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and the Art of Music
by Dane Rudhyar

Chapter 7

The Harmonic Series
Part Two

The Seven Levels of Being
and the Symbolism of Number

According to the great religions of the last five millennia, and to most of the metaphysical systems dealing with the origin of the universe (or more generally with the origin of being), all there is began in unity. The religious mind usually personalizes the concept of unity as God. Metaphysicians speak of "the One." Sankaracharya, founder of India's Advaita (or nondual) system of metaphysics, speaks of "the One without a second." The great (and actually insoluble) problem of metaphysics and religious cosmogonies is how to explain or interpret the passage from unity to duality, and from duality to the quasi-infinite multiplicity of entities active in the universe. Religions speak of God's desire to create, of the primordial Eros that moves the One to produce out of its unity a second, perhaps a mirror, image. Hindu metaphysics interprets such a process of doublement or replication as the great illusion, the essential Maya, root of all existence. The harmonic series of fundamental and overtones provides a very significant and experienceable realization of the relation between pure unity (the One) and duality (the second) by referring to the unique and mysterious character of the octave in music.
      The remarkable fact is that two sounds an octave apart are given the same name, even though one of their frequencies is twice that of the other. They have for our ears an identical nature. They are the same note, even though they are obviously not the same sound. Are we conditioned by our culture to feel that two sounds at an octave interval are the same note, or is the feeling of their identity innate — that is, rooted in an intuitive grasp of the nature of a metaphysical-spiritual process, which is none other than the basic process of cosmic existence and the primary manifestation of what we call life?
      Although the harmonic series of fundamental and overtones is an arithmetic series, and the archetype of all such series is the series of whole numbers created by the endless addition of number one to itself, the term addition may be misleading. Philosophically the series refers to the self-reproduction, self-multiplication, or self-replication of the One. All numbers are born out of number one. The birth process begins with the characteristic act of self-duplication. Duality emerges out of unity: the One produces the Other, which is identical to itself — a mirror image (as it were) — yet itself in a new role. This duplication process can be repeated; its repetition produces a geometrical series: two, when duplicated, produces four, which when duplicated produces eight; the eight duplicates into the sixteen, and so on.
      This series might be considered a repeated process of reflection, giving rise to a series of mirror images. But sonically the series produces octave-sounds. They are not merely reflections of one another, for each one is the source of series of overtones, and each new octave of the harmonic series contains more overtones than the preceding one. Each new octave symbolizes a level of being one more step removed from the original unity — sonically the fundamental, philosophically the One.
      Some of the religions of India speak of the One as Shiva, and the second as Shiva's shakti — his power, which is personified as his feminine counterpart, Shakti, the beloved. In the Tantric cosmogony, once Shiva has created Shakti and consummates his union with her, he retires (as it were) and becomes a mysterious presence beyond the cosmic manifestation to which Shakti gives birth. The mother, having produced the child, becomes the manager of the generative process and of its results. She rules over the universe of concrete and multiple entities — over all subsequent generations, each of which begins with a reflection of the primordial mother. Each of these mothers (like each of the subsequent octave-sounds of number two) also manages and rules over her own progeny and her own level of being.
      The initial process of duplication of the One into the second has its source in a release of power from the One. This is what religions interpret as God's "desire" for creation, for self-revelation, or for the exteriorization of the immense potentialities of his infinite being — the One desiring to be many. More impersonally, this desire is the motion that operates throughout the universe. Motion is everywhere. Matter is the incredibly rapid motion of subatomic particles, which themselves are nothing more than whirlpools of motion. All life is God's self-revelation through rhythmic, self-duplicating motion. In its primary spiritual aspect, this motion is Sound — the descending power of the One into multiplicity, the descending harmonic series.
      Is this descent endless? The rational intellect can find no reason for an end to the process of self-replication. The harmonic series issued from the fundamental One can theoretically extend ad infinitum. But infinity is only an intellectual concept; it is the negation of limit. The concept of existence, however, must include limitation. Existence can only be conceived in terms of wholes, and all wholes must have limits or boundaries, metaphysical if not physical.
      Thus the octave symbolizes and defines a whole of sound-the limits within which motion, as a creative factor, cyclically operates. Metaphysically, the octave is the most fundamental whole because it originates in the first act of self-duplication, of which all further acts are replications. But the momentum of the creative release of the power of the One does not stop with number two. The power release acting through number two produces number three, the symbolic child. A new relationship is established between the mother principle and the child principle. This relationship also replicates itself, generating in music a series of fifths (the ratio 3:2) — a new limiting and cyclic factor.
      The geometric series of octaves and the geometric series of fifths interact; and a time comes when both series reach almost the same vibratory frequency: twelve fifths extend a little farther than seven octaves, the difference between them being the Pythagorean comma. What this means becomes clear once we understand the character of the interval of fifth and experience the psychic response it normally produces in human beings. To do so, however, we have first to deal in some detail with the field of cosmic and psychic activity and consciousness represented by each successive octave of the harmonic series. What we will discuss is a series of abstract numbers and proportions, the harmonic series as an archetypal pattern that can be interpreted numerologically, descending or ascending as the occasion requires.

