The sense which the Greeks gave to this word in their music, is so much less easy to be determined, because, the word itself being originally a substantive proper, it has no radical words by which we might analyse it, to discover its etymology. In the ancient treatises which remain to us, harmony appears to be that department whose object is the agreeable succession of sounds, merely considered as high or low; in opposition to the two others called rhythmica and metrica, which have their principle in time and measure. This leaves our ideas concerning that aptitude of found vague and undetermined; nor can we fix them without studying for that purpose all the rules of the art; and even after we have done so, it will be very difficult to distinguish harmony from melody, unless we add to the last the ideas of rhythmus and measure; without which, in reality, no melody can have a distinguishing character: whereas harmony is characterised by its own nature, independent of all other quantities except the chords or intervals which compose it.

It appears by a passage of Nicomachus, and by others, that they likewise gave the name of harmony to the chord of an octave, and to concerts of voices and instruments, which performed in the distance of an octave one from the other, and which is more commonly called antiphone.

Harmony, according to the moderns, is a succession of chords agreeable to the laws of modulation. For a long time this harmony had no other principle but such rules as were almost arbitrary, or solely founded on the approbation of a practised ear, which decided concerning the agreeable or disagreeable succession of chords, and whose determinations were at last reduced to calculation. But Father Mersenne and M. Sauveur having found that every sound, however simple in appearance, was always accompanied with other sounds less sensible, which constitute with itself a perfect chord-major; with this experiment M. Rameau set out, and upon it formed the basis of his harmonic system, which he has extended to a great many volumes, and which at last M. D'Alembert has taken the trouble of explaining to the public.

Signior Tartini, taking his route from an experiment which is newer and more delicate, yet no less certain, has reached conclusions similar enough to those of Rameau, by pursuing a path whose direction seems quite opposite. According to M. Rameau, the treble is generated by the bass; Signior Tartini makes the bass result from the treble. One deduces harmony from melody, and the other supposes quite the contrary. To determine from which of the two schools the best performances are likely to proceed, no more is necessary than to investigate the end of the composer, and discover whether the air is made for the accompaniments, or the accompaniments for the air. At the word System in Rousseau's Musical Dictionary, is given a delineation of that published by Signior Tartini. Here he continues to speak of M. Rameau, whom he has followed through this whole work, as the artist of greatest authority in the country where he writes.

He thinks himself obliged, however, to declare, That this system, however ingenious it may be, is far from being founded upon nature; an affirmation which he incessantly repeats: "That it is only established upon analogies and congruities, which a man of invention may overturn to-morrow, by substituting others more natural: that, in short, of the experiments from whence he deduces it, one is detected fallacious, and the other will not yield him the consequences which he would extort from it." In reality, when this author took it in his head to dignify with the title of demonstration the reasoning upon which he established his theory, every one turned the arrogant pretence into ridicule. The Academy of Sciences loudly disapproved a title so ill founded, and so gratuitously assumed; and M. Elève, of the Royal Society at Montpellier, has shewn him, that even to begin with this proposition, That according to the law of nature, sounds are represented by their octaves, and that the octaves may be substituted for them, there was not any one thing demonstrated, or even firmly established, in his pretended demonstration." He returns to his system.

"The mechanical principle of resonance presents us with nothing but independent and solitary chords; it neither prescribes nor establishes their succession. Yet a regular succession is necessary; a dictionary of selected words is not an oration, nor a collection of legitimate chords a piece of music: there must be a meaning, there must be connections in music as well as in language: it is necessary that what has preceded should transmit something of its nature to what is subsequent, so that all the parts conjoined may form a whole, and be stamped with the genuine character of unity.

"Now, the complex sensation which results from a perfect chord must be resolved into the simple sensation of each particular sound which composes it, and into the sensation of each particular interval which forms it, ascertained by comparison one with another. Beyond this there is nothing sensible in any chord; from whence it follows, that it is only by the relation between sounds, and by the analogy between intervals, that the connexion now in question can be established; and this is the genuine, the only source, from whence flow all the laws of harmony and modulation. If, then, the whole of harmony were only formed by a succession of perfect chords-major, it would be sufficient to proceed by intervals similar to those which compose such a chord; for then some one or more sounds of the preceding chord being necessarily protracted in that which is subsequent, all the chords would be found sufficiently connected; and the harmony would, at least in this sense, be one.

