Home | Bio | Art | Music | Literature | Civilization & Culture | Philosophy of Wholeness | Theosophy & Spirituality | Astrology
and the Art of Music
by Dane Rudhyar

Chapter 8

The Septenary Tone Cycle
and the Psychoactive Modes Issued
from its Fundamentals
Part Two

The Organization of Fundamentals

Sound as the means for the transmission of creative power has a septenary operation. At the human level, this creative power takes the limited form of the will or desire to perform an act which contracts and moves muscles, including those of the vocal organs. Each of the seven types of Sound's descending motion arouses in matter a characteristic resonance, one of seven Fundamentals. The basic question is, how are these seven Fundamentals related? They must be related because they are differentiated aspects of the single source of power from which they branched. They branched because each has a characteristic function to perform as it strikes matter. A scale, considered as a group of seven Fundamentals, is a functional whole — a system of organization, a musical organism
      In the philosophy of number, seven represents the possible ways three principles can operate; that is, each singly, by pair and all three together. Thus one, two, and three can operate in seven ways as 1, 2, 3, 1 + 2, 1 + 3, 2 + 3, and 1 + 2 + 3. The number three results from duplication, which gives rise not only to number two, but to number three (1 + 2 = 3). By adding the seven combinations of the first three numbers we obtain number twenty-four (twice twelve).
      In ancient Greece, the seven Fundamentals were presumably called arches. Each of these had a function to perform in an organized life field. Each arche, however, could act as the origin or initial tone of a mode which dealt with the unfoldment of the arche's special function in the sevenfold scale of fundamentals (the grama).
      As the creative Sound strikes potentially resonant matter, it becomes the life force (prana in India, chi in China), and this life force circulates through the nadis of the human body (the meridians in the philosophy of Chinese acupuncture). The cosmic Sound Nada becomes in living matter the nadis, which are concentrated into the seven chakras (wheels or whorls of energy in the body). Esoteric tradition refers to three sets of seven chakras. One set along the spinal column is the downward path of Sound ending in the muladhara chakra at the base of the spine (where, it is said, the power of Kundalini is coiled, sleeping, like a snake). Another set of seven chakras radiates from the spinal set and is broadly related to biological organs (especially endocrine glands) and their functions. A third set is said to exist within the head, and are sometimes called the master chakras.
      These three sets of chakras can be related to the three gramas of ancient India. The Gandhara grama presumably refers to the master chakras within the head. The mysterious sage and adept Narada is said to have heard this grama sung by singers (gandharvas) in the celestial realm, but it is inaudible for ordinary mortals whose consciousness is bound to the activities of the biophysical level of existence.(1)
      Thus the seven Fundamentals exist as centralizing areas of tone potency in human beings. They are symbolized by the seven sacred planets and associated with the chakras. They are also associated with seven vowel sounds, which symbolize the seven aspects of the life force in human manifestation. Thus the Christian Gnostics — who not only once represented the esoteric aspect of Christianity but (though persecuted by the official Church) have never ceased to do so throughout the entire span of European culture (as the Sufis represent the inner, spiritual aspect of Islam) — had their sacred vowel chants. The echo of such chants is heard in Alexander Scriabin's symphonic poem, Prometheus (The Poem of Fire), when the chorus intones a mysterious word, OEAOHOO. This word should be pronounced with seven vowel sounds (which nevertheless are only three, 0, E, A). It is mentioned in H. P. Blavatsky's Secret Doctrine, which relates it to the descent of a group of promethean spiritual beings from a higher planetary scheme into the etheric realm of the earth. These beings are said to have bestowed the gift of self-consciousness (objective or reflective consciousness) upon an animal-like mankind.
