The diaschisma is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds (in just intonation

Just intonation

In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...

). It can be represented by the ratio 2048:2025 and is about 19.5 cents

Cent (music)

The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...

. The use of the name diaschisma for this interval is due to Helmholtz; earlier Rameau

Jean-Philippe Rameau

Jean-Philippe Rameau was one of the most important French composers and music theorists of the Baroque era. He replaced Jean-Baptiste Lully as the dominant composer of French opera and is also considered the leading French composer for the harpsichord of his time, alongside François...

 had called that interval a "diminished comma" or comma minor.

Medieval theorists Boethius

Anicius Manlius Severinus Boethius

Anicius Manlius Severinus Boëthius, commonly called Boethius was a philosopher of the early 6th century. He was born in Rome to an ancient and important family which included emperors Petronius Maximus and Olybrius and many consuls. His father, Flavius Manlius Boethius, was consul in 487 after...

 and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would give an interval of 45 cents.

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

Limit (music)

In music theory, limit or harmonic limit is a way of characterizing the harmony found in a piece or genre of music, or the harmonies that can be made using a particular scale. The term was introduced by Harry Partch, who used it to give an upper bound on the complexity of harmony; hence the name...

 temperament as the one tempering out both the syntonic comma

Syntonic comma

In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 cents...

 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

22 equal temperament

In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the tempered scale derived by dividing the octave into 22 equal steps . Each step represents a frequency ratio of 21/22, or 54.55 cents ....

, 34

34 equal temperament

In musical theory, 34 equal temperament, also referred to as 34-tet, 34-edo or 34-et, is the tempered tuning derived by dividing the octave into 34 equal-sized steps...

 and 46 notes all temper it out.