"Maximum Clarity" and Other Writings on Music

Rational Structure in Music

rational structure in music 1976 “Over the whole of the historical period of instrumental music, Western music has based itself upon an acoustical lie. In our time this lie—that the normal musical ear hears twelve equal intervals within the span of an octave —has led to the impoverishment of pitch usage in our music.”1 We lie especially when we pretend to ourselves that vertical combinations of these pitches constitute harmony. We do not avoid the lie if we abandon harmony in music, so long as we retain a tempered scale. Feeling that the harmonic mode of pitch perception is far too important a resource of human capability for it to be allowed to fall into disuse, I have set about to reestablish ratio scale usage in pitch organization.This has entailed a number of radical means (large numbers of microtones, for instance, entailing new performing techniques, especially for wind players), some strongly conservative practices such as the resumption of a sharp awareness of degrees of consonance and dissonance as a major musical parameter (which amounts to revoking Schoenberg’s much-touted “emancipation of the dissonance”), and even some radical reactionary attitudes, for example, the rejection of the idea that noise, “randomness,” and ultracomplex pitch are the primary frontiers for avant-garde exploration. I have been concerned to reopen doors closed by the acceptance of the twelve-tone equal-tempered scale as the norm of pitch usage. My focus is upon complexity arrived at as perceptible order rather than as seeming disorder . I am especially interested in the role played by proportional order in the domains of rhythm, harmony, and melody. Since as a culture we have developed not only a tolerance but also a taste for a high level of complexity in many areas of experience, this effort necessarily involves a very highly developed proportional ordering system in order to cope with such levels of complexity in pitch and rhythm. We must learn to differentiate sharply between complexity due to large numbers and complexity which delineates subtleties of relationship. If one purifies Western pitch usage of late adulterations traceable to the adoption of equal temperament,the two most complex examples of systems of proportional relations in existence are the harmonic and metrical systems of Western art music. Rhythm requires no corrective, only the long-sinceachieved abolition of the tyranny of the bar line and the fixed repetitive metrical schemes proper to common-practice-period music. Extrapolating the basic logic from the harmonic practice of traditional Western music is only a first step. A much more challenging and interesting follow-up is the generalization of this logic so that it becomes applicable to unfamiliar pitch materials. Once this has been achieved, the door closed by the acceptance of equal temperament is reopened. In measurable physical terms,there are only two parameters of sound,duration and energy (measurable as the amount of displacement of molecular particles in a vibrating medium).These are interpreted phenomenologically as a great variety of parameters,a differentiation assisted enormously by our facility in perceiving gestalt phenomena on various scales of time. On an ordinary scale of time (countable time), the patterning, due always to vibratory events, is intelligible as rhythm. As we move up into larger amounts of time, our ability to count diminishes and the role played by memory greatly increases. Macrorhythmic events, characterizing longer durations , enable us to acquire a sense of the overall shape of music or sound compositions.We also perceive patterning on a scale of time much too rapid to count, but clearly we have nevertheless a marvelously precise ability to measure the duration patterns involved in these microrhythmic events. Since air or any other vibrating medium can respond to the periodicities of diverse sound sources simultaneously, these different rates of vibration are constantly interacting with one another. If the pattern of interaction is relatively simple, the sound complex exhibits a type of blend traditionally called consonant (as defined in, for instance, Helmholtz’s On the Sensations of Tone). This kind of consonance, though not independent of context and function in a melodic or harmonic pattern, does exhibit, simply in its blend, a greater simplicity than the concomitant kind of dissonance, in the same way that superimposed rhythmic groupings such as 3:2 and :3 are clearly easier to perform and to analyze by ear than, say, 9: or 1:8. We also identify such combinations by their relative “size,” as measured for instance in half steps or in cents...