121/120
Ratio | 121/120 |
Factorization | 2^{-3} × 3^{-1} × 5^{-1} × 11^{2} |
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 | [math]\text{d1}^{11,11}_{5}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 13.8258 |
Weil height (log_{2} max(n, d)) | 13.8377 |
Wilson height (sopfr (nd)) | 36 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~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".