{{Short description|Musical interval}} thumb|Diaschisma on C {{audio|Diaschisma on C.mid|Play}}. thumb|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<ref>Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxviii. {{ISBN|0-8247-4714-3}}. Diaschisma.</ref> 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'''.

A diaschisma is the difference between a schisma and a syntonic comma,<ref>"[http://www.merriam-webster.com/dictionary/diaschisma Diaschisma]", ''Merriam-Webster.com''.</ref> as well as the difference between the greater chromatic semitone (135:128 = 92.18 cents) and the just minor second (16:15 = 111.73 cents).<ref>(1897). ''[https://books.google.com/books?id=n5pRAAAAYAAJ&dq=Diaschisma&pg=PT354 Columbian cyclopedia, Volume 9]'', np. Garretson, Cox & Company. pre-ISBN.</ref> Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would make the other half either 25/24 (70.67 cents) or about 45 cents. The diaschisma may be approximated by 89/88, 19.56 cents.

thumb|center|300px|three octaves (above) and four perfect fifths plus two major thirds (below)

Tempering out the diaschisma, in the modern meaning of the term, leads to a '''diaschismic temperament'''. The diaschisma is tempered out in the usual system of 12 equal temperament; in fact, 12 equal temperament can be characterized as the 5-limit temperament that tempers 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== {{reflist}}

{{Intervals|state=expanded}}

Category:5-limit tuning and intervals Category:Commas (music) {{music-theory-stub}}