The fundamental harmonic diagram, which Thimus called the “Lambdoma” because it is drawn in the shape of a Greek lambda (Λ), and to which I gave the designation “partial-tone coordinates” because it is best for us to notate it in the familiar form of a coordinate grid, is (like all harmonic diagrams) not simply a mathematical-logical scheme that could be drawn with any other symbols. The form of these tone-number groups is also justified optically through the geometric-arithmetical arrangement of their contents, as is shown by the construction of the monochord, on which every tone-value in the diagram can be realized by means of the “equal-tone lines.” In pure numeric terms, this is a division canon that rationally subdivides any linear unit. Regarding the tonal content, these partial-tone coordinates provide, for the first time in the history of acoustics and music theory, a system of tones, which science has lacked before now. Since this system is based on the natural law of the overtone series, and its group-theoretical form also appears to be based in nature in other ways-and since, on the other hand, all the tone-values in it correspond to forms present in our psyche, as the “monochord test” demonstrates-this fundamental harmonic diagram contains one of those rare coincidences of the natural and the psychic, of matter and spirit, which promises to impart completely different findings from those of a merely logical (mathematical) formulation, or from a merely psychological analysis of inner forms and experiences.
“Theology in the form of mathematical figures is taught by Plato, the Pythagorean scriptures, and Philolaus,” says Proclus in his Commentary on Euclid. With this we return once again to Pythagoreanism itself. It is my firm belief that the only way to orient oneself in the great maze of Pythagorean traditions and their “authentic” and “inauthentic” theorems is to starts with the central idea of Pythagoreanism-namely with the tone-number, and the geometric-tonal configurations developing from it. I made a first attempt at this orientation in my essay on Pythagoras, and even in those initial harmonic analyses showed that many of the previously “obscurest” Pythagorean theorems could be illuminated with comparative ease; indeed, a few previously considered “foreign” and “un-Greek,” such as the doctrine of the transmigration of souls, can be derived directly from the Lambdoma. The reader will find various such analyses mentioned in this book.
Pythagoreanism had an enormous influence in all of antiquity with its double concept of number and harmony. This effect spread both into the most problematic individual phenomena and into the great universal akróatic concepts, as we have already learned (the harmony of the spheres, for example). Pythagoras taught in two ways. With one section of his students, the mathematikoi, he approached problems discursively, working through proofs; with the others, the akusmatikoi (= hearers), he taught symbolically by means of concise, easily remembered epigrams (akusmata). Of the many akusmata that remained in circulation throughout antiquity, an especially tenacious one has been preserved in different variations. Reduced to a common denominator, its translation reads: “Number is the wisest of things, and the name of things the next wisest.”
Plato's and Aristotle's position on akróasis
The position on akróasis of the two great ancient philosophers, Plato and Aristotle, is interesting to us. Today it is agreed that for the ancient Greeks, “music” (understanding this concept in its broadest meaning, i.e. “akróasis”), like poetry (which is also perceived through the medium of the ear), was not merely an art, but that they sensed the singing and the order of the cosmos in the phenomenon of tone. Physiologically, the eye was more spiritual for Plato; for Aristotle, the ear. Plato gives the eye the predicate “sun-like,” and speaks of an “eye of the spirit.” Aristotle was of the opinion that the ear is the most spiritual organ of the human senses (!). For both however, Plato and Aristotle, the high value of “music” and the musical in educational and ethical terms is self-evident. The two thinkers only differ regarding their physiological priorities in that Aristotle, especially in his Metaphysics, argues against the Pythagorean speculations numbers. The examples he gives show clearly, for those who have worked over the actual Pythagorean tone-number system and analyzed its forms, that Aristotle did not know the concrete basis of Pythagorean harmonics, and therefore did not understand many of the traditional Pythagorica. Plato, on the other hand, only objects fundamentally to the “haptification” of those Pythagoreans who treated tone-number like “hair splitting,” and seeks, in the acoustic phenomena in question, an ascent to the spiritual, to the Idea. In the Philebus, Plato introduces the arrangement of the sound system in speech with these words: “Some god or divine man observed that the voice [phonè] was infinite...” In his later works, he returns openly to Pythagoreanism, presumably as a result of personal contact with Pythagoreans in Sicily and southern Italy. His harmonic derivation of the soul of the world in the Timaeus is both famous and infamous. Since Plato was avowedly an initiate (see his Seventh Letter), he gave this derivation only in veiled