# 936/935

 Ratio 936/935 Factorization 23 × 32 × 5-1 × 11-1 × 13 × 17-1 Monzo [3 2 -1 0 -1 1 -1⟩ Size in cents 1.8505978¢ Names ainisma,ainic comma Color name 17u3o1ug1, sutholugu unison FJS name $\text{P1}^{13}_{5,11,17}$ Special properties superparticular,reduced Tenney height (log2 nd) 19.7392 Weil height (log2 max(n, d)) 19.7407 Wilson height (sopfr (nd)) 58 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.23106 bits Comma size unnoticeable S-expression S52 × S53 × S54 open this interval in xen-calc

936/935, the ainisma or ainic comma, is a 17-limit unnoticeable comma with a size of roughly 1.85 cents. It arises as the amount by which a stack consisting of 18/17 and 13/11 exceeds 5/4, as well as the amount by which a stack consisting of 10/9 and 17/16 falls short of 13/11. Moreover, it is also the interval that differentiates the tannisma (273/272) from the keenanisma (385/384), and the septendecimal kleisma (256/255) from the minthma (352/351). Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See #Commatic relations for more.

## Commatic relations

This comma is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

## Temperaments

When tempered out in the full 17-limit, the resulting rank-6 temperament is called the ainismic temperament, or in the 2.3.5.11.13.17 subgroup, the rank-5 ainic temperament. Both are characterized by the presence of essentially tempered chords called ainismic chords.

### Ainic

Subgroup: 2.3.5.11.13.17

Comma list: 936/935

 [⟨ 1 0 0 0 0 3 ], ⟨ 0 1 0 0 0 2 ], ⟨ 0 0 1 0 0 -1 ], ⟨ 0 0 0 1 0 -1 ], ⟨ 0 0 0 0 1 1 ]]
sval mapping generators: ~2, ~3, ~5, ~11, ~13
• CTE: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~11/8 = 551.7011, ~13/8 = 840.0893
• CWE: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5772, ~11/8 = 551.8274, ~13/8 = 840.2857

Optimal ET sequence22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624

### Ainismic

Subgroup: 2.3.5.7.11.13.17

Comma list: 936/935

 [⟨ 1 0 0 0 0 0 3 ], ⟨ 0 1 0 0 0 0 2 ], ⟨ 0 0 1 0 0 0 -1 ], ⟨ 0 0 0 1 0 0 0 ], ⟨ 0 0 0 0 1 0 -1 ], ⟨ 0 0 0 0 0 1 1 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
• CTE: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~7/4 = 968.8259, ~11/8 = 551.7011, ~13/8 = 840.0893
• CWE: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5773, ~7/4 = 968.9509, ~11/8 = 551.8275, ~13/8 = 840.2857

## Etymology

This comma was named by Aura in 2020. Its names come from the Ancient Greek word aînos ("tale", "story" or "fable"), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word aínigma ("riddle"), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.