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 theoricians 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 melopoe, 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 rhythmopoe, 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, conti- 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 singers execute on the stage. It is in this music alone, and not in harmonies 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 characterised by these pathetic and imitative powers, deserves no better name than that of a musical jargon, and can only be effectuated by such a complication and intricacy of harmony, as may confound, but cannot entertain the audience. This character, therefore, ought to be added as essential to the definition of music; and it must be attributed to our neglect of this alone, whilst our whole attention is bestowed on harmony and execution, that the best performances of our artists and composers are heard with listless indifference and oscillation, 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 quire 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 humanised the character, and softened those habits of roughness and ferocity by which men might otherwise have degenerated into savages. The gradations by which voices were exerted and tuned, by which the invention of one instrument succeeded to another, or by which the principles of music were collected and methodised in such a manner as to give it the form of an art and the dignity of a science, are topics so fruitful of conjecture and so void of certainty, that we must leave them to employ minds more speculative and inventions more prolific than ours, or transfer them to the History of music as a more proper place for such disquisitions. For the amusement of the curious, Rousseau in his Musical Dictionary, Plates C and N, has transcribed some fragments of Grecian, Persian, American, Chinese, and Swiss music, with which performers may entertain themselves at leisure. When they have tried the pieces, it is imagined they will be less sanguinely fond than that author of ascribing the power of music to its affinity with the national accents where it is composed. This may doubtless have its influence; but there are other causes more permanent and less arbitrary to which it owes its most powerful and universal charms.

The music now most generally celebrated and practised is that of the Italians, or their successful imitators. The English, from the invasion of the Saxons, to that more late though lucid era in which they imbibed the art and copied the manner of the Italians, had a music which neither pleased the soul nor charmed the ear. The primitive music of the French deserves no higher panegyric. Of all the barbarous nations, the Scots and Irish seem to have possessed the most affecting original music. The first consists of a melody characterised by tenderness: it melts the soul to a pleasing pensive languor. The other is the native expression of grief and melancholy. Tassoni informs us, that in his time a prince from Scotland had imported into Italy a lamentable kind of music from his own country; and that he himself had composed pieces in the same spirit. From this expressive though laconic description, we learn that the character of our national music was even then established; yet so gross is our ignorance and credulity, that we ascribe the best and most impassioned airs which are extant among us to David Rizzio; as if an Italian lutenist who had lived so short a time in Scotland, could, at once, as it were by inspiration, have imbibed a spirit and composed in a manner so different from his own. It is yet more surprising that Geminiani should have entertained and published the same prejudice, upon the miserable authority of popular tradition alone; for the fact is authenticated by no better credentials. The primitive music of the Scots may be divided into the martial, the pastoral, and the festive. The first consists either in marches, which were played before the chieftains, in imitation of the battles which they fought, or in lamentations for the catastrophes of war and the extinction of families. These wild effusions of natural melody preserve several of the rules prescribed for composition. The strains, though rude and untutored, are frequently terrible or mournful in a very high degree. The port or march is sometimes in common, sometimes in treble time; regular in its measures, and exact in the distance between its returning cadences; most frequently, though not always, loud and brisk. The pi-broch, or imitation of battles, is wild and abrupt in its transitions from interval to interval and from key to key; various and desultory in its movements; frequently irregular in the return of its cadences; and in short, through the whole, seems inspired with such fury and enthusiasm, that the hearer is irresistibly infected with all the rage of precipitate courage, notwithstanding the rudeness of the accents by which it is kindled. To this the pastoral forms a striking contrast. Its accents are plaintive, yet soothing; its harmony generally flat; its modulations natural and agreeable; its rhythmus simple and regular; its returning cadences at equal distance; its transitions from one concinnous interval to another, at least for the most part; its movements slow, and may be either in common or treble time. It scarcely admits of any other harmony than that of a simple bass. A greater number of parts would cover the air, and destroy the melody. To this we shall add what has been said upon the same subject by Dr Franklin. Writing to Lord K———, he proceeds thus:

"Give me leave, on this occasion, to extend a little the sense of your position, 'That melody and harmony are separately agreeable, and in union delightful,' and to give 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 acceptation, 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 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 pith 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 stopt the moment a succeeding note begins. To avoid actual discord, it was therefore necessary that the succeeding emphatic 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 manoeuvre of the Irish harp, know well that there is a method of discontinuing sounds no less easy and effectual than upon the harpsichord. When the performer finds it proper to interrupt a note, he has no more to do but return his finger gently upon the string immediately struck, which effectually stops its vibration.

That species of Scots music which we have distinguished by the name of festive seems now limited to reels and country-dances. These may be either in common or treble time. They most frequently consist of two strains: each of these contains eight or twelve bars. They are truly rhythmical; but the mirth which they excite seems rather to be inspired by the vivacity of the movement, than either by the force or variety of the melody. They possess a manoeuvre 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 dawnsings 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 and of Plato, there is reason to suppose, that in very ancient times the study of music in Egypt was confined to the priesthood, who used it only on religious and solemn occasions; that, as well as sculpture, it was circumscribed by law; that it was esteemed sacred, and forbidden to be employed on light or common occasions; and that innovation in it was prohibited: But what the style or relative excellence of this very ancient music was, there are no traces by which we can form an accurate judgment. After the reigns of the Pharaohs, the Egyptians fell by turns under the dominion of the Ethiopians, the Persians, the Greeks, and the Romans. By such revolutions, the manners and amusements of the people, as well as their form of government, must have been changed.

In the age of the Ptolemies, the musical games and contests instituted by those monarchs were of Greek origin, and the musicians who performed were chiefly Greek.

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 300 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 rossa, or the broken pillar, which during the sacking of the city in 1527 was thrown down and broken, still lies in the Campus Martius. On it is seen the figure of a musical instrument of two strings, and with a neck. It resembles much the calascione still used in the kingdom of Naples.

This curious relic of antiquity is mentioned, because it affords better evidence than, on the subject of ancient music, is usually to be met with, that the Egyptians, at so very early a period of their history, had advanced to a considerable degree of excellence in the cultivation of the arts. By means of its neck, this instrument was capable, with only two strings, of producing a great number of notes. These two strings, if tuned fourths to each other, would furnish that series of sounds called by the ancients heptachord, which which consists of a conjunct tetrachord as B, C, D, E; E, F, G, A; if tuned fifths, they would produce an octave, or two disjunct tetrachords. The calascione is tuned in this last manner. The annals of no nation other than Egypt, for many ages after the period of the obelisk at Heliopolis, exhibit the vestige of any contrivance to shorten strings during performance by a neck or finger-board. Father Montfaucon observes, that after examining 500 ancient lyres, harps, and citharas, he could discover no such thing.

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

The Hermes or Mercury of the Egyptians, surnamed 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 animals."

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

The monaulos, or single flute, called by the Egyptians photinx, was probably one of the most ancient instruments used either by them or any other nation. From various remains of ancient sculpture, it appears to have been shaped like a bull's horn, and was at first, it may be supposed, no other than the horn itself—Before the invention of flutes, as no other instrument except those of percussion were known, music must have been little more than metrical. When the art of refining and lengthening sounds was first discovered, the power of music over mankind, from the agreeable surprise occasioned by soft and extended notes, was probably irresistible. At a time when all the rest of the world was involved in savage ignorance, the Egyptians were possessed of musical instruments capable of much variety and expression.—Of this the astonishing remains of the city Thebes still subsisting afford ample evidence. In a letter from Mr Bruce, ingrossed in Dr Burney's history of Music, there is given a particular description of the Theban harp, an instrument of extensive compass, and exquisite elegance of form. It is accompanied with a drawing taken from the ruins of an ancient sepulchre at Thebes, supposed by Mr Bruce to be that of the father of Sesostris.

