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and the Art of Music
by Dane Rudhyar

Chapter 4

Number and the Quantification
of Tone Relationship
Part One

Protagoras (500?-411 B.C.) said, "Man is the measure of all things." A more significant statement would be, man is the being who measures all things. Einstein's theory of relativity is explained by reference to yardsticks and clocks as instruments of measure. Such reliance on measurement reveals a basic belief in number and the subservience of the mind to the concept of quantity. Modern Western civilization worships quantity and pays only attenuated homage to quality. It is ruled by number — a tyrannical rule barely modified by the ideal of so-called democracy. Science is dominated by statistics, politics by popular polls and the apportionment of voting units and favors, and business by the expectation of quantitative production and profits.
      Music too is dominated by number and measurements, by the quantity and length of musical products. The performance of music is evaluated according to the quantitatively defined accuracy (the exact pitch) of the sounds produced and of their relationship to other preceding, simultaneous, and following sounds. Here one should speak of notes rather than sounds, for classical Western music is divorced from sound; it is defined by the musical score, a spatialized complex of relationships between notes, which actually are only thepotentiality of sound.
      One of the great failings of Western society is to confuse potentiality and actuality. The rule of number is the rule of potentiality. Ten units are potentially more powerful than one; nevertheless, most decisions are actually made by a very small minority of qualitatively more valuable, significant, and effectual individuals who are (in some ways) the spearhead of human evolution. Quantity comes to dominate when beings who were called upon to act in the name of a particular quality of organization are no longer able to perform their work of destiny — their dharma.
      The great problem is how to define and recognize the process of being called upon. To define it in terms of biological heredity and social inheritance is only partially valid. What we call education should be the process whereby a human being becomes aware of what his or her society and culture needs, and of what his or her ability is to participate effectively in the satisfaction of those needs — thus of what he or she is called upon to do, his or her vocation. But a society ruled by quantitative values and measurements (tests and statistics) obscures the deep, intuitive, and qualitative feeling of individual vocation. In American Indian society, every adolescent child (at least every male child) went into the wilderness and fasted until he received his vision and was given his sacred Name. Western culture is one of visionless and nameless individuals who, as citizens, are only numbers in a variety of statistics.
      Similarly Western music is a highly complex organization of notes which constitute a score — a musical work. All the notes in a score are interrelated, but the relationships are defined in terms of intervals — numerical ratios — not in terms of the quality and meaning of sounds which can be considered tones because they have an inherent quality and convey a message.
      It is probably impossible to ascertain when the concept of number, exact measurements, and proportions entered and came to dominate the field of sacromagical incantations and ritualistic tone production. Traditionally it comes from Pythagoras during the sixth century B.C. But great as Pythagoras undoubtedly was, he can hardly be made entirely responsible for so important a development. He certainly had traveled widely, and he may have learned in the sanctuaries of Egypt and Chaldea much of what he taught to a small group of the Greek aristocracy. It is also said that he received much of his knowledge from the Orphic Mysteries, but where the Orphic tradition originated is uncertain. One may speculate that it came from beyond Thrace and even Chaldea, from a very ancient center of secret knowledge in northwestern India. A Brahminical tradition claims that the Chaldean culture, at least in its more esoteric aspect, resulted from the westward migration of Indian people under the rule of the Lunar Dynasties. On the other hand, European historians believe that the ancient culture of the Indus valley was a colony of the older Chaldean people. Yet it seems certain that the Sumerians came from the north. They were succeeded by Babylonian peoples.
      Pythagoras was one of the great pioneers (if not the greatest in the Mediterranean world) in the development of a new level of the human mind. He impersonalized the gods and revealed — not so much instead of them, but beyond and through them — cosmic principles as the foundation of all forms of existence. But this development alone did not negate what the mythic mode of communication of psychic power and of experiential knowledge had built. Pythagorean principles simply gave a new character to the psychic energies of the sacred rituals of the Near Eastern Orphic tradition. He undoubtedly intended to make possible a more conscious, more objective, and more accurate use of these energies by human beings eager to act as individuals with relative intellectual freedom and personal independence. This relatively new sense of individuality and intellectual freedom developed under the sociocultural and political conditions which had led to the city-state.
      Pythagoras was also a reformer, just as was his contemporary, Gautama Buddha. Both communicated to a few followers a new approach, which removed some of the basic uncertainties of the generations preceding them. These uncertainties had arisen when the old tribal and vitalistic cults of the Greek world and India's rigid society controlled by the Brahmin caste had lost much of their efficacy and prestige. When the great reformers' disciples began to spread what they had understood from their teachers, the approach was new insofar as the general public was concerned; but the principles on which it was based had probably been known for a long time among initiates and adepts who had been living in secluded places or in the protective fields of temples. They were known in India as well as in the Sumerian and Babylonian cultures for at least twenty-five centuries, according to Brahminical chronology, since the Kali Yuga began.
      Kali Yuga is usually considered an age of spiritual darkness, but more significantly it is the period of gestation of a new humanity. This gestation process is very long and difficult; it requires the development of a clear and objective mind increasingly detached from the instinctual compulsions of biological drives and the collectively accepted and unquestioned rules and taboos of culture. All cultures are exclusivistic and jealous of their prerogatives, as well as innately bound to a particular territory and the particular way of life that territory fosters.
