4000/3969
Ratio | 4000/3969 |
Factorization | 2^{5} × 3^{-4} × 5^{3} × 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 (log_{2} nd) | 23.9203 |
Weil height (log_{2} 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 * S20^{2} |
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 S20^{2} * 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.