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 == | == Temperaments == | ||
Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[ | 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}}... | 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 == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== Notes == | |||
[[Category:Octagar]] | |||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 12:59, 3 November 2024
| 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 10/9s and a stack of two 7/6s. As per its S-expression of S202 * S19, being a lopsided comma, it is also equal to (10/9)/(21/20)2.
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.
It is also tempered out in the following edos (by simple map): 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[1]. It is not clear how it later dropped the last letter i.