Schisma

Schisma

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. The term was coined 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.

Because the difference between a grad and a schisma is so small, 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 schismic temperament.