"But besides that these successions must exclude all melody by excluding the diatonic series which forms its foundation, Harmony. foundation, it would not arrive at the real end of the art; because, as music is a system of meanings like a discourse, it ought, like a discourse, to have its periods, its phrases, its suspensions, its cadences, its punctuation of every kind; and because the uniformity of a harmonical procedure implies nothing of all this, diatonic procedures require that major and minor chords should be intermixed; and the necessity of dissonances has been felt in order to distinguish the phrases, and render the cadences sensible. Now, a connected series of perfect chords-major can neither be productive of perfect chords-minor nor of dissonances, nor can sensibly mark any musical phrase, and the punctuation must there be found entirely defective.

"M. Rameau being absolutely determined, in his system, to deduce from nature all the harmony practised among us, had recourse, for this effect, to another experiment of his own invention, of which I have formerly spoken, and which by a different arrangement is taken from the first. He pretended, that any simple sound whatever afforded in it multiplies a perfect minor or flat chord, of which it was the dominant or fifth, as it furnished a perfect chord-major by the vibration of its aliquot parts, of which it is the tonic or fundamental sound. He has affirmed as a certain fact, that a vocal string caused two others lower than itself to vibrate through their whole extent, yet without making them produce any sound, one to its twelfth major and the other to its seventeenth; and from this joined to the former fact, he has very ingeniously deduced not only the application of the minor mode and of dissonances in harmony, but the rules of harmonic phrases and of all modulation, such as they are found at the words Chord, Accompaniment, Fundamental Bass, Cadence, Dissonance, Modulation.

"But first (continues Rouffleau), the experiment is false. It is discovered, that the strings tuned beneath the fundamental sound do not entirely vibrate when this fundamental sound is given; but that they are divided in such a manner as to return its unison alone, which of consequence can have no harmonics below. It is moreover discovered, that the property of strings in dividing themselves, is not peculiar to those which are tuned by a twelfth and seventeenth below the principal sound; but that oscillations are likewise produced in the lower strings by all its multiples. Whence it follows, that, the intervals of the twelfth and seventeenth below not being singular phenomena of their kind, nothing can be concluded in favour of the perfect minor chord which they represent.

"Though the truth of this experiment were granted, even this would by no means remove the difficulty. If, as M. Rameau alleges, all harmony is derived from the resonance of sonorous bodies, it cannot then be derived only from the vibrations of such bodies as do not resound. In reality, it is an extraordinary theory, to deduce from bodies that do not resound the principles of harmony; and it is a position in natural philosophy no less strange, that a sonorous body should vibrate without resounding, as if sound itself were anything else but the air impelled by these vibrations. Moreover, sonorous bodies do not only produce, besides the principal sound, the other tones which with itself compose a perfect chord; but an infinite number of other sounds, formed by all the aliquot parts of the bodies in vibration, which do not enter into that perfect harmony. Why then should the former sounds produce consonances, and why should the latter not produce them, since all of them equally result from nature?

"Every sound exhibits a chord truly perfect, since it is composed of all its harmonics, and since it is by them that it becomes a sound. Yet these harmonics are not heard, and nothing is distinguished but a simple sound, unless it be exceedingly strong: whence it follows, that the only good harmony is an unison; and that, as soon as the consonances can be distinguished, the natural proportion being altered, the harmony has lost its purity.

"That alteration is in this case produced two different ways. First, by causing certain harmonics to resound, and not the others, the proportion of force which ought to prevail in all of them is altered, far producing the sensation of a single sound; whence the unity of nature is destroyed. By doubling these harmonics, an effect is exhibited similar to that which would be produced by suppressing all the others; for in that case we cannot doubt, but that, along with the generating sound, the tones of the other harmonics which were permitted to sound would be heard: whereas, in leaving all of them to their natural operations, they destroy one another, and conspire together in forming and strengthening the simple sensation of the principal sound. It is the same effect which the full sound of a stop in the organ produces, when, by successively removing the stopper or register, the third and fifth are permitted to sound with the principal; for then that fifth and third, which remained absorbed in the other sounds, are separately and disagreeably distinguished by the ear.

