Diaschisma

Diaschisma on C  Play (help·info).

Diaschisma as four perfect fifths plus two major thirds.

The diaschisma (or diacisma) is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds (in just intonation). It can be represented by the ratio 2048:2025^[1] and is about 19.5 cents. The use of the name diaschisma for this interval is due to Helmholtz; earlier Rameau had called that interval a "diminished comma" or comma minor.

Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would give an interval of 45 cents.

Tempering out the diaschisma, in the modern meaning of the term, leads to diaschismic temperament. The diaschisma is tempered out in the usual system of 12 equal temperament; in fact, this temperament can be characterized as a 5-limit temperament as the one tempering out both the syntonic comma of 81/80 and the diaschisma. However, it is possible to improve the tuning a good deal over that of 12-et and still temper out the diaschisma; the equal temperaments with 22, 34 and 46 notes all temper it out.

See also

• Comma (music)

References

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxviii. ISBN 0824747143. Diaschisma.