The first octave, considered in terms of a descending harmonic series, refers to the pre-cosmic realm of being. The human mind cannot conceptualize or formulate the quality of this realm, and the word realm is obviously inadequate because space does not yet exist. To say that it is the realm of changeless being also means very little, for time does not exist yet, either. The human mind can only conceive of it as pure void, nothingness; yet in that void the potentiality of all existence is implicit. Motion inheres in it, but only in the sense that God's desire is in itself the cause of motion. When anthropomorphized, it is the emotion inevitably leading to objective muscular movements. This first octave in the descending series symbolizes the purely subjective relationship of the One and the other that is its image. In the terminology of the Tantric systems, it symbolizes the mysterious love of Shiva and Shakti before any manifested forms of existence appear. It is the realm of God's desire for seeing himself reflected in a multiplicity of potentially creative and individualized centers.
      The first octave in an ascending harmonic series — that is, in the rebounding of the descending current of will, emotion, or creative power from the material instrument that gave it a concrete, limited, and audible reality — symbolizes the sexual love union of male and female as it reflects the divine love of Shiva and Shakti. God's desire for self-revelation has become the dynamic power we call life. Life acts in and through the lovers. The two sexually complementary bodies are merely instrumentalities which life sets into resonant vibration in order to perpetuate one of its specialized forms (or modes of activity and consciousness) which we categorize as homo sapiens. A modern biologist would therefore say that, in sex and in instinctual love (the glamorization of sex) the bodies of the two lovers are merely convenient apparatuses for the perpetuation of genes. (1)
      What we call life is therefore the symmetrical reflection of the process, following which a creative release of energy from the precosmic union of the One and its image sets into vibration a physical organism. Before sexual differentiation occurs in biological evolution, life perpetuates itself through mitosis, the division of one cell into two. When reproduction is sexual, two complementary factors temporarily unite to produce a third. However, in some biological species the female, after being fecundated, kills and eats the male. If we translate this into musical symbolism, the second partial (the octave-sound of the fundamental) alone remains active and gives birth to number three.
      There are indeed instances when this octave-sound (often confusingly referred to as the first overtone) is the sound we actually hear instead of the fundamental. In any case, this octave-sound (number two of the harmonic series), as the mother, rules the home as well as is the source of a progeny. The prototype of all children is symbolized by number three in the series of whole numbers. In ancient tribal and in many more recent systems of family and social organization it represents the first son. However, in the cosmic scheme it has a much deeper character and meaning.
      Number three is the result of the operation of the One through its image and duplication, number two. Number three represents the desire to exteriorize all that is inherent in the One producing the first result that is not merely a mirror image. Number three is the origin of a potentially quasi-infinite series of diverse yet complementary realizations, all of which were latent and implicit in the One. If number two is (metaphysically) the projected reflection of the One, number three is the projection of the love of the One for this reflection. It is the desire for exteriorization of the One operating as will, the first manifestation of cosmic motion.

The second octave begins with number two. If we think of the harmonic series as a descending current of creative energy radiating from God, the second octave represents the first realm of manifestation of the principles according to which the cosmos will be built. In the first octave, duality was implicit; in the second octave it is explicit. The first octave is the noumenon of space as a field of potential activity. The potentiality is there because of the desire of the One for a second; but this second is a mirror image of the One. The One and the second are identical. We can hardly speak of a relationship, because identity is not really relatedness. Yet there is an implied difference between One and two. Two is One charged with the power to be the source of an immensely varied progeny. This power is Sound, Nada Brahman. This power has a dual nature, and the second octave is divided by number three into two unequal intervals, a fifth (the ratio 3:2) and a fourth (the ratio 4:3).(2)
      We can state this another way: love as a subjective desire is unitary; creative power is bipolar and operates through the interplay of two principles, expansion and contraction. The interval of fifth is expansive; the fourth is contractive since it has to balance and counteract the centrifugal power of the fifth in order that number four may be the exact duplication of number two. Such an exact process of duplication reflects the pre-cosmic, primordial love of the One for the second — producing a geometric series of octaves. Each new octave-sound begins a new level of cosmic manifestation, thus giving birth to a new rhythm of activity and consciousness.
      As a centrifugal power the fifth represents the will to self-exteriorization, the power to make what is potential actual, and what is implicit explicit — thus the cosmogonic, creative mind. The fifth symbolizes electricity; the fourth, magnetism. The second octave, which contains both a fifth and a fourth, is a realm in which electromagnetism is the primordial mode of motion. At a lower and human (or psychological) level the dualism is that of mind and feelings.
      In Chinese philosophy two principles, yang and yin, constitute the primordial dualism of motion within the circle of Tao; but yang and yin are equal as well as opposites. In music, the fifth and the fourth are not equal intervals, even though they, too, are contained within a circular and cyclic pattern, the octave. But twelve fifths are slightly more extensive than seven octaves. Thus the universe of the creative mind is a spiral, not a circle; there is no Nietzschean eternal return, no unceasing repetition. Even though the octaves within the harmonic series repeat themselves, the contents of the octaves potentially expand infinitely, each new octave containing a greater number of overtones than the preceding one. What also expands are the ramifications and diversifications of the original power radiating from the fundamental, One.
      As the interval of fourth symbolizes contraction, it balances the centrifugal, open quality of the fifth. Twelve fifths plus twelve fourths thus cover the same musical space as twelve octaves. But human beings do not have the capacity to hear twelve octaves of sound.
      The harmonic series considered merely as a geometric series of octaves refers to the reflection, level after level, of what the first octave means — the One's desire to be many. The geometric series of fifths and fourths refer symbolically to the many's development of consciousness; and consciousness oscillates between two poles, creative expansion and enjoyment of being. In Indian philosophy, this enjoyment of being is ananda, a word usually translated as bliss but really meaning the return of the many to the One — as One can be understood and experienced by the returning consciousness of one of the many. Thus the one to which it returns is not the original One but its reflection in an octave-sound. This is why Tantric devotees worship the mother force (number two or its octave-sounds), believing the One (the hidden Father) to be unreachable. The interval of fourth thus symbolizes the return to the mother. At the human level, such a return may compensate for psychological defeat and neurosis, or it can mean that the negative aspects of mind — egocentric ambition and pride — have been overcome by a surrender of the ego. Ideally, the ego is surrendered to the impersonal cosmic principle of motherhood, but more often it is surrendered to a personalization of this principle, to a woman who becomes the symbol of the universal mother force the cosmic Mahashakti (the Great Mother). (3)
      Metaphysically and metacosmically in the descending harmonic series, number three refers only to the idea of a future universe — thus to what H. P. Blavatsky's Secret Doctrine calls "cosmic ideation." The second octave deals with the two great noumena of manifested being. The third octave, between harmonics four and eight, is the realm of archetypes in which number three operates through its octave-sound (its reflection) as number six. Each harmonic whose frequency is twice that of a preceding one restates the character and function of the earlier one at a more concrete level of being. Numbers twelve and twenty-four are therefore new manifestations of the creative imagination and will symbolized by number three. These manifestations actualize potentialities symbolized by the fourth and fifth octaves of the harmonic series.

1. See Lifetide, Lyall Watson (New York: Simon & Schuster, 1979).  Return

2. These terms, fifth and fourth, are unfortunate and may be confusing. They originated in the fact that in our ascending diatonic scale (C, D, E, F, G, A, B) the F which ends the interval of a fourth (C to F) is the fourth note. G is the fifth note, and thus the interval C to G is called a fifth.  Return

3. This process is the foundation of the path of devotion (bhakti marga in Sanskrit). A less well known, more esoteric path, is symbolized by the direct relation between number One and number three. This implies a direct channeling of the power of One — which is Sound (or creative motion) — to the mind represented by number three (in the descending harmonic series). But this mind is not a product of cogitating, classifying, and generalizing brain activity; it is mind acting as a formative power through creative imagination and centralized will (kriyashakti and ichchashakti in Sanskrit). This process could be called rakti, from the Egyptian root ra, the power of the spiritual sun (sometimes called ra-orakti). its path could be called the way of the avatar, provided one realizes that besides the mythified great avatars of the Hindu tradition, who perform planetary or cosmic functions, there are many other avatars charged with various kinds of messages which they formulate in words, deeds, or other modes of spirit-impelled creativity. This avataric way would thus be symbolized by the ratio 3: 1. In the diatonic musical system this ratio defines the interval of twelfth.  Return

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