Diaschisma

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 height (log2 nd)	21.9837
Weil height (log2 max(n, d))	22
Wilson height (sopfr(nd))	44
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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 the diaschismic family of temperaments. 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.

Example

parizek1 A comma pump progression that assumes that the diaschisma is tempered out (i.e. equates two notes that are separated by a diaschisma).

See also

• Comma