1. Aristotle says, in Politics, Book 1, that nature constantly combines, in music, command with obedience.
2. I will give my readers the literal translation of a passage from Plutarch, Dialogue on Music. I think you will be grateful to me for a quotation which should surprise to the supreme degree. Plutarch speaks there as one would still do today; I know nothing more decisive than this passage and more potent against the constantly reviving objection against enharmony; if we are not convinced, we should despair. Plutarch says, page 168, Dialogue on music, translation by Burette, in the Home of the Memoirs of the Academy of inscriptions and belles-lettres, volume X, old series. After expressing how much enharmonic was cultivated by the ancients and by Pythagoras himself: Our modern musicians have entirely banished the most beautiful of all these genres (the enharmonic genre), and that which, by its seriousness, was the most esteemed and the most cultivated among the ancients: so that there is very little of people who have the slightest perception of enharmonic intervals.
The negligence of our moderns goes so far as to maintain that the enharmonic sharp is not among the number of things that fall under the senses of hearing, and consequently to the point of excluding it from their chants: adding that those which have known cases of this kind and that have put it in use gave in the trifle. The most substantial proof they believe they bring of the truth of such a proposition consists in their insensitivity: as if all that escapes them did not exist and became absolutely impracticable. They further assure that this interval cannot enter into what is called symphony or consonance, as do the semitone, the tone, and the other intervals.
But they do not notice that, according to this principle, they should also give exclusion to the third, fifth, and seventh interval, of which one is three sharps, the other five and the last seven, and that, in general, it would be good to reject as useless all the odd intervals, because no consonance can be derived from them. Of this number would be all those which the smallest sharp can only measure unequally; whence it would follow that any division of the tetrachord would be useless, except those alone which make all the intervals even and would only cease that of the diatonic and that of the tonic chromatic. It belongs to advance, not even to imagine such propositions, only to people who want to fight the evidence and contradict themselves. For it seems that they are the first to use these divisions of the tetrachord, according to which most of the intervals are either odd or irrational.
Indeed, they always release and soften the lichanos and the paranetes, without counting that after having lowered some of the fixed sounds (and that according to an irrational interval), they still release the trites and the paranetes. So that in The Use of Harmonic Systems, they value nothing so much as those where most of the intervals are irrational, releasing not only those sounds which by their nature are mobile and variable but also some of those which are fixed and motionless, as distinctly felt by musicians who have a keen enough ear to perceive all these differences.
3. Mersenne has a particular idea of the enharmonic genre in his Harmonie Universelle, but all this is very confused and through an ignorant imitation of the Greeks. Nevertheless, he was a man who was looking for real difficulty; he says himself that the Platonists regarded the world as formed according to universal harmony, and, on page 249, we see that he approaches the principle of attraction of notes singularly.
4. It is curious to see what Meibomius thinks in his preface, page 1: Barbaros Graeci reliquos populos olim vocabant, quod ad suam elegantiam in omni rerum ac scientiarum tractatione non accederent: nunc Barbaros novi homines Graecos nominant, non alia de causa, quam quod illos non intelligant. Formerly the Greeks called other peoples barbarians because they did not approach their refinement in all the treatment of things and sciences. Now, the new men call the Greeks barbarians for no other reason than that they do not understand them. (See additional note).
5. Despite what the authors report on the discovery of Pythagoras passing in front of a blacksmith’s workshop and what I quoted from Gaudentius, page 3 (note), one can still wonder whether the Greeks, who so well defined the dissonances, the perfect and imperfect consonances, were not reduced to a purely theoretical knowledge of these phenomena, without having in this use beyond a few elements. It was difficult to escape harmoniously from these series by fourths, of which they had composed their scale, and one can see, by the richness and variety of their melodic combinations, that the poetic rhythm, to which they sacrificed everything, had prevented them from ever dreaming of a simultaneous broadcast which would inevitably have broken it.
6. Modern didactic authors on music have generally shown themselves incredibly powerless to understand what remains to us of the ancients. After some searching for detail and enumeration, as dry as it is erroneous, they have, so to speak, apologized for occupying the reader’s attention for so long on things of no application, if not ridiculous; and they quickly pass to the glorification of our present system. As if Euclid, for example, of whom we have an admirable treatise on music, had amused himself by writing charades for the amusement of posterity! Meibomius has collected in several parts the works on the music of the Greeks and Romans.
We can add to it what is disseminated in the polygraph authors Plato, Aristotle, Plutarch, and others. The more significant part of the treatises included in the collection of Meibomius bears the title: introduction to Music. Instead of lamenting the singular hazard that gives us so many introductions and leaves us so few complete systems, he had to look for the reason for this oddity. It wasn’t hard to find, though. In fact, it was enough to see that these works, which among us now bear the name of essays, are the deepest and most complete we have in the respective genre they have treated. Essays by Montaigne, Essays by Montesquieu, Essays by Locke, Guizot, etc. The title, Introduction to Music, stems from this way of acting. At the same time, it shows us that the ancients carefully divided the study of music into pure theoretical or speculative (see the Meibomius collection) and practical application.
