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and the Art of Music
by Dane Rudhyar



1. Communication: Man's Primordial Need

2. Sound as Carrier-Wave for Tone

3. The Magical and the Sacred

4. Number and the Quantification of Tone Relationship
     Part One
   »Part Two

Chapter 4

Number and the Quantification
of Tone Relationship
Part Two

The difference between scales and modes is basic though subtle and deals with the consciousness of music more than with the sounds and intervals the ear perceives. In archaic times when shamans and priests intoned magical incantations, the tone relationships (intervals) they used might have been almost indistinguishable from those of the Pythagorean scale; but they were not measured! They could not be measured if the tones were produced by the human voice. If they were mathematically accurate the accuracy was unconscious and instinctual. The shaman chanted as birds sing or cats in sexual circumstances moan and yell in intense melodic developments. The shaman was not preoccupied with the possibility of uttering "wrong" notes. He had learned through imitation and oral transmission the correct way (in Sanskrit, rita) of chanting in order to obtain effective results; and archaic man's memory was undoubtedly remarkable. A bard could remember not only the words of a long epic narrative but the traditional way of intoning the words, of sliding from tone to tone, and of obeying complex rhythmic patterns. Of course, singers today memorize long parts in operas, and orchestra conductors hold in their minds a prodigious number of complex orchestral scores. But their capacity for memorization does not belong to the same level of consciousness. Magical results are very different from intellectual and esthetic responses.
      Similarly, one may think of archetypes in at least two basic ways. A typically intellectual person might consider archetypes as abstractions, as a set of characteristics extracted (or abstracted) from a vast number of concrete data. He or she will think of archetypes as the product of a mental operation for which the human mind seems to have a unique ability. Number five, it may be said, is the abstraction of the universal human experience of having five fingers on each hand. Number one is the abstraction of the experience of being distinct from everything else and possessing characteristics which, being solely one's own, define one's basic sense of being "I." By extension of the idea, anything is a one which, in one's experience, is not duplicated, or which becomes the source of an ever-repeated process of reproduction.
      On the other hand, for Pythagoras, Plato, and philosophers, mystics, and cosmologists of ancient eras, archetypes belonged to a realm superior to and (in terms of cyclic time) antedating human thinking. Archetypes were usually considered the results of the creative activity of the divine mind. They constituted the foundation on which all concrete forms or modes of existence were built; yet the term foundation is not quite right because one usually thinks of foundations as made of solid and resistant materials, while archetypes are more like seeds imbued with the latent power of life — the power to transform themselves into plants and trees through germination and growth.
      Archetypes thus were not originally considered abstractions from a multitude of similar or analogous particulars. Each archetype was understood to be the seed-origin of a multitude of forms and modes of existence possessing identical characteristics.
     ; As I use the term, an archetype is a concentrate of creative energy as well as an ideal structure establishing a definite set of relationships among its components. The word structure in its nonmaterial sense is a special arrangement or pattern of organization by which material entities constitute the many parts of an all-encompassing whole. (1)
      The Pythagorean scale is an archetype in this sense. It is a structure giving a definite form to the relationships among its components; but these components are not abstractions or mere musical notes, but rather are tones imbued with an archetypal potency. When tones became mere notes in classical European music, it was because the potency of the creative human mind when attuned to the harmony and rhythm of the universe (or its postulated divine source, "the One") had been replaced by an intellectual and formalistic capacity for organization.
      The shift from creative and transformative archetypes to intellectual organization according to abstract models characterizes the relative failure of the Greek culture. Europe inherited the legacy (the karma) of that failure. After the emergence of a complex structural polyphony and the adoption of a rigid system of notation and measures, European music developed the system of tonality and its prototypal C-major scale. The character and meaning of such a development will be discussed in a subsequent chapter.
      An interesting though limited parallel could be made between Pythagoras and Francis Bacon, the man who established the scientific method. Both men sought to provide a universally valid foundation for knowledge and the practical application of that knowledge. Pythagoras lived at the beginning of the classical age of Greek culture, an age that eventually lost respect for the cults that were beginning to proliferate in the eastern Mediterranean regions. The great century of Athenian domination was marked by a fascination with reason and a sense of the Beautiful and the True. The Good, was revered secondarily, though apparently Pythagoras emphasized the necessity to live a pure life based on loving kindness, virtue, and harmony in all relationships. Francis Bacon lived at a time when Englishmen and Europeans sought to expand the new data provided by Copernicus into a humanistic knowledge free from the dogmatism of the revelatory doctrines of the Medieval Church. Bacon's empiricism (in his Novum Organum) was a method for reaching an objective and rational knowledge of the world of human experience and its infinite varieties of relationships.
      Truth, to the classical Greeks, was based on reason and harmonic proportion. The True could be proven by any rational person properly making use of measurements; the Beautiful was the spatialization of harmony. What the Greeks meant by harmony in music is what we call melody, for Greek music was essentially melodic (or rather monodic), and Pythagoras's concepts dealt with a single series of tones, though one wonders whether his "music of the spheres" did not also refer to a harmonic polyphony.
      Pythagoras's use of the monochord in order to check the accuracy of the relationship (interval) between two or more tones was both empirical and rational. While it was based on strict and objective observation, it was also a powerful means to make the student think in terms of cosmic principles. When that thinking became pervaded and dynamized by the will to the Good, it became illumined by healing power — the power to harmonize the psychic natures of human beings who, having partially overcome their bondage to a collective, cultural psychism, were tense and emotionally confused.
      The practice of healing (or "whole-making") was an important part of what Pythagoras taught in Krotona. But healing can be approached in several ways. In archaic times the shaman healed by bringing the sick person back to the reservoir of power, the collective psychism, of his or her tribe. The priests of vitalistic cults healed by invoking the god or goddess he and the sick person worshipped as a fountainhead of the powerful flow of the One Life. With Pythagoras, healing became the harmonizing of discords in the partially individualized (thus relatively isolated) and psychically disturbed person.
      The healing power Pythagoras used was that of Sound itself — sound used as a power of harmonization. To harmonize in the Greek sense was to deal with the unceasing process of change that is life itself, to make this change resonant with the rhythmic flow of universal change. The universe was not seen as a static whole, but rather — as Heraclitus emphasized — a dynamic process of rhythmic formation and transformation. Pythagoras presumably emphasized the formative aspects, while Heraclitus stressed the transformative phase, symbolized as fire.
      The basic premise Pythagoras impressed upon the collective mind of pre-classical Greece was that the process giving form to all things operates through number. The formative process operating through number was not, as Pythagoras formulated it, a magical or divine operation, but one based on ratio and, more abstractly, on reason. This operation could be understood by the human mind and applied in the simple act of measuring.
      The dangerous and potentially negative aspect of such an approach to existence is that it tends to substitute quantitative concepts and practices for qualitative values. It also tends to stress the importance of matter and material bodies because these can be easily measured, while psycho-spiritual realities do not lend themselves to quantitative analysis. In music a transformation of sacromagical tones into abstract notes which are but the edges of intervals becomes likely once the tone producer becomes a quasi-mathematical theorist or technician haunted by accuracy and mechanical (that is, measurable) perfection. The Greek trinity of the Good, the True, and the Beautiful can take the form of ethics, science and esthetics; but if scientific knowledge is pursued in lonely splendor by technicians intent only on measuring everything regardless of human consequences, and the arts stress the concept of form regardless of content or meaning, ethics, as the development of interpersonal relationships on the basis of an all-encompassing harmony, tends to be either forgotten or sentimentalized by the paternalism of priests and moralists.
      Then two basic concepts arise: knowledge for the sake of more knowledge (regardless of what its application will mean), and art for art's sake, which in the broadest sense of the term is formalism. Musicians then speak of "pure music," free from any connection with poetry or any association with concrete events or appearances. The problem then is to define what the music communicates. We shall return to this question in subsequent chapters.

1. In our century the word archetype is associated in many people's minds with its use by the depth-psychologist, C. G. Jung. Jung, however, seems to have oscillated between two ways of thinking about archetypes. Originally he defined archetypes as powerful concentrates of human experience in the "collective unconscious," where they exist as numinous entities which we have to deal with during "the process of individuation." On the other hand, in his later books Jung seems to consider archetypes as preexisting psychic structures characterizing and inherent in the human species. Perhaps this latter concept developed in Jung's mind when he studied alchemy and reinterpreted it in psychological terms. Jung vehemently disclaimed being a metaphysician, yet his concept of the psyche has a metaphysical character. For the ancient Greeks, the word Psyche referred only to the lower, emotional level of the soul; its higher, emotional and archetypal level was called nous, from which the adjective noetic is derived.  Return

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