121/120: Difference between revisions

(11 intermediate revisions by 7 users not shown)

Line 1:

{{Infobox Interval

| Name = biyatisma, undecimal seconds comma

| Color name = 1oog1, Lologu 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.

In [[~~just intonation~~]]~~, '''121/120''', otherwise known as~~ the ~~'''biyatisma''', or '''undecimal seconds comma''', is a~~ [[~~superparticular~~]] ~~interval of around 14.4¢ which makes~~ the ~~difference between two undecimal neutral seconds of~~ [[~~11/10~~]] ~~and~~ [[~~12/11~~]]. ~~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~~]]).

== 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 ==

* [[Biyatismic chords]]

* [[Rank-4 temperament #Biyatismic (121/120)]]

* [[Biyatismic clan]], the clan of rank-3 temperaments where it is tempered out

* [[Small comma]]

* [[List of superparticular intervals]]

== Notes ==

[[Category:Biyatismic]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = biyatisma, undecimal seconds comma
-| Color name = 1oog1, Lologu 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.
-In [[just intonation]], '''121/120''', otherwise known as the '''biyatisma''', or '''undecimal seconds comma''', is a [[superparticular]] interval of around 14.4¢ which makes the difference between two undecimal neutral seconds of [[11/10]] and [[12/11]]. 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]]).
+== 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 ==
-* [[Biyatismic chords]]
-* [[Rank-4 temperament #Biyatismic (121/120)]]
-* [[Biyatismic clan]], the clan of rank-3 temperaments where it is tempered out
 * [[Small comma]]
 * [[List of superparticular intervals]]
+== Notes ==
 [[Category:Biyatismic]]
+[[Category:Commas named after musical traditions]]