      Both Pythagoras and the Buddha were universalists. When Pythagoras spoke of numbers he did not mean mere arithmetical abstractions but universals — that is, realities of a realm of being transcending local conditioning, the cultural-mythical personifications having meaning and power only in terms of a particular culture-whole and, within it, the prerogatives of a particular class or caste. Similarly when the Buddha spoke of Nirvana he meant a state of consciousness no longer attached to or even especially conditioned by the long-held beliefs and rituals of ancient Vedic India still dominating the consciousness of the people. He tried to spread the direct realization that there exists in all human beings a power of mind which can analyze away and destroy any attachment to and identification with all forms of desire, especially the desire for individual, exclusivistic, and separate selfhood. He thus tried to evoke a universal state of consciousness and being.
      Most of these great reformers' disciples probably did not understand that what their teachers had tried to formulate was a practice or technique for freeing the mind from the power of privileged castes and traditional methods handed down orally by families jealously guarding their secrets. What the Buddha taught, anyone could use; and if a person suddenly understood, his or her consciousness could be instantaneously liberated. When Pythagoras used the monochord (1) to show the exact value and meaning of the relationships between the tones of a chant, he made it possible for anyone to understand tone relationships and to experiment with them, while before him, the use of tones and inflections was reserved to a few trained poet-musicians probably using strict rules derived from old magical and sacred traditions.
      Pythagoras was very careful in teaching these universal principles of sound, and particularly how to use the sound-relationships his monochord revealed, for communicating spiritual and healing energies. His school in Krotona operated at three levels, not unlike the three degrees of Freemasonry. In the first grade, which could only be reached after severe tests of character and moral strength, the acoustici learned how to recognize and apply the various musical proportions demonstrated to them through the use of the monochord. In the second grade, the mathematici had to deal more specifically with individual purification and mental self-control. Presumably the aspirant at that level was made to realize the nature of the shift in the level of his or her consciousness which was at the core of the new spiritual-mental reform. In the third degree the esotericists were probably taught the secret processes of psychic transmutation and the control of forces needed for accomplishing the "great work" of perfection, and also for healing, for Pythagoras apparently emphasized the therapeutic power of sound when these sounds were tones able to communicate the compassionate energy and will of the purified tone-producer attuned to the rhythms of the universal life-force (see Appendix 1). The significant fact is that Pythagoras sought to free music from the limitations of traditional practices based on the mythic type of consciousness. The music he pioneered drew its power from mind, but mind as a cosmic, formative power.
      It is not clear whether Pythagoras used what we call the Greek modes. As the names they bore indicate — Dorian, Phrygian, Lydian, for example — modes were rooted in the performance of sacromagical ceremonies by particular races of people. They were series of relationships between vocal tones nearly always associated with words. When musical instruments were used they were intimately related to the sacred intonation of divine Names and, elemental powers. Instrumental melodies achieved a complete independence from words only at a later period, probably in Greece during the fourth century (though it is possible that some of them were used previously for popular dancing or to imitate bird songs, animal cries, or the sound of thunder). In India much was made of Krishna playing the flute, but it is impossible to know when this mythical story originated, for the worship of the child Krishna began long after the Buddha, when the old Hinduism regained its power. The mythical Orpheus was also said to play the lyre, probably as an accompaniment for sacromagical chants.
      The significance of the scale Pythagoras used was that it did not have a special connection with local and ritualistic events. The melodic sequence of tones could be intoned at any time and any place because it had a universal validity rather than a mythic and cultural character. It was based on not only universal but observable facts. Anyone who knew how could easily ascertain the accuracy of the sounds and their sequential relationships by measuring lengths of vibrating strings. Through this act of measuring, the formative processes of the realm of the cosmic mind — the mind of reason and harmony — could now be understood and unvaryingly applied to the needs of emerging individuals eager to free themselves from a collective existence.
      When, through travel and commerce, local conditions lose much of their fundamental meaning and root power, the myths, cults, and sacred ceremonies of a culture are deprived of biopsychic efficacy. The power of reason gradually supersedes the magical foundations of the vitalistic age. This is a slow process to which only a "creative minority" (to use Arnold Toynbee's phrase) can effectively resonate. The new mental concepts take the form of theories, which may be officially taught, but the official teachings do not radically alter the general practice of the people. Confusion, therefore, results.
      The Pythagorean scale is not a mode, for a mode is the product of special conditions belonging to the realm of culture and myth. The Pythagorean scale is an unconditioned, archetypal manifestation of cosmic principles. Number and proportions, as Pythagoras understood them, belong to the realm of archetype. In order to effectively operate in that realm man needs to develop a mind that has basically freed itself from bondage to biological energies and mythic-cultural specialization and exclusivism. When conceived by the archetypal mind, music can become, at least potentially, a universal, supercultural language.

1. A monochord is simply a string stretched between two pegs over a kind of yardstick, with a movable fret gliding over the stick. By moving the fret one can easily measure the exact length of the string which one sets in vibration. One can start with a definite unit of vibrating string, say two inches, and by plucking successive lengths of four, six, eight, ten, and twelve inches of string one obtains a descending Harmonic Series. One can set the whole length of the string vibrating, then one half of it, a third, a fourth, a fifth, and so on. One thus obtains an ascending Harmonic Series. The meaning of these Series is discussed in chapter 7.  Return

By permission of Leyla Rudhyar Hill
Copyright © 1982; by Dane Rudhyar
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