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. 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. | |||
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. | |||
== Temperaments == | == 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. | ||
== Etymology == | == 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>. | 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>. | ||
== | == References == | ||
[[Category:Octagar]] | [[Category:Octagar]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 14:18, 13 March 2026
| Interval information |
The octagar comma is a 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.
Etymology
This comma was named as octagari by Gene Ward Smith in 2005 as a contraction of octacot and garibaldi[1]. The last letter i was dropped by 2010, however[2].