121/120: Difference between revisions

Line 5:

}}

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]]).

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 ==

* [[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]]

[[Category:Biyatismic]]

@@ Line 5: / Line 5: @@
 }}
-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]]).
+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 ==
-* [[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]]
 [[Category:Biyatismic]]