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In just intonation the quarter tone can be represented by the septimal quarter tone, 36:35 (48.77 cents), or by the undecimal quarter tone (i.e. the thirty-third harmonic), 33:32 (53.27 cents), approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone.
Dialogue, for two pianos tuned a quarter-tone apart, eight hands, W.o.O. (1959) Dithyrambe, for two pianos tuned a quarter-tone apart, Op. 12 (1923–1924) Études sur les mouvements rotatoires, for two pianos tuned a quarter-tone apart, eight hands, Op. 45a.; for chamber orchestra, Op. 45c (1961)
Major microtonal composers of the 1920s and 1930s include Alois Hába (quarter tones, or 24 equal pitches per octave, and sixth tones), Julián Carrillo (24 EDO, 36, 48, 60, 72, and 96 equal pitches to the octave embodied in a series of specially custom-built pianos), Ivan Wyschnegradsky (third tones, quarter tones, sixth tones and twelfth ...
Comparison between tunings: Pythagorean, equal-tempered, quarter-comma meantone, and others.For each, the common origin is arbitrarily chosen as C. The degrees are arranged in the order or the cycle of fifths; as in each of these tunings except just intonation all fifths are of the same size, the tunings appear as straight lines, the slope indicating the relative tempering with respect to ...
The septimal quarter tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between the two different types of minor thirds is lost. The septimal quarter tone may be derived from the harmonic series as the interval between the thirty-fifth and thirty-sixth ...
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Four of the scale notes – the tonic (C in the example), subdominant (F), dominant (G), and octave (C′) – are all fixed: They are nearly exactly the same relative pitches in all three categories of ancient Greek scales (enharmonic, chromatic, and diatonic), [4] and in ancient Greek music, the fixed tones relative pitches were very nearly the same as the corresponding notes in the modern ...