language. However, for those who know, there is no doubt that the two series given by Plato, 1 2 4 8 and 1 3 9 27, joined in the correct way, produce what is still the only correct formula for the diatonic scale, and therefore a law on which not only all practical music is based, but also, for the ancients, the music of the cosmos; which is exactly what Plato wished to show. Plato's thoughts are even closer to Pythagoreanism in his enigmatic posthumous work, the Epinomis. This has long been assumed to be the work of his student Philippos of Opus, but arguments are now being made for its authenticity. It is possibly a transcription of one of Plato's later lectures. “If the Epinomis is authentic, then its special significance lies in the fact that it represents Plato's closest approach to Pythagoreanism.” The subject of the Epinomis is the question: what must mortal men learn in order to be wise? The individual observations of this work continually lead back to number. Everything unintelligent, incalculable, unordered, non-rhythmical, and inharmonic is lacking in number-ratio. Number is the gift of the divine universe. The harmonic idea of unity rules the forms of the upper and the lower world, and also determines that in which man is absent: at death the multitude of sensory perceptions are extinguished, the dying go from the condition of multiplicity to that of unity and thus attain perfect wisdom and happiness. Looking at the “Lambdoma” or simply at the “partial-tone coordinates,” one can see the tendency of all tone-values to return to the unity of the generator-tone line, and from there to achieve the “perfect wisdom and happiness” of the 0/0. In the series of mathematical sciences, from arithmetic to geometry and stereometry to the harmonic intervals, the Epinomis gives special attention to the arithmetic, geometric, and harmonic proportions. I suggest that the reader look at Fig. 179 in this book. These three proportion types were therefore present in the original Pythagorean diagram, which may serve as further proof of the connection between Plato's later works and Pythagoreanism.
In this section we will trace the influences of Pythagoreanism from ancient times and late antiquity to the Middle Ages, and in the next will show, with the aid of concrete examples, the akróatic elements in various domains in modern times, and finally, especially in poetry, right up to the present. In sections I through V of this Introduction, my primary task is to collect the information on akróasis up until now in a condensed selection, so that one can see and hear how the characteristic peculiarity of this mode of thought and inner attitude has manifested again and again in all periods. This information, together with the summary of the history of harmonics in §55, can then provide future research with the foundations of a universal history of akróasis.
Hippocrates; Alcmaeon; Empedocles
Pythagorean tendencies in medicine appearing with Hippocrates (around 400 B.C.) can be traced to Alcmaeon, a doctor from Croton and a student of Pythagoras. A fragment from Alcmaeon tells us: “Health depends on the correct proportions of the qualities.” The philosopher Empedocles of Agrigentum (490-430 B.C.) gives us some very concrete harmonic rules for these proportions. On the construction of bones, for example, one of his fragments reads:
“But the earth took up lovingly, in spacious crucible,
Of her 8 parts in all, 2 from Nestis [water]
And from Hephaistos [fire] 4, which became glowing bones,
Thus glued by harmony into a wondrous image.”
This is the harmonic octave proportion 8 : 4 : 2, or in string lengths on the monochord, 4 c,, : 2 c, : 1 c. These two octaves are the range of an average human voice! Desire, flesh, and blood obey the proportions 2 : 1 : 1. All beings are put together from the elements through sound proportions (harmosthenta). The following wonderful fragment from Empedocles-one of those that may have inspired Hölderlin to write his Empedocles-tells how, from these primal phenomena, fire, water, and earth (which it is a great mistake to understand in our modern material sense), all form themselves, in hate and love, up to the highest ones, the gods:
“But come, see testimony to the earlier words,
Lest they still be lacking for the making of things,
See how the sun shines warm and bright on all sides,
And the immortal bodies, replete with light and warmth,
And the water, which is in all things, dark and cool,
And springs from the earth, which has foundation and fixed form.
In hate, all this is torn asunder and made different,
But it yearns and comes together again in love.
For thence comes all that was and is and will be,
Trees grow from it, men and women grow,
Beasts and birds, and fishes feeding in the water,
And long-lived gods, foremost in power and noblesse.”
The Number Seven
The significance of the number seven is dominant in this early iatro-mathematics, and even more so later. The “tyranny” of this number can predominantly be traced harmonically to the norm of the seven-stepped diatonic scale existing in our psyche. The analogy of the 7 tones to the 7 planets is well known. As an iconographic element, the harmonic scale number 7 has typological significance far into the Middle Ages, and also in art history (e.g. the 7 church modes on the capitals of the 12th century Cathedral of Cluny).