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

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

It cannot be doubted that during the reigns of the Ptolemies, who were voluptuous princes, music must have been much cultivated and encouraged. The father of Cleopatra, who was the last of that race of kings, derived his title of auletes, or flute-player, from his excessive attachment to the flute. Like Nero, he used to array himself in the dress of a 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 hereditary and by office. The prophets appear to have accompanied their inspired effusions with music; and every prophet, like the present improvisatori of Italy, seems to have been accompanied by a musical instrument.

Music, vocal and instrumental, constituted a great part of the funeral ceremonies of the Jews. The pomp and expense used on these occasions advanced by degrees to an excessive extent. The number of flute-players in the processions amounted sometimes to several hundreds, 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.

Cadmus, with the Phoenician colony which he led into Greece, imported at the same time various arts into that country. By the assistance of his Phoenician 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 deified a prince or hero of their own country, they usually assigned him an Egyptian name, and with the name bestowed on their new divinity all the actions, attributes, and rites of the original.

The Grecian lyre, although said to have been invented by Mercury, was cultivated principally by Apollo, who first played upon it with method, and accompanied it with the voice. The celebrated contest between him and Marsyas is mentioned by various authors; in which, by conjoining the voice with his lyre (a combination never before attempted), his music was declared superior to the flute of Marsyas. The progress of the lyre, according to Diodorus Siculus, is the following. "The muses added to the Grecian lyre the string called mese; Linus that of lichanos; and Orpheus and Thamyras those strings which are named hypate and parhypate." It has been already mentioned, that the lyre invented by the Egyptian Mercury had but three strings. By putting these circumstances together, we may perhaps acquire some knowledge of the progress of music, or at least of the extension of its scale in the highest antiquity. Mese, in the Greek music, is the fourth sound of the second tetrachord 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 meson, parhypate meson, and meson diatonic. 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 diffusive, and involve too much foreign matter for the plan we have chosen to adopt. We cannot avoid, however, making a few observations on the poems of Homer, in so far as connected with our subject. It has been imagined, with much appearance of probability, that the occupation of the first poets and musicians of Greece resembled that of the Celtic and German bards and the scalds musicians of Iceland and Scandinavia. They sang their poems in Greece, in the streets of the 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.

(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 still extant of the three great tragic poets, Aeschylus, Sophocles, and Euripides, together with those of Plato, Aristotle, Aristoxenus, Euclid, Theocritus, Callimachus, Polybius, and many others, produced all within a space less than 300 years, distinguish this illustrious and uncommon period as that in which the whole powers of genius seem to have been exerted to illuminate and instruct mankind in future ages. Then it was that eloquence, poetry, music, architecture, history, painting, sculpture, like the spontaneous blossoms of nature, flourished without the appearance of labour or 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 that 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 £81l. 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. Amoebeus, a harper, was paid an Attic talent, or £93l. 15s. per day for his performance (b).

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 sects, and of much diversity of opinion.—The founders of the most distinguished sects were Pythagoras and Aristoxenus.

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

The excessive vanity of Nero with respect to music, displayed in his public contentions for superiority with the most celebrated professors of the art in Greece and Rome, is known to every one conversant in the history of Rome. The solicitude with which that detestable tyrant attended to his voice is curious, and will throw some light on the practices of singers in ancient times. He was in use to lie on his back, with a thin plate of lead on his stomach. He took frequent emetics and cathartics, abstained from all kinds of 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 (Phonascus) to regulate his tones in speaking.

Most nations have consented in introducing music into their religious ceremonies. That art was early admitted into the rites of the Egyptians and Hebrews; and that it constituted a considerable part of the Greek 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.

(b) Roscius gained 500 sestertia, or £93l. 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 Stillington, 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 hydraulican 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, seem 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 of the 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 at least as 1483. John de Muris, however, who there is some cause to believe was an Englishman, though not the inventor of the cantus mensurabilis, did certainly by his numerous writings greatly improve it. His tract on the Art of Counterpoint is the most clear and useful essay on the subject of which those times can boast.

In the 11th century, during the first crusade, Europe began to emerge from the barbarous stupidity and ignorance which had long overwhelmed it. While its inhabitants were exercising in Asia every species of rapine and pious cruelty, art, ingenuity, and reason, insensibly civilized and softened their minds. Then it was that the poets and songsters, known by the name of Troubadours, who first appeared in Provence, instituted a new profession; which obtained the patronage of the count of Poictou, and many other princes and barons, who had themselves cultivated music and poetry with success. At the courts of their magnificent patrons the troubadours were treated with respect. The ladies, whose charms they celebrated, gave them the most generous and flattering reception. The success of some inspired others with hopes, and excited exertions in the exercise of their art; impelling them towards perfection with a rapidity which the united force alone of emulation and emulation could occasion. These founders of modern versification, constructing 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 of the scale attributed to Guido, and the invention of the time-table ascribed to Franco, no remains of secu- lar music can be discovered, except those of the trou- badours or Provençal poets. In the simple tones of these harps no time indeed is marked, and but little variety of notation appears: It is not difficult, how- ever, to discover in them the germs of the future me- lodies, 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 cho- sen that subject, it would have been discovered to be worthy of attention; the poetry, as interesting to li- terature; 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 ori- gin. The most ancient strains that have been spared by time, are such as were set to the songs of the trouba- dours. 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 violiers, or performers on the vielle or viol, juglers, 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 compris- ed 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 musi- cians were employed often to sing the verses of trouba- dours, 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- triers, 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 an- cient or modern times, only during the early dawning of literature.

In the 13th century the songs were on various sub- jects; moral, merry, amorous: and at that time me- lody 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 move- ment and embellishments of the air depended on the abilities of the singer. Since that time, by the culti- vation of the voice modern music has been much ex- tended, for it was not till towards the end of St Lewis's reign that the fifth line began to be added to the stave. The singer 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 estima- tion 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 violins holds the first place among the treble instrumen- ts. 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 con- quest. 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 ex- tensive 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 num- bers, and with acquisitions from France and Italy aug- mented our store of knowledge (Chaucer), entitles one of his poems "The History of St Cecilia;" and the ce- lebrated patroness of music must no doubt be men- tioned in a history of the art. Neither in Chau- cer, however, nor in any of the histories or legendary accounts of this saint, does anything appear to au- thorize the religious veneration paid to her by the vo- taries 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 Spel- man, the appellation of Doctor was not among the de- grees granted to graduates in England sooner than the reign of King John, about 1207; although, in Mrs. Wood's history of Oxford, that degree is said to have been conferred, even in music, in the reign of Hen- ry 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 ex- tended to it.

After the invention of printing, an art which has tended to disseminate knowledge with wonderful ra- pidity among mankind, music, and particularly com- puterpoint, 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 consi- 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 Bayntyne'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 descant 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 Books. 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 master now in Europe to enable him to play one of them to the end. Tallis, singularly profound in musical composition, and Bird his admirable scholar, were two of the authors of this famous collection.

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

The most eminent musical theorists of Italy, who flourished in the 16th century, were, Franchinus Gaffurius, or Gafforio of Lodi, Pietro Aaron of Florence, Lodovico Fogliano, Giov. Spato, Giov. Maria da Terentio Lanfranco, Stefano Uanaco, Antonio Francesco Doni, Luigi Dentice, Nicolo Vicentino, and Gioseffo Zarlino, the most general, voluminous, and celebrated theorist of that period, Vincentio Galilei, a Florentine nobleman, and father of the great Galileo Galilei, Maria Artuse of Bologna, Orasco Tegrimi, Pietro Pontio, and Lodovico Zacconi.

