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and the Art of Music
by Dane Rudhyar

Chapter 6

Descending and Ascending
Musical Progressions

Books dealing with the music of ancient Greece usually state, without comment, that the tetrachords apparently constituting the original organization of Greek music had a descending slope; their tones were listed from higher to lower pitch. In several histories of music I read in the summer of 1917, I found brief statements, at times merely footnotes, that the standard musical progressions (or scales) of all ancient cultures descended from high to low notes.
      The implications of this are vast and profound, indicating that a total reversal of human consciousness of sound has occurred since ancient Greece. Yet historians and musicologists have not given any serious attention to this matter. This makes me wonder about the reliability and depth of understanding of these students of the musical past.
      Would anyone singing or playing scales today start with high-pitched sounds and gradually descend to lower pitches? Is not the feeling and thought of rising scales absolutely ingrained in present-day musical consciousness? What could have occurred to produce such a reversal in musical consciousness?
      In primitive societies and ancient races that still cling to traditions, the use of descending musical progressions remains. Around 1900 the French writer Pierre Loti described the melodically prolonged shout used by the Basque people when successfully completing a contraband expedition across the French-Spanish border. A Basque woman recently performed this remarkable shout for me. She started with a loud, high tone and gradually descended to a low pitch. She had learned it in childhood, and she told me how it was traditionally used by the whole community, men and women, in warlike adventure, to startle and frighten adversaries. In the Japanese martial arts a violent shout is said to be able to kill by acting on an opponent's nerve centers. Similar descending chants are intoned by Navajo medicine men for healing. It seems therefore that the traditional procedure of magical tone production is to start with an explosive release of energy, perhaps to bring a superphysical power down (as it were) into physical manifestation.
      Chapter 2 refers to inaudible Sound as vibratory power, which when mobilized and released brings archetypal forms and creative ideas into concrete manifestation. Sound is, in ancient religions and cosmologies, the divine creative power, the energy inherent in the creative Word, the Logos. It is also the power of will, which in a mysterious way makes it possible for an idea (and particularly a decision) to compel the muscles of the body (those of the limbs, vocal organs, and eyes) to move in the precise way required for making the idea or decision work out.
      We know that the efferent volitional nervous system is the apparent agency making possible the exteriorization of a decision in the form of an action. We know too that our emotions are also exteriorized into actual movements — even emotions or feelings of which we are not conscious — and we now pay much attention to psychosomatic processes and the organic disturbances they cause. But while we speak of electrochemical currents passing along the nerves, the nature of these currents is only superficially known. The old Indian and Chinese concept of a field of energy (etheric body) pervading and sustaining the entire space of the body — and the aura beyond it — might well be an aspect of the creative Sound that descends, level by level, to the life field of the earth and the subtle body of all living organisms.
      Such a descent is the involution of Sound into whatever material organization is able to resonate to it. A material organization may be a living body, but it can also be a musical instrument like a violin, a flute, or a gong. When the human body utters a vocal tone, or when a gong vibrates at the strike of a mallet, a physically audible sound is produced. But this sound is the response of the human body or the gong to a muscular act which was the exteriorization of a decision to produce the audible tone in order to communicate information or a state of consciousness. The physical sound is the repercussion in matter of the inaudible Sound (the current of will through the nerves), just as light and color are the reflections of solar rays striking the atmosphere or a material object.
      The vocal and instrumental sounds we hear are only the resonance of matter, including the air molecules contained within the resonant cavities of the human body or an instrument. The audible sounds produced by this resonance rise. They rise symmetrically to the series of steps taken by the descent of the activity-producing Sound — the energy of the will or the emotions. We do not hear this Sound, but only the wave motion of the resonant material; and as the resonant material usually has a complex nature, what we hear is an equally complex set of vibrations. Nearly all the sounds we hear are combinations of vibrations. In acoustics these are called partials. One partial is normally dominant in the sounds produced by musical instruments and the human voice. We call this dominant vibration the fundamental; the hardly perceptible ones are called overtones or harmonics.
      The concept of fundamentals and overtones is, however, not basic and natural (as musicians usually believe). Tone analysis is not instinctive. When the modern acoustician hears a trumpet and a violin produce the same note, say a middle C, he or she may think of the two sounds as combinations of the same dominant vibrations and the different overtones characteristic of trumpet tones and violin tones. The acoustician hears this way because he or she has been trained to do so. An untrained hearer will have a non-analytical feeling-reaction to the sounds of the instruments, perhaps because the sounds are associated with pleasant or unpleasant past experiences. The difference between the two reactions is even more evident if we compare an Indian scout traveling through a dark forest ahead of his tribe to an acoustician studying the cries of animals in the safety of a zoo. The Indian scout listens for the tones of living beings to discover the nature and temperament of the animals producing them; the scientist applies his intellectual training to learn more about sounds as composite waves.