"Moreover, the harmonics which we cause to sound have other harmonics pertaining to themselves, which cannot be such to the fundamental sound. It is by these additional harmonics that the sounds which produce them are distinguished with a more sensible degree of harshness; and these very harmonics which thus render the chord perceptible, do not enter into its harmony. This is the reason why the most perfect chords are naturally displeasing to ears whose relish for harmony is not sufficiently formed; and I have no hesitation in thinking, that even the octave itself might be displeasing, if the mixture of male and female voices did not insure us to that interval from our infancy.

"With dissonance it is still worse, because, not only the harmonics of the sound by which the discord is produced, but even the sound itself, is excluded from the natural harmony of the fundamental; which is the cause why discord is always distinguished amongst all the other sounds in a manner shocking to the sense.

"Every key of an organ, with the stop fully opened, gives a perfect chord with its third major, which are not distinguished from the fundamental sound, if the hearer is not extremely attentive, and if he does not find the whole stop in succession; but these harmonic sounds are never observed in the fundamental, but on account of the prodigious noise, and by such a situation of the registers as may cause the pipes which produce the fundamental sound to conceal by their force the other sounds which produce these harmonics. Now, no person observes, nor can observe, this continual proportion in a concert; since, by the manner of inverting the harmony, its greatest force must in every instant be transferred from one part to another; which is not practicable, and would destroy the whole melody.

"When we play upon the organ, every key in the bass causes to resound the perfect chord-major; but because that bass is not always fundamental, and because the music is often modulated in a perfect minor chord, this perfect chord-major is rarely struck with the right hand; so that we hear the third minor with the major, the fifth with the triton, the seventh redundant with the octave, and a thousand other cacophonies, which, however, do not much disgust our ears, because habit renders them tractable: but it is not to be imagined that an ear naturally just would prove so patient of discords, when first exposed to the test of this harmony.

"M. Rameau pretends, that trebles composed with a certain degree of simplicity naturally suggest their own basses; and that any man having a just, though unpractised ear, would spontaneously sing that bass. This is the prejudice of a musician, refuted by universal experience. Not only would he, who has never heard either bass or harmony, be of himself incapable of finding either the bass or the harmony of M. Rameau, but they would be displeasing to him if he heard them, and he would greatly prefer the simple unison.

"When we consider, that, of all the people upon earth, who have all of them some kind of music and melody, the Europeans are the only people who have a harmony consisting of chords, and who are pleased with this mixture of sounds: when we consider that the world has endured for so many ages, whilst, of all the nations which cultivated the fine arts, not one has found out this harmony; that not one animal, not one bird, not one being in nature, produces any other chord but the unison, nor any other music but melody; that the eastern languages, so sonorous, so musical; that the ears of the Greeks, so delicate, so sensible, practised and cultivated with so much art, have never conducted this people, luxurious and enamoured of pleasure as they were, towards this harmony which we imagined so natural; that without it their music produced such astonishing effects; that with it ours is so impotent; that, in short, it was reserved for the people of the north, whose grog and callous organs of sensation are more affected with the noise and clamour of voices, than with the sweetness of accents and the melody of inflections, to make this grand discovery, and to vend it as the essential principle upon which all the rules of the art were founded; when, in short, attention is paid to all these observations, it is very difficult not to suspect that all our harmony is nothing but a Gothic and barbarous invention, which would never have entered into our minds, had we been truly sensible to the genuine beauties of art, and of that music which is unquestionably natural.

"M. Rameau affirms, however, that harmony is the source of the most powerful charms in music. But this notion is contradictory both to reason and to matter of fact. To fact it is contradictory, because, since the invention of counter-point, all the wonderful effects of music have ceased, and it has lost its whole force and energy. To which may be added, that such beauties as purely result from harmony are only perceived by the learned; that they affect none with transport but such as are deeply conversant in the art; whereas the real beauties of music, resulting from nature, ought to be, and certainly are, equally obvious to the adept and the novice. To reason it is contradictory; since harmony affords us no principle of imitation by which music, in forming images and expressing sentiments, can rise above its native excellence till it becomes in some measure dramatic or imitative, which is the highest pitch of elevation and energy to which the art can aspire; since all the pleasures which we can receive from the mere mechanical influence of sounds are extremely limited, and have very little power over the human heart."

