79edo

79edo divides the octave into 79 equal parts of 15.190 cents each.

Theory

It tempers out 3125/3072 in the 5-limit, 4000/3969, 1728/1715 and 4375/4374 in the 7-limit, 99/98, 1331/1323, 243/242, 385/384 and 4000/3993 in the 11-limit, and 275/273, 169/168, 640/637, 1188/1183, 325/324, 351/350, 1575/1573, 2080/2079 and 2200/2197 in the 13-limit. It provides the optimal patent val for sentinel temperament. 79 is the 22nd prime EDO number.

79edo adequately represents the temperament where a tone is considered to be 10/9 instead of 9/8. In most temperaments, when the difference betweein 10/9 and 9/8 is tempered out, what really happens is that the 9/8 only note is used, and 10/9 is raised to be equal to 9/8. 79edo misses 9/8 while having a near-perfect representation of 10/9 as 12\79. Proposed name: decaononic, from "10 over 9".

A maximum evenness variant of such scale can be generated by naively stacking 6 12edo diatonic majors and 1 Lydian tetrachord. Since the final tetrachord doesn't have a 2nd degree, this results in 6 II's stretched over 6+7/12 octaves, which is just enough to make the log2 of the number to be equal to 10/9. Proposed name: Auramagnesic, from 79 (gold) and 12 (magnesium).

Scales

Decaononic[7] - also glacial Auramagnesic[46]

Music

Saint Sebastian, By the Hands of Reni by Silence and Secrecy (Julian Malerman)