Diaschisma

2048/2025, the diaschisma, an interval of 19.553 cents, is the difference between four perfect fifths plus two major thirds and three octaves. Tempering it out leads to diaschismic temperament. It may also be defined as the difference between a Pythagorean minor seventh (16/9) and a just augmented sixth (225/128), as the difference between two classic diatonic semitones (16/15) and the major whole tone (9/8), that is, (9/8)/(16/15)², or as the difference between the 5-limit tritone 45/32 and its enharmonic equivalent 64/45.

Interval information

Ratio	2048/2025
Factorization	211 × 3-4 × 5-2
Monzo	[11 -4 -2⟩
Size in cents	19.55257¢
Name	diaschisma
FJS name	[math]\displaystyle{ \text{d2}_{25} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	21.9837
Weil norm (log2 max(n, d))	22
Wilson norm (sopfr(nd))	44
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See also

• Comma