Wilschisma

Interval information

Ratio	532480/531441
Factorization	213 × 3-12 × 5 × 13
Monzo	[13 -12 1 0 0 1⟩
Size in cents	3.3813652¢
Name	wilschisma
Color name	s3oy2, sathoyo 2nd, Sathoyo comma
FJS name	[math]\text{d2}^{5,13}[/math]
Special properties	reduced
Tenney height (log2 nd)	38.0419
Weil height (log2 max(n, d))	38.0447
Wilson height (sopfr (nd))	80
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math])	~2.44821 bits
Comma size	unnoticeable
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The wilschisma (monzo: [13 -12 1 0 0 1⟩, ratio: 532480/531441) is a 13-limit (also 2.3.5.13 subgroup) unnoticeable comma measuring about 3.38 cents. It is the difference between the wilsorma (65/64) and the Pythagorean comma, hence the name. The wilschisma can be viewed as a counterpart of the symbiotic comma – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an ibnsinma. In addition, the wilschisma is the difference between the garischisma and the schismina.

Temperaments

Tempering out this comma in the full 13-limit results in the rank-5 wilschismic temperament. You may find a list of good equal temperaments that support this temperament below. Adding the ibnsinma and thus the symbiotic comma to the comma list gives symbiotic (→ Rank-4 temperament #Symbiotic (19712/19683)), with virtually no additional error, so it is highly recommendable. Otherwise, retracting it to the 2.3.5.13 subgroup gives the rank-3 will temperament.

Wilschismic

Subgroup: 2.3.5.7.11.13

Comma list: 532480/531441

Mapping:

[⟨	1	0	0	0	0	-13	],
⟨	0	1	0	0	0	12	],
⟨	0	0	1	0	0	-1	],
⟨	0	0	0	1	0	0	],
⟨	0	0	0	0	1	0	]]

mapping generators: ~2, ~3, ~5, ~7, ~11

Optimal ET sequence: 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef

Will

Subgroup: 2.3.5.13

Comma list: 532480/531441

Sval mapping: [⟨1 0 0 -13], ⟨0 1 0 12], ⟨0 0 1 -1]]

Optimal tuning (CTE): ~3/2 = 702.2227, ~5/4 = 386.2658

Optimal ET sequence: 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf

Badness: 0.132 × 10^-3

See also

• Unnoticeable comma