4000/3969: Difference between revisions

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The '''octagar comma''' is a [[small comma|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s.

The '''octagar comma''' is a [[small comma|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s. [[Square_superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29|As per its S-expression of S20<sup>2</sup> * S19]], being a lopsided comma, it is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>.

== Temperaments ==

Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[~~octagar~~ family]] for the family of rank-3 temperaments where it is tempered out. See [[~~octagar~~ temperaments]] for a collection of rank-2 temperaments where it is tempered out.

Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[Octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[Octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.

It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}...

== Etymology ==

This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later dropped the last letter ''i''.

== See also ==

* [[Gallery of just intervals]]

== Notes ==

[[Category:Octagar]]

[[Category:Commas named by combining multiple temperament names]]

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-The '''octagar comma''' is a [[small comma|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s.
+The '''octagar comma''' is a [[small comma|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s. [[Square_superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29|As per its S-expression of S20<sup>2</sup> * S19]], being a lopsided comma, it is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>.
 == Temperaments ==
-Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.
+Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[Octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[Octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.
 It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}...
+== Etymology ==
+This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later dropped the last letter ''i''.
 == See also ==
 * [[Gallery of just intervals]]
+== Notes ==
+[[Category:Octagar]]
+[[Category:Commas named by combining multiple temperament names]]