Schisma

Interval information

Ratio	32805/32768
Factorization	2-15 × 38 × 5
Monzo	[-15 8 1⟩
Size in cents	1.953721¢
Name	schisma
FJS name	[math]\displaystyle{ \text{d}{-2}^{5} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	30.0016
Weil height (log2 max(n, d))	30.0033
Wilson height (sopfr(nd))	59
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The schisma, 32805/32768, is the difference between the Pythagorean comma and the syntonic comma. It is equal to (9/8)⁴/(8/5) and to (135/128)/(256/243) and also to (9/8)³/(64/45). Tempering it out gives a 5-limit microtemperament called schismatic, schismic or Helmholtz, which if extended to larger subgroups leads to the schismatic family of temperaments.

English Wikipedia has an article on:

Schisma

Trivia

The schisma explains how the greatly composite numbers 1048576 (2²⁰) and 104976 (18⁴) look alike in decimal. The largest common power of two between these numbers is 2⁵, and when reduced by that, 1049760/1048576 becomes 32805/32768.

See also

• Unnoticeable comma