Schisma

In music, the schisma, also spelled skhisma, is the ratio between a Pythagorean comma and a syntonic comma and equals 32805/32768, which is 1.9537 cents ( Play (help·info)). It may also be defined as:

• the ratio between 8 perfect fifths plus a just major third and 5 octaves;
• the ratio between major limma and pythagorean limma;
• the ratio between the syntonic comma and the diaschisma.

Schisma is a Greek word meaning a split (see schism). Its musical sense was introduced by Alexander J. Ellis, but earlier theorist Andreas Werckmeister defined the grad as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth and the equally tempered fifth of 700 cents, and this interval of 1.9550 cents is also sometimes called a schisma.

Curiously, 2^1/12 5^1/7 appears very close to 4/3, the just perfect fourth. That's because the difference between a grad and a schisma is so small. So, a rational intonation version of equal temperament may be realized by flattening the fifth by a schisma rather than a grad, a fact first noted by Johann Kirnberger, a pupil of Bach. Twelve of these Kirnberger fifths of 16384/10935 exceed seven octaves, and therefore fail to close, by the tiny interval of 2¹⁶¹ 3⁻⁸⁴ 5⁻¹², the atom of Kirnberger of 0.01536 cents.

Tempering out the schisma leads to schismatic temperament.

See also

• Comma (music)

External links

• Septimal Comma, Encyclopedia of Microtonal Music Theory; Tonalsoft.
• List of Intervals