      Ancient Chinese music used five or seven Fundamentals, called by various names, which can be translated as either degrees or beginnings. The five Fundamentals were manifestations of the five elements (fire, water, wood, metal, earth), the five colors, the five planets, and the five aspects of Chinese culture (the king, his administration, the people, business, and the material products of the kingdom).
      The problem that had to be solved to establish a particular musical system' was how to define the relationships between these Fundamentals — that is, the musical intervals both separating and linking them. In archaic times this problem probably did not arise. Deliberate and conscious choices of tones had to be made only when the concepts of number and proportion were introduced into a musical consciousness which previously had been mainly spontaneous and instinctive. A musical system was therefore built on the basis of principles which defined the particular character of a culture, even though the principles were believed to be universal.
      If one believes that the series of whole numbers reveals a universal principle, the problem of choosing tones is solved by selecting from the variety of possibilities revealed by the series. The relationships between the Fundamentals have to be measured: they take on the objective character of intervals between entities spread in visual space. The Pythagorean monochord — which may have been used in Chaldean and Egyptian sanctuaries centuries before Pythagoras — is the simplest and most characteristic instrument for identifying sounds and numbers and for experiencing descending and ascending series of tones. In China decreasing or increasing lengths of tubes of bamboo served the same purpose.
      Two procedures are possible. The first is to select a section of the harmonic series bounded by two sounds in octave relationship and to use only the overtones within this octave interval. This is the kind of natural intonation Kathleen Schlesinger believed was universally used before theorists formulated a more intellectual system. Natural intonation implies the primacy of instrumental music, for it is only through man-made instruments that overtones can be measured. Yet the earliest production of intentional series of tones (such as mantrams) was undoubtedly by the human voice. True, a specially trained human voice can produce overtones (as in Tibetan sacred chanting), but such a deliberate production seems to belong to a later period; above all, its overtones cannot be directly and concretely measured. Moreover, within a scale, no two intervals produced by such a selection are the same, for the ratios between tones represented by two successive whole numbers constantly diminish.
      In the second procedure, the relationships between primary numbers are used as interval units on which to build a scale — an archetype of relationship. The primary numbers one, two, three, and four constitute the Pythagorean tetraktys, a sacred symbol for the Greek philosopher. These numbers define the octave (the ratio 2: 1), the fifth (3:2), and the fourth (4:3).
      Musicians tuning their instruments (particularly the lyre) and writers attempting to present Pythagoras's ideas have usually taken for granted that the proper procedure was to start from the fundamental (let us say C), move upward a fifth to G, then descend by a fourth from G to D. The interval C to D is the whole tone (a 9:8 ratio). By adding another wholetone to D the note E would be reached, and a semitone would be left between E and F — the interval C to F being a fourth (the tetrachord in the ascending scale). However, Greek tetrachords were always presented as a descending sequence of four notes. Pythagoras perhaps sought to establish a structure indicating that humanity had reached a point at which man could reproduce the descent of the creative power of Sound by an upward kind of resonance symmetrically reflecting the first steps in the creative process, from the ineffable One, to the two, and from this mother tone to the three, the cosmic mind.

