525/512
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Ratio
525/512
Factorization
2-9 × 3 × 52 × 7
Monzo
[-9 1 2 1⟩
Size in cents
43.408335¢
Names
Avicenna's enharmonic diesis,
avicennma
Color name
Lzyy1, lazoyoyo unison
FJS name
[math]\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]\sqrt{nd}[/math])
~4.51024 bits
Comma size
medium
open this interval in xen-calc
| Interval information |
avicennma
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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