By Ben Johnston
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Extra resources for Maximum Clarity and Other Writings on Music
Indd 18 on music t heor y 8/31/06 3:37:48 PM figure 6. Pythagorean pentatonic scale, derived from cyclic tuning in perfect fifths; the scale in the second measure is, in ratios starting from C, 1/1–9/8–4/3–3/2–16/9–2/1. figure 7. Pythagorean heptatonic scale, derived from cyclic tuning in perfect fifths; the scale in the second measure is, in ratios starting from C, 1/1–9/8–32/27–4/3–3/2–27/16–16/9–2/1. interval between these two alternative possibilities is called the Pythagorean comma. The Pythagorean twelve-tone scale can also be derived from cyclic tuning in perfect fifths (Figure 8).
Both works consciously evoke earlier classical idioms as part of a new emphasis that becomes increasingly apparent in Johnston’s music of these years, and which he discusses in a “Position Paper” published in Perspectives of New Music: that of exploring how European music might have developed had it been freed of the constraints of equal temperament. This is a form of musical revisionism, distinct in technique and intent from the neoclassicism of his earlier work. 1989 Completes the song cycle Calamity Jane to Her Daughter for soprano and small ensemble, which is premiered by Dora Ohrenstein in New York to great acclaim.
The subsequent development of extended modulation and chromaticism only intensified a tendency already fully developed in the European musical tradition. : The implied definition of consonance given here—“the simpler a ratio the more consonant the interval”—is consistent throughout Johnston’s writings but is only one of several definitions that have been proposed, historically, to explain the phenomenon of consonance and dissonance. ” Beats are more rapid the more dissonant the tones. indd 9 8/31/06 3:37:39 PM sc al ar order a s a compositional resource 1962– 63 When listening to music we hear changing sound qualities in rhythmic patterns which create an illusion of growth.