121/120: Difference between revisions
The 1-11/8-15/8 chord is essentially just |
m Set the links straight |
||
| (8 intermediate revisions by 6 users not shown) | |||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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]], between [[11/8]] and [[15/11]], and also the difference between [[6/5]] and two [[12/11]]'s. | |||
== Temperaments == | |||
[[Tempering out]] this comma in the 2.3.5.11 [[subgroup]] gives the rank-3 [[protomere]] temperament. See [[Biyatismic clan]] for extensions of protomere. Tempering it out in the full 11-limit gives the rank-4 biyatismic temperament (→ [[Rank-4 temperament #Biyatismic (121/120)]]). In such systems, 11/10 and 12/11 are equated, enabling [[biyatismic chords]]. This is similar 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 {{EDOs| 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<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13575 ''Small comma'' (Revision as of 23:54, 1 June 2010 by Wikispaces>genewardsmith)]</ref>. The name seems to come from {{w|Bayati (maqam)|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", although likely it is a pun using the prefix "bi" given that it splits the interval [[6/5]] in two parts. | ||
== See also == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Biyatismic]] | [[Category:Biyatismic]] | ||
[[Category:Commas named after musical traditions]] | |||
Latest revision as of 11:33, 26 April 2025
| 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, between 11/8 and 15/11, and also the difference between 6/5 and two 12/11's.
Temperaments
Tempering out this comma in the 2.3.5.11 subgroup gives the rank-3 protomere temperament. See Biyatismic clan for extensions of protomere. Tempering it out in the full 11-limit gives the rank-4 biyatismic temperament (→ Rank-4 temperament #Biyatismic (121/120)). In such systems, 11/10 and 12/11 are equated, enabling biyatismic chords. This is similar 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", although likely it is a pun using the prefix "bi" given that it splits the interval 6/5 in two parts.