# Wilschisma

 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 $\text{d2}^{5,13}$ 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, $\sqrt{nd}$) ~1.30587 bits Comma size unnoticeable open this interval in xen-calc

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

 [⟨ 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

### 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