      Pythagoras thus built his scale on the interpenetration and interaction of a descending and an ascending fifth within an octave. The result of the interpenetration is the whole tone. The Roman philosopher-harmonicist Boetius (480-524 A.D.) states that this was the way Mercury's lyre was tuned. (2) The center of such a scheme is F-sharp, the midpoint of the octave; I believe it symbolizes the tone of the earth that was stressed in Chinese music. This tone approximates the eleventh harmonic of an ascending harmonic series starting with C. (Kathleen Schlesinger found that the mode most frequently used in ancient Egypt and in India was a series of eleven notes to the octave, thus the section of the harmonic series between the eleventh and the twenty-second harmonic. See The Greek Aulos.) For many centuries the music of India has featured a series of twenty-two srutis, selecting from these (so relatively late writers report) the seven notes of the sa grama.

      However Pythagoras conceived the formation of the whole tone (the ratio 9:8), his disciples' disciples believed that he selected the seven notes of his scale by using the initial notes produced by an ascending series of exact fifths, C, G, D, A, E, B, and bringing these notes back to the limited field of a single octave. But this series does not provide an F-natural, because its seventh fifth sound is an F-sharp (which differs noticeably from the F-sharp of the harmonic series, being a somewhat larger interval). Thus there is something awkward and illogical about such a scheme of scale formation, and we have to believe that the F-natural was the product of a descending fifth.
      It seems that the method used for tuning instruments like the kithara was based on the partial alternation of ascending fifths and descending fourths, but opinions vary considerably and authorities disagree. The same thing happened in China where the series of twelve fifths — the cycle of lyus —formed the basis for calculating intervals.
      The Pythagorean scale — the condensation of seven notes derived from a series of intervals of fifths — is a diatonic scale. Considered as a series of intervals, it is a succession of whole tone (9:8), whole tone, hemitone (256:243), wholetone, wholetone, wholetone, hemitone.(3) In the traditional Greek view, the series includes two tetrachords (whole tone, whole tone, hemitone) separated by one whole tone. Whether Pythagoras actually thought of it in such a manner is questionable. It may represent an interpretation by Greek musicians (and later theorists) used to dealing with tetrachords of what Pythagoras had in mind, especially when he spoke of the "music of the spheres."
      This series of intervals produces sounds which could be considered overtones of a low fundamental tone and represented by the numbers 384, 432, 486, 512, 576, 648, and 729. The number 384 is the seventh octave-sound of 3 (3, 6, 12, 24, 48, 96, 192, and 384); and in the series of whole numbers beginning with 1, 3 gives birth to the interval of fifth. Thus the Pythagorean scale is also potentially a section of the harmonic series. The so-called natural scale of European tonality (before equal temperament) can be considered a series of overtones beginning with number 24 (24, 27, 30, 32, 36, 40, and 45). It therefore also begins with an overtone belonging to the fifth octave of the harmonic series starting with 1.
      In India it appears that the twenty-two srutis within an octave provided the musical substance from which the seven tones of the sa or ma grama were selected; tables survive showing the manner in which a number of srutis were found between the seven basic notes. But here, too, actualities are uncertain. I believe that the seven components of the grama were used in ancient sacromagical incantations (for example, in intoning the Vedas) long before the series of twenty-two srutis came to dominate classical Hindu music.(4)

1. See Fox Strangeway's The Music of Hindustan (Oxford: Clarenden Press, 1914), P. 70. The name Narada is probably symbolic. Man is referred to in some ancient Hindu scriptures as Nara, and Nada is the creative Sound.  Return

2. In J. Marnold in Les Fondements Naturels de la Musique Grecque (International Music Gesellshaft, 1907-09).  Return

3. The hemitone (limma) is what remains of an exact fourth (4:3) when two whole tones are taken away from it.  Return

4. In the sa grama the twenty-two srutis are divided as follows: 4, 3, 2-4-4, 3, 2. In the ma grama the distribution is 4, 3, 4-2-4, 3, 2. But are the srutis small equal intervals, or harmonics of a fundamental tone?
      The reader interested in the philosophical meaning of numbers and proportion will perhaps have realized that the ratio 22:7 is a very close approximation of the magical value of the relationship between the length of the circumference of a circle and its diameter. This value, pi, is a never-ending number, 3.14159 . . . The ratio 22:7 is also never-ending, as its series of decimals keep repeating endlessly (3.142857142857, etc.).
      Raga music in India probably started after the rebirth of Hinduism and the Medieval triumph of the spread of bhakti devotionalism of the Radha-Krishna movement. During the Buddhist and perhaps pre-Buddhist era another type of musical organization prevailed following the jati system. Still earlier in Vedic and post-Vedic times music most likely was mainly associated with Vedic rituals and the recitation of sacred texts and mantrams.  Return

By permission of Leyla Rudhyar Hill
Copyright © 1982; by Dane Rudhyar
All Rights Reserved.

Visit CyberWorld Khaldea

Web design and all data, text and graphics appearing on this site are protected by US and International Copyright and are not to be reproduced, distributed, circulated, offered for sale, or given away, in any form, by any means, electronic or conventional.

See Notices for full copyright statement and conditions of use.

Web design copyright © 2000-2004 by Michael R. Meyer.
All Rights Reserved.