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Interval information
Ratio 4000/3969
Factorization 25 × 3-4 × 53 × 7-2
Monzo [5 -4 3 -2
Size in cents 13.469325¢
Name octagar comma
Color name Rurutriyo comma
FJS name [math]\text{d}{-2}^{5,5,5}_{7,7}[/math]
Special properties reduced
Tenney height (log2 nd) 23.9203
Weil height (log2 max(n, d)) 23.9316
Wilson height (sopfr (nd)) 51
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~2.68919 bits
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. As per its S-expression of S202 * S19, being a lopsided comma, it is also equal to (10/9)/(21/20)2.


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...


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