121/120: Difference between revisions
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In [[just intonation]], '''121/120''', otherwise known as the '''biyatisma''', or '''undecimal seconds comma''', is a [[superparticular]] interval of around 14. | In [[just intonation]], '''121/120''', otherwise known as the '''biyatisma''', or '''undecimal seconds comma''', is a [[superparticular]] interval of around 14.4 [[cent]]s which makes the difference between two undecimal neutral seconds of [[11/10]] and [[12/11]]. | ||
== Temperaments == | |||
Tempering out this comma in the 11-limit gives the rank-4 biyatismic temperament (→ [[Rank-4 temperament #Biyatismic (121/120)]]), enabling [[biyatismic chords]]. See [[biyatismic clan]] for the clan of rank-3 temperaments where it is tempered out. | |||
Equal temperaments in which 121/120 is [[tempered out]] include {{EDOs| 15, 22, 29, 31, 46, 53 }} and others; in such systems, 11/10 and 12/11 are equated. 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]]. Along with being the difference between 11/10 and 12/11, 121/120 is the difference between [[11/8]] and [[15/11]], so that tempering out 121/120 allows for the [[Dyadic chord|dyadic triad]] which has intervals of 11/8, 11/8, and 16/15 ([[biyatismic chords]]). | |||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Biyatismic]] | [[Category:Biyatismic]] | ||
Revision as of 08:10, 11 January 2023
| Interval information |
undecimal seconds comma
Lologu comma
reduced
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.
Temperaments
Tempering out this comma in the 11-limit gives the rank-4 biyatismic temperament (→ Rank-4 temperament #Biyatismic (121/120)), enabling biyatismic chords. See biyatismic clan for the clan of rank-3 temperaments where it is tempered out.
Equal temperaments in which 121/120 is tempered out include 15, 22, 29, 31, 46, 53 and others; in such systems, 11/10 and 12/11 are equated. 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. Along with being the difference between 11/10 and 12/11, 121/120 is the difference between 11/8 and 15/11, so that tempering out 121/120 allows for the dyadic triad which has intervals of 11/8, 11/8, and 16/15 (biyatismic chords).