Homer's Odyssey, XIX, 456-7, reads:
“And as for the wound of the noble godlike Odysseus,
They bound it up skillfully, and stayed the black blood with a song of healing.”
An ancient commentator already remarked upon “songs of healing”: “One must know that ancient medicine was founded upon singing.” This refers to staunching bleeding with the magic of tones and words, and presumably this is the oldest form of acoustic therapy: the healing song.
Athanasius Kircher made the first comparison of nerves with strings: “The nerves receive the same impression through the outer air / as strings have / when they are pulled over a smooth and resonant piece of wood / and just like these, they become excited / not only through the outer air / but also through the inner air / when it is in proportion / thus nervi and musculi are also agitated and moved / through the inwardly implanted air and spirit / which is like the conductor of the motive power in man / and this proportioned form / in that it concerns the soul, works on it all sorts of alterations / of happiness or sadness.” This passage should comfort all those sensitive to drafts! Examples of this theme of tone and healing could easily be multiplied hundredfold; they serve merely as preparatory illustrations.
It is interesting, and in a certain sense relevant to this topic, how widespread this theory of the number seven was in ancient times. Solon, the famous Athenian lawmaker (around 600 B.C.), wrote an elegy on the hebdomads (sevens) of human life: new teeth at age 7, puberty at 14, beard growth at 21, the greatest bodily strength at 28, the time to marry and produce children at 35, the full development of character at 42, the mature development of understanding and speech at 49 and 56 (through 2 hebdomads), a reversion at 63 (= 9 × 7), and finally, at 70, nothing further until death. This poem of Solon later influenced Aristotle and others; but his theory of the number seven received its highest intensification in the pseudo-Hippocratic writing On the Hebdomads, which abounds with septenary analogies. The purpose of this single example of numeric symbolism is merely to show that harmonics, in this somewhat disparaged domain of “number superstition,” may provide quite definite clarifications: the first numbers in the whole number series are present in our psyche as tone proportions!
On the “well-sounding and bad-sounding” in musical rhythm, Plato says: “Painting and all other works of this type are full of it, as are also weaving, both simple and artistic, and architecture and the manufacture of all other implements; also the nature of the body and all other growing things; because in all these dwells a propriety or an impropriety, and impropriety, boundlessness, and dissonance [!] are kindred to evil babble and evil-mindedness, but the opposite is kindred to the opposite, the rational and good spirit and its representation.” Truly, this is the harmonic ethos reduced to a formula!
Heraclitus said: “Things repelling each other unify, from multiple tones emerges the most beautiful harmony, and everything emerges from strife.” The Stoics preserved these ideas in their own way: “Perfect serenity will be that” which “is firmly rooted in the knowledge of the divine and human things, through which it holds the opposites in the world as the most beautiful harmony in creation.” Compare to this the inner “opposites” of our fundamental harmonic diagram, through which the “harmony” (i.e. order) of the cosmos of the tones first emerges! In the Stoa, etymology (the study of the origins of words) was practiced vigorously; indeed, the word “etymology” supposedly originates from it. For example, they derived the word phònè = φωνή (voice) from phòs nou = φω̃ς νου̃ (light of the spirit)!
Hippolytus, in his account of the heresies of the Phrygians, reports that they called reborn spiritual people by the name “Papa,” and meant all heavenly, earthly, and subterranean beings when they said: “Paue, paue-stop, stop the dissonance of the cosmos!” Again and again, the mysterious power of the call, the voice, and the name breaks through. “Simon Magus the Gnostic teaches that there is an unlimited power and calls it the origin of everything, stating the following: 'This writing of the proclamation of a voice and a name comes from the decree of the great, unlimited power.'” The verse at the beginning of Genesis: “And God made two great lights: a great light to rule the day and a lesser light to rule the night,” is interpreted by Simon thus: the sun and moon are the powers of the voice and the name, the speaking and the spoken. According to the Gnostic Marcus, the hidden, beingless deity opens its mouth and emits the word (Logos) that is its likeness. This Logos now speaks various archetypical names: “Each of the letters [of the names] has its own sign, its own character, its own pronunciation, its own form, its own appearance, and none of them knows the form of that of which it is only a letter, indeed it does not even comprehend the utterance of its neighbor; with the sound that it makes itself, it believes that it is naming everything. Marcus is the “Greek classicist of letter-metaphysics.” Thus the “dieresis” of the letters goes forth into infinitude; but everything returns to the letters from whose pronunciation it emerged, back into the lost unity, and sounds therein as on the first day: one day everything will resound in a World-Amen.