The principal Roman authors were, Giovanni Annuccia, 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, Costanzo Porta, Gastoldi, Bissi, Cima, Vocchi, and Monteverde.

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

Francisco Cortecchia, a celebrated organist and composer, and Alessandro Striggio, a lutanist 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 Ornithorparcus, Paul Hofhaimer, Luscinius, Henry Loris or Lorit, Faber, Fink, Hosman, and many others whom it would be tedious to mention; and for a particular account of whose treatises and compositions we must refer to more voluminous histories of music.

In France, during the 16th century, no art except the art of war made much progress in improvement. Ronsard, Baif, Goudimel, Claud le Jeune, Cauroy, 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 Alfonzo 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; ther... of whom we may mention Verletot, Gombert, Arka- delt, Berchem, Richafort or Ricciafort, Crequillon 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- thanana Giles, Thomas Tomkins, and his son of the same name; Elway Bevin, Orlando Gibbons, Dr Wil- liam Child, Adrian Batten, Martin Pierson, William Lawes, Henry Lawes, Dr John Wilson, John Hilton, John Playford, Captain Henry Cook, Pelham Hum- phrey, John Blow, William Turner, Dr Christopher Gibbons, Benjamin Rogers, and Henry Purcell. Of these, Orlando Gibbons, Pelham Humphrey, and Hen- ry Purcell, far excelled the rest.

About the end of the reign of James I, a music-lec- ture 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 cultivated in Italy with diligence, and in a learned and elaborate style, till near the middle of the century; yet a revo- lution in favour of melody and expression was prepar- ing, 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 pre- ferred to music of many parts; in which canons, fugues, and full harmony, had been the productions which chiefly employed the master's study and the hearer's attention.

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 com- posers flourished in that country."

The list of great musicians which France produced during the early part of the same century is not nu-

(b) The most celebrated violin players of Italy, from the 16th century to the present time, have been Farina, M. Angelo Rossi, Bassani the violin-master of Corelli, the admirable Angelico Corelli himself, Torrelli, 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 about the 1600s, 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 Don d'Amore, set by the famous organist Bernardo Pasquini, was represented at Nilla Sala de Signori Copranica; a theatre which still subsists. In the year 1680, L'Onceta 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 sackbutts, 6 great flutes, 6 minstrels 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 English poets from the beginning of the last century, and 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 risen 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: Psyche 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 Arsiné 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 Cross, and Mrs Lyndsey. The translation of Arsiné, and the music to which it is set, are execrable; yet such is the charm of novelty, that this miserable performance, deserving neither the name of a drama by its poetry, nor of an opera by its music, sustained 24 representations, and the second year 11.

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

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

The first truly great singer who appeared on the stage of Britain was Cavalier Niccolino Grimaldi, commonly known by the name of Niccolini. He was a Neapolitan; and though a beautiful singer indeed, was still more eminent as an actor. In the Tatler, see also No. 115, the elegance and propriety of his action are Spectator, particularly described*. Recently before his appearance, Valentin Urban, and a female singer called the Baroness, Baroness arrived. Margarita del'Epini, who afterwards married Dr Pepusch, had been in this country some time before.

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

The year 1710 is distinguished in the annals of music by the arrival in Britain of George Frederic 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 100l., 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 1729, 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, then king of Poland. Here Handel engaged Senesino-Berenstadt, Boschi, and the Duranstanti.

In the 1723, the celebrated Francesca Cozzoni 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 Hasse, 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 singer. 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 Senesino, 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 Signior Bernacchi, Signora Merighi, Signora Strada, Signior Anibale Pio Fabri, his wife, Signora Bertoldi, and John Godfrid Reimschneider.

The sacred musical drama, or oratorio, was invented early in the 14th century. Every nation in Europe seems first to have had recourse to religious subjects for its dramatic exhibitions. The oratorios had been common in Italy during the last century. They had never been publicly introduced in England, till Handel, stimulated by the rivalryship 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 Senesino; Senesino 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 Senesino, 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 Hasse, as well as other eminent professors, 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 singer seems to have transcended the limit 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, Senesino, 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.

After a fruitless attempt by Heidegger, the coadjutor of Handel in the conduct of the opera, and patience 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 expense of Mr Tyers, proprietor of those gardens.

The next year (1739) Handel carried on oratorios at the Haymarket, as the opera there was suspended. The earl of Middlesex now undertook the troublesome office of impresario of the Italian opera. He engaged the King's theatre, with a band of singers from the continent almost entirely new. Calluppi 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 Calluppi, was exhibited, which surpassed in musical merit all the comic operas performed in England till the *Bicona Figliuola*. 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 Manzoli, 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 some time before, and was now returned much improved, performed in the station of second man to Manzoli.

Gaetano Guadagni made a great figure at this time. He had been in this country early in life (1748), as Guadagni, serious man in a burlesque 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 remembered his voice when formerly in England were now disappointed: It was comparatively thin and feeble: He had now changed it to a soprano, and extended its compass from six or seven notes to fourteen or fifteen. The music he sang was the most simple imaginable; a few notes with frequent pauses, and opportunities of being liberated from the composer and the band, were all he required. In these effusions, seemingly extemporaneous, he displayed the native power of melody unaided by harmony or even by unisonous accompaniment: The pleasure he communicated proceeded principally from his artful manner of diminishing the tones of his voice, like the dying notes of the Æolian 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 ascendant over music by the superior talents of Mademoiselle Heinei, whose grace and execution were so perfect as to eclipse all other excellence.

In the first opera performed this season (*Lucco Vero*) appeared Miss Cecilia Davies, known in Italy by the name of L'Inglesina. 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 slurredness of the French cadence. The flexibility of her throat rendered her execution equal to the most rapid divisions.

Next season introduced Venanzio Ravignini, 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.

The season 1775 and 1776 was rendered memorable by the arrival of the celebrated Caterina Gabrielli, styled early in life La Cucchetina, 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.

About the time of which we have been treating, the proprietors of the Pantheon ventured to engage Aguari at the enormous salary of 100l. per night, for singing two songs only: Lucrezia Aguari 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.

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.

After the departure of Aguari 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 Roman singers at the opera in London were Francesco Roncaglia and Francesca Danze, afterwards Madame Le Brun.

Roncaglia possessed a sweet toned voice; but of the three great requisites of a complete stage singer, pathos, grace, and execution, which the Italians call cantabile, graciosia, and bravura, he could lay claim only to the second. His voice, a voce de camera, when confined to the graciosia 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 Gasparo 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 Gain, 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'Ainé, 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 sang, 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 Theodore, the Coulons, the Hillingsburgs; while the slighted singers 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 manner in which the birth and genius of Handel were celebrated in Westminster Abbey and the Pantheon, by five performances of pieces selected from his own works, and executed by a band of more than 500 voices and instruments, in the presence and under the immediate auspices of their majesties and the first personages of the kingdom. The commemoration of Handel has been since established as an annual musical festival for charitable purposes; in which the number of performers and the perfection of the performances have continued to increase. In 1785 the band, vocal and instrumental, amounted to 616; in 1786 to 741; in 1787 to 806; 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.

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 ecstasy and rapture.

In 1786 arrived Giovanni Rubinelli. 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.

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

This year arrived Signor Luigi Marchesi, a singer whose talents have been the subject of praise and admiration on every great theatre of Europe. Marchesi's style of singing 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.

