Plato himself, as we shall see, owed much of his numerical codes to the influence of Pythagoreanism, and that in turn owed much to Mesopotamian civilizations. A proper understanding of the Grid system and the cosmologies that underwrote it cannot therefore be had without a consideration of the massive influence that the civilizations “between the rivers” had on its development, and in particular, on the development of music. In this understanding, no work is more magisterial and important than that of Professor Ernest G. McClain.
A. The Unified Intention of Symbol and Musical Codes
In my previous books I have spoken at length about a conception that I call “the unified intention of symbol,” i.e., the idea that ancient myths were carefully composed, multi-leveled structures designed to encode a massive amount of technical information that could be decoded when science had advanced to a similar state of development as the society that originally created the myths.3 It has been my assumption that this “mythological creation” was the deliberate act of a post-cosmic war elite or elites seeking a method to enshrine and transmit technical information in a form that would last over time. If studies such as De Santillana and Von Dechend’s Hamlet’s Mill, or Ernest G. McClain’s Pythagorean Plato and The Myth of Invariance are any indicators, the program was wildly successful, for those myths, from Scandinavia to Polynesia, encode a wealth of astronomical, geometric, and musical data.
1. Music as the First Physical Unification and the Musical
Meanings of Pantheons
I am not the only one, by any means, to have noticed this multi- leveled, almost paronomasial symbolism at work in ancient myths. Commenting on this phenomenon in the Vedic texts, McClain observes that there are at least four “languages” or modes of expression at work simultaneously:
1) the language of Non-Existence (Asat),
2) the language of Existence (Sat),
3) the language of Images and Sacrifice (Yajna), and
4) the language of Embodied (Rta) Vision (Dhih).
These four languages are the expressions of a sensorium which organizes itself primarily on a model of sound.4
It is the recurrence of similar numbers, in a similar order, from the Rig Vedas of India, and on into Babylon, Egypt, and Greece that indicates an underlying, common spiritual and philosophical tradition. Indeed, for McClain, music was “the one force capable of projecting a philosophical synthesis” because music was the first physical unification.5 This musical code manifests itself, within the Vedic tradition, as hymns and musical numerology that link Sun, Moon, the planets, to the Indian pantheon “in which sons create their own mothers and all are counted.”6
In the effort to decode these musical-numeric codes, Plato is, for McClain, a kind of Rosetta Stone “to the more obscure science of earlier cultures.”7 Of all these cultures, the Vedic was by far the oldest, and its myths and hymns were, in fact, codes of a musical science:
The numbers Rgvedic man cared about define alternate tunings for the musical scale. The hymns describe the numbers poetically, distinguish “sets” by classes of gods and demons, and portray tonal and arithmetical relations with graphic sexual and spatial metaphor. Vedic concerns were with those invariances which became the focus of attention in Greek tuning theory. Because the poets limited themselves to integers, or natural numbers, and consistently used the smallest integers possible in every tonal context, they made it possible for us to rediscover their constructions by the methods of Pythagorean mathematical harmonics.8
We may now add to the accumulated levels of meaning associated with the “unified intention of symbol” a new understanding of “gods:”
1) At the most prosaic level, the gods represent real “people” or beings who interact with humanity;
2) At a second, deeper level, the names of gods might be titular, as denoting a planet or its ruler, or ruling house;9 and now we have, in addition to this,
3) At a third level, the names of classes of gods also represent sets of notes generated by certain mathematical relationships.
There is a clue here, for as was seen in my book The Cosmic War, there is yet another formula which emerges from Mesopotamian and Egyptian texts:
Mountains ≈ Planets ≈Gods ≈ Pyramids,10 where the symbol ≈ means “is associated with.”
We may now add a new component to this formula: Mountains ≈ Planets ≈ Gods ≈ Pyramids ≈ Music.
But why associate music with mountains, pyramids and planets?
The answer to that question emerges from a careful consideration of McClain’s decoding of the “musical paleophysics” of the myths of Pythagoreanism and Platonism. It is music that adds a hierarchy of order to the otherwise infinite and chaotic series of numbers:
What we are investigating then, is actually a realm of number theory in which music sets the problems, since musical patterns elevate certain numbers to a prominence pure number theory would not accord them. Musical values introduce a hierarchy into the number field: as we shall show… even numbers which define the octave matrix are “female,” odd numbers which fill the matrix with “tone-children” are “male,” and the smaller numbers define intervals of greater importance.11
Or to put it into terms reminiscent of Rene Schwaller de Lubicz, music denotes the functions that numbers symbolize.
What certain numerical relationships in ancient mythological texts are actually doing, in other words, are defining systems of tuning in the attempt to reduce the chaos of the harmonic series to an engineerable order. Why this is so requires a little explanation by way of a simple illustration.
