The smallest interval in 31 equal temperament (the "diesis" of 38.71 cents) is half a chromatic semitone, one-third of a diatonic semitone and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-tone or a sixth-tone. 72-TET also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. 22-TET contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas 53-TET has an interval of 45.28 cents, slightly smaller. Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems. The 8-TET scale is composed of three-quarter tones. A semitone is thus made of two steps, and three steps make a three-quarter tone or neutral second, half of a minor third. In this scale the quarter tone is the smallest step. 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). For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g., D ♯–E ♭). The term quarter tone can refer to a number of different intervals, all very close in size. It approximates the harmonic seventh, B ♭.
The "subminor seventh": B = A, 19 quarter tones.
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