4000/3969: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Created page with "{{Infobox Interval | Ratio = 4000/3969 | Name = octagar comma | Color name = Rurutriyo comma | Comma = yes }} The '''octagar comma''' is a small 7-limit [..."
 
Expansion
Line 9: Line 9:


== 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.


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]]

Revision as of 11:39, 2 January 2024

Interval information
Ratio 4000/3969
Factorization 25 × 3-4 × 53 × 7-2
Monzo [5 -4 3 -2
Size in cents 13.46933¢
Name octagar comma
Color name Rurutriyo comma
FJS name [math]\displaystyle{ \text{d}{-2}^{5,5,5}_{7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 23.9203
Weil norm (log2 max(n, d)) 23.9316
Wilson norm (sopfr(nd)) 51
Comma size small
S-expression S19⋅S202
Open this interval in xen-calc

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.

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.

See also

Notes