Every musical tone has a natural harmonic series of overtones extending above and below it into infinity. The problem is, that each “overtone” or “harmonic” decreases in interval relationship to its fundamental the higher one goes. If one sits at an acoustic piano, presses the note “C” down silently, and then hits the note “C” an octave lower, one will hear this silently pressed “C” vibrating in sympathetic resonance with the struck note. Now, go up a fifth to the note “G”, and repeat the experiment. Silently press down “G” while hitting the note “C”. Again, one will hear the silently held note “G” vibrating sympathetically with the struck note “C”. Again, go up a fourth — note that the interval is diminishing — to another note “C,” press it silently, and hit the note “C” two octaves below it. Again, the silently held “C” will vibrate.
Repeating this process will inevitably lead to a note that does not exist on the piano keyboard, but that does exist in the natural harmonic series of “C”, and that note lies in the crack between A and Bb. And as the intervals continue to diminish, more and more notes are added that do not exist on the keyboard. Our modern music, and particularly keyboard instruments, have been tempered or tuned to an artificially engineered overtone series that allows all twelve notes within an octave on the keyboard to function in any key of music, without having to stop to retune the whole instrument in order to do so.
Plato, in his Republic, encoded this “equal tempering” as a political philosophy: “The necessity of tempering the pure intervals, defined by the ratios of integers” that is to say, the harmonic series as it naturally occurs with its infinite overtones for each note, “is one of the great themes of Plato’s Republic. In his allegorical form, ‘citizens’ modeled on the tones of the scale must not demand ‘exactly what they are owed,’ but must keep in mind ‘what is best for the city.’”12 That is to say, they must be willing to submit to a slight mathematical adjustment to allow them to function with each other in a harmonious fashion.
The number twelve here is a key, for it points directly to Mesopotamia and to its “sexagesimal” numerical system, a system that as we shall see was taylor-made to solve the tuning problem, and to a secret held by those cultures and passed down through the Pythagoreans. It points also to the twelve houses of the zodiac, and with that, the connection between music and astronomy comes a little closer into view.
B. Music, the Alchemical Medium
, and Astronomy
The Vedic tradition is full of allusions to the “luminous nature of sound”. Indeed, the word for light (svar) is similar to the word for sound (svara).13 This, as I have observed elsewhere, is another clue that perhaps we are viewing a legacy of a lost sophistication in physics, for the idea of a “sound-light” can also be understood as “electro-acoustic,” i.e., as longitudinal electrical waves in the medium, recalling the “Sound-Eye” spoken of in the Egyptian Edfu texts.14
The regularity of that physical medium was, for the ancient mind, expressed in the regularity of the cyclic nature of the heavens, and the precession of the equinoxes through a long cycle through the twelve houses of the Zodiac. Twelve, then, became the number of choice for expressing the musical harmony of the spheres. We may illustrate this by again sitting at an acoustic piano, and playing through the circle of perfect fourths and fifths:
Circle of Fourths (Asdending)
1) C
2) F
3) Bb
4) Eb
5) Ab
6) Db
7) Gb/F#
8) B
9)E
10) A
11) D
12) G
13) (C)
Circle of Fifths, Descending (Reading the above chart bottom to top)
Again, the notes we play are not the result of the natural overtone series, but of a tempering or “tampering with” by means of a mathematical adjustment to harmonize with the celestial motions of precession through the twelve houses of the Zodiac. As McClain states it, “Ancient cosmology required just enough number theory and just enough musical theory to harmonize the heavens with the scale and the calendar.”15 The musical allegory is expressed in poetic terms in the Rig Veda
Formed with twelve spokes, by length of
time, unweakened, rolls round the
heaven, this wheel of during order.
Twelve are the fellies, and the wheel is single.16
This astronomical and calendrical correspondence is even evident if one plays the white keys of the C major scale: C, D, E, F, G, A, B, for these seven tones were understood to represent not only the seven day week, but, in Vedic tradition, the Seven Rishis or Seven Sages.17
The Rig Veda also knows and speaks of the primary “tripartation” that we discovered in connection with Angkor Wat and Vishnu’s triadic self-manifestation:
The Gods are later than this world’s production,
Who knows then whence it first came into being?18
That is to say, all the multiplicities of the god-notes follow upon that first tripartation.
But what happens, then, if we take thirds, or the powers of three, and follow those around “a circle of thirds”? The result is perplexing, for if we start again at C, and follow intervals of a major third, we get the following:
1) C
2) E
3) G#/Ab
4) C
We are far short of generating the twelve equidistant tones of the circles of fourths and fifths. In other words, the primary mathematical and musical problem faced by ancient civilizations, was how to reconcile the two “sets” of god-tones into a harmonious whole.
This leads us inevitably to a consideration of the “female” and “male” numbers of the ancient tuning systems.
C. The Male and Female Numbers and the Physical Medium
The image of the musical circle was one that haunted the Vedic literature.
