Thediaschisma (ordiacisma) is a smallmusical interval defined as the difference between threeoctaves and fourperfect fifths plus twomajor thirds (injust intonation). It can be represented by the ratio 2048:2025[1] and is about 19.5cents. The use of the name diaschisma for this interval is due toHelmholtz; earlierRameau had called that interval a "diminished comma" orcomma minor.
A diaschisma is the difference between aschisma and asyntonic comma,[2] as well as the difference between thegreater chromatic semitone (135:128 = 92.18 cents) and thejust minor second (16:15 = 111.73 cents).[3] Medieval theoristsBoethius andTinctoris described the diaschisma as one-half of thePythagorean minor second, or 256/243, which would make the other half either 25/24 (70.67 cents) or about 45 cents. The diaschisma may be approximated by 89/88, 19.56 cents.
Tempering out the diaschisma, in the modern meaning of the term, leads to adiaschismic temperament. The diaschisma is tempered out in the usual system of12 equal temperament; in fact, 12 equal temperament can be characterized as the5-limit temperament that tempers 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 with22,34 and46 notes all temper it out.
| Twelve- semitone (post-Bach Western) |
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| Other tuning systems |
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| Other intervals |
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