The philosophers called upon to study theoretical music by the desire to discover universal harmony, which was the philosopher’s stone of the time, exercised themselves in turn in this part of science which lent itself to the aspirations of pure speculation. We find among the didactic authors of music all the great names of ancient thought. We would therefore be very mistaken if we thought that they followed their work to the point of descending into practice, into what they called empirical education; if they did, it was summarily, as a verification of the proposed theories. The set of all these introductions, identical in the basics of the doctrine, proves that the Greeks never produced multiple combinations of successive resonance in music, at least importantly and consciously.
Out of misunderstood curiosity, we persist in seeking in the Greek books anything other than what Euclid, Aristoxenes, Aristide Quintilian, and others can provide us now. Our available documents should suffice for an imaginative individual whose firmly established principles can supplement what may seem lacking in the Greek science of musical note combinations. If I had the time to translate Euclid, I would show, in a commentary of only a few pages, how little remains for us to learn to be entirely in possession of the Greeks’ beautiful, admirable melodic system. This is so true that it may safely be said that we have scarcely a shadow of a treatise that approaches their grave deduction, so denoting in such men the highest power of learned and philosophical thought.
7. I say Indians, although the Egyptians are always indicated as direct intermediaries. These last peoples having themselves received their system from the Indians, it is better to go immediately to the source.
8. Euclid says moving intervals (page 9, collection Meibomius): Rationadilis & irrationabilis diſferentia est, qua intervallorum alia sunt rationabilia, alia irrationabilia. Rationabilia sunt, quorum magnitudines exhibere possumus: ut tonus, hemitonium, ditonum, tritonum, et similia. Irrationabilia, quae hasce magnitudines: variant vel in majus, vel in minus, magnitudine aliqua irrationabili. There is a difference between rational and irrational, where some intervals are rational, others irrational. Those of which are rational we can present the magnitudes: as a tone, a hemitone, a ditone, a tritone and the like. In the Irrationals, these quantities vary, either to a greater or lesser extent, in some irrational quantity.
9. It is easy to see that the Greek enharmony was broken down into sharps of thirds and quarter tones. (Euclid, page 141 of the Meibomius collection.) Gaudentius (page 6) completes this assertion by showing us that the enharmonic genre: Incompositum primum, was divided by quarter tones, intervallum est quarta part toni. The chromatic genre admits the sharp by third of a tone: in chromatico, toni triens; vocatur que diezis, chromatica minima. In the diatonic genre they had a tone divided into two only: in diatonico (maxime eo quod synthonium dicitur), hemitonium primum est and incompositum. Here, then, our barbarian Greeks, our ignoramuses, are convinced of possessing the most complete divisions of the tone of which we are aware and uniting in their system that of the Hindus and the Arabs. Here is, the diatonic step was presented, according to Gaudentius: descending: fa, mi, re, do (A = la, B= si, C = do, D = re, E = mi, F = fa, G = sol).
The opposite on the way up.
The chromatic march was: fa F, mi E, re D ♯, do C 1/3 of ♯.
The enharmonic march was: fa F, do C ♯, do C 1/4 of ♯and do C♮.
10. See, page 28, the note where Aristide Quintilien says that the enharmony servait coagmentando dictum, it kept on assembling what was said.
11. Here is a little known passage from Aristide Quintilian which defines in two words the three genders of the Greeks (Meibomius, a, 9, 18):
Harmonia appellatur illud genus, quod minimis abundat intervallis, a COAGMENTANDO dictum.
Diatonum, quod tonis abundat; quandoquidem in ipso vox vehementius distenditur.
Chroma, quod per hemitonia contenditur.
12. It is the same for the song of our peasants; which would lead one to believe that the enharmonic genre is the first that comes in the natural order by imitating the song of birds, the cries of animals, and the innumerable noises of matter. In fact, seek to translate by the stiffness, the original melodies of Brittany, Normandy, etc., you will almost always discolor them, and will only retain a species of skeleton which will render nothing at all. This is what happened in particular at the Ambigu theater, in the Closeris des Genéts by Frédéric Souliè. The most famous popular musician in Bretagne, Mathurin the blind, had been summoned from Quimperlé; but in vain, the poster carried the enunciation of this fact; the ears refused to see anything else in this old Breton than a corypheus in disguise. It was because the orchestration had broken the native melodies, and the obligatory flourishes of the genre, the gymnastics of ordinary transitions, became impossible or were stifled.
I do not come here to establish out of time the superiority of Breton melodies over our systematically measured singing; I am only saying that if we thought we had them in their essence, we would be strangely mistaken.
In the countryside, there are old shepherds and old spinners who take advantage of their long memories to impose sad lamentations which are taken for the ne plus ultra of art and which are basically only hiccups of drunk or meowing from a toothless mouth. But choose one of those young girls from Brittany, melancholic, with a pure and naive voice; listen to the progress of its song, of its bizarre though systematic accentuation: you will have the most complete representation of a musical element which you believed to have been lost for two thousand years, the enharmonic genre in all its purity. The motif rolls over such a small number of real notes that they can often be squeezed into a single tetrachord.
