The diaschisma (or diacisma) is a small musical interval defined as the difference between four perfect fifths plus two major thirds (in just intonation) and three octaves. It can be represented by the ratio 2048:2025 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". In music theory, an interval is the difference (a ratio or logarithmic measure) in pitch between two notes and often refers to those two notes themselves (otherwise known as a dyad). ... In music, Just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by whole number ratios; that is, by positive rational numbers. ... The cent is a logarithmic unit of measure used for musical intervals. ... Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist. ... Jean-Philippe Rameau Jean-Philippe Rameau (September 25, 1683 - September 12, 1764) was one of the most important French composers and music theorists of the Baroque era. ...

Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would give an interval of 45 cents. There are several persons called Bo thius: Philosophers: Anicius Manlius Severinus thius - to many scholars this is the Bo thius, a late-Roman writer best known for his works in philosophy and theology. ...

Tempering out the diaschisma, in the modern meaning of the term, leads to diaschismic temperament. The diaschisma is tempered out in the usual system of 12 equal temperament; in fact, this temperament can be characterized as a 5-limit temperament as the one tempering 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. Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. ... In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. ...