4000/3969: Difference between revisions
m Readability |
+ another reference |
||
| Line 13: | Line 13: | ||
== 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>. | ||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== | == References == | ||
[[Category:Octagar]] | [[Category:Octagar]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Revision as of 12:21, 25 November 2025
| 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 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.
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]. The last letter i was dropped by 2010, however[2].