But they are overloaded with embroidery and, above all, with enharmonic and enharmonic modulations. It is one of those old Breton ballads which, in the mouth of a beautiful, lonely, restless, dreamy child, takes on all the shades of amorous cooing, of a sentimental complaint, or sometimes of an erotic and even hysterical ardor. , depending on the circumstances of position and season. It is obvious that nature has put the most complete force into expressing instincts and passions in this decomposition of sound to infinity. Listen and analyze the sounds made by a dog crying because you have punished and confined it; you recognize, if you want, all the accents of submission, repentance and prayer. The cats push the game of melody even further in these nocturnal cries, which surprisingly imitate the human voice in emotion, especially when crying is involved.
If we had thought of all this, would I need to recall today that Therpander was condemned at Lacedaemon, not only because of the richness of imitation of his enharmonic singing but above all because of the scandal he lifted awkwardly? Indeed, in his indictment and judgment, it was established that he had impiously reproduced the cries of Latona in labor pains. Now, I ask you, what means will you have of rendering the cries, as the peasants say, the groans of a woman in childbirth, if not by the infinite division of the vibratory cord? The analysis of a painful complaint, launched in a single jet, gives us a division less than one of our semitones. So, without going to look for the Orientals, who do not want to hear about another system, it is clear that this so ignored enharmonic is on our stage, and at our doorstep, in the peasant with ancient traditions.
But we laugh at all these traditions, without understanding anything about them; yet I am convinced that it would be very easy to appropriate this rather limited vocabulary of birds and animals, which responds to instinct alone; that by studying it from the point of view of melodic combination, we would make of it a system as exact as many others to which we give full credence. The singers didn’t wait that long to capitalize on that thought.
Without harmony no complete imitation; the bayaderes of Egypt, who are called almees in the country, have kept the habit of expressing through music all the circumstances of romantic episodes, not figuratively like us, by determining a general and indeterminate sensation, but by an exact imitation of all realizable phenomena. (See Villoteau.) This is still the most popular and sought-after genre in a country where enharmonic reigns supreme. All the times we wanted to do powerful imitations, it was necessary to return to an indeterminate harmony, not as to the principle, but as to the result. This is proven by several passages from Beethoven and Mozart, the great poets par excellence, and particularly certain parts of the overture to the Freischutz, where we hear the fantastic sound of the clarinets which are sol G, mi E in the low registers.
13. We have always been driven by the mathematical idea, in music; making us neglect the so important phenomenon of attraction, which has given us too rigid a formula for division with respect to sharps and flats.
The Arabs, who, according to Villoteau, owe the remains of their music to the Greeks and to the Indians, did not fall into the same error as us. They have three ways of cutting off a semitone.
When they want to throw cold on a piece, they choose division by semitones to nullify the attractive character. When it is ardor, energy that is to be produced, they use thirds and quarter tones. In this way, they have, like us, not unique signs, sharp, flat, which are consistent at least in theory, but a true sharp, a true flat: the sharp both the appellative rising, the flat the appellative descending.
Because for them, men of an exquisite sense of delicacy, a perfectly equal cut, in any division whatsoever, always generates a difficulty of attraction due to the equal force that exists in the bilateral appellation.
When we compare these ideas with the passage of the anonymous Arab quoted by Villoteau, we see clearly that this alleged division of seconds, so incoherent for us, is infinitely more logical than ours mathematically and phenomenally.
Here is the quoted passage as given in the literal translation:
“The basis of natural singing is made up of eight melodious sounds which come naturally from the throat, and of which the first is in direct relation to the last; none other than that can be produced naturally by the voice. It is called the proper circulation (range) of the rast. They were so called because rast, in Persian, means straight. They are also called the circulation of degrees or the circulation of consecutive (diatonic) intervals; when we have reached the eighth, the circulation is finished: we call this the complete interval and we begin another circulation.
When one has read this extraordinary testimony of a nation that presents a subdivision of tone in such a capricious way, it is clear that this flagrant recognition of our consonances first, then of their immediate subdivision, the seconds, demonstrates to There can be no doubt that the inner divisions only bear on the individual connection of the names against their point of support, and that all these peoples are neither as ignorant nor as dissident as one would have us believe.
Villoteau completes this datum by saying that, as with the fourth above the first low sound and the fifth above the last high sound.
Since with them, as with us, the division of a tone is made into two parts called comma, they are therefore better justified than we in invoking the logic of the calculation, which indicates three cuts of three commas, as more natural than that employed by we in two unequal semitones, one of five commas, the other of only four.
Descartes and the mathematicians were right about the division of octaves into unequal parts; only they have completely misunderstood the attraction first, and all that is contingent, dialectical in music.
Mathematics cannot, any more than chemistry or physics, provide anything other than facts for analysis. It is logic and deduction which must take advantage of it in order to rise to the great considerations which probe the sciences. The musicians, too ignorant in general to know the resources of metaphysics, delivered themselves hand and foot to the mathematicians, whom they believed to be men to solve everything, and the mathematicians remained in the material analysis without giving the solution.