# Diaschisma

### From Encyclopedia of Microtonality

**Diaschisma**

2048 / 2025 ►

19.55257 cents

2^{11} : 3^{4}· 5^{2}

greater chromatic semitone** 135 / 128 ►**
92.17872 cents

3

^{3}· 5 : 2

^{7}

just minor second

**111.73129 cents**

16 / 15 ►

16 / 15 ►

2

^{4}: 3 · 5

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**.

A diaschisma is the difference between a schisma and a syntonic comma,^{[2]} 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).^{[3]} 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.

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[edit | edit source]

## References[edit | edit source]

- ↑ Haluska, Jan (2003).
*The Mathematical Theory of Tone Systems*, p.xxviii. ISBN 0-8247-4714-3. Diaschisma. - ↑ "Diaschisma",
*Merriam-Webster.com*. - ↑ (1897).
*Columbian cyclopedia, Volume 9*, np. Garretson, Cox & Company. pre-ISBN.

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