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{n\cdot d}[/math]) |
~2.81184 bits |
| Comma size | small |
| open this interval in xen-calc | |
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