121/120

(Redirected from Biyatisma)
 Ratio 121/120 Factorization 2-3 × 3-1 × 5-1 × 112 Monzo [-3 -1 -1 0 2⟩ Size in cents 14.36717¢ Names biyatisma,undecimal seconds comma Color name 1oog1, lologu 1sn,Lologu comma FJS name $\text{d1}^{11,11}_{5}$ Special properties square superparticular,reduced Tenney height (log2 nd) 13.8258 Weil height (log2 max(n, d)) 13.8377 Wilson height (sopfr (nd)) 36 Harmonic entropy(Shannon, $\sqrt{n\cdot d}$) ~3.16917 bits Comma size small S-expression S11 open this interval in xen-calc

In just intonation, 121/120, otherwise known as the biyatisma, or undecimal seconds comma, is a superparticular interval of around 14.4 cents which makes the difference between two undecimal neutral seconds of 11/10 and 12/11, as well as between 11/8 and 15/11.

Temperaments

Tempering out this comma in the 11-limit gives the rank-4 biyatismic temperament (→ Rank-4 temperament #Biyatismic (121/120)). Tempering it out in the 2.3.5.11 subgroup gives the rank-3 protomere temperament. See biyatismic clan for extensions of protomere. In such systems, 11/10 and 12/11 are equated, enabling biyatismic chords. This is in contrast to the more familiar tempering out of 81/80, which results in meantone and other temperaments, in which 10/9 is equated with 9/8. Equal temperaments in which 121/120 is tempered out include 15, 22, 29, 31, 46, 53 and others.

Etymology

The biyatisma was presumably named by Gene Ward Smith in 2010 since it seems this wiki was the place where it made its first appearance[1]. The name seems to come from maqam bayati, which features a neutral second. It is yet to be found out why it is spelt with an "i" instead of an "a".