936/935: Difference between revisions

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'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together.

'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.

== Commatic relations ==

It factors into ~~two~~ superparticular ~~intervals~~: [[1701/1700]] × [[2080/2079]].

This comma is the difference between the following superparticular pairs:

* [[78/77]] and [[85/84]]

* [[144/143]] and [[170/169]]

* [[221/220]] and [[289/288]]

* [[256/255]] and [[352/351]]

* [[273/272]] and [[385/384]]

* [[351/350]] and [[561/560]]

* [[364/363]] and [[595/594]]

* [[375/374]] and [[625/624]]

* [[441/440]] and [[833/832]]

* [[540/539]] and [[1275/1274]]

* [[676/675]] and [[2431/2430]]

* [[715/714]] and [[3025/3024]]

It factors into the following superparticular pairs:

* [[1716/1715]] and [[2058/2057]]

* [[1701/1700]] and [[2080/2079]]

* [[1156/1155]] and [[4914/4913]]

* [[1089/1088]] and [[6656/6655]]

* [[1001/1000]] and [[14400/14399]]

== Temperaments ==

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-'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together.
+'''936/935''', the '''ainos''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.
 == Commatic relations ==
-It factors into two superparticular intervals: [[1701/1700]] × [[2080/2079]].
+This comma is the difference between the following superparticular pairs:
+* [[78/77]] and [[85/84]]
+* [[144/143]] and [[170/169]]
+* [[221/220]] and [[289/288]]
+* [[256/255]] and [[352/351]]
+* [[273/272]] and [[385/384]]
+* [[351/350]] and [[561/560]]
+* [[364/363]] and [[595/594]]
+* [[375/374]] and [[625/624]]
+* [[441/440]] and [[833/832]]
+* [[540/539]] and [[1275/1274]]
+* [[676/675]] and [[2431/2430]]
+* [[715/714]] and [[3025/3024]]
+It factors into the following superparticular pairs:
+* [[1716/1715]] and [[2058/2057]]
+* [[1701/1700]] and [[2080/2079]]
+* [[1156/1155]] and [[4914/4913]]
+* [[1089/1088]] and [[6656/6655]]
+* [[1001/1000]] and [[14400/14399]]
 == Temperaments ==