Thus far we have heard M. Rousseau, in his observations on harmony, with patience; and we readily grant, that the system of harmony by M. Rameau is neither demontrated, nor capable of demonstration. But it will not follow, that any man of invention can so easily and so quickly subvert those aptitudes and analogies on which the system is founded. Every hypothesis is admitted to possess a degree of probability proportioned to the number of phenomena for which it offers a satisfactory solution. The first experiment of M. Rameau is, that every sonorous body, together with its principal sound and its octave, gives likewise its twelfth and seventeenth major above; which being approximated as much as possible, even to the chords immediately represented by them, return to the third, fifth, and octave, or, in other words, produce perfect harmony. This is what nature, when solicited, spontaneously gives; this is what the human ear, unprepared and uncultivated, imbibes with ineffable avidity and pleasure. Could any thing which claims a right to our attention and acceptance from nature, be imprest with more genuine or more legible signatures of her function than this? We do not contend for the truth of M. Rameau's second experiment. Nor is it necessary we should. The first, expanded and carried into all its consequences, resolves the phenomena of harmony in a manner sufficient to establish its authenticity and influence. The difficulties for which it affords no solution are too few and too trivial either to merit the regard of an artist, or a philosopher, as M. D'Alembert in his elements has clearly shewn. The facts with which M. Rousseau confronts this principle, the armies of multiplied harmonics generated in infinitum, which he draws up in formidable array against it, only show the thin partitions which sometimes may divide philosophy from whim. For, as bodies are infinitely divisible, according to the philosophy now established, or as, according to every philosophy, they must be indefinitely divisible, each infinitesimal of any given mass, which are only harmonics to other principal sounds, must have fundamental tones and harmonics peculiar to themselves; so that, if the reasoning of Rousseau has any force against M. Rameau's experiment, the ear must be continually distracted with a chaos of inappreciable harmonics, and melody itself must be lost in the confusion. But the truth of the matter is, that, by the wise intuition of nature, there is such a conformity established between our senses and their proper objects, as must prevent all these disagree- Harmony. able effects. Rousseau and his opponent are agreed in this, that the harmonics conspire to form one predominant found; and are not to be detected but by the nicest organs, applied with the deepest attention. It is equally obvious, that, in an artificial harmony, by a proper management of this wise precaution of nature, dissonances themselves may be either entirely concealed or considerably softened. So that, since by nature sonorous bodies in actual vibration are predisposed to exhibit perfect harmony; and since the human ear is, by the same wise regulation, fabricated in such a manner as to perceive it; the harmonical chaos of M. Rousseau may be left to operate on his own brain, where it will probably meet with the warmest reception it can expect to find*. Nor does it avail him to pretend, that before the harmonics can be distinguished, sonorous bodies must be impelled with a force which alters the chords, and destroys the purity of the harmony: for this position is equally false both in theory and practice;—in theory, because an impulse, however forcible, must proportionally operate on all the parts of any sonorous body, so far as it extends; in practice, because the human ear actually perceives the harmony to be pure. What effects his various manoeuvres upon the organ may have, we leave to such as have leisure and curiosity enough to try the experiments; but it is apprehended, that when tried, their results will leave the system of Rameau, particularly as remodelled by D'Alembert, in its full force.