The chariot of the gods is actually a “wheel-less car… fashioned mentally” (10.135.3). The Celestial Race itself “was made by singers with their lips,” and the same singers “with their mind formed horses harnessed by a word” to drive the chariot,” a light car moving every way (1.20.1–3). Of the car itself, in what I assume to be an allusion to rotation and counter-rotation in the tone-circle, we hear that it “works on either side,” the car-pole to which the horses are harnessed thus “turning every way” (10.102.1 and 10.135.3).19
In other words, the primary feature of the physical medium in view in the ancient cosmology was its rotational frequency, and the resulting “music” therefrom.
Frequency is the key here, for it shows how and why the ancients approached the subject of tuning via whole number integers and ratios. Suppose you are sitting at the massive console of a pipe organ. Before you are five octaves on its various keyboards, beginning with the lowest note, “C” on your left. You pull an eight foot stop, say, the stop Prinzipal. On the stop knob there is a number 8 followed by a foot sign, thusly: 8’.20 This means that the pipe, from the mouth to the tip, is exactly eight feet long, and will sound the note “C”. Go up an octave, and the pipe will be exactly four feet long, and so on.
We thus have the ratio 8:4, which reduces to 2:1, which reduces even further, to 2. Two thus becomes the ancient number assigned to the octave of any note. It is a “female” number, and with this, occurs another problem:
The number 2 is “female” in the sense that it creates the matrix, the octave, in which all other tones are born. By itself, however, it can only create “cycles of barrenness.” In Socrates’ metaphor, for multipication and division by 2 can never introduce new tones into our tone-mandala. In musical arithmetic, the powers of 2 (2±n) generate cyclic identities; that is, they leave the musical relationship of the octave cycle invariant.21
Previously we saw how the primordial Nothing tripartitioned itself into Vishnu’s primordial trinitarian manifestation.
McClain speaks of this same thing, and now we come to the musical application of our previous topological analysis. McClain obserfved that “the starting point of the Rg Veda’s intentional life is the Asat, the non-existent, “the whole undifferentiated primordial chaos…”22 Thus, the sexual metaphor also enters the picture:
It is a theme of much ancient mythology that the Divine Unity is a hermaphrodite, producing a daughter, “2,” by a process of division without benefit of of a mother. God is “1”, but he cannot preocreate except via his daughter, “2,” the female principle and mother of all.23
But this, as we saw in our topological commentary on Angkor Wat, is not strictly true. It is not the number two which is first produced, but the number three, corresponding to the two regions of “differentiated Nothing” sharing a common surface. The common surface of the two regions becomes the topological symbol of the octave matrix, the regions defined by it.
To put it in terms of the numerical ratios that would have been used by the ancients, a primordial unity, once differentiated, gave rise to a primordial “triad,” and two is the arithmetic mean between the two: 1+3=4/2=2. In other words, our “ancient topological metaphor” is also a musical metaphor. The odd numbers are thus “male” numbers, including 1, 3, and especially 5, since these numbers, 3 and 5, generate the differentiation of tones within the octave “mother” or matrix.24 In this, the “female principle was deified, but it was exclusively the male element on which the world developed and differentiated itself.”25 Thus, Plato could define a father as “‘the model in whose likeness that which becomes is born.’ The only fathers we need from here on are ‘3’ and ‘5,’ which appear to have meant in the Rg Veda exactly what they meant long afterward in the Republic.”26 The powers of three, and the multiples of three and five, define the eleven tones of our modern equally-tempered chromatic scale.27
But why would ancient cosmological-musical systems equate femininity with the octave, and masculinity with the differentiating process that gave rise to (tonal and topological) diversity? We are perhaps here in the presence of another clue to the degree of sophisticated scientific knowledge bequeathed as a legacy to these ancient civilizations, for as modern genetics now knows, females carry only the female sexual chromosome, but males carry both sexual chromosomes and are capable of biologically reproducing either a male or female offspring. There is, as it were, a kind of inbuilt androgyny to the male that does not exist in the female. This might account for the assignation of “maleness” to those arithmetic ratios of odd n
umbers that produced differentiation in the generation of musical tones.
Why give such prominence to the “male” numbers? And what other numbers do they generate. Again, the answer is cosmological in nature:
The male odd numbers take precedence over their female octave “doubles” not only because they lie closed to god = 1, but presumably because they permit the divine unity to be subdivided rigorously according to the principle of unity; if we limit generative ratios, as Greek musical theory did traditionally, to those between two consecutive intergers… then each odd number (oddness itself being due to an element of unity) functions as the arithmetic mean for an earlier superparticular ratio, and subdivides it according to the same principle. We can schematize this subdivision as follows:
Note carefully the implications of this musical-topological metaphor, for clearly, it is not impaled on the horns of the either-or dialectic of having to choose between “pure monotheism” — a “feminine” principle in terms of the ancient worldview — nor a “pure polytheism”, or “masculine” principle in terms of the ancient worldview. The metaphor is an acid drip on that conventional opposition, for what one is looking at is an “androgynous both-and,” one encompassing both unity and diversity, and attempting to relate the two in a carefully conceived topological and musical metaphor.
Grid of the Gods Page 25