Kleisma

In music theory and tuning, the kleisma (κλείσμα), or semicomma majeur,[1] is a minute and barely perceptible comma type interval important to musical temperaments.

It is the difference between six justly tuned minor thirds (each with a frequency ratio of 6/5) and one justly tuned tritave or perfect twelfth (with a frequency ratio of 3/1, formed by a 2/1 octave plus a 3/2 perfect fifth).

It can be also defined as the difference between five justly tuned minor thirds and one justly tuned major tenth (of size 5/2, formed by a 2/1 octave plus a 5/4 major third) or as the difference between a chromatic semitone (25/24) and a greater diesis (648/625).

The interval was named by Shohé Tanaka after the Greek for "closure",[2] who noted that it was tempered out to a unison by 53 equal temperament.

[2] Larry Hanson[4] independently discovered this interval which also manifested in a unique mapping using a generalized keyboard capable of accommodating all the above temperaments as well as just intonation constant structures (periodicity blocks) with these numbers of scale degrees.