kleisma

The kleisma is a small interval composed of 6 major thirds up and 5 fifths down [= 3^-55⁶].



Its ratio is 15635/15552 [= 0.08 Semitones = ~8.10728 cents].

The term was introduced by Shohé Tanaka.

[from John Chalmers, Divisions of the Tetrachord]

. . . . . . . . . . . . . . . . . . . . . . . .

Another interval that has become known as a kleisma (and in fact is now the one most commonly referred as such) is the one which forms the difference between the 5-limit "augmented 6th", with the ratio 225:128 [= 2^-73²5² = 9.77 Semitones = ~976.5374295 cents], and the harmonic "7th", with the ratio 7:4 [= 2^-27¹ = 9.69 Semitones = ~968.8259065 cents]. This kleisma's ratio is thus 225:224 = 0.08 Semitones = ~7.711522991 cents.

[from Joe Monzo, JustMusic: A New Harmony]

REFERENCE: Tanaka, Shohé. "Studien im Gebiete der reinen Stimmung", Vierteljahrsschrift für Musikwissenschaft vol. 6 no. 1, Friedrich Chrysander, Philipp Spitta, Guido Adler (eds.), Breitkopf und Härtel, Leipzig, 1890, pp. 1-90. English translation of pages 8 to 18 by Daniel J. Wolf, "Studies in the Realm of Just Intonation", Xenharmonikôn vol. 16, autumn 1995, pp. 118-125; reproduced on the web at The Wilson Archives (requires free Adobe Reader).

see also anomaly, unison vector, xenharmonic bridge, diesis, comma, skhisma, 5-limit intervals, 100 cents and under

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