936/935
Ratio | 936/935 |
Factorization | 2^{3} × 3^{2} × 5^{-1} × 11^{-1} × 13 × 17^{-1} |
Monzo | [3 2 -1 0 -1 1 -1⟩ |
Size in cents | 1.8505978¢ |
Names | ainos comma, ainma |
FJS name | [math]\text{P1}^{13}_{5,11,17}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} n⋅d) | 19.7392 |
Weil height (max(n, d)) | 936 |
Benedetti height (n⋅d) | 875160 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.41335 bits |
Comma size | unnoticeable |
S-expression | S52 × S53 × S54 |
open this interval in xen-calc |
936/935, the ainos comma or ainma, 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. When tempered out in a linearly independent fashion, the resulting temperaments are called "ainos temperaments", and are characterized by the presence of essentially tempered chords called "ainic chords".
This comma's names come from the Ancient Greek word "aînos" (meaning "tale", "story" or "fable"^{[1]}), 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" (meaning "riddle"^{[2]}), 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.
It factors into two superparticular intervals: 1701/1700 × 2080/2079.