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.

Mathematical observations

The schisma is the reason for why the greatly composite numbers 1048576 (2²⁰) and 104976 (18⁴) look alike. 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
• Wikipedia: Schisma