The three greatest Italian singers of these times were certainly Pacchierotti, Rubinelli, 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 Rubinelli's voice, the fulness, steadiness, and majesty, the accuracy of his intonations, his judicious graces: Of Marchesi's voice, the elegance and flexibility, his grandeur in recitative, and his boundless fancy and embellishments.—Having mentioned Dr Burney, we are in justice bound to acknowledge the aid we have derived from his history; a work which we greatly prefer to every other modern production on the subject.

During the latter part of the 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 Prince Lobkowitz, as eminent dilettanti of modern times.

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, Favorite Clegg, Clarke, and Festing, on the violin; Kyteh musicians, 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, Roseingrave, Green, Robinson, Magnus, Jack James, and the blind Stanley, who seems to have been preferred. The favourite playhouse singer was Salway; and at concerts Mountier of Chichester.

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

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

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

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

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

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

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 judgment 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 Crosdill, 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 viol da gamba, that remnant of the old chest 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 viol 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, Lolle, came to England in 1785. Such was his caprice, that he was seldom heard; and so eccentric was his style and composition, that by many he was regarded as a madman. He was, however, during his lucid intervals a very great and expressive performer in the serious style.

Mrs Billington, after distinguishing herself in childhood as a neat and expressive performer on the pianoforte, appeared all at once in 1786 as a sweet and captivating singer. In emulation of 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 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 Grassini 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 she 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 Grassini.—This eminent performer is a native of Sinigaglia in Italy, where her father was a singer of the comic order.

She was educated in a convent. The virtuous impressions 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 singer 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.

Theoretical and Practical (c).

PRELIMINARY DISCOURSE.

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 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 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 throughout 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 anything 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 observations, 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 shun the appearance of affectation, we shall use the ordinary terms by which musical sensations, or the mediums by which they are conveyed, are generally denominated.

(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, 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 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.

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.

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 traditionary manner through the Roman provinces from a more remote period of antiquity.

(1) See M. Rameau's letter upon this subject, Merc. de Mai, 1752. scribed 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 these 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 sought in the mixture and protraction of tones produced by a sonorous body; persuaded as we are, that M. Rameau was under no necessity of paying the least regard to these proportions, which we believe to be not only useless, but even, if we may venture to say so, fallacious when applied to the theory of music. In short, though the relations produced by the octave, the fifth, and the third, &c. were quite different from what they are; though in these chords we should neither remark any progression nor any law; though they should be incommensurable one with another; the protracted tone of the 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 in vain to expect what is called demonstration: it is much to have reduced the principal facts to a consistent and connected system; to have deduced them from one simple experiment; and to have established upon this foundation the most common and essential rules of the musical art. But 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 contiguity, 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 recognise 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 conductress 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 Rameau's to reject this principle, because certain phenomena appear to be deduced from it with less success than others. It is only necessary to conclude from this, either that by future scrutinies means may be found for reducing counted for these phenomena to this principle; or that harmony all the phenomena of music 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 some other is only a branch; or, lastly, that we ought not perhaps to attempt the reduction of the whole science of music to one and the same principle; which, however, is the natural effect of an impatience so frequent even among philosophers themselves, which induces them to take a part for the whole, and to judge of objects in their full extent by the greatest number of their appearances.

In those sciences which are called physico-mathematical (and amongst this number perhaps the science of sounds may be placed), there are some phenomena which depend only upon one single principle and one single experiment: there are others which necessarily suppose a greater number both of experiments and principles, whose combination is indispensable in forming an exact and complete system; and music perhaps is in this last case. It is for this reason, that whilst we bestow on M. Rameau all due praise, we should not at the same time neglect to stimulate the learned in their endeavours to carry them still to higher degrees of perfection, by adding, if it is possible, such improvements as may be wanting to consummate the science.

Whatever the result of their efforts may be, the reputation of this intelligent artist has nothing to fear: he will still have the advantage of being the first who rendered music a science worthy of philosophical attention; 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 Preliminary Discourse 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 an information, of which in composing this article we were ignorant: M. Romien, a member of the Royal Society at Montpelier, had presented to that society in the very 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 judgment 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

(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 sound unison with its lowest generator; from the fourth, one which is an octave lower than the highest of its generators; from the third major, one which is an octave lower than its lowest; and from the sixth minor (whose highest note forms an octave with the lowest in the third formerly mentioned) will be produced a sound lower by a double octave than the highest of the lesser sixth; from the third minor, one which is double the distance of a greater third from its lowest; but from the sixth major (whose highest note makes an octave to the lowest in the third minor) will be produced a sound only lower by double the quantity of a greater third than the highest; from the second major, a sound lower by a double octave than the lowest; from a second minor, a sound lower by triple the quantity of a third major than the highest; from the interval of a diatonic or greater semitone, a sound lower by a triple octave than the highest; from that of a minor or chromatic semitone, a sound lower by the quantity of a fifth four times multiplied than the lowest, &c. &c.

But that these musical phenomena may be tried by experiments proper to ascertain them, two hautboys tuned with scrupulous exactness must be procured, whilst the musicians are placed at the distance of some paces one from the other, and the hearers in the middle. The violin will likewise give the same chords, but they will be less distinctly perceived, and the experiment more fallacious, because the vibrations of other strings may be supposed to enter into it.

If our English reader should be curious to examine these experiments and the deductions made from them in the theory of music, he will find them clearly explained and illustrated in a treatise called Principles and Power of Harmony, printed at London in the year 1771. 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 inappreciable 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 fond vague and unsatisfactory; much less is it their province to exhaust their powers in vain attempts to cal conclude above their sphere into a region still more remote, less 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 judgments? Besides, why should certain chords which are extremely pleasing in themselves, such as the fifth, lose almost nothing of the pleasure which they give us, when they are altered, and of consequence when the simplicity of their relations are destroyed; whilst other chords, which are likewise extremely agreeable, such as the third, become harsh almost by the smallest alteration; nay, whilst the most perfect and the most agreeable of all chords, the octave, cannot suffer the most inconsiderable change? Let us in sincerity confess our ignorance concerning the genuine causes of these effects (h). The meta-

(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... physical conjectures concerning the acoustic organs are probably in the same predicament with those which are formed concerning the organs of vision, if one may speak so, in which philosophers have even till now made such inconsiderable progress, and in all likelihood will not be surpassed by their successors.

Since the theory of music, even to those who confine themselves within its limits, implies questions from which every wise musician will abstain; with much greater reason should they avoid idle excursions beyond the boundaries of that theory, and endeavours to investigate between music and the other sciences chimerical relations which have no foundation in nature. The singular opinions advanced upon this subject by some even of the most celebrated musicians, deserve not to be rescued from oblivion, nor refuted; and ought only to be regarded as a new proof how far men of genius may 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 harmony may be deduced from one single experiment; Preliminary Discourse for which, if we may speak so, preceding artists have been under the 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 defined the technical terms most frequently used in this treatise; 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 singer 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. believing all this arithmetic necessary to form an artist. Calculations may indeed facilitate the understanding of certain points in the theory, as of the relations between the different notes in the gammut and of the temperament; but the calculations necessary for treating of these points are so simple, and 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.

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.

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 number of objects and precepts, we have transferred to the notes in the second part several rules and observations which are less frequently put in practice, which perhaps it may be proper to omit till the treatise is read a second time, when the reader is well acquainted with the essential and fundamental rules explained in it.

This second part 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 composition, and especially those which direct the rules of composition of music in several parts, and which, being composition not less severe and indispensable, may be chiefly acquired by practice, by studying the most approved models, in the assistance of a proper master, but above all by bentenary 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 explication 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 mistress of explained in this treatise? Here can only be learned musical composition 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.

I. 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.

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. A single chord is...

(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, 1800; 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.

