4000/3969

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]\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
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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. It is not clear how it later dropped the last letter i.

See also

• Gallery of just intervals