121/120: Difference between revisions

(21 intermediate revisions by 13 users not shown)

Line 1:

In [[~~Just Intonation~~]], 121/120 (the biyatisma) is a [[superparticular]] interval of around 14.4¢ which makes the difference between two undecimal neutral seconds of [[11/10]] and [[12/11~~]]. Temperaments in which 121/120 is tempered out include [[15edo|15~~]], [[~~22edo|22]], [[29edo|29]], [[31edo|31]], [[46edo|46]], [[53edo|53]] EDOs 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 triad which has intervals of 11/8, 11/8, and 16/15~~.

{{Infobox Interval

| Name = biyatisma, undecimal seconds comma

| Color name = 1oog1, lologu 1sn,<br>Lologu comma

| 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.

See: [[~~Gallery~~ of ~~Just Intervals~~]]

== Temperaments ==

[[Category:~~11-limit~~]]

[[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.

[[Category:~~superparticular~~]]

== 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 ==

* [[Small comma]]

* [[List of superparticular intervals]]

== Notes ==

[[Category:Biyatismic]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
-In [[Just Intonation]], 121/120 (the biyatisma) is a [[superparticular]] interval of around 14.4¢ which makes the difference between two undecimal neutral seconds of [[11/10]] and [[12/11]]. Temperaments in which 121/120 is tempered out include [[15edo|15]], [[22edo|22]], [[29edo|29]], [[31edo|31]], [[46edo|46]], [[53edo|53]] EDOs 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 triad which has intervals of 11/8, 11/8, and 16/15.
+{{Infobox Interval
+| Name = biyatisma, undecimal seconds comma
+| Color name = 1oog1, lologu 1sn,<br>Lologu comma
+| 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.
-See: [[Gallery of Just Intervals]]
+== Temperaments ==
-[[Category:11-limit]]
+[[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.
-[[Category:superparticular]]
+== 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 ==
+* [[Small comma]]
+* [[List of superparticular intervals]]
+== Notes ==
+[[Category:Biyatismic]]
+[[Category:Commas named after musical traditions]]