In music, the schisma (also spelled skhisma) is the interval between the syntonic comma (81:80) and the Pythagorean comma which is slightly larger. It equals or ≈ 1.00113,[1] [2] which corresponds to 1.9537 cents . It may also be defined as:
Schisma is a Greek word meaning a split or crack (see schism) whose musical sense was introduced by Boethius at the beginning of the 6th century in the 3rd book of his De institutione musica. Boethius was also the first to define the diaschisma.
Andreas Werckmeister defined the grad as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth (3:2) and the equally tempered fifth of 700 cents (2).[3] This value, 1.955 cents, may be well approximated by converting the ratio 886:885 to cents.[4] This interval is also sometimes called a schisma.
Curiously,
21/12 51/7
| 2161 | |
| 384 512 |
,
Tempering out the schisma leads to a schismatic temperament.
Descartes used the word schisma to mean that which multiplied by a perfect fourth produces 27:20 (519.55 cents); his schisma divided into a perfect fifth produces 40:27 (680.45 cents), and a major sixth times a schisma is 27:16 (905.87 cents).[5] However, by this definition a "schisma" would be what is better known as the syntonic comma (81:80).