F. Dornseiff believes that this idea “is not lacking in grandeur,” and as harmonists, we see in this an astonishing concordance with the value-formal content of the fundamental Pythagorean diagram of the “P.” The reader will be able to judge this for himself after studying the relevant chapters of this book.
Proclus; Plotinus; Prudentius
The last great synthesist of the Greek philosophers, the Neoplatonist Proclus (410-485), believed (like Kepler, who quotes him extensively) that the psyche contains the “harmonically making” (harmonika) before the “harmonically made” (harmosmenoi); or as we would express it: some psychic prototypes must be within us a priori, otherwise we would not be able to tell whether a harmony is in tune or not.
“Since it is thus that the whole world attains existence, look upon it: then perhaps you will hear its voice,” says Plotinus (205-270), the most important Neoplatonist. And Prudentius, the master of Christian poetry, tells his spirit: “Let loose your voice, sonorous spirit, free your noble tongue, tell of the triumphal signs of the Passion.” Both are typical akróatica, referring repeatedly to the toning magic of voice and word. “Just as the individual string is set in its proper place corresponding to the ratio of its tones, just as it appears with its ability to sound,” so the soul enters into the poetry of the world: “Every soul sings the song from its place, harmonizing both with the place and with the collective all.” “The unutterable names of the Gods, so the theurgists say, fill the whole world, and not only this world but all powers over the world. Before the souls come into being, they see that the Gods fill the whole world with themselves and their names. They long to be like them when they have come into being,” says Proclus in his Commentary on Plato's First Alcibiades.
Kepler emphasizes in his Harmonice Mundi that in opposition to the “meaningless symbolizations” of Ptolemy and the old speculations about harmonies of the spheres, he has reestablished harmonics upon scientific theorems, in astronomy: “Therefore, with an improved astronomy that establishes the true and simple movements of the planets, eliminating the apparent, the things that rest upon the deception of our sense of sight, I have shown that all harmonic proportions appear in the heavens according to a true and real proportion, quantitative and measurable, not according to a mere meaningless symbolization, as well as the keys, the musical system or the scales and most of their notes, the differences of the modes, the imitation of polyphonic music by the planets, and finally the collective counterpoint of the six primary planets, which varies according to the keys and modes.” In the dedication of his work to King James of England, he supports this, and his investigations, with the words: “The reasons for thinking of this patrocinium in terms of my harmonics originated from that manifold dissonance in human affairs that is too well-known not to affect one, but which is built from true and plainly perceptible intervals, whose nature it is to soothe the hearing amidst dissonance by promising a pleasant concord to follow, and to keep it in happy expectancy.” Throughout the entire work the numbers found in the sky are harmonized, i.e. converted to tone-numbers and “scientifically” analogized: “As the simple or monophonic song known as plainsong, which alone was known in ancient times, is to the polyphonic so-called figured song, which is an invention of the last century, so the harmonies made by the individual planets are to the harmonies of the planet pairs.” “Harmonies” is no vague concept for Kepler, no “hint,” no epitheton ornans as is has been considered by all of modern science since Whewell: instead, it conforms to tone-numbers, intervallic proportions, scale steps. It was by means of these tone-numbers, i.e. through harmonic analyses, that he discovered his Third Law! For Kepler, the formative idea lies in these harmonies, not just in the geometric figures: “Thus I came gradually, especially in recent years, upon the harmonies, tolerating very small variations in the spatial figures. The thought came to me that on the one hand, the harmonies played the role of form, applied by the final touch, whereas the figures played the role of the material that is in the number-world of the planetary bodies and is the gross extent of spatial domains. The harmonies, on the other hand, also provided eccentricities, which the spatial figures never offered.” And precisely through this harmonic and not “physical” observation-that the tone-numbers and tone proportions play a decisive role in the eccentricities of the planetary orbits, and that through them the Creator “applied the final touch”-Kepler found his famous Third Law. Because for him, the harmonist, the discovery of the exponent 3/2 was the fifth, the interval that generates all diatonic steps, and in the formula p2 = cr3 (p = orbital period, c = a constant, r = radius vector) he saw, behind the relationship of orbital period and orbital radius, the background of the psychic form of the “dominating” interval, the fifth! Later in this book, the reader will discover other “harmonies” in this main work of Kepler's, as well as other “Kepleriana.”
