3042/3025
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Ratio
3042/3025
Factorization
2 × 32 × 5-2 × 11-2 × 132
Monzo
[1 2 -2 0 -2 2⟩
Size in cents
9.7020128¢
Name
diagassormisma
Color name
3oo1uugg2,
bitholugu 2nd,
Bitholugu comma
FJS name
[math]\text{d2}^{13,13}_{5,5,11,11}[/math]
Special properties
reduced
Tenney height (log2 nd)
23.1335
Weil height (log2 max(n, d))
23.1416
Wilson height (sopfr(nd))
66
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~2.03076 bits
Comma size
small
open this interval in xen-calc
| Interval information |
bitholugu 2nd,
Bitholugu comma
(Shannon, [math]\sqrt{nd}[/math])
3042/3025, the diagassormisma is a 13-limit interval measuring about 9.7¢. It forms the difference between two 55/39s and an octave.
Temperaments
Tempering out this comma leads to the diagassormismic temperament, which splits the octave into two equal parts, each representing 55/39 (small gassormic tritone) and its octave complement, 78/55 (large gassormic tritone). Odd-numbered EDOs cannot temper it out.
2.3.5.11.13 diagassormismic
Subgroup: 2.3.5.11.13
Comma list: 3042/3025
Mapping: [⟨2 0 0 0 -1], ⟨0 1 0 0 -1], ⟨0 0 1 0 1], ⟨0 0 0 1 1]]
- Mapping generators: ~55/39, ~3, ~5, ~11
Optimal tuning (POTE): ~55/39 = 1＼2, ~3/2 = 701.7083, ~5/4 = 387.2538, ~11/8 = 553.2831
Optimal ET sequence: 8, 10, 12e, 12f, 14cf, 16, 22, 24, 34, 58, 72, 96, 130, 282f