936/935

Interval information

Ratio	936/935
Factorization	23 × 32 × 5-1 × 11-1 × 13 × 17-1
Monzo	[3 2 -1 0 -1 1 -1⟩
Size in cents	1.850598¢
Name	ainos comma
FJS name	[math]\displaystyle{ \text{P1}^{13}_{5,11,17} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	19.7392
Weil height (log2 max(n, d))	19.7407
Wilson height (sopfr(nd))	58
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936/935, the ainos comma is an unnoticeable 17-limit comma with a size of roughly 1.85 cents. It forms the interval between the interval between 18/17 and 55/52 as well as the interval between 13/11 and 85/72, the interval between the tannisma (273/272) and the keenanisma (385/384), and, the interval between the septendecimal kleisma (256/255) and the minthma (352/351). Thus, tempering out this comma is a good way to extend Neo-Gothic and Minthmic harmonies to the 17-limit, as well as a good way to bring Keenanismic and Tannismic harmonies together. Furthermore, it is also the interval that differentiates 17/13 from 72/55, 24/17 from 55/39, and 117/64 from 935/512. When tempered out in a linearly independent fashion, the resulting temperaments are called "ainic temperaments".

This comma's name comes from an Ancient Greek word "aînos" (meaning "tale", "story" or "fable") which is fitting due to 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"), 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.