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 14.4 [[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.

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]], ~~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 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.

[[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".

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 ==

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[[Category:Biyatismic]]

[[Category:Commas named after musical traditions]]

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+In [[just intonation]], '''121/120''', otherwise known as the '''biyatisma''', or '''undecimal seconds comma''', is a [[superparticular]] interval of around 14.4 [[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.
-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]], 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 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.
+[[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".
+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 ==
@@ Line 20: / Line 19: @@
 [[Category:Biyatismic]]
+[[Category:Commas named after musical traditions]]