      The sound waves the acoustician analyzes originate from the vibrations of material substances. Whether these are musical instruments or the parts of a body that produce vocal sounds, the material substance is usually not homogenous; its vibrations are therefore complex, and so is the form of the sound wave. Secondary wavelets affect the main wave, producing overtones or harmonics characteristic of the instrument or body that produced the sounds. This characteristic quality of the sounds an instrument or voice produces is its timbre — the proportional relationships and relative intensities of the partials it produces.
      What is striking and not easily explained is that all the overtones vibrate at rates related to the fundamental vibration according to an arithmetic series of simple ratios. The prototype of all such series is the series of whole numbers (or integers), 1, 2, 3, 4, 5, and so forth. The frequency of all the vibrations (overtones), which define the, particular timbre (or quality) are in the same relation to the frequency of the fundamental vibration as any whole number is to 1. A particular musical instrument may produce overtones 3, 5, 6, 7; another may emphasize overtones 2, 4, 5. But the overtones cannot vibrate at the rate of 2.45 or 5.17 vibrations of the fundamental. Only frequencies represented by whole numbers — if the fundamental tone is 1 — are possible. Why is it so, if overtones are due only to the complex nature of the resonating materials of and in the instrument?
      Such a question may be like asking why all snowflakes have a six-pointed crystalline organization. All modes and forms of existential activity (and cosmic motion) embody simple, harmonic relationships. The science of harmonics attempts to show how these relationships are the structural foundations upon which the universe as well as microcosmic living beings are built as complex material wholes. Greek philosophers spoke of such structural foundations as archetypes constituting an aspect of the mind of the deity. The basic question is whether these archetypal forms or geometric structures are prior to existential activity — matter and life — of which they are the universal and essential molds or models, or if they are the product of the human mind abstracting from a multiplicity of shared and transmitted human experiences principles of organization having a universal validity. If the second alternative is true, then the human mind is imposing upon earth nature and the universe an organization which is only in the human mind. Material substances that do not absolutely fit the archetypal model, science allows for in the "coefficient of inefficiency" inherent in any experiment or in the principle of indeterminacy that results from the effect of the observer upon what is being observed. If one believes in the primacy of archetypes and in their reality in a realm of pure mind, inaccuracies in measurements and actual shapes that do not conform exactly to archetypal structures and proportional form are interpreted as the results of deviations introduced into the perfection of archetypes by the confusing and centrifugal power of material activities and (at the higher level of human existence) of interpersonal relationships.
      The question has a practical bearing on musical concepts and the philosophy of music. The difference between a descending and an ascending progression of sounds has to do not only with the sources of the progressions but with the character of what is progressing, that is, either descending or ascending. If Sound is the descent of an energy released cosmically in the divine creative act and humanly in a willful decision or an emotional impulse, it is the carrier of a message (information or communication) into a material form (an instrumentality, natural or man-made) organized to transmit this message more or less adequately. As the instrumentality resonates to the impact of Sound (and responds to it, if it has a consciousness), this resonance is a tone. This vocal, instrumental, or elemental tone is a combination of the Sound that descended into (or embodied itself in) the resonant instrumentality and the nature or character of the instrumentality. The tone is transmitted as sound waves to human ears.
      As it rebounds from the material it has set into resonance, the energy of Sound should theoretically follow a rising structure of harmonics or overtones, symmetrical to that of its descent. This ideal course is the harmonic series. But because what we hear is the resonance of the material instrument, this resonance introduces selection in the rebounding Sound energy; it emphasizes only certain sections of the harmonic series in which the energy of the resonant tone is condensed (the formant). The result is the timbre (or tone quality) of the voice or musical instrument.
      The series of fundamental and overtones produced by the vibrations of a material body is neither a complete nor an infinite series. A biological (vocal) organism or a man-made instrument able to vibrate in response to nerve stimulation or to a physical impact releases what it can of the energy that moved it. The character or quality of the release is largely determined by the nature and form of the vibrating body. The tone is a combination of a relatively few harmonics of varying intensities. The concept of a complete harmonic series represented by a sequence of notes on a musical staff is either abstract or the intellectual interpretation in Western musical terms of an inaudible process — the descent of a current of cosmic or human energy (Sound) issued from a single source, a One.
      Metaphysically, this current of energy is released by the creative activity of "the One," the Creative Word (Verbum or Logos). Ancient Hindu philosophers called it Nada Brahman, and symbolized it by the mystical sound AUM. In a human sense, the energy is either that of the will or of a biopsychic state seeking exteriorization (an emotion). A current of energy is a mode of motion. Pythagoras and other philosophers taught that motion operates according to the principle of number. This principle is most simply revealed in the series of whole numbers, the prototype of all arithmetic series. As Sound is the power that transmits an originating idea or decision to material substances and bodies able to actualize it more or less effectively, sonic energy operates according to the principle of number, thus in terms of an arithmetic series. It descends from level to level of material organization until it reaches the level of the instrument or body that will effectively resonate to it in order to actualize the creative will or originating decision. The motion is a descent, but a more proper term is exteriorization.
      In The Rebirth of Hindu Music and other early writings, when I spoke of a descending harmonic series, I also spoke of a "spiritual Fundamental," and a series of "undertones." (1) This now seems irrelevant or confusing. More significant is the understanding that the descending motion of Sound (which the human ear cannot hear) is a process of differentiation, for at its source Sound has a unitary character. This leads to the conclusion that when archaic peoples instinctively organized the tone sequences of their magical chants and mantrams in descending progressions, their sacromagical musical consciousness reflected the process of Sound descending from its unitary source and differentiating into material bodies and instruments and into a few fundamental tones. These tones constituted the archaic grama — perhaps the legendary Gandhara grama which the seer and musician Narada is said to have heard in the celestial realm.
      The descending tetrachord on which ancient Greek music was based indicates that the same feeling for descending musical progression originally existed there, probably in the Orphic chants before Pythagoras. The Pythagorean meaning of the tetraktys is related to the mystic properties of number 4, even though it was also applied to the basic musical intervals — octave, fifth, fourth, and whole tone.
      Pythagoras dealt primarily with the concepts of number and proportional form, that is, with the relationship between numbers and their visual manifestations as geometrical forms. He was not concerned with the timbre or quality of tones produced by material bodies, but rather with the development of the mind of reason — the archetypal mind dealing with number and form. Such a development had become historically imperative to help human beings overcome their involvement in the biopsychic realm of instincts, emotions, and collective cults, symbols, and myths personifying natural forces and cosmic processes. Pythagoras sought to demythify music. This reform attempted to substitute number and proportion for gods. In the process, however, it intellectualized and spatialized what may have still been the direct experience of the descending energy of Sound. If Pythagoras himself effectively used the power of Sound as a healing force, it was by providing adequate vocal and instrumental embodiment for its audible resonance in matter.
      A music with descending progressions of tones indicates that the musicians are still at least subconsciously attuned to the flow of Sound. Their psyches are still open to the direct impact of its descending energy. Later, music loses this attunement; it deals instead with tones generated by the complex vocal organs and resonant cavities of the human body and, more and more, by musical instruments able to provide an even richer resonance to Sound. Musicians increasingly think in terms of measurable and exact relationships between tones — that is, in terms of intervals.
      In music, any series of sounds (melody, for example) can be considered from two different points of view: as a sequence of separate sounds of varying pitches, or as a series of either ascending or descending intervals (a second, a third, a fifth, and so on). An interval is defined by the mathematical ratio between the frequencies of two tones.
      When musicians or acousticians speak of the harmonic series of fundamental and overtones, they can refer either to the individual notes of the series (for example, C1, C2, G2, C3, E3, G3, Eb3, C4), or to the intervals between them, that is, an octave (C1 to C2), a fifth (C2 to G2), a fourth (G2 to C3), a major third (C3 to E3), a minor third (E3 to G3), and so on. In the first case, attention is focused on each note as a vibratory unit; in the second, on the relationship between two succeeding notes.
      Behind these two approaches (both of which are concerned with music as an art shaped by a particular culture), there is always, however, the possibility of experiencing Sound as a continuous current of creative and transformative power. In this continuum, single tones arise and fade away as temporary focal points around which fields of sonic energy are formed and interpenetrate. Similarly, distances between these focalizing tones, instead of being considered precisely measured intervals, may be experienced as the many differentiated aspects of a fullness of vibrating space. This space can be experienced as a pleroma of interpenetrating and interacting tones, an immense and multitudinous resonance of the orchestra of cosmic existence to the creative, then form-maintaining, transforming, and, disintegrative will of God, the One source of manifested being.
      In a reflected sense, man can also be a true tone producer. He can sound in a physically concrete manner — through words charged with dynamic, image-evoking energy — the fundamental tone of a culture in the making. He can act as the sacromagical poet or bard. He can use Sound as a carrier wave to communicate the regenerative answer to the new human need.

1. The concept of "undertones," the actual existence of which many experimenters and theorists deny, probably originated in the work of Jean-Phillipe Rameau (1725).  Return

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