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 whose ear or voice is not extremely false naturally modulates. The following observations will occur to us in singing this scale.

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 F, &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 (s).

5. In general, the interval between two sounds is proportionally greater, as one of these sounds is higher or lower with relation to the other: but it is necessary to observe, that two sounds may be equally high, or low, though unequal in their force. The string of a violin touched with a bow produces always a sound 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 the intervals between C and D, between D and E, between E and F, 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 recognised by every one: the reason for it shall be given in the sequel; in the mean time every one may ascertain its reality by the assistance of an experiment.

(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; insomuch, 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, 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. 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, and A and B, are tones.

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

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

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.

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

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

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

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.

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

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

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

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

And in short, an interval consisting of five tones and two semitones, as from C to e' 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.

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

11. If two sounds form between them any interval, whatever it be, we say, that the highest when ascending is in that interval with relation to the lowest; and when descending, we pronounce the lowest in the same interval with relation to the highest. Thus in the third minor, E, G, where E is the lowest and G the highest sound, G is a third minor from E ascending, and E is a 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. 2. 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 what 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 fifth, and twelfth &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.

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

IV.

(*) 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,

1st. 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.

2ndly. 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.

3rdly. 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, while the other only completes one; and a string which is only the fifth part of another, will perform five vibrations in the same time which is occupied by the other in one.

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

It is for that reason, that if we represent any sound whatever by 1, one may represent the octave above by 2; that is to say, by the number of vibrations formed by the string which produces the octave, whilst the longest string only vibrates once; in the same manner we may represent the twelfth above the sound 1 by 3, the seventeenth IV. What is meant by Sharps and Flats.

15. It is plain that one may imagine the five tones which enter into the scale, as divided each into two semitones; thus one may advance from 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 ♯: thus C ♯ 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, ♭: thus A ♭ signifies A flat, or A depressed by a semitone.

V. What is meant by Consonances and Dissonances.

16. A chord composed of sounds whose union or coalescence pleases the ear is called consonance; and the sounds which form this chord are said to be consonant one with relation to the other. The reason of this denomination is that a chord is found more perfect, as the sounds which form it coalesce more closely among themselves.

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

18. A number of sounds simultaneously produced whose union is 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 C D, C B, or F B, &c. simultaneously heard, form a dissonance. See 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.

PART I. THEORY OF HARMONY.

CHAP. I. Preliminary and Fundamental Experiments.

EXPERIMENT I.

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

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

---

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 denote 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 to than compare among themselves the number of vibrations which are formed in a given time by the strings that produce these sounds.

(a) Since the octave above the sound 1 is 2, the octave below the same sound shall be ½; 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.

It is for that reason that if any sound whatever, for instance C, is denominated

| Its octave above will be | 2 | |-------------------------|---| | Its double octave above | 4 | | Its triple octave above | 8 | | In the same manner its octave below will be | ½ | | Its double octave below | ¼ | | Its triple octave below | ⅛ |

And so of the rest.

| Its twelfth above | 3 | |------------------|---| | Its twelfth below | ⅓ | | Its 17th major above | 5 | | Its 17th major below | ⅕ |

The fifth then above the sound 1 being the octave beneath the twelfth, shall be, as we have immediately observed, 21. The principal sound is called the generator*, and the two other sounds which it produces, and with which it is accompanied, are, inclusive of its octave, called its harmonics†.

Experiment II.

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

Let it be supposed that any person has an inclination to sing a tune, and having at first begun this air

Vol. XIV. Part II.

served, \( \frac{3}{2} \), which signifies that this string performs \( \frac{3}{2} \) vibrations; that is to say, one vibration and a half during a single vibration of the string which gives the sound \( r \).

To obtain the fourth above the sound \( r \), we must take the twelfth below that sound, 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 \( r \) is \( \frac{3}{2} \), it follows that the double octave above this twelfth, that is to say, the fourth from the sound \( r \) in ascending, will be \( \frac{3}{2} \) multiplied by \( 4 \), or \( \frac{6}{2} \).

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

The third major of a sound, for instance the third major \( E \), from the sound \( C \), and its fifth \( G \), form between them a third minor \( E, G \); now \( E \) is \( \frac{3}{2} \), and \( G \) \( \frac{5}{4} \), 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 \( \frac{3}{4} \) to the fraction \( \frac{5}{4} \).

To determine this relation, it is necessary to remark, that \( \frac{3}{4} \) are the same thing with \( \frac{1}{2} \), and that \( \frac{1}{2} \) are the same thing with \( \frac{3}{2} \); so that \( \frac{3}{4} \) shall be to \( \frac{1}{2} \) in the same relation as \( \frac{3}{2} \) to \( \frac{1}{2} \); that is to say, in the same relation as \( 10 \) to \( 12 \), or as \( 5 \) to \( 6 \). If, then, two sounds form between themselves a third minor, and that the first is represented by \( 5 \), the second shall be expressed by \( 6 \); or, what is the same thing, if the first is represented by \( 1 \), the second shall be expressed by \( \frac{6}{5} \).

Thus the third minor, an harmonic sound which is even found in the protracted and coalescent tones of a sonorous body between the sound \( E \) and \( G \), an harmonic of the principal sound, may be expressed by the fraction \( \frac{6}{5} \).

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

Such is the manner in which we may compare two sounds one with another whose numerical value is known.

We shall now show the manner how the numerical expression of a sound may be obtained, when the relation which it ought to have with another sound is known whose numerical expression is given.

Let us suppose, for example, that the third major of the fifth \( \frac{3}{4} \) is sought. That third major ought to be, by what has been shown above, the \( \frac{3}{4} \) of the fifth; for the third major of any sound whatever is the \( \frac{3}{4} \) of that sound. We must then look for a fraction which expresses the \( \frac{3}{4} \) of \( \frac{3}{4} \); which is done by multiplying the numerators and denominators of both fractions one by the other, from whence results the new fraction \( \frac{9}{16} \). It will likewise be found that the fifth of the fifth is \( \frac{3}{4} \), because the fifth of the fifth is the \( \frac{3}{4} \) of \( \frac{3}{4} \).

Thus far we have only treated of fifths, fourths, thirds major and minor, in ascending; now it is extremely easy to find by the same rules the fifths, fourths, thirds major and minor in descending. For suppose \( C \) equal to \( 1 \), we have seen that its fifth, its fourth, its third, its major and minor in ascending, are \( \frac{3}{2}, \frac{4}{3}, \frac{5}{4}, \frac{6}{5} \). 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 \( \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6} \).

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

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 proportioned 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; 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 it is evident that the third from C to E b is minor; nor and such is the origin of that mode which we call minor (s).

32. The most perfect chords then are, 1. All chords related one to another, as C, E, G, 'c', consisting of any sound, of its third major, of its fifth, and of its chords, octave. 2. All chords related one to another, as C, E b, G, 'c', consisting of any sound, 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 F 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. Chap. III. Of the Succession by Fifths, and of the Laws which it Observes.

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 bass by thirds, deduced from the two seventeenth parts, 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 bases 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:

\[ E\sharp, B\flat, F, C, G, D, A, \&c. \]

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

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

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, 'e', and D, F\(\sharp\), 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.

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 harmonies of each of these three sounds, that is to say, Harmony, 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 regarded as representing the mode of C. One may likewise take the series of fifths, or fundamental bass, of fifths, C, G, D, as representing the mode of G; in the same manner B\(\flat\), 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 mode, and are called its two adjuncts.

