Schisma

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.

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 (27/12).

So, a rational intonation version of equal temperament may be obtained 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 16 384 : 10 935 exceed seven octaves, and therefore fail to close, by the tiny interval of

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).