Of all the whims and paradoxes maintained by this philosopher, none is more extravagant than his assertion, that every chord, except the simple unison, is displeasing to the human ear; nay, that we are only reconciled to octaves themselves by being inured to hear them from our infancy. Strange, that nature should have fixed this invariable proportion between male and female voices, whilst at the same time she inspired the bearers with such violent propensities against it as were invincible but by long and confirmed habit! The translator of D'Alembert's Elements, as given under the article Music in this Dictionary, has been at peculiar pains to investigate his earliest recollections upon this subject; and has had such opportunities, both of attending to his original perceptions, and of recognising the fidelity of his memory, as are not common. He can remember, even from a period of early childhood, to have been pleased with the simplest kinds of artificial harmony; to have distinguished the harmonics of sonorous bodies with delight; and to have been struck with horror at the sound of such bodies as, by their structure, or by the cohesion of their parts, exhibited these harmonics false. This is the chief, if not the only cause, of the tremendous and disagreeable sensation which we feel from the sound of the Chinese ghong. The same horrible cacophony is frequently, in some degree, produced by a drum unequally braced: from this sound the translator often remembers to have started and screamed, when carried through the streets of the town in which he was born in the arms of his nursery-maid; and as he is conscious, that the acoustic organs of many are as exquisite as his own, he cannot doubt but they may have had the same sensations, though perhaps they do not recollect the facts. So early and so nicely may the sensations of harmony and discord be distinguished. But after all, it seems that harmony is no more than a modern invention, and even at this late period only known to the Europeans. We should, however, be glad to know, from what oracle our philosopher learned that harmony was not known to antiquity. From what remains of their works, no proof of his position can be derived; and we have at least mentioned one probability against it in our notes to the Preliminary Discourse to the article Music, (see note B). But though Rousseau's mighty objections were granted, that harmony can only be endured by such ears as are habitually formed and cultivated; that the period of its prevalence has been short, and the extent of its empire limited to Europe; till his conclusion, that it is a Gothic and barbarous invention, is not fairly deducible even from these premises. Must we affirm, that epic poetry has no foundation in nature, because, during the long interval which happened from the beginning of the world to the destruction of Troy, no epic poem seems to have appeared? Or because a natural and mellifluous verification is less relieved by an unpolished taste, than the uncoth rhymes of a common ballad, shall we infer, that the power of numbers is merely supposititious and arbitrary? On the contrary, we will venture to affirm, that though harmony cannot, as Rameau supposes, be mathematically demonstrated from the nature and vibrations of sonorous bodies; yet the idea of its constituent parts, and of their coalescence, is no less established, no less precise and definite, than any mode or property of space or quantity to be investigated by geometrical researches or algebraical calculations. It is certain, that the mimetic or imitative power of music chiefly consists in melody; but from this truth, however evident, it cannot be fairly deduced that harmony is absolutely unfascicible of imitation. Perhaps every musical sound, even to the most simple, and all modulations of sound, are more or less remotely connected with some sentiment or passion of the human heart. We know, that there are instinctive expressions of pain or pleasure in their various modes and degrees, which, when uttered by any sensitive, and perceived by any conscious being, excite in the mind of the percipient a feeling sympathetic with that by which they are prompted. We likewise know from experience, that all artificial sounds modulated in the same manner, have similar, though not equal, effects. We have seen that, in order to render harmony compatible with itself, the melody of each part must be congenial; and, for that reason, one kindred melody results from the whole. So far, therefore, as any composer has it in his power to render the general melody homogeneous, so far the imitation may be preserved, and even heightened: for such objects as are majestic and august, or the feelings which they excite, are more aptly expressed by a composition of kindred sounds, than by any simple tone whatever. They who suppose the mimetic powers of music to be consummated in the imitation of mere unmeaning sounds or degrees of motion, must entertain limited and unworthy ideas of its province. It is naturally a representative almost of every sentiment or affection of the soul; and, when this end is gained, the art must have reached its highest perfection, and produced its noblest effects. But these effects, however sensible among the ancients, may in us be superceded by other causes which remain yet unexplored. Harmony explored. Theatrical performances are likewise, by them, said to have produced the most wonderful effects; yet thele we do not recognise amongst ourselves, though we have dramatic entertainments perhaps not inferior to theirs.

Rousseau proceeds to tell us, that among the ancients the enharmonic species of music was sometimes called harmony.

Direct Harmony, is that in which the bas is fundamental, and in which the upper parts prelve among themselves, and with that fundamental bas, the natural and original order which ought to subfit in each of the chords that compose this harmony.

Inverted Harmony, is that in which the fundamental or generating sound is placed in some of the upper parts, and when some other found of the chord is transferred to the bas beneath the others.