Speaking of Kepler, here is a quote from the second great harmonist of modern times, A. von Thimus, which gives, in a certain sense, a concentrated summary of his way of thinking: “Only by means of thought, and only with the inner ear of a God-enlightened sense, can the indescribable sound of this harmony, eternally exalted above human earthly music due to its impressiveness and beauty, be surmised. Only by the Creator himself, and by the blessed spirits joined with him, is it beheld and known in its entirety. Its sounds come together from the opposition and gradation of powers concurring and unifying harmonically in a higher accord, as well as from the diversity and yet the strict order of the movement that forms itself through the action and reaction of these powers in colorful multiplicity according to the laws of an entirely musical number, faster or slower, greater or smaller, more closely bounded or reaching into the outermost distance.”
In Jakob Böhme's theosophy, “reverberation” or “resonance” is the sixth nature-form, concluding the evolution of the “eternal nature.” The Aurora, Ch. 10, 1, reads: “The sixth source spirit in the divine power is the resonance or tone / that clangs and rings everything within / from there comes speech and difference of all things / as well as sound and song of holy angels / and therein is the formation of all colors and beauty / and the heavenly domain of joy.” In this doctrine of nature forms or “qualities”-a type of metaphysical principle-“tone” therefore means grasping and becoming conscious of things. From this comes the “speech and the difference” of all things, articulation and “formation” in the broadest sense.
Franz Baader, the great commentator on Böhme and profound theosophist, part of that German idealism which continually surpasses itself intellectually, carries this idea of Böhme's further, in his own way: “All movement [e.g. of the stars] is figure writing, and these natures write because they cannot speak.” Here, the replacement of speech with “figure writing,” mute speech, changes through movement into form! Schelling, who was strongly influenced by Böhme and Baader in his later work, writes of a “wonderful” explanation of the “resonance-principle” as of an “inner light.” However, the only modern philosopher who has declared possible the restitution of harmonics as a science is Schopenhauer.
After deep reflection upon the nature of music in the 3rd book of his main work, Die Welt als Wille und Vorstellung, Schopenhauer writes: “One could call the world embodied music just as much as embodied will.” His view is that “the apparent world, or nature, and music are two different expressions of the same thing,” and in conclusion he summarizes as follows: “If I am given the task, in this whole illustration of music, of making it clear that it declares in a most universal language the inner nature, the In-Itself of the world (which we think of, according to its most usual utterance, as the concept of Will) in a unique medium, namely simple tones, and does so with great certainty and truth; if, moreover, in my opinion and aspiration, philosophy is nothing other than a complete and correct repetition and enunciation of the nature of the world in universal concepts, since only thus is a sufficient and correct overview of this whole being possible, then those who follow me and have entered into my way of thinking will find it not so paradoxical when I say: supposing that a complete, correct, and detailed clarification of music, hence an exhaustive repetition of that which it expresses, were given in concepts, this would also immediately be a sufficient recapitulation and clarification of the world in concepts, or something equal to that, and would therefore be the true philosophy; and that consequently we can parody the saying of Leibniz quoted above [music is a mysterious arithmetical exercise of the soul = 'Musica exercitium arithmeticae occultum nescientis se numerare animi'], which is completely correct from a lower viewpoint, in the sense of our higher viewpoint of music, as follows: 'Music is a mysterious metaphysical exercise of the spirit, unconscious of its philosophizing' ['Musica est exercitium metaphysices occultum nescientes se philosophari animi']. For scire, to know, always means to have set down in abstract concepts. Since further, by virtue of the much-supported truth of Leibniz's pronouncement, music, disregarding its aesthetic or inner meaning and observing it merely outwardly or empirically, is nothing other than the means of grasping, directly and in concreto, greater numbers and more complicated number-ratios than we would otherwise be able to know indirectly through grasping them in concepts; thus, through unification of these two so different and yet correct views of music, we can make for ourselves a concept of the possibility of a number philosophy, like that of Pythagoras or the Chinese in the I Ching, so as to then interpret, in this sense, that saying of Pythagoras which Sextus Empiricus presents: 'τω̃ ̕αριθμω δὲ τὰ πάντ' ̕επέοικεν = all is assimilated through number.'” Here one must naturally abstract from the familiar concept of “music” and understand it in its broadest sense: just as broadly as Schopenhauer does.
We modern harmonists admittedly consider our discipline as one, but not the “true philosophy”; the possibility of a “number philosophy,” on the other hand, emerges of itself within harmonic symbolism.
