4000/3969: Difference between revisions

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| Comma = yes

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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. It is also equal to ([[10/9]])/([[21/20]])2, with [[S-expression]] ~~S19 × S20~~2, making it a lopsided comma.

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. It is also the difference between [[50/49]] and [[81/80]], and is equal to ([[10/9]])/([[21/20]])2, with [[S-expression]] S19⋅S202, making it a lopsided comma.

== 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>. The last letter ''i'' was dropped by 2010, however<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92281.html Yahoo! Tuning Group | ''Octagar (4000/3969) planar temperament'']</ref>.

~~== See also ==~~

* [[Gallery of just intervals]]

== References ==

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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. It is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>, with [[S-expression]] S19 × S20<sup>2</sup>, making it a lopsided comma.
+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. It is also the difference between [[50/49]] and [[81/80]], and is equal to ([[10/9]])/([[21/20]])<sup>2</sup>, with [[S-expression]] S19⋅S20<sup>2</sup>, making it a lopsided comma.
 == 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>. The last letter ''i'' was dropped by 2010, however<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92281.html Yahoo! Tuning Group | ''Octagar (4000/3969) planar temperament'']</ref>.
-== See also ==
-* [[Gallery of just intervals]]
 == References ==