great sixth, is called a subdominant, (art. 97. and 42.) and is marked with a 6. Thus in the example 111. F carries the chord of F A C D. The sixth should always be major, (art. 97. and 109.).

185. In every chord, whether perfect, or a chord fundamental 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 C in the example 1. D and C in the example 11. and F in the example 111. are fundamental notes.

186. In every chord of the seventh, and of the great sixth, the note which forms the seventh or sixth above of a chord, the fundamental, that is to say, the highest note of the chord, is called a dissonance. Thus in the chords of the seventh G B D F, D F A C, F and C are the dissonances, viz. F with relation to G in the first chord, and C with relation to D in the second. In the chord of the great sixth F A C D, D is the dissonance (art. 120.); but that D is only, properly speaking, a dissonance with relation to C from which it is a second, and not with respect to F from which it is a sixth major (art. 17. and 18.).

187. When a chord of the seventh is composed of 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 G B D F, the fundamental G is the tonic dominant; but in the other chords of the seventh, as C E G B, D F A C, &c. the fundamentals C and D are simple dominants.

188. In every chord, whether perfect, or of the Major seventh, or of the sixth, if it is meant that the third above the fundamental note should be major though it be naturally minor, a sharp must be placed above the

where the groups of quavers in the second measure are triplets, and each triplet occupies the time of two quavers only. Triplets also occur in triple time, fig. 12.

Certain other characters will be with propriety explained here.

The Pause signifies that the regular time is to be delayed, and the note marked with the pause protracted. See fig. 13. where the pause is on the last note of the second measure.

The Repeat, a character resembling an S, denotes, that the following part of the movement must be repeated. See fig. 14.

The Dirò (fig. 15.) is placed at the end of the staff, to shew upon what degree the first note of the following staff is placed.

When the inner sides of two bars are dotted, the measures between them are to be repeated (fig. 16.). The word bis is sometimes placed over such passages.

The double bar distinguishes the end of a movement or strain, (fig. 17.). If the double bar be dotted on one or both sides, the strain is to be repeated, (fig. 18.). The double bar does not affect the time; so that when the strain terminates before the end of a measure, as is often the case, the double bar only marks the conclusion of the strain, but the time is kept exactly as if it were not inserted. See fig. 19.

The graces of exertion and expression, such as the appoggiatura, the shake, the slur, the crescendo, the diminuendo, &c. are not necessary to the consideration of the theory of music or principles of composition, but belong to the performer only. See SHAKE, &c.

(3 R) In this part of our subject, we shall, in mentioning the harmonics of the chords, make use of the capital letters only, as the general names of the notes, without distinguishing octaves by minuscule or italic letters. The harmonics may be arranged in different octaves. Their different positions will be most easily seen and best understood from the examples in the plates.

fundamental note. For example, if we would mark the perfect major chord D F♯ A D, as the third F above D is naturally minor, we place above D a sharp, as in Example IV. In the same manner, the chord of the seventh D F♯ A C, and the chord of the great sixth D F♯ A B, is marked with a ♯ above D, and above the ♯ a 7 or a 6 (see v. and vi.).

On the contrary, when the third is naturally major, and if we would render it minor, we place above the fundamental note a ♭. Thus the examples VII. VIII. IX. show the chords G B♭ D G G B♭ D F, G B♭ D E (38).

CHAP. V. Of the Fundamental Bass.

189. LET a modulation be invented at pleasure; and under this modulation let there be set a bass 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 bass, may be one of those which enters into the chord of that note in the bass; this bass being composed according to the rules which shall be immediately given, will be the fundamental bass of the modulation proposed. See Part I. where the nature and principles of the fundamental bass are explained.

Thus (Exam. XVI.) it will be found that this modulation, C D E F G A B C, has or may admit for its fundamental bass, C G C F C D G C.

In reality, the first note C in the upper part is found in the chord of the first note C in the bass, which chord is G E G C; the second note D in the treble is found in the chord G B D G, which is the chord of the second note in the bass, &c. and the bass 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 Bass.

190. ALL the notes of the fundamental bass 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 bass 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 that the note which constitutes the seventh, or dissonance, should likewise be found in the preceding chord.

RULE III.

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 F A C D, it is necessary that F, A, or C, which are the consonances

(38) We may only add, that there is no occasion for marking these sharps or flats when they are originally placed at the clef. For instance, if the sharp be upon F which indicates the key of G (see Exam. x.) it is sufficient to write D, without a sharp, to mark the perfect chord major of D, D F♯ A D. In the same manner, in the Example XI. where the flat is at the clef upon B, which denotes the key of F, it is sufficient to write G, to mark the perfect chord minor of G B♭ D G.

But where there is a sharp or a flat at the clef, if we would render the chord minor which is major, or vice versa, we must place above the fundamental note a ♯ or a ♭. Thus the Example XII. marks the minor chord D F A D, and Example XIII. the major chord G B D G.—Sometimes, in lieu of a natural, a flat is used to signify the minor chord, and a sharp to signify the major. Thus Example XIV. in the key of G, marks the minor chord D F A D, and Example XV. in F, the major chord G B D G.

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 clef, we write before or after the 6 a ♯; and if this sixth should be flat according to the clef, we 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, we 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 one sharp at the clef, and if we would mark the chord G B D F♯, or the chord A C E F♯, we ought to place before the seventh or the sixth a ♯ or a ♭.

In the same manner, if there be one flat at the clef, and if we would mark the chord C E G B♭, we ought to place before the seventh a ♭ or a ♮; and so of the rest.

All these intricate combinations of figuring shew the superior convenience of the modern method of writing the notes themselves instead of the figures, which has the farther advantage of exhibiting the proper arrangement of the chord, see Example II.

Principles of Composition. consonances of the chord, should be found in the chord preceding. The dissonance D 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; 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 will presently be seen. For, let us assume the succession of the two chords A C E G, D F A C (see Exam. xvii.), this succession is by no means legitimate, though in it the first dominant descends by a fifth; because the C 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, we take away the sharp carried by the C in the first; or if, without meddling with the first chord, we render C and F sharp in the second (3T); or, if we simply render the D of the second chord a tonic dominant, in causing it to carry F# instead of F (119. and 122.).

It is likewise by the same rule that we ought to reject the succession of the two following chords, D F A C, G B D F#; (see Exam. xviii).

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

Other rules substituted. Of the five fundamental rules which have now been given, instead of the three first, one may substitute the three following, which are consequences from them.

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 xix. and xx. (3U); a tonic dominant (124.), see xxi. and xxii.; or a sub-dominant (124.), see xxiii. and xxiv; or, to express the rule more simply, that second note may be any one, 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. xxv. and xxvi.; or a tonic dominant, or a simple dominant, yet in such a manner that the rule of art. 192. may be observed (124.), see xxvii. xxviii. xxix. and xxx.; or a sub-dominant (124.), see xxxi. and xxxii.