The Harmony of the Spheres
The concept and worldview of the harmony of the spheres is common to almost all classical and pre-classical peoples. But in it we find not only the “cosmic” content of akróasis, expressed in myths and legends and interwoven in numerous forms, but even more, we find that specialized harmonic research since the earliest antiquity repeatedly sought concrete connections between the stars and the laws of tones, until Kepler and modern harmonics proved these connections. I will give a few examples so that a few of these mythological forms of the celestial world can be “heard.” Lucian writes: “Thus the lyre served Orpheus, its inventor, as the noblest instrument of his clandestine religion; but this lyre, which had seven strings, was to him a symbol indicating the harmonies of the planets. It was with this secret science that he charmed and mastered all: his concern was not the lyre he had made himself, nor what one generally thinks of as music.” In the Orphic hymns, Helios Apollo is entreated: “You who with golden lyre guide the harmonic progression of all”; Pan is addressed as “under the stars playing / the harmonies of the world on a jesting flute”; and Apollo is sung to thus: “With your bright playing you guide / the whole pole; now changing to the lowest string / now to the highest, and now, in the Dorian mode / completely harmonizing the pole”-the celestial pole, of course. Franz Cumont found depictions of the Muses on seven Roman sarcophagi from the 1st to the 4th centuries, and comments on them as follows: “The sister goddesses who oversee the harmony of the spheres awaken in people's hearts, through music, the passionate longing for those divine harmonies and the yearning toward the heavens. At the same time the daughters of Mnemosyne recall to consciousness the memory of the truths she knew in an earlier life. They share their wisdom with her, the pledge of immortality. Thanks to them, thought rises up to the ether, is initiated into the secrets of nature, and reaches the circle of the choir of the stars. It is relieved of the worries of this world, is transported to the world of ideas and of beauty, and cleansed of material passions. And after death the heavenly maidens summon the soul they have consecrated in their service to the celestial sphere, and allow it to take part in the blissful life of the immortals.” Of the eight heavenly spheres, Plato writes that on each circle sits “a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony; and round about, at equal intervals, there is another band, three in number, each sitting upon her throne: these are the Fates, daughters of Necessity, who are clothed in white robes and have chaplets upon their heads, Lachesis and Clotho and Atropos, who accompany with their voices the harmony of the sirens-Lachesis singing of the past, Clotho of the present, Atropos of the future.”
The singing swan also reaches the stars. Virgil tells of the legend:
“For it is told that Cygnus [the swan], mourning for beloved Phaeton,
Under budding poplar branches and the shadows of the sisters,
As he sought to ease the sorrow of his love by singing songs,
Old age hastened in upon him, silver-gray with tender down,
And flying up from earth, he pursued the stars with chanting.”
There are many more examples of ancient poetry and speculation relating to the harmony of the spheres. We will mention only a few others.
Pindar, a contemporary of Pythagoras (6th century B.C.), sang:
Apollo plays you above in heaven,
and you rule the dance and song
of the violet-ringlet Muses.
Below on Earth the choirmasters
hear these sounds,
and the singers follow the directions
when you strike up the prelude
giving beat and tone to the song.”
Willamowitz-Moellendorf, from whom this translation is quoted, recognizes in this poem a poetic veiling of the harmony of the spheres. The dance, so closely bound up with music for the Greeks, is a symbol of the heavenly dance of the stars: “For what is this round dance of the stars, this regular interwoven movement of the planets in relation to the fixed stars, and the rhythmical unification and beautiful harmony of their movements, if not proof of a great primal dance?” writes Lucian. Cicero moves entirely in the akróatic realm of ideas when he writes of soul, tone, and cosmos: “Indeed, Socrates asks Xenophon from whence we have conceived the soul, if there is none in the world. And I ask, whence speech, whence the regular harmony of speech, whence song? We would have to assume that the sun converses with the moon when they approach each other, or that the world sings in harmony, as Pythagoras says. These are works of nature, Balbus, not of an artificially intrusive nature, as Zeno expresses it, but one that stimulates and drives everything through its own motions and changes.”
We will remark only in passing that the ancients closely studied the analogies of the elements of speech, of vowels and consonants to the tones of the planets and celestial spheres, through which they regained a connection to the most ancient cosmic meaning of sound and of the word itself; we will return to this later. But the reader will agree with me that a name, indeed an entire realm of concepts, can now no longer be avoided: Pythagoras.