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In the quarter-tone scale, also called 24-tone equal temperament (24-TET), the quarter tone is 50 cents, or a frequency ratio of 24 √ 2 or approximately 1.0293, and divides the octave into 24 equal steps (equal temperament). In this scale the quarter tone is the smallest step.
Brian Ferneyhough (Great Britain, b. 1943, quarter tones, 31ET in Unity Capsule for solo flute, 1976; quarter tones and eighth tones in La Chute d'Icare, 1988) Jukka Tiensuu (Finland, b. 1948, quarter tones, non equal temperament tunings) Mathius Shadow-Sky (France, b. 1961, introduces acyclic nonoctave scales in 1980) [111]
More generally, three genera of seven octave species can be recognized, depending on the positioning of the interposed tones in the component tetrachords: The diatonic genus is composed of tones and semitones, the chromatic genus is composed of semitones and a minor third, the enharmonic genus consists of a major third and two quarter-tones or ...
As discussed above, in the quarter-comma meantone temperament, the ratio of a semitone is S = 8 : 5 5 ⁄ 4, the ratio of a tone is T = √ 5 : 2. The tones in the diatonic scale can be divided into pairs of semitones. However, since S 2 is not equal to T, each tone must be composed of a pair of unequal semitones, S, and X:
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The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament, the distance between each successive note being a quarter tone (50 cents). Each tone has its own name not repeated in different octaves, unlike systems featuring octave ...