The succession of the bass C E G C, F A C E, 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 xxxiv. and xxxv. (3X).

We must here advertise our readers, that the examples xxxvi. xxxvii. xxxviii. xxxix. belong to the fourth rule above, art. 194.; and the examples xl. xli. xlii. 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 employed. See xliii. xliiv. xlv. xlvj.

197. We must avoid, as much as we can, syncopation in the fundamental bass; that the ear may accurately distinguish the primarily accented part of a measure, by means of a harmony different from that which it had before perceived in the last unaccented part of the preceding measure. Nevertheless, syncopation may be sometimes admitted in the fundamental bass, but it is by a license (3Y).

(3T) In this chord it is necessary that the C and F should be sharp at the same time; for the chord D F A C#, in which C would be sharp without the F, is excluded by art. 179.

(3U) 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 we ascend from the tonic C to the tonic E, the major mode of C, C E G C, will be changed into the minor mode of E, E G B E. We must never ascend from one tonic to another, when there is no found common to both their modes: for example, we cannot rise from the mode of C, C E G C, to the minor mode of E, E G B E (91.).

(3X) Thus all the intervals, viz. the third, the fifth, and second, may be admitted in the fundamental bass, except that of a second in descending. The rules now given for the fundamental bass are not, however, 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 enter into 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.

(3Y) There are notes which may be found several times in the fundamental bass in succession with a different

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. XVI. the scale C D E F G A B C, is a treble with respect to the fundamental bass C G C F C D G C.

199. We are 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 C E G E C, may have for its fundamental bass the note C alone, because the chord of that note comprehends the sounds C, E, G, which are found in the treble.

2. In like manner, a single note in the treble may, for the same reason, answer to several notes in the bass. For instance, G alone may answer to these three notes in the bass, C G C (32).

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 dissonance prepared (122). For instance, let us suppose that the note of the fundamental bass shall be D, bearing the chord of the simple dominant D F A C; and that this C, 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 a C.

201. According to the rules which we have given for the fundamental bass, C will always be found in the chord of that note in the fundamental bass which precedes the simple dominant D. See XLVIII. XLIX. I. In the first example the dissonance is C, in the second G, and in the third E; and these notes are already in the preceding chord (4A).

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 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 saved or resolved (129, 130.) See III. LIII. LIV.

203. According to the rules for the fundamental bass which we have given, the note upon which the dissonance

ferent harmony. For instance, the tonic C, after having carried the chord C E G C, may be followed by another C which carries the chord of the seventh, provided that this chord be the chord of the tonic dominant C E G B_b. In the same manner, the tonic C may be followed by the same tonic C, which may be rendered a sub-dominant, by causing it to carry the chord C E G A.

A dominant, whether tonic or simple, sometimes descends or rises to another by the interval of a tritone or false fifth. For example, the dominant F carrying the chord F A C E, may be followed by another dominant B carrying the chord B D F A. 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 C to which F and B belong. If one should descend from F to B_b by the interval of a just fifth, he would then depart from that scale, because B_b is no part of it.

(32) 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 Example XLVII. (Plate CCCLVIII.) in which this modulation C D E F G, may be regarded as equivalent to this other, C E G, as D and F are no more than notes of passage. So that the bass of this modulation may be simply C G.

When the notes are of equal duration, and arranged in a diatonic order, the notes which are accented ought each of them to carry chords. Those which are unaccented, are mere notes of passage. Sometimes, however, the unaccented note may be made to carry harmony; but the duration of this note is then commonly increased by a point placed after it, which proportionably diminishes the continuance of the accented note, 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.

(4A) 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, while the dominant is still retained. For instance, let us imagine this modulation,

C | D C B C | D ;
and this fundamental bass, C | D G C | G ;

(see example II.) ; the D of the fundamental bass answers to the two notes D C of the treble. The dissonance C has no need of preparation, because the note D of the fundamental bass having already been employed for the D which precedes C, the dissonance C is afterwards presented, below which the chord D may be preserved, or D F A C.

Principles of Composition. ance ought to descend or rise will always be found in the subsequent chord (4 B).

and a sixth, is called the chord of the tritone, and is marked as in Example LXI. (4 D). Principles of Composition.

CHAP. VIII. Of the Continued Bass, and its Rules.

See Continued Bass. 204. THE continued bass, is 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 G B D F, we should say B D F G or D F G B, &c. the chord is inverted.

Chords inverted; how. The ways in which a PERFECT CHORD may be INVERTED.

205. The perfect chord C E G C may be inverted in two different ways.

1. E G C E, which we call a chord of the sixth, composed of a third, a sixth, and an octave; and in this case the bass note E is marked with a 6. (See LXI.)

2. G C E G, 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 $\backslash frac\{4\}\{6\}$. (See LXII.)

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 G B D F, the third major B above the fundamental note G is called a sensible note (77.); and the inverted chord B D F G composed of a third, a false fifth and sixth, is called the chord of the false fifth, and is marked as in examples LXIII. and LXIV.

The chord D F G B, composed of a third, a fourth, and a sixth, is called the chord of the sensible sixth, and marked as in Example LX. (4 C). In this chord, the third is minor, and the sixth major.

The chord F G B D, composed of a second, a tritone,

207. In the chord of the simple dominant D F A C, we find,

1. F A C D, a chord of the great sixth, which is composed of a third, a fifth, and a sixth, and which is figured with a $\backslash frac\{6\}\{5\}$. See LXII. (4 E).

2. A C D F, a chord of the lesser sixth, which is figured with a 6. See LXIII. (4 F).

3. C D F A, a chord of the second, composed of a second, a fourth, and a sixth, and which is marked with a 2. See LXIV. (4 G).

The ways in which the CHORD of the sub-DOMINANT may be INVERTED.

208. The chord of the sub-dominant, as F A C D, 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 A C D F (LXIII.), and the chord of the seventh D F A C. See LXV.

ROLES 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 LXVI. in which the fundamental bass which in itself is monotonous and little suited for singing, C G C G C G C, produces, by inverting its chords, this continued bass highly proper to be sung, C B C D E F E, &c. (4 H.)

The continued bass then is properly a treble with respect to the fundamental bass. Its rules immediately follow, which are properly those already given for the treble.

RULE I.

210. Every note which carries the chord of the false fifth,

(4 B) When the treble syncopates in descending diatonically, it is common enough to make the second part of the syncope carry a discord, and the first a concord. See Example LV. where the first part of the syncopated note G, is in concord with the notes C E G C, which answers to it in the fundamental bass, and where the second part is a dissonance in the subsequent chord A C E G. In the same manner, the first part of the syncopated note F is in concord with the notes D F A C, which answer to it; and the second part is a dissonance in the subsequent chord G B D F, which answer to it, &c.

