176/175
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| Ratio | 176/175 |
| Factorization | 24 × 5-2 × 7-1 × 11 |
| Monzo | [4 0 -2 -1 1⟩ |
| Size in cents | 9.8646082¢ |
| Name | Valinorsma |
| FJS name | [math]\text{d1}^{11}_{5,5,7}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 n⋅d) | 14.9106 |
| Weil height (max(n, d)) | 176 |
| Benedetti height (n⋅d) | 30800 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.79305 bits |
| Comma size | small |
| S-expressions | S8 / S10, S22 × S23 × S24 |
| open this interval in xen-calc | |
176/175, the valinorsma, is a 11-limit small comma measuring about 9.9 cents. It is amount by which 11/7 exceeds two 5/4's stacked, that is, the difference between 11/7 and 25/16, 8/7 and 25/22, 14/11 and 32/25, 15/11 and 48/35, or 22/15 and 35/24. Tempering it out leads to the rank-4 valinorsmic temperament.
176/175 factors neatly into two 13-limit superparticular commas: 352/351 × 351/350.
See also
- Valinorsmic chords
- Rank-4 temperament #Valinorsmic (176/175)
- Valinorsmic clan, the clan of rank-3 temperaments where it is tempered out
- Small comma
- List of superparticular intervals