41. It is then, in some measure, indifferent to the ear whether a transition be made to the one or to the other of these adjuncts, since each of them has equally two sounds in common with the principal mode. Yet it seems that the mode of G seems a little more eligible: for G is heard amongst the harmonics of C, and of consequence is 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 Dominant 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 having passed from the mode of C to that of G, one may thence proceed to the mode of D. And on how to be the other hand, having passed from the mode of C to managed, that of F we may then pass to the mode of B\(\flat\). 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 (v) 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 Theory of form this modulation, or this fundamental bass, by Harmony, fifth:

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

45. Each of the sounds which forms this modulation brings necessarily along with itself its third major, its fifth, and its octave; insomuch 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,

G, C, G, C, F, C, F,

gives the following diatonic series,

B, c, d, e, f, g, a;

which is precisely the diatonic scale of the Greeks. We are ignorant upon what principles they had formed this scale; but it may be sensibly perceived, that that series arises from the bass G, C, G, C, F, C, F; and that of consequence this bass is justly called fundamental, as being the real primitive modulation, that which conducts the ear, and which it feels to be implied in the diatonic modulation, B, c, d, e, f, g, a' (x).

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

In the modulation B, c, d, e, f, g, a', the sounds d' and f' form between themselves a third minor, which Harmony, is not so perfectly true as that between c' and g' (y). 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.

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

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

the use of the word phrase when transferred from language to that art, we have thought proper to insert the definition of Rousseau.

A phrase, according to him, is in melody a series of modulations, or in harmony a succession of chords, which form without interruption a sense more or less complete, and which terminates 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 \(\frac{3}{2}\) and \(\frac{4}{3}\); from whence it follows,

1. That 'c' in the scale is the octave of C in the bass; that is to say, 2. 2. That 'b' is the third major of G; that is to say \(\frac{5}{4}\) of \(\frac{3}{2}\) (note q), and of consequence \(\frac{15}{8}\). 3. That 'd' is the fifth of G; that is to say \(\frac{5}{4}\) of \(\frac{3}{2}\), and of consequence \(\frac{15}{8}\). 4. That 'e' is the third major of the octave of C, and of consequence the double of \(\frac{5}{4}\); that is to say, \(\frac{15}{8}\). 5. That 'f' is the double octave of F of the bass, and consequently \(\frac{15}{8}\). 6. That 'g' of the scale is the octave of G of the bass, and consequently 3. 7. That 'a' in the scale is the third major of 'f' of the scale; that is to say, \(\frac{5}{4}\) of \(\frac{15}{8}\), or \(\frac{15}{8}\).

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

| Diatonic Scale | Fundamental | Bass | |----------------|-------------|------| | B, c, d, e, f, g, a | G, C, G, C, F, C, F | \(\frac{1}{2}\), \(\frac{3}{2}\), \(\frac{5}{4}\), \(\frac{4}{3}\), \(\frac{5}{4}\), \(\frac{3}{2}\), \(\frac{1}{2}\) |

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

\[ \begin{align*} \text{B} & : \text{c} : \text{d} : \text{e} : \text{f} : \text{g} : \text{a} \\ & = \frac{1}{2} : \frac{3}{2} : \frac{5}{4} : \frac{4}{3} : \frac{5}{4} : \frac{3}{2} : \frac{1}{2} \end{align*} \]

(y) In order to compare d' with f', we need only compare \(\frac{5}{4}\) with \(\frac{3}{2}\); 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. In reality, in order that the sound 'b' may succeed immediately in the scale to the sound '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 sound '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 proximabonomena, 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 c, f, g, a'. These two tetrachords are exactly similar; for from c' to f' there is the same interval as from B to c', from f' to g' the same as from c' 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 'c', 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 'c, 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, Theory of which is evident; for the third major from 'f' to 'a' is Harmony, 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 Another is absolutely perfect in each tetrachord taken by itself; but that there is some alteration in passing from the one tetrachord to the other. This is a new reason for distinguishing the scale into these two tetra-chords.

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 'c, 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.; Greater and the lesser †, from 'd' to 'e', from 'g' to 'a', &c. Lesser

**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, 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.

56. Hence

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

(AA) The proportion of 'c' to 'c' is as \( \frac{3}{4} \) to 1 , or as 5 to 4 , which is a true third major; that from 'd' to 'b' is as \( \frac{3}{4} \) to \( \frac{7}{8} \); 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 \( \frac{3}{4} \) to \( \frac{7}{8} \); 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 \( \frac{3}{4} \) to 1 , or as 9 to 8 ; that of 'e' to 'd' is as \( \frac{4}{5} \) to \( \frac{3}{4} \), that is to say, as 40 to 36 , or as 10 to 9 : now \( \frac{3}{4} \) is less removed from than \( \frac{4}{5} \); 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 \( \frac{3}{4} \) bear to \( \frac{4}{5} \), 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 harmonical, and the same chord when it suffers alteration 'd', 'f', of which we have taken notice in the scale (note r); 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... 56. 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.

57. For this reason the note 'g' is twice repeated in immediate succession in this scale; once as the fifth of 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 sound 'f'. There is no person who does not perceive this whilst he himself sings the scale.

58. The scale of the moderns, then, may be considered as consisting of two tetrachords, disjunctive indeed, but perfectly similar one to the other, '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.

59. 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'; insomuch, that the three tones 'f, g, a, b,' are supposed to belong to two different tetrachords.

60. It ought not then any longer to surprise us, Change of mode 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 sings pauses in the same mode, the fourth sound above the first note will never be higher than a semitone above the tones succeeding '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,' 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 form true with the third major from 'f' to 'a,' but each of these consonant sounds forms otherwise consonances perfectly true, with their corresponding sounds in the fundamental bass.

62. The thirds 'a,' c, 'f a,' 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; and this likewise happens from the introduction of the mode of G into the fundamental bass.

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 $\frac{6}{7}$, its fifth will be expressed by $\frac{3}{7}$; so that the scale will be numerically signified thus:

$$\begin{array}{cccccc} 1 & \frac{2}{3} & \frac{4}{5} & \frac{5}{6} & \frac{7}{8} & 2 \\ c, & d, & e, & f, & g, & a, & b, & c, \end{array}$$

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 $\frac{7}{8}$ to $\frac{5}{6}$, that is to say, as 81 to 80; these two 'a's then will 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, 'f a' and 'a' c; and likewise a fifth altered, 'a' c 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 sound c, and it is in reality from that sound that we ought to begin; it is from this that all the others naturally arise, and upon this that they depend; nay, if we 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 sound C is here the genuine guide of the ear, that if, before we modulate the sound 'c', we should should be the interval of a fifth; so that the D in the Theory of first scale will be a true fourth below the G of the same Harmony.

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 in 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.

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', 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 harpsichord 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.

The A considered as the fifth of D is $\frac{5}{7}$, and the fourth beneath this A will constitute $\frac{4}{5}$ of $\frac{1}{2}$; that is to say, $\frac{5}{7} \times \frac{4}{5} = \frac{2}{3}$; 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 $\frac{3}{4}$; these two E's then are between themselves in the proportion of $8:1$ to $8:1$; thus it is impossible that E should be at the same time a perfect third major from C, and a true fourth beneath B.

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 $\frac{3}{4}$, D $\frac{5}{7}$, E $\frac{4}{5}$, &c. and so of the rest till you arrive at B, which will be found $\frac{2}{3}$. 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 $\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$, which is evidently greater than C represented by unity. This last fraction $\frac{2}{3} \times \frac{1}{2} = \frac{1}{3}$ 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 sound C, though upon the harpsichord, B and C are identical. This fraction rises above unity by $\frac{1}{3}$, that is, by about $\frac{1}{3}$; 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 $\frac{1}{3}$.