(4 C) This chord is called by English musicians, the chord of the third and fourth, and generally figured $\backslash frac\{4\}\{3\}$.

(4 D) This chord is in England called the chord of the second and fourth, and is figured $\backslash frac\{4\}\{2\}$.

(4 E) We are obliged to mark likewise, in the continued bass, the chord of the sub-dominant with a $\backslash frac\{6\}\{5\}$ 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 LXVI. and LXVII.) 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 C E G B, gives the chord of the great sixth E G B C, thus improperly called, since the sixth from E to C is minor.

(4 F) M. Rameau has justly observed, that we ought rather to figure this lesser sixth with a $\backslash frac\{4\}\{6\}$, 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 notation, though we thought with him, that it would be better to mark this chord by a particular figure.

(4 G) The chord of the seventh B D F A gives, when inverted, the chord F A B D, composed of a third, a tritone, and a sixth. The 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 F be a tritone or a fourth redundant.

One may figure this chord thus, $\backslash frac\{4\}\{6\}$.

(4 H) The continued bass is proportionably adapted to singing, as the sounds which form it more scrupulously observe

Principles of Composition. 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 1.XIV. the note B, carrying the chord of the false fifth, rises diatonically upon C (41).

211. Every note carrying the chord of the tritone should descend diatonically upon the subsequent note. Thus in the same example LXVI. F, which carries the chord of the tritone figured with a 4^th, descends diatonically upon E (art. 202.)

212. The chord of the second is commonly put in practice upon notes which are syncopated in descend-

ing, because these notes are dissonances which ought to be prepared and resolved (200. 302.) See the example LXVII. where the second C, which is syncopated, and which descends afterwards upon B, carries the chord of the second (4K).

213. THE broken cadence is executed by means of a Broken cadence, which rises diatonically upon another, or upon some, how a tonic by a license. See, in the example LXIV. G A, (132, and 134.)

214. The interrupted cadence is formed by a dominant, how formed. Interrupted cadence, how formed. cd.

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.

(41) 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 D, carrying a chord of the seventh D F A C, to which the chord of the sub-dominant F A C D corresponds in the fundamental bass, ought to rise diatonically upon E, (art. 129. N^o 1. and art. 202.)

(4K) When there is a reprise in the treble, the note of the continued bass ought to be the same with that of the fundamental bass, (see Example LXVIII.) In the closes which are found in the treble at D and C (measures second and fourth), the notes in the fundamental and continued bass are the same, viz. G for the first cadence, and C for the second. This rule ought above all to be observed in 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 first note of the second measure in Example LXIX. D is found at the same time in the continued bass and in the treble; but the treble rises from C to D, and from D to E, whilst the bass descends from E to D, and from D to C.

Two octaves, or two fifths, in succession, must likewise be avoided. For instance, in the treble sounds G E, the bass must be prevented from sounding G E, C A, or D B; because in the first case there are two octaves in succession, E against E, and G against G; and because in the second case there are two fifths in succession, C against E, and A against G, or D against G, and B against E. 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 LXX. (Plate CCCLIX.) where the fundamental bass C gives the continued bass C E G E; the two E's ought in this bass to carry the chord 6, and G the chord 4; but as these chords are comprehended in the perfect chord C E G C, which is the first of the continued bass, we place nothing above C, only we draw a line over C E G E.

In like manner, in the second measure of the same example, the notes F and D of the continued bass, arising from the note G alone of the fundamental bass which carries the chord G B D F, we think it sufficient to figure F only, and to draw a line above F and D because the same harmony is used with both.

It should be remarked, that this F ought naturally to descend to E; but this note is considered as subsisting so long as the chord subsists; and when the chord changes, we ought necessarily to find the E, 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 LXXI. where this continued bass, C B D B G C, is reckoned the same with this C, B C. (Example LXXII.)

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 G in a continued bass may answer to this fundamental bass C G C, (see Example LXXIII.) in this case, we may regard the note G as divided into three parts, of which the first carries the chord 4, 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

Principles of Composition. minant which descends by a third upon another (136.). See, in the example LXXV. G E (4.1.). These cadences ought to be permitted but rarely and with precaution.

Chord by supposition what. 215. When a dominant is preceded by a tonic in the fundamental bass, we add sometimes, in the continued bass to the chord of that dominant, a new note which is a third or a fifth below; and the chord which results from it in this continued bass is called a chord by supposition.

See Supposition. For example, let us suppose, that in the fundamental bass we have a dominant G carrying the chord of the seventh G B D F; let us add to this chord the note C, which is a fifth below this dominant, and we shall have the total chord C G B D F, or C D F G, which is called a chord by supposition (4 M).

216. Chords by supposition are of different kinds. For instance, the chord of the tonic dominant G B D F gives,

1. By adding the fifth C, the chord C G B D F, These different chords what, and how figured. called a chord of the seventh redundant, and composed of a fifth, seventh, ninth, and eleventh. It is figured with a ♯7; see LXXVI. (4 N). This chord is not practised but upon the tonic. They sometimes leave out the sensible note, for reasons which we shall give in the note (4 O), upon the art. 219; it is then reduced to C F G D, and marked with ♯ or ♯.

2. By adding the third E, we shall have the chord E G B D F, called a chord of the ninth, and composed of a third, fifth, seventh, and ninth. And it is figured with a 9. This third may be added to every third of the dominant. See LXXVII.

and elsewhere. These rules, which are proper for a complete dissertation, did not appear indispensably necessary in an elementary essay on 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.

(4 L) One may sometimes, but very rarely, cause several tonics in succession to follow one another in ascending or descending diatonically, as C E G C, D F A D, B D F B; but, besides that this succession is harsh, it is necessary, in order to render it practicable, that the fifth below the first tonic should be found in the chord of the tonic following, as here F, a fifth below the first tonic C, is found in the chord D F A D, and in the chord B D F B (37. and note T).

(4 M) Though supposition be a kind of license, yet it is in some measure founded on the experiment related in the note (S), where you may see that every principal or fundamental found causes its twelfth and seventeenth major in descending to vibrate, whilst the twelfth and the seventeenth major ascending resound: which seems to authorize us in certain cases to join with the fundamental harmony this twelfth and seventeenth in descending; or, which is the same thing, the fifth or the third beneath the fundamental found.

Even without having recourse to this experiment, we may remark, that the note added beneath the fundamental found, causes that very fundamental found to be heard. For instance, C added beneath G, causes G to resound. Thus G is found in some measure to be implied at C.

If the third added beneath the fundamental found be minor, for example, if to the chord G B D F, we add the third E, the supposition is then no longer founded on the experiment, which only gives the seventeenth major, or, what is the same thing, the third major beneath the fundamental found. In this case the addition of the third minor must be considered as an extension of the rule, which in reality has no foundation in the chords emitted by a sonorous body, but is authorized by the function of the ear and by practical experiment.

(4 N) Many musicians figure this chord with a ♯7; M. Rameau suppresses this ♯, and merely marks it to be the seventh redundant by a ♯ or ♯7. But it may be said, how shall we distinguish this chord from the seventh major, which, as it would seem, ought to be marked with a ♯7? M. Rameau answers, that there is no danger of mistake, because in the seventh major, as the seventh ought to be prepared, it is found in the preceding chord; and thus the sharp subsiding already in the preceding chord, it would be useless to repeat it.

Thus D G, according to M. Rameau, would indicate D F ♯ A C, G B D F ♯. If we would change F ♯ of

the second chord into F ♯, it would then be necessary to write D G. In notes such as C, whose natural seventh is major, the figure 7 preceded or followed by a sharp will sufficiently serve to distinguish the chord of the seventh redundant C G B D F, from the simple chord of the seventh C E G B, which is marked with a 7 alone. All this appears just and well founded.

(4 O) Supposition introduces into a chord dissonances which were not in it before. For instance, if to the chord E G B D, we should add the note of supposition C descending by a third, it is plain that, besides the dissonance between E and D which was in the original chord, we have two new dissonances, C B, and C D; 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.)

3. If to a chord of the simple dominant, as D F A C, we should add the fifth G, we would have the chord G D F A C, called a chord of the eleventh, and which is figured with a $\backslash frac\{3\}\{4\}$ or $\backslash frac\{4\}\{5\}$. (See LXXVIII.)

217. WHEN the dominant is not a tonic dominant, we often take away some notes from the chord. For example, let us suppose that there is in the fundamental bass this simple dominant E, carrying the chord E G B D: if there should be added the third C beneath, we shall have this chord of the continued bass C E G B D; but we suppress the seventh B, for reasons which shall be explained in the note upon art. 210. In this state the chord is simply composed of a third, fifth, and ninth, and is marked with a 9. See LXXIX. (4 P.)

218. In the chord of the simple dominant, as D F A C, when the fifth G is added, we frequently obliterate the sounds F and A, that too great a number of dissonances may be avoided, which reduces the chord to G C D. 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 (4 Q.) (See LXXX.)

219. Sometimes we only remove the note A, and then the chord ought to be figured with $\backslash frac\{1\}\{4\}$ or $\backslash frac\{4\}\{5\}$ (4 R.)
220. Finally, in the minor mode, for example, in that of A, where the chord of the tonic dominant (109), is E G B D; if we add to this chord the third C below, we shall have E G B D, called the chord of the fifth redundant, and composed of a third, a fifth redundant, a seventh, and a ninth. It is figured as in LXXXI. (4 S.)

221. In the minor mode, for instance, in that of A, E a fifth from A is the tonic dominant (109), and carries the chord E G B D, in which G is the sensible

note. For this chord we sometimes substitute G B D F, (116), all composed of minor thirds; and which has for its fundamental sound the sensible note G. This chord is called a chord of the flat or diminished seventh, and is figured with a $\backslash sharp$ in the fundamental bass, (see LXXXIV.); but it is always considered as representing the chord of the tonic dominant.

222. This chord by inversion produces in the continued bass the following chords:

1. The chord B D F G, composed of a third, false fifth, and sixth major. They call it the chord of the sixth sensible and false fifth; and it is figured as in Exam. LXXXV. (Plate CCCLX.)

2. The chord D F G B, composed of a third, a tritone, and a sixth. It is called the chord of the tritone and third minor; and marked as in LXXXVI.

3. The chord F G B D, composed of a second redundant, a tritone, and a sixth. It is called the chord of the second redundant, and figured as in LXXXVII. (4 T.)

223. Besides, since the chord G B D F represents the chord E G B D, it follows, that if we operate by supposition upon the first of these chords, it must be performed as one would perform it upon E G B D; that is to say, that it will be necessary to add to the chord G B D F, the notes C or A, which are the third or fifth below E, and which will produce,

1. By adding C, the chord C G B D F, 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 marked as in LXXXVIII.

2. By adding A, we shall have the chord A G B D F, 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 as in LXXXIX. It is of all chords the most harsh, and the most rarely practiced (4 U.)

(4 P.) 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 $\backslash frac\{7\}\{9\}$; 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.

(4 Q.) In England it is figured $\backslash frac\{1\}\{4\}$.

(4 R.) We 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 C is preceded by the sensible note B carrying the chord of the false fifth, and that we should choose to form upon this note C the chord C E G B D, we must obliterate the seventh B, because in retaining it we should destroy the effect of the sensible note B, which ought to rise to C.

In the same manner, if to the harmony of a tonic dominant G B D F, one should add the note by supposition C, it is usual to retrench from this chord the sensible note B; because, as the D ought to descend diatonically to C, and the B to rise to it, the effect of the one would destroy that of the other. This above all takes place in the suspension, concerning which we shall presently treat.

(4 S.) Supposition produces what we call suspension; and which is almost the same thing. Suspension 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, in Example LXXXII. the C bearing $\backslash sharp$ is a supposition; but in Example LXXXIII. it is a suspension, because it suspends or retards the perfect chord C E G C which the ear expects after the tonic dominant G B D F.

(4 T.) The chord of the diminished seventh, and the three derived from it, are termed chords of substitution. They are in general harsh, and proper for imitating melancholy objects.

(4 U.) As the chord of the diminished seventh G B D F, and the chord of the tonic dominant E G B D, only differ

where the note D, which is added, passes under the chord C E G C.

License 1^st. 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 license ought to be rarely practiced.

226. As the continued bases alone appears in practical compositions, it becomes necessary to know how to find the fundamental bases when the continued bases is figured. This problem may be easily solved by the following rules.

In like manner, in a continued bases, the dissonance in a chord of the sub-dominant inverted, as A in the chord A C E G, inverted from C E G A, may sometimes descend diatonically instead of rising as it ought to do, art. 129. N^o 2; but in that case the note ought to be repeated in another part, that the dissonance may be there resolved in ascending.

227. 1. Every note which has no figure in the continued bases, ought to be the same, and without a figure in the fundamental bases; it is either a tonic, or reckoned such (4 X).

License 2^d. 225. SOMETIMES likewise, to render a continued bases more agreeable by causing it to proceed diatonically, we place between two sounds of that bases a note which belongs to the chord of neither. See Example XCII. in which the fundamental bases G C produces the continued bases G A B G C, where A is added on account of the diatonic modulation. This A has a line drawn above it, to show its resolution by passing under the chord G B D F.

2. Every note which in the continued bases carries a 6, ought in the fundamental bases 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. gave. and the note (4 Y).

3. Every note carrying $\backslash frac\{7\}\{4\}$ gives in the fundamental bases 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 bases, and with the same figure (4 Y).

5. Every note figured with a 2 gives in the fundamental bases the diatonic note above figured with a 7. See LXIV. (4 Z).

6. Every note marked with a 4 gives in the fundamental

differ one from the other by the notes E and F; one may form a diatonic modulation of these two notes, and then the fundamental bases 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 XC.)

For the same reason, as the chord of the diminished seventh G$\backslash flat$ B D F, and the chord B D F A, which carries the fifth B of the tonic dominant E, only differs by the sensible note G$\backslash flat$, and the tonic A; one may sometimes, while the treble modulates G$\backslash flat$ A G$\backslash flat$ A G$\backslash flat$ A, ascend in the fundamental bases, from the bases note to the third above, provided one descend at last from thence to the tonic dominant, and from thence to the tonic; (see XC.) This and the preceding examples are licenses.

(4 X) We 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 G, carrying a perfect chord, is preceded by D a simple dominant, carrying the chord D F A C, that note G is not a real tonic; because, in order to this, it would have been necessary that D should have been a tonic dominant, and should have carried the chord D F$\backslash flat$ A C; and that a simple dominant, as D, carrying the chord D F A C, should only naturally descend to a dominant, (art. 194.)

(4 Y) SOMETIMES a note which carries a 7 in the continued bases, gives in the fundamental bases its third above, figured with a 6. For example, this continued bases A$\backslash flat$ B C gives this fundamental bases C$\backslash flat$ G C; but in this case it is necessary that the note figured with a 6 should rise by a fifth, as we see here C rise to G.

(4 Z) A note figured with a 2, gives likewise sometimes in the fundamental bases its fourth above, figured 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 4 Y.)

These variations in the fundamental bases, 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'Abbé Roussier, to redress this deficiency, had invented a new manner of figuring the continued bases. His method is most simple for those who know the fundamental bases. 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 $\backslash frac\{7\}\{4\}$, or a 6, in order to mark all the discords. Thus the fundamental chord of the seventh D F A C is expressed by a D; and the same chord, when it is inverted from that of the sub-dominant F A C D, is characterized by F; the chord of the second C D F A, inverted from the dominant D F A C, is likewise represented by D; and the same chord C D F A, inverted from that of the sub-dominant F A C D, is signified by F; the case is the

compose the major mode of C, because the third E above C is major. If therefore we would have a modulation in the major mode of C, no other sounds must enter into it than those which compose this scale; in such a manner that if, for instance, we should find F# in this modulation, this F# discovers to us that we are not in the mode of C, or at least that, if we have been in it, we are no longer so.

232. In the same manner, if we form this scale in ascending A B C# D E F# G# A, which is exactly similar to the scale C D E F G A B C of the major mode of C, this scale, in which the third from A to C# is major, shall be in the major mode of A; and if we incline to be in the minor mode of A, we have only to substitute for C sharp C natural; so that the major third A C# may become minor A C: we shall have then

A B C D E F# G# A,

which is (§5.) the scale of the minor mode of A in ascending; and the scale of the minor mode of A in descending shall be (90.),

A G F E C D B A,

in which the G and F 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 (§9.).

Hence it appears what sharps and flats should be placed at the cleff in the major mode of A, and why they are omitted in the minor mode in descending.

233. This is the reason why, when we wish to begin a piece in the major mode of A, we place three sharps at the cleff upon F, C, and G; and on the contrary, in the minor mode of A, we place none, because the minor mode of A, 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.

(See Ex. xciv.)

Minor Modes.

3 Z 2

(§5 B) The major mode of F#, of C#, and of G#, are not much practised.

When a piece begins upon C#, there ought to be seven sharps placed at the cleff: but it is more convenient only to place five flats, and to suppose the key D#, which is almost the same thing with C#. For this reason we substitute here the mode of D#, for that of C#.

It is still much more necessary to substitute the mode of A# for that of G#; for the scale of the major mode of G# is,

G#, A#, B#, C#, d#, e#, f#, g#.

in which it appears that there are at the same time both a 'g#' and a 'g#': it would then be necessary, even at the same time, that upon G there should and should not be a sharp at the cleff; which is inconsistent. It is true that this inconvenience may be avoided by placing a sharp upon G at the cleff, and by marking the note G 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. We might likewise in this series, instead of G natural, which is the note immediately before the last, substitute F##, that is to say, F twice sharp: which, however, is not absolutely the same found with G natural, especially upon instruments whose scales are fixed, or whose intervals are invariable. But in that case two sharps must be placed at the cleff upon F, which would produce another inconvenience. But by substituting A# for G#, the trouble is eluded.

The double sharp, however, is incidentally used, when in a composition in the key of F# there is an occasional modulation into the dominant of that key, and it is distinguished by the character X or ##.

Of E♯ or F♯.
In descending. f f e♯ d♯ c B♭ A♭ G F.
In rising. F G A♭ B♭ c d e f.

Of C.
In descending. c B♭ A♭ G F E♭ D C.
In rising. C D E♭ F G A B c.

Of G.
In descending. g f e♭ d c B♭ A G.
In rising. G A B♭ c d e f♯ g.

Of D.
In descending. d c B♭ A G F E D.
In rising. D E F G A B c♯ d (5 c).

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, the piece begins in the major mode of C, or in the minor mode of A.

2. That when there is one sharp, it will always be placed upon F, and that the piece begins in the major mode of G, or the minor of E, in such a manner that it may be sung as if there were no sharp, by singing B instead of F♯, and in singing the tune as if it had been in another cleff. For instance, let there be a sharp upon F in the cleff of G upon the first line; one may then sing the tune as if there were no sharp; and as if, instead of the cleff of G upon the first line, it were the cleff of C; for the F♯, when changed into B, will require that the cleff of G should be changed to the cleff of C, as may be easily seen. This is what we call transposition (5 D).

237. It is evident, that when F♯ is changed into B,

(5 c) 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 below 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 below the tonic, and which is a third major from the dominant, is called a sensibile 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 D in the mode of C, and B in that of A is termed a super-tonic; the following note, which is a third major or minor from the tonic, according as the chord is major or minor, such as E in the major mode of C, and C in the minor mode of A, is called a mediant; and the note which is a tone above the dominant, such as A, in the mode of C, and F♯ in that of A, is called a super-dominant.

(5 d) 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, for instance, your air should begin upon C, requiring the natural diatonic series through the whole gammut, in which the distance between E and F, as also that between 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 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 G, the note with which you propose to begin, the three tones immediately succeeding are full; but the fourth C is only a semitone; it may therefore be kept in its place. But from F, the seventh note above, to G, the eighth, the interval is a full tone, which must consequently be redressed by raising the F a semitone higher. Thus the situations of the semitonic 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.

The order to be observed in these alterations of the intervals, is deduced from the relation which the fifth ascending and descending bear to the fundamental (art. 34, 35.); and therefore the farther we depart from the natural fundamental C by a series of fifths ascending or descending, the alterations, and consequently the number of sharps or flats indicating them, will be the greater.

Thus if G, which is the perfect fifth ascending from C, therefore the note most nearly allied to C (art. 39, 40.),

B, G must be changed into C, and E into A. Thus, by transposition, the air has the same melody as if it were in the major mode of C, or in the minor mode of A. The major mode then of G, and the minor of E, are by transposition reduced to those of C major, and of A minor. It is the same case with all the other modes (5 E).

238. As we have reduced to a very small number the rules of the fundamental basis, and those which in the treble ought to be observed with relation to this

be taken for a fundamental, F, which is the seventh of the scale of G, must be made sharp, that it may be a whole tone from the sixth E, and only a semitone from the key note G, according to the laws of the diatonic scale (art. 77.). See Ex. XCIV. 1. 2.

Again, if D, the perfect fifth ascending from G, and the second in the series of progressive fifths ascending from C, be used as a fundamental, C, which is the seventh of the scale of D, must, to render it the sensible or leading note (art. 77.), be made sharp in addition to F; so that in the scale of D, there are two sharps, F and C. See Ex. XCIV. (3.).

If A, the perfect fifth above D, and the third in the series of fifths ascending from C, be the fundamental, the seventh G must, in addition to F and C, be made sharp, for the same reason (4.); and so on, in the scale of E, which is next in order, F, C, G, and D, must be sharp (5.): in that of B, the sharps must be F, C, G, D and A (6.).

The perfect fifth above B is F#, and in that scale F, C, G, D, A, and E, must be sharp (7.). And in the next scale C# all the notes of the system are sharp (8.).

This, for the reasons mentioned in the note (5 B), is the last scale to which we can properly go by the progressions of fifths ascending.

Returning to the natural scale of C, if, instead of assuming G, the perfect fifth above, for a fundamental, we take F, the perfect fifth below; B, which is the fourth note above F, and forms a tritone or sharp fourth to it, must, to become a perfect fourth, according to the laws of the diatonic scale, (art. 60.) be made flat (12.).

Proceeding with the series of fifths descending, if Bb, which is the perfect fifth below F, be taken for a fundamental; E, which, in its natural state, is the tritone or sharp fourth to Bb, must, to become the diatonic fourth (art. 60.), also be rendered flat (11.).

If Eb, which is the perfect fifth below Bb, and the third in the series of fifths descending from C, be made the fundamental, A, the sharp fourth, must, to become the diatonic fourth, be made flat, and the flats marked at the cleff are B, E and A (10.).

To form the next scale in the series of fifths descending, which is that of A flat, D must be flattened; and B, E, A, and D, are marked flat at the cleff (9.).

The next scale, that of D flat, is formed by flattening G, and adding its flat to the others at the cleff (8.). This is the scale recommended to be used rather than that of C# (See note 5 B).

We do not proceed farther with the series of fifths descending, since the next scale, that of Gb, would just or very nearly exhibit the sounds already represented by the scale of F# (7.). This scale is, however, sometimes written in the key of G flat, and we even meet with the scale of its fifth below, C flat, and, with an occasional modulation from that key into its fifth below, F flat, where B being necessarily twice flattened, is distinguished by this character $\backslash flat$, or bb, called a double flat.

We have thus seen, 1st, That each of the notes of the diatonic scale of C, and each of the semitones into which the whole tones of that scale are divided, may be taken for the fundamental note of a diatonic scale, called the scale of that note. 2dly, That the notes of the natural scale are more or less altered, as the note assumed for a fundamental is more or less distant from C, in a progression of fifths ascending or descending. 3dly, That in the progression by fifths ascending, the notes are altered by sharps, and in the progression by fifths descending, the alterations are by flats. 4thly, That in the alteration by sharps, the last sharp is always on the seventh or sensible note of the scale; and where there are more than one, is always on the fifth above the sharp immediately preceding; and in the alteration by flats, the last flat is always on the fourth of the scale; and where there are more than one, is always on the fifth below the flat immediately preceding.

The signatures of sharps and flats at the cleffs, belonging to the twelve major scales, are also used for their relative minor scales. The occasional elevation and depression of the sixths and sevenths of the minor scales, are denoted by occasional sharps or flats placed before these notes.

(5 E) 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 D, they place neither sharp nor flat at the cleff; in the minor mode of G, one flat only; in the minor mode of C, 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.

bass, it should no longer be difficult to find the fundamental bass of a given modulation, nay, frequently to find several; for every fundamental bass 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 bass, will both be prepared, if it is necessary that they should be so, and always resolved (5 F).

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 that bass should correspond.— But it is difficult in this matter to assign general rules, and such as are absolutely without exception, in which nothing may be left that appears indifferent or discretionary; because sometimes we seem to have the free choice of referring a particular melody either to one mode or another. For example, this melody G C may belong to all the modes, as well major as minor, in which G and C are found together; and each of these two sounds may even be considered as belonging to a different mode.

240. We 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 (chap. vi.) for the procedure of the fundamental bass.

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 C is C, and A in that of A, &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 distinguishing the major mode of C from the minor of A. 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 C E G in the one, and A C E in the other; so that if a piece should, for instance, begin thus, A C E A, it may be almost constantly concluded, that the tone or mode is in A minor, although the notes A C E belong to the mode of C.

2. From the sensible note, which is B in the one, and G♯ in the other; so that if G♯ appears in the first bars of a piece, we may be certain that we are in the mode of A.

3. From the adjuncts of the mode, that is to say, the modes of its two-fifths, which for C are F and G, and D and E for A. For example, if after having begun a melody by some of the notes which are common to the modes of C and of A (as E D E F E D C B C), we should afterwards find the mode of G, which we ascertain by the F♯, or that of F which we ascertain by the B♭ or C♯, we may conclude that we have begun in the mode of C; but if we find the mode of D, or that of E, which we ascertain by B♭, C♯, or D♯, &c. we conclude from thence that we have begun in the mode of A.

4. A mode is not usually changed, especially in the beginning of a piece, unless in order to pass into one or other of the modes 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 C, are the major mode of G, and that of A minor. From the mode of C 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. 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 F and E for the mode of C (5 C).

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,

(5 F) We often say, that we are upon a particular key or scale, instead of saying that we are in a particular mode. The following expressions therefore are synonymous; such a piece is in C major, or in the mode of C major, or in the key of C major, or in the scale of C major.

(5 G) It is certain that the minor mode of E has an extremely natural connection with the mode of C, 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 D may be joined to the major mode of C: and thus in a particular sense, this mode may be considered as relative to the mode of C, but it is still less so than the major modes of G and F, or than those of A and E minor; because we cannot immediately, and without licence, pass in a fundamental bass from the perfect minor chord of C to the perfect minor chord of D; and if you pass immediately from the major mode of C to the minor mode of D in a fundamental bass, it is by passing, for instance, from the tonic C, or from E G C, to the tonic dominant of D, carrying the chord A C♯ E G, in which there are two sounds, E G, which are found in the preceding chord, (Ex. xcv.) or otherwise from C E G C to G B♭ D E, a chord of the sub-dominant in the minor mode of D, which chord has likewise two sounds, G and E, in common with that which went immediately before it. See Ex. xcv.

Principles of Composition. closes *, is always easy to be found. For the sounds which occur in the treble, M. Rameau may be consulted, p. 54. of his Nouveau Systeme de Musique theorique et pratique (58).

* See Conclusion. Having ascertained the mode, the fundamental bass not difficult.

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 C, C E G 'c'.

Minor mode of A, A C E A.

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 C, G B D 'f'.

Tonic dominant.

Minor mode of A, E G 'B' d'.

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 C, F A C 'd'.

Minor mode of A, D F A B.

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 C, and that we find in the melody these two notes A B in succession; if we confine ourselves to place in the fundamental bass one of the three sounds C G F, we shall find nothing for the sounds A and B but this fundamental bass F G; now such a succession as F to G is prohibited by the fifth rule for the fundamental bass according to which every sub-dominant, as F, should rise by a

fifth; so that F can only be followed by C in the fundamental bass, and not by G.

To remedy this, the chord of the sub-dominant F A C 'd' must be inverted into a fundamental chord of the seventh, in this manner, D F A 'c', which has been called the double employment (art. 105.) because it is a secondary manner of employing the chord of the sub-dominant. By these means we give to the modulation A B this fundamental bass D G; which procedure is agreeable to rules. See Ex. xcvii.

Here then are four chords, C E G 'c', G B D 'f', F A C 'd', D F A 'c', which may be employed in the major mode of C. We shall find in like manner, for the minor mode of A, four chords.

A C 'e' a', E G 'B' d',

D F A B, B D 'f' a'.

And in this mode we sometimes change the last of these chords into B D 'f' a', substituting the 'f' for 'a'. For instance, if we have this melody in the minor mode of A, E F 'G' A, we would cause the first note E to carry the perfect chord A C E A; the second note F to carry the chord of the seventh B D F 'A'; the third note G, the chord of the tonic dominant E G 'B' d', and the last the perfect chord A C E A. See Ex. xcviii.

On the contrary, if this melody is given always in the minor mode, A A G 'A', the second A being syncopated, it might have the same bass as the modulation E F 'G' A, with this difference alone, that F might be substituted for F in the chord B D F 'A', the better to mark out the minor mode. See Exam. xcix.

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,

C A D G C F B E A D G C,

which are terminated equally in the tonic C, either entirely belong, or at least may be reckoned as belonging (51) to the mode of C; because none of these dominants are tonic dominants, except G, which is the tonic dominant of the mode of C; and besides, because the chord of each of these dominants forms no other

(51) 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, E C G, we must not with too much precipitation conclude from thence that we are in the major mode of C, although these three sounds, E C G, be the principal and characteristic sounds in the major mode of C: we may be in the minor mode of E, especially if the note E should be long.

(51) 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 C, viz. C carrying the perfect chord, F carrying that of the sub-dominant, and G that of the tonic dominant, to which we may join the chord of the seventh, D F A C (art. 105.): but we here regard as extended the series of dominants in question, as belonging to the mode of C, 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 A belongs naturally to the mode of G, the simple dominant B to that of A, &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 C.

considering the last C as a tonic dominant in this manner, C E G B^b; the mode would then be changed at the second C, and we should enter into the mode of F, because the chord C E G B^b indicates the tonic dominant of the mode of F; besides, it is evident that the mode is changed, because B^b does not belong to the scale of C. See Ex. ci.

In the same manner, were we to form this fundamental bass

considering the last C as a sub-dominant in this manner, C E G A; this last C would indicate the mode of G, of which C is the sub-dominant. See Ex. cii.

In like manner, still, if in the first series of dominants, we caused the first D to carry the third major, in this manner, D F^♯ A^♯ C^♯; this D having become a tonic dominant, would signify to us the major mode of G, and the G which should follow it, carrying the chord B D^♯ F^♯, would relapse into the mode of C, from whence we had departed. See Ex. ciii.

Finally, in the same manner, if in this series of dominants, we should cause B to carry F^♯ in this manner, B D F^♯ A, this F would show that we had departed from the mode C, to enter into that of G. See Ex. civ.

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.

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, it cannot be ascertained from this dominant alone, whether the mode be major or minor: but it is only necessary to examine the following note, which must be the tonic of the mode in which he is; by the third of this tonic it will be discovered 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 (5 K).

CHAP. XIV. Of the Chromatic and Enharmonic.

245. We call that melody chromatic which is chromatic, posed of several notes in succession, whether rising or what, descending by semitones. See cv. and cvi.

246. When an air is chromatic in descending, the most natural and ordinary fundamental bass is a con-
catenated series of tonic dominants; all of which fol-
low one another in descending by a fifth, or which
is the same thing, in rising by a fourth. See Ex. cv. fundamental bass, (5 L).

(5 K) 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 C and the major of G, or the major mode of C and the minor of A: 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 C and the minor of B, &c.

When the composer, 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, he ought to continue in it but for a short time, because the ear is always impatient to return to the former mode.

(5 L) 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 cvii, 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 seventh diminished, and that in this bass there is a false fifth from D to G^♯, and a fifth redundant from G^♯ to C.

The reason of this licence is, at it appears to us, 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

(see Example cviii.) may be considered as representing (art. 116.) that which is written below,

Now this last fundamental bass is formed according to the common rules, unless that there is a broken cadence from D to E, and an interrupted cadence from E to C, which are licences (art. 213 and 214.)

Fig. 1. Tone Tone Semi-T. Tone Tone Tone Tone Semi-T.
C D E F G A B c

Fig. 9. Scale
{ c d e f g a b c
C G C F C D G C

Fig. 2. C D E F G A B c d e f g a b c d e f g a b
Scale First Scale Second Scale Third
H I

Fig. 3. K L M N
R S T U V W

The Diatonic Scale of the Graks

Fig. 4. { B c d e f g a
G C G C F C F

The Fundamental Bass

The Chromatic Species Scale

Fig. 10. { g g# &c
C E G#

The Fund. Bass

Fig. 5. { c d e f g g a b c
C G C F C G D G C

The Fundamental Bass

Fig. 11. { c e b#
C E G#

Fig. 6. C, C#, D, D#, E, E#, F, F#, G, G#, A, A#, B, B#, c, c#, d, d#, e, e#
Scale First Scale Second

The first Scale of the Minor Mode

Fig. 7. { G A B c d e f
Third Minor Third Minor Third Minor
E A E A D A D

The Fundamental Bass

Scale

Fig. 12. { f e e d#
F C E B

The Fund. Bass

The Second Scale of the Minor Mode

Fig. 8. { A B c d e e f# g# a
A E A D A E B E A

The Fundamental Bass

Scale

Fig. 13. { eb e e e e#
C C A C# C#

The Fund. Bass

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

Fig. 12.

Fig. 13.

Fig. 14.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18. Rests.

Rests of several Bars.

Semibreve } Min. Rest Crot. Rest Quav. Rest Semiq. Rest Demis. Rest 2 Bar Rest 3 Bar Rest 4 Bar Rest 5 Bar Rest.
or Bar Rest }

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

Fig. 12.

Fig. 13. Pause

Fig. 14. Repeat.

Fig. 15. Direct.

Fig. 16.

Fig. 17.

Fig. 18.

Fig. 19.

MUSIC.

Plate CCCLVII.

Ex. I. II. III. IV. V. VI. VII. VIII. IX. X.

XI. XII. XIII. XIV. XV. XVI.

XVII. XVIII. XIX. XX. XXI. XXII. XXIII. XXIV.

XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI. XXXII.

XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XL.

XLI. XLII. XLIII. XLIV. XLV. XLVI.

Perfect Cadence.

Imperfect Cadence.

Perf. Cad.

MUSIC.

Plate CCCLVIII.

XLVII. XLVIII. XLIX. L. LI.

Diss. prepared. Diss. prep. Diss. prep.

LII. LIII. LIV. LV. LVI. LVII. LVIII.

Diss. resolved. Diss. res. Diss. res. Continued Bass. Fund. Bass.

LIX. LX. LXI. LXII. LXIII. LXIV. LXV. LXVI.

Cont. Bass. Fund. Bass.

LXVII. LXVIII. LXIX.

Cont. Bass. Fund. Bass.

Handwritten musical score on aged paper, featuring multiple staves with notes and rests. The page is heavily stained with brown spots, obscuring much of the original text and notation. The staves are arranged vertically, and the handwriting is in a cursive script. The overall appearance is that of an old, weathered document.

LXX. LXXI. LXXII.

Cont. Bass.

Fund. Bass.

LXXIII. LXXIV. LXXV. LXXVI. LXXVII. LXXVIII.

Cont. Bass.

Fund. Bass.

LXXIX. LXXX. LXXXI. LXXXII. LXXXIII. LXXXIV.

Cont. Bass.

Fund. Bass.

MUSIC.

Plate CCCLX.

LXXXV.

LXXXVI.

LXXXVII.

LXXXVIII.

LXXXIX.

XC. Diatonic Modulation.

XCI.

XCII.

XCIII.

XCIV. Major Scales.

1. of C.

2. of G.

3. of D.

4. of A.

5. of F.

6. of B.

7. of F#.

8. of Db.

9. of Ab.

10. of Eb.

11. of Bb.

12. of E.

MUSIC.

Plate CCCLXI.

XCV.      XCVI.      XCVII.      XCVIII.      XCIX.

Fund. Bass.

C.      CI.

F.B.

CII.      CIII.      CIV.

F.B.

CV. Chromatic Modulation descending.      CVI. Chromatic Modulation ascending.

F.B.      F.B.

Cont. Bass.

C.B.

Fund. Bass.

F.B.

1^st & 2^d Parts.

3^d & 4^th Parts.

Fund. Bass.

1^st & 2^d Parts.

3^d & 4^th Parts.

Fund. Bass.

THE treatise of D'Alembert 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

(5 M) Compositions in strict canon, where one part begins with a certain subject, and the other parts are bound to repeat the very same subject, or the reply, as it is called, in the unison, fifth, fourth, or octave, depend on the following rules, which are nothing more than a summary of the system explained by our author.

1. 1. The chords to be employed are the tonic, and its two adjuncts; the subdominant, susceptible of an added sixth, and the dominant, susceptible of an added seventh.
2. 2. The subject must begin in the harmony of the tonic, and as the fundamental progression from the dominant to the subdominant is not permitted (art. 33. 36.), the subdominant must follow the tonic, and the dominant the subdominant, thus,

C, F, G, C, F, G, C, &c.

3. As the diatonic scale consists of two tetrachords, of which the first is also the second tetrachord of the mode of the sub-dominant, and the second the first tetrachord of the dominant; so, in canon, when the reply is meant to be in the mode of the dominant, the subject must be in the first tetrachord of the tonic, by which means the corresponding first tetrachord of the dominant being the second tetrachord of the tonic, the whole piece is truly in that mode. On the other hand, if the reply is to be in the mode of the sub-dominant, the subject must be in the second tetrachord of the tonic, the corresponding tetrachord of the sub-dominant being the first tetrachord of the tonic, and the mode of the tonic being thus preserved.

4. For the same reason, where the reply is in the dominant, the subject is only allowed to modulate into the mode of the sub-dominant, and the reply of course into that of the tonic. And where the reply is in the dominant, the subject is to modulate only into the mode of the sub-dominant, the reply following of course into that of the tonic. Were the contrary modulation permitted, the reply would depart too far from the mode of the tonic.

Lossly, When the reply is to be in the mode of the dominant it must commence in the measure bearing that harmony; and in the same way, the reply in the sub-dominant must begin in the measure which bears the harmony of the sub-dominant.

If these rules be observed, and due attention paid to the preparation and resolution of dissonances, composition in strict canon, in any number of parts, will be found to be by no means difficult. See Ex. CIX. and CX.

(5 N) 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 F D, and the other 'c' a' in rising, C is the fifth of F, and 'a' the twelfth of D.

General
Observa-
tions on
Harmonies.

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 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 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.

Aristoxenes, 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 velo-

cities, 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, the opinions of Pythagoras 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 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.

Music.
Musimon.

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,

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,