525/512

Interval information

Ratio	525/512
Factorization	2-9 × 3 × 52 × 7
Monzo	[-9 1 2 1⟩
Size in cents	43.40834¢
Names	Avicenna's enharmonic diesis, avicennma
Color name	Lzyy1, lazoyoyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5,5,7} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	18.0362
Weil height (log2 max(n, d))	18.0723
Wilson height (sopfr(nd))	38
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.51024 bits
Comma size	medium
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525/512, known as Avicenna's enharmonic diesis or avicennma, is the 7-limit medium comma between 64/63 and 25/24, or between 32/25 and 21/16.

Temperaments

Tempering it out equates 64/63 with 25/24 and leads to the avicennmic temperament.

Avicennmic temperament

Subgroup: 2.3.5.7

Comma list: 525/512

Mapping: [⟨1 0 0 9], ⟨0 1 0 -1], ⟨0 0 1 -2]]

POTE generators: ~3/2 = 695.5265, ~5/4 = 374.1745

Optimal ET sequence: 7, 9, 10, 16, 19, 45, 64cd, 93cdd, 119bccdd, 138bccdd

Badness: 0.4765 × 10^-3

See also

• Medium comma
• Avicennmic temperaments, a collection of rank-2 temperaments where it is tempered out