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 $\frac{3}{4}$, G to $\frac{5}{7}$, and B to $\frac{4}{5}$, whose octave below is $\frac{2}{3}$; from whence it appears, that this last B is less than unity (that is to say than C), by $\frac{1}{3}$, or by $\frac{1}{3}$, 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 $\frac{2}{3}$ is to $\frac{3}{4}$: that is to say, in multiplying by 524288, as 125 multiplied by 4996 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 $\frac{1}{3}$.

Moreover, if, after having found the G equal to $\frac{3}{4}$, 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 $\frac{2}{3}$; its difference, then, from unity, or, in other words, from C, is $\frac{1}{3}$, that is to say, about $\frac{1}{3}$; a comma still less than any of the preceding, and which the Greeks have called apotome minor. Theory of not to be different from the octave above C: for every Harmony. 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×, e×, 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, ii; after having found E equal to \( \frac{4}{5} \) 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 \( \frac{3}{4} \times \frac{5}{4} \), and which will not differ from unity but by about \( \frac{1}{5} \), 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, F×, &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 twelves 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.

| C | C× | D | D× | E | F | F× | G | G× | |---|----|---|----|---|---|----|---|----| | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) | \( \sqrt{\frac{2}{3}} \) |

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 \( \frac{4}{5} \), ought to be diminished by about \( \frac{1}{5} \) of \( \frac{4}{5} \); that is to say, by \( \frac{1}{5} \), a quantity almost inconceivably 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 \( \frac{1}{5} \); 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, C×, 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 it the third be more altered than the fifth, it is a consequence of the difference which we find between the degrees of perfection in these intervals; a difference with which, if we may speak so, the temperament proposed conforms itself. Thus this diversity of alteration is rather advantageous than inconvenient. In this, then, the theory of temperament consists; but as it would be difficult in practice to tune a harpsichord 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.

Take any key of the harpsichord 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 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 the fifth, may be identical with the sound C, with which you began, or at least the octave of that sound perfectly just: it will be necessary then to try if this C, or its octave, forms a just fifth with the last sound E or F, which has been already tuned. If this be the case, we may be certain that the harpsichord is properly tuned. But if this last fifth be not true, in this case it will be too sharp, and it is an indication that the other fifths have been too much diminished, or at least some of them; or it will be too flat, and consequently discover that they have not been sufficiently diminished. We must then begin and proceed as formerly, till we find the last fifth in tune of itself, and without our immediate interposition (11).

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(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 harpsichord. 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; insomuch, that upon a harpsichord 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 anything. 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 judgment, 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 harpsichord.

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 Harmony, one of the scales shall be tuned; nothing is necessary but to tune with the greatest possible exactness their octaves in the other scales, and the harpsichord shall be well tuned.

We have given this rule for temperament from M. Rameau; and it belongs only to disinterested artists to judge of it. However this question be determined, and whatever kind of temperament may be received, the 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; insomuch 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 sound as might offend!

In a fundamental bass whose procedure is by fifths, there always is, or always may be, a repose, or imperfect crisis, in which the mind acquiesces in its transition what and 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.).

Amongst absolute reposes, there are some, if perfect 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 G 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.

We may still add, that what is commonly called Cadence 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 advanced 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 Repose, in Rousseau's Musical Dictionary. In the first case, the 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 presages, a repose, either present or impending, in the fundamental bass (ll.).

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.

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.

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.

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 convenience, another chord, which is likewise minor and exactly similar to the former, of which all the notes are found in the scale.

79. The scale affords us three chords of this kind, viz. 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 diatonic scale of the minor mode. We might in the same manner have chosen any other minor chord; and it is Harmony, only, as we have said, for greater ease and convenience that we fix upon this.

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

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 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,

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 the third rises to the fundamental sound A.

83. It is true, that, in causing E to imply its third minor G, one might also rise to A by a diatonic progression. 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.

84. We may remark this first difference between the scales

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 'e' 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 not the only discrimination which may be found between the scales of the two modes.

(ll.) 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,

\[A, E, A, D, A, E, B, E, A,\]

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 modes greater than those of the major.

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

89. It is not the same case in descending. For \(E\), different in the fifth of the generator, ought not to imply the third descending 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'.

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,

\[a, g, f, e, e, d, c', B, A.\]

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 Harmony '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, in descending, ('a, g, f, e, d, c', B, A,) 'g' may be regarded simply as a note of passage, merely added to give yet another sweetness to the modulation, and as a diatonic gradation factory, 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 what 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 \(C\).

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(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 'g', 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. 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, e', 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.

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, E, G, 'c', has two sounds, C and G, in common with the perfect major chord C, E, G, 'c'. Nor is there anything more common than a transition from the major mode of C to the minor mode, or from the minor to the major.

**CHAP. XI. Of Dissonance.**

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.

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 Harmony 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.

Let us now see what may be added to the harmony of F, A, C, of the fifth F below the generator, to treat and distinguish this harmony from that of the generator continued.

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 mode should be determined; but this introduction of G, in the chord F, A, C, would produce two seconds in succession, F G, G A, that is to say, 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.

For this reason, instead of G, we shall take its chord of fifth 'd', the sound that approaches it nearest, and the great 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.

The fifth G, in rising above the generator, gives a chord entirely consisting of thirds ascending from G, of dissonances 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.

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.**

It is evident by the resemblance of sounds to Account of their octaves, that the chord F, A, 'c', 'd', is in effect the double same as the chord D, F, A, 'c', taken inversely employment, that the inverse of the chord C, A, F, D, has been found (art. 98.) in descending by thirds, from the generator C (pp.).

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(oo) 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 whose 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.

(pp) 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... 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 Harmony, by M. Rameau its double office or employment+. This Double Employment is the source of one of the finest varieties in harmony, and we shall see in the following chapter the advantages what, and why so.

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 primitive-ly composed of two similar tetrachords, one in the chord 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 accord-

ing

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 sound in the chord of the sub-dominant. 2. Because that without having recourse, with M. Rameau, to harmonical and arithmetical progressions, of which the consideration appears to us quite foreign to the question, we have found a probable and even a satisfactory reason for adding the note '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', d, e, f, g, a, b', 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 bass 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'. 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 a', which will exhibit the double employment of dissonances in the minor mode.

One may employ this chord B d f a', 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 a, 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.

Hence the minor mode is susceptible of a much greater number of varieties than the major: the major mode is found 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.**

The dissonance added to the chord of the dominant and of the sub-dominant, 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, Theory of Harmony may not still be carried farther.

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.

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:

According to what has been said above, if we would add a seventh to the chord C E G, to make last describe a dominant of C, one can add nothing but Bb; and ed admission in this case C E G Bb would be the chord of the tonic ble, and 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 Bb 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 eb'; in which one may substitute for "eb", "e" natural, to preserve the impression of the mode of C, or 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 "e" of the same chord. All together then seem to allow the artist to introduce the note B and "e" into these two chords (rr).

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 continued and explained.

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 Eb. It is the same case with several other chords, such as B D F A X, B D X 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 X; and this D X 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. Theory of the dominant and of the sub-dominant in the minor Harmony 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', f, a'. Now, if we should suffer this chord to remain thus, it would be disagreeable to the ear, by its multiplicity of dissonances, D 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 D 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 (ss).

117. Since, then, from the chord E G B d', we may pass to the perfect A C e a', and vice versa, we may in like manner pass from the chord G B d' to the chord A C e a', 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 Discords.**

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. 102.) which is not composed of a third major followed by two thirds minor, the dissonance which this chord pertains forms ought to stand as a consonance in the chord which precedes it.

This is what we call a prepared dissonance.

