176/175
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Ratio | 176/175 |
Factorization | 2^{4} × 5^{-2} × 7^{-1} × 11 |
Monzo | [4 0 -2 -1 1⟩ |
Size in cents | 9.8646082¢ |
Name | Valinorsma |
Color name | 1orgg1, lorugugu 1sn, Lorugugu comma |
FJS name | [math]\text{d1}^{11}_{5,5,7}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 14.9106 |
Weil height (log_{2} max(n, d)) | 14.9189 |
Wilson height (sopfr (nd)) | 36 |
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.
176/175 factors neatly into two 13-limit superparticular commas: (352/351)(351/350).
Temperaments
Tempering out this comma leads to the rank-4 valinorsmic temperament (→ Rank-4 temperament #Valinorsmic (176/175)), and enables valinorsmic chