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and the Art of Music
by Dane Rudhyar

Chapter 9

The European Spirit in Music:
Pluralism, Tonality and Equal Temperament
Part Two

In the fifth century B.C. in Greece the traditionally intimate association between poetry and specific musical intonation was already being broken, if we are to believe Plato, who frowned on the practice. A similar situation developed during the twelfth and fourteenth centuries of Christianized Europe (and probably before, at least in some places) when unorthodox combinations of popular songs and traditional Church chant aroused the ire of the popes.
      In India the development of ragas as melodies still imbued with a magical if not sacred character did not mean the use of what we are calling tonality. As we already saw, ragas are modes in which the voice, or instruments imitating the expressiveness of the voice (especially the vina and saranji but also, especially in Japan, the bamboo flute), develops a modal material relating to a fundamental unceasingly sounded by a tambura. The ragas have no integrated polyphonic texture, but they can become heterophonic as instruments join in the melodic stream that flows uninterruptedly, often scanned by the complex rhythms of the drummer.
      Europe developed the system of tonality because the pluralism of a definitely built polyphonic structure demands it. And because the new polyphony sought to combine the popular with the religious (Nordic or Celtic folk melodies or Arabic-Sufi tunes brought back from the Crusades combined with the thoroughly diatonized and simplified Church plainchant), a new type of musical scale emerged and gradually spread. It became definitely operative as the tonality system when the complexification of Baroque music led to an increasing demand for chords, for a system of tonal harmony insuring a constant sense of unity. This harmonic tonality system grew synchronously with the centralizing power of national kings justifying by the principle of divine right their totalitarian possession of the kingdom and all it contained. In music this sociocultural trend was experienced as the "divine right" of the tonic assisted by the prime minister and the minister of finance, the dominant and subdominant (the fifth and fourth above the kingly tonic).

The three components of the diatonic scale the tonic — dominant and subdominant — are the foundations of the harmono-melodic tonality system. They were also the basis of the Pythagorean scale whose application, at least in its origin, was monodic rather than melodic. Melody comes into music, we can assume, with the popular or folk element. This element had its concentrated appeal in the natural intonation interval of third — the relationship between the fourth and fifth harmonics of the harmonic series. On the other hand, the Pythagorean third (C to E) apparently was derived from the fifth note of a series of exact fifths (C, G, D, A, E) reduced to the musical space of an octave. The difference between a Pythagorean third and a natural" third (the 5:4 ratio) could be compared to the difference between the theoretically impersonal relationship of a monk and nun, or between any two members of an ashram, and the personal love of an ordinary man and woman.
      Pythagoras selected only the interval of fifth (3:2) to build his scale. He used the very first type of differentiation from unity or identity (the octave symbol) appearing in the still-precosmic realm of the second octave of the harmonic series. Everything else had to be derived from the fifth and a series of fifths. This impersonal derivation befitted Pythagoras's apparent attempt to establish a cosmic canon of proportions which, we should not forget, was meant to be applied only to monodic music. But such a canon of proportions became obsolete when human emotions and the drama of personal relationships sought to find musical expression within the developing European culture. The realm of personal emotions is filled with confusion, restlessness, and uncertainties, especially when it is stirred by a spiritual fire of discontent and a passion for transcending natural conditions — even the human condition. This is the Faustian spirit in European man. The culture must therefore build strictly limiting patterns and structures of containment which are sanctified by religion, the unifying power within the collective psyche. Thus during the seventeenth and eighteenth centuries a strongly centralized state developed in politics, and the tonality system developed in music.
      In order to operate most effectively, tonality took the form of a harmonic system providing order, direction, and the resolution of tension into the "perfect chord," the major triad (C, E, G). Thus the divine Trinity, Father, Holy Spirit, and Son (in other religions the Holy Spirit is the divine Mother, Shakti or Shekinah) is reflected in the human being. The "natural third" relationship generates the energy of love which, though at first strictly human in its expression, can be transmuted into agape, divine love.
      This interval of natural third was accepted into music during the centuries of the Crusades. Its acceptance was synchronous with the extraordinary development in southern France of an idealization of womanhood and the spiritualization of love. The nonbiological expression of love — courtly love — became a strong motive in chivalry. The ancient Greek culture did not know of such a love, for "platonic love" had another meaning, that of pure friendship. Medieval Europe, however, glorified the devotion of the knight for his lady. It also knew of the tragic love of Abelard and Heloise, and of Lancelot for Guinivere in the Round Table myth; for this personal love, when it leads to biological union, turns out to be asocial and ultimately tragic, as for Tristan and Isolde, and the sin of Amfortas in the Parsifal legend.
      The tragedies of love and frustration also had to find their field of expression in music. They are associated with the minor mode in which the first third interval is flattened (C to E flat), evoking a descent of the energy of love to the physical level and a deep feeling of the futility or tragedy of the ascent of human nature (at least at our stage of humanity's development).

In Greek music the basic pattern of containment was the descending tetrachord. In the music of a post-Medieval Europe dominated by the pluralistic drive toward physical expansion and religio-emotional transcendence symbolized by the Gothic cathedral with its skyflung ogives and spires-the basic pattern is the triad, whose ascending energy is represented by the ascending fifth. The Perfect System of ancient Greece encompassed essentially four descending tetrachords. In European music the vertical extension of the triadic formation led to Debussy's and Ravel's chords of ninths, elevenths, thirteenths, and so on. It also led to the principle of modulation from key to key based on the centrifugal fifth interval. Thus the field of usable sound vibrations was extended to the space defined by seven successive octaves which, as we already saw, corresponds (almost) to a series of twelve intervals of fifths. Figure 3 makes this point clear.
      The series of seven octaves and the series of twelve fifths are both (geometric) series of equal intervals, but the octave series includes only whole numbers, while only the first two terms of the fifth series are whole numbers. (These twelve fifths produce the twelve notes of our chromatic scale.) We would have to go to very large numbers to find a series of twelve fifths whose sound frequencies measure in terms of whole numbers and therefore can be considered parts of a harmonic series. In figure 3, the twelfth fifth-sound, B-sharp (259.48), is higher in vibration than the seventh octave sound. The difference between them is the Pythagorean comma, approximately half a quartertone.
      This is a small but still perceptible interval. It symbolizes the centrifugal or Faustian character of the fifth interval. On the piano keyboard, however, B-sharp and C-natural are the same note. An untrained person would hardly be able to distinguish between them because for two and a half centuries we have use a system of piano tuning called equal temperament, of which Bach is the most well-known endorser. According to this system every one of the series of twelve fifths is slightly clipped, the twelfth part of a comma being taken away from it. In itself such a very small interval is not perceptible, but persons with a sensitive ear will feel the difference between a natural and a tempered fifth.
      In the process of temperament all intervals except the octave are affected. We can give a visual interpretation to the process by saying that the geometrical figure produced by a series of twelve natural fifths would be a spiral. Equal temperament reduces the spiral to a circle. It establishes the boundaries of a musical field limited to octaves, each being divided into twelve equal intervals.
      This field differs essentially, at least from a philosophical point of view, from the span of vibrations covered by the Perfect System of ancient Greece. The latter was based on the range of the human voice and had a descending slope. This naturally resulted from the intimate association and even identification of music with poet — poetry being considered a rhythmic, magically creative act using intoned words to evoke sacred or heroic deeds whose meaning was essential to the formation and sustainment of a culture-whole. Such an intimate association of monodic music with words and ritual existed in Christian Europe during the early Middle Ages, but it had a devotional rather than magical or theurgic character. With the appearance of polyphony and visual notation music began to gain an independence which acquired a radically new meaning with the increasing use of man-made instruments — until the human voice itself assumed the character of a melodic instrument much of the time.
      Archaic monodies have a descending character because they reflect a basic awareness of the descent of spiritual power (will and creative imagination) into matter. As monodies are essentially identified with words and names, the range of possible intonation is controlled by the limitations of the human voice, limitations which in subsequent cultural periods are extended by special training. In contrast, folk and later in Europe classical melodies do not have a magical character. They deal with the expression of personal emotions or are parts of collective cultural festivities, particularly dancing.
      Personality is the resonance of a human body (or in a collective sense of a closely united group of people) to various biological and cultural changes and pressures. In some cultures, for instance in India, personality operates in close attunement with natural forces and seasonal or daily changes. In Europe the sociocultural level of consciousness, deeply influenced by a religion of transcendence and other-worldliness, dominates the natural, biological-psychic level at which the mass of people nevertheless still act and react. Because the exclusivistic and centralizing ideal of the culture-whole was impregnated by the restless and centrifugal spirit of civilization (the Promethean or Faustian drive), the field of musical possibilities had to expand. It expanded as trade, commerce, and travel partially vitiated provincialism and ethnic exclusivism. Yet, in order not to become lost in the centrifugal personalism of the Renaissance, the music of a still-cohesive European culture deeply influenced by church tradition (in spite of the rising analytical spirit of science) had to stress the binding power of tonality.
      If tonality is formally defined as a system represented by a ladder with rigidly spaced rungs, and the entire ladder can be moved up and down without losing its structure, technical problems of determining pitch arise. A new kind of motion enters the field of music, and music becomes irrevocably linked with instruments. No longer of primary significance is the movement of one tone away from and toward another tone, which is the essence of melody. Focal instead is the displacement of the tonality ladder from one "key" (or placement of the tonality ladder) to another. This new type of motion is called modulation. It may have been known to some extent in non-European musical cultures, but never with the special and dynamic character it acquired in European music. With Beethoven, the concept of a musical idea or theme needing to be developed in many ways, and with Wagner the concept of the leitmotif, further increased the possibility of producing the feeling of dynamic change by moving a fixed pattern of intervals from one key to another.
      This modulating movement — the transposition of a pattern from one pitch level to another — made the development of the equal temperament system inevitable, considering the increasing complexity of the melodic and harmonic components of a "musical work," now an objective entity whose constituting cells constantly move within a culturally predetermined "musical form."
      When one moves the fixed pattern of intervals constituting the basic C-major scale up and down, notes that were not parts of the original diatonic series are required to sound where the rungs of the ladder now hit the musical space. A violin might be able to produce these new notes, but on the fixed keyboard of an instrument that has seven notes to the octave, these new notes do not exist. This is why the piano keyboard has black and white keys.
      When a melody is transposed from the key of C to that of G (that is, when the diatonic scale that once began with C has now G as its starting point, its tonic) one black key, F-sharp, has to be added to the original seven white keys. Each modulation to the next higher key (whose tonic occurs one interval of fifth above) introduces an added sharp. A symmetrical process of modulating to a lower key requires the technical use of flats instead of sharps, but on the piano keyboard no distinction can actually be made between sharps and flats. The distinction is theoretical and applies only to the written score, though performers on some instruments without fixed keyboards can respond to it.
      Thus, because of the particular kind of musical motion called modulation, and because of the increasing use of the piano or similar instruments with fixed keyboards, a chromatic division of the octave into twelve equal intervals has become the fundamental feature of Western music. The equalized series of octaves and twelve fifths produces a musical space divided into eighty-four equal intervals. This has become for two and a half centuries the materia prima of Western music. This music has spread all over the globe, together with technological products and a personalistic way of life. As we shall see in greater detail in chapter 1 1, the piano keyboard can be made to represent the entire world of now-usable musical sounds. It can also be considered a symbol of the sociopolitical and ethical organization of theoretically free and equal individuals, without any functional or generic, religious or financial, ideological or characterological differentiation — the organization called democracy.
      We should realize, however, that there is no equality in nature. All units of activity (molecules, cells, species within one biosphere) operate on the basis of functional differentiation. There was also no equality in aristocratic or feudal societies, which were dominated by castes or classes. In the modern world, whether democratic or socialist, equality is an ideal, not a fact.
      What then does this concept mean? What does it point to as a future possibility? The question has a deep meaning in both musical and sociopolitical terms, because in complex modern symphonies calling for large orchestras the musical note is an excellent symbol of the citizen operating within even more complex modern democracies. Both the note and the citizen are abstract units. The democracy of New England towns before the Industrial Revolution, the railroads, and the Civil War still had a cohesive religious and ethical characters character of tonality. But modern megalopoles resemble atonal constructions a la Schönberg, held together by a police force and the emotionalism of unresolved tensions tightly boxed within obsolete forms of quasi-traditional behavior.
      If by tonality, we mean loyalty to a tonic, or even preference to the tonic as the tonal center to which all others are related, the concept of atonality (the absence of tonality) can be very meaningful. The basic issue is the quality of the relationship (or loyalty) to a tonic or any single tone. In classical Europe such a relationship in music paralleled the relationship of the people with their king, whose rule was religiously sanctioned by the convenient idea of "divine right." If tonality means the divine right of the tonic, then the rise of individualism in the Romantic era was bound to manifest in music as the gradual breakdown of tonality. Liszt and Wagner became powerful agents in fostering such a process. Chromaticism was used by these composers not in a decorative sense as in Bach's Chromatic Fantasy; it rather was meant to convey to a stolid, materialistic, and egocentric bourgeoisie the usually tragic consequences of asocial love and of longing for an elusive transcendence of biocultural patterns.(1)
      Schönberg's profound error was to cling to the belief that rigid rules and patterns were needed to replace the discarded tonality order. It was like substituting totalitarianism for the divine right of kings. It meant replacing the attachment of a people to a king and religion with a deliberate, computative structural order enforced by the analytical and formalistic mind. It meant a change from a collective cultural order to the artificial rule of an overly deliberate and, to a large extent, fashion-inspired intellectual system. The psychocultural ground of Schönberg's atonalism and its complex procedures was the disintegration of the Austro-Hungarian Empire. His system can be related to the psychological reductionism of Freud; and Jung's psychology is not alien in practice, even if not in its deepest spirit, to Neo-classicism. (Jung actually promoted a freer, more individualized and conscious return to the great aristocratic European tradition, especially in its more esoteric aspects, gnosticism and alchemy, which fascinated the Swiss psychologist.)
      The Viennese school of music from Mahler to Schönberg, Alban Berg, and Webern, is the musical expression of the breakdown of the European spirit in its Germanic aspect, and in Webern's music its almost total atomization. Yet these composers were still profoundly European in spirit, and their music should be approached and performed in that spirit. The same is also true of Stravinsky, and in general of all neoclassical or formalistic music. In the more recent avant-garde music, however, a basically different trend is at work. It affects not only the outer form of music and the musical relationship between notes but the consciousness seeking expression and communication in musical organization. It is a revolutionary endeavor to find a new answer to the question "what is music for?"
      European music in the past gave to this question three successive answers: the religious Medieval answer, the Baroque and Classical answer, and the Romantic and, later, Expressionistic answer. But the answer given by the most genuine and deeply motivated avant-garde musicians has an essentially non-European character, and the same can be said of at least some aspects of recent popular music. It is the music of youths eagerly, emotionally, and also tentatively and confusedly, seeking to experience a process of deconditioning. Such a process has been catalyzed by Oriental philosophies and practices, and by the consciousness destructuring effects of psychedelic drugs.
      Deconditioning and destructuring are, however, indications that a process of radical transformation is at work. What is occurring in music today is more crucial than the process that transformed church plainchant into the music of the fifteenth century and into the music of the classical era. What occurred some six centuries ago was an integral part of the evolution of the European culture. Today there are very strong indications that this culture and its prolongations in the Americas and elsewhere are disintegrating, perhaps much as the Roman Empire broke down 1500 years ago. Moreover, every other culture in the world is also disintegrating. A new planet-wide descent of creative spirit may therefore be taking place, a release of "seed ideas," which sooner or later may inspirit a radically new kind of musical as well as social organization.
      The essential purpose of this book is to evoke the possibility of such a new type of organization in music. To envision the potential future we have to understand what the past has been, how it has evolved into the present, and where the dynamism of sociocultural processes is leading. If we do not understand the beginning of music there is no place in our mind for the rebirth of our consciousness of music. But to understand need not mean to return to and imitate.
      While a cycle begins in unity it ends in a state of multi-unity. In music this cyclic consummation may take a complex form merely announced by the large orchestras of today. Or perhaps music will acquire a new simplicity, not by being reduced to a slightly evolving monotone, but by the rich variety of orchestral tones being "condensed" into what I call "pleromas of sound." This presumably would require a new kind of tone producing instrument. The piano and today's still-primitive electronic instruments may be forerunners of such a panharmonic instrument, in whose tones the whole of musical space may be at least implied and ultimately brought to a focus in an all-inclusive fullness of sonic vibration.
      Before we can try to formulate a philosophy of music defining an approach to such panharmonic achievements, it is necessary to examine as objectively as possible what the various aspects of the musical avant-garde have been and have meant since the beginning of World War II.

1. The realization that the traditional sense of tonal relationship had sooner or later to be transcended came to Franz Liszt as early as 1832, when he developed the concept of an "ordre omnitonique" and composed a Prélude Omnitonique which, most unfortunately, has disappeared, "though it was seen in manuscript in London in 1904." (See Liszt, by Eleanor Perényi [Boston: Little, Brown and Company, 1974], p. 321.
      Bela Bartok gave a great deal of attention to what he called "pan-tonality," as I can personally testify. In a long, private meeting I had with him in the mid-thirties at the New York apartment of Blanche Walton — the patroness of Henry Cowell and the New Music group to which I more or less belonged — he spoke at length about a non-exclusivistic type of tonality which could accept the presence of any note, provided the musical piece would have a recognizable tone-center. Bartok did not think of such a tone-center as a fundamental, of which the other notes would be overtones. What he seemed eager to convey as he demonstrated this idea on the piano was that every conceivable note and type of sound should be allowed as long as it could be felt to be part of a musical whole in which a centralizing vibration established the character of the composition.  Return

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