525/512

Interval information

Ratio	525/512
Factorization	2-9 × 3 × 52 × 7
Monzo	[-9 1 2 1⟩
Size in cents	43.40834¢
Names	avicennma, Avicenna's enharmonic diesis
Color name	Lzyy1, lazoyoyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5,5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	18.0362
Weil norm (log2 max(n, d))	18.0723
Wilson norm (sopfr(nd))	38
Comma size	medium
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525/512, the avicennma, also known as Avicenna's enharmonic diesis, is a medium 7-limit comma measuring about 43.4 cents. It is the difference between 64/63 and 25/24, or between 32/25 and 21/16.

In the 11-limit, it factors into (45/44)⋅(385/384), and in the 2.3.5.7.13 subgroup, (65/64)⋅(105/104).

Temperaments

Tempering out this comma equates 64/63 with 25/24 and leads to the avicennmic temperament. Because it flattens 3/2 and 5/4, it is a natural choice to further temper out 81/80, resulting in flattone temperament.

See Avicennmic temperaments for a collection of rank-2 temperaments where it is tempered out.