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 a', 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 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 make in some measure, as much the character of an harmonic sound as may be possible, it is necessary that this in the 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 is the chord of the tonic dominant which ought to be the dissonance of the chord of the tonic dominant.

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(ss) We have seen (art. 109.) that the chord B d f a', 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 a' may be considered as composed of the two chords F B d f', F A c d' of the dominant and of the sub-dominant of the major mode of their 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 this chord B d f a'. The chord B d f a', considered in this point of view, may be understood as belonging to the major mode of C upon certain occasions. 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 'e' 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).

First part, - 'f' 'e' Second, - 'd' 'c' Third, - B 'c' Fourth, - G G Fundamental bass, - G C

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

2° In every chord of the 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 DFA 'c', though it should even be considered as the inverse of FA '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 DFA '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 DFA 'c', to C E G 'c', it is necessary that DFA 'c' should in this case be understood as the inverse of FA 'c d'. Now the chord DFA 'c' can only be conceived as the inverse of FA 'c d', when this chord DFA 'c' precedes or immediately follows the C E G 'c'; in every other case the chord DFA 'c' is a primitive chord, formed from the perfect minor chord DFA, to which the dissonance 'c' was added, to take from D the character of a tonic. Thus the chord DFA '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', DFA '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', FA '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 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, the test of there is always, as we have formerly observed (chap. viii.), a repose more or less perfect from one sound to another; and of consequence there must likewise be a repose more or less perfect from one sound to another in the diatonic scale, which results from that bass.

It may be demonstrated by a very simple experiment, that the cause of a repose in melody is solely in the fundamental bass expressed or understood. Let any person sing these three notes '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 anything 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 e' 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 e' 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 cadence, like the double employment, only the double consists in a diatonic procedure of the bass ascending employment (chap. xii.). In effect, nothing hinders us to descendment of from the chord GB 'd f' to the chord CEGA 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 GB 'd f' to CEGA is the same thing as to rise from the chord GB 'd f' to the chord A 'c e g', in changing the chord of the sub-dominant CEGA 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 performing the fifth of the subsequent chord. For instance, in this case, the broken cadence GB 'd f', A 'c e g', the dissonance 'f' is resolved by descending diatonically upon the fifth 'e'.

136. There is another kind of cadence, called an interrupted cadence, where the dominant descends by a what, third to another dominant, instead of descending by a fifth upon the tonic, as in this succession of the bass dence. 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 sound 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 base C, E, G, A, the first two first sounds 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 (xx); 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 modulation 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 section minor tone 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 CF, 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 from the succession of thirds in ascending. The series of thirds minor in descending, CA, gives, C, Cb, the fundamental bass by thirds; 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 semitones, diatonic intervals, resulting from the succession of thirds (chap. v. and vi.), it comprehends the whole of the melody.

**CHAP. XIX. Of the Enharmonic Species.**

144. The two extremes, or highest and lowest notes, Diesis or C G, of the fundamental bass by thirds major CEG, give this modulation c' Bx; and these two sounds c'val, what is called the diesis, or enharmonic fourth* of a tone (3a), formed which* See Fourth of Tone.

(tt) In reality, C being supposed 1, as we have always supposed it, E is $\frac{4}{5}$ and $\frac{5}{6}$; now G being $\frac{2}{3}$, Gx then shall be to G as $\frac{5}{6}$ to $\frac{4}{5}$; that is to say, as 25 times 2 to 3 times 16: the proportion then of Gx 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 Fx by the interval of a minor semitone, the interval from E to Fx will be a minor tone. For let us suppose E to be 1, F will be $\frac{4}{5}$, and Fx will be $\frac{5}{6}$; that is to say, 25 times 16 divided by 24 times 15, or $\frac{5}{6}$; E then is to Fx as one is to $\frac{5}{6}$, 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, $\frac{5}{6}$ multiplied by $\frac{5}{6}$ gives $\frac{25}{36}$, which is greater than $\frac{4}{5}$, 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, à fortiori, two minor semitones would still give less.

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

(zy) A being $\frac{5}{6}$ Cx is $\frac{4}{5}$ of $\frac{5}{6}$; that is to say, $\frac{5}{6}$, and C is 1: the proportion then between C and Cx is that of 1 to $\frac{5}{6}$, or of 24 to 25.

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

(3a) Gx being $\frac{5}{6}$ and Bx being $\frac{4}{5}$ of $\frac{5}{6}$, we shall have Bx equal (note q) to $\frac{5}{6}$, and its octave below shall be $\frac{5}{6}$; an interval less than unity by about $\frac{1}{20}$ or $\frac{1}{10}$. It is plain then, from this fraction, that the Bx in question must be considerably lower than C. 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 \( \frac{3}{4} \), and its difference from unity being \( \frac{1}{4} \), the difference of this quarter tone from unity will be almost the fourth of \( \frac{1}{4} \); that is to say, \( \frac{1}{8} \).

2. The fourth of a tone minor; and as a tone minor, which is \( \frac{5}{6} \), differs from unity by \( \frac{1}{6} \), the fourth of a minor tone will differ from unity about \( \frac{1}{12} \).

3. One half of a semitone major; and as this semitone differs from unity by \( \frac{1}{12} \), one half of it will differ from unity about \( \frac{1}{24} \).

4. Finally, one half of a semitone minor, which differs from unity by \( \frac{1}{24} \): its half then will be \( \frac{1}{48} \).

The interval, then, which forms the enharmonic fourth of a tone, as it does not differ from unity but by \( \frac{1}{48} \), 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 cu) 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 \( \frac{1}{2} \), F will be \( \frac{3}{4} \); and \( F^+ \) \( \frac{5}{6} \): the proportion then between \( F^+ \) and F is that of \( \frac{3}{4} \) to \( \frac{5}{6} \) (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. Theory of ed as nothing, because it is inappreciable 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, e, d' in which the semitones from 'f' to 'e', and from 'e' to 'd', 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, C, C, we shall form this modulation 'c, b, e, c, e, e', 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 inappreciable 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 G, C, is susceptible of 20 different fundamental basses. Now the same fundamental bass, as may be seen in our second part, will afford several continued or thorough basses. How many means, of consequence, may be practised to vary the expression of the same modulation?

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,

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(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 3, and 'e' of the scale 4 of 3, that is 1/2; the proportion of 'f' to 'e' is as 2 to 1/2, or as 1 to 1/4. Now E of the bass being likewise 4 of 3, or 1/2; B of the bass is 1/2 of 3, and its third major D is 1/2 of 1/2, or 1/4 of 1/2; this third major, approximated as much as possible to 'e' in the scale by means of octaves, will be 1/2 of 1/2; 'e' then of the scale will be to 'd' which follows it, as 1/2 is to 1/2 of 1/2, that is to say, as 1 to 1/2. The semitones then from 'f' to 'e', and from 'e' to 'd', are both major.

(3 E) It is evident that 'c' is 1/2 (note Q), and that 'e' is 1/2; these two 'e's, then, are between themselves as 1/2 to 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 1/2, and C is 1/2 of 1/2, or 1/4 of 1/2; 'e' then is 1/2 of 1/2, the 'e' in the scale is likewise to the 'e' 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 PART II. PRINCIPLES AND RULES OF 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.

CHAP. I. Of the Different Names given to the same Interval.

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.

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 in descending.

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 G).

161. 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 has been called a second redundant, we likewise call redundant, the interval from C to G in ascending, a fifth redundant, what clant, or from B to E in descending, each of which intervals is composed of four tones (3 H).

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

163. For the same reason, an interval composed of seventh diminished, 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).

CHAP. II. Comparison of the Different Intervals.

165. If we sing c B in descending by a second, and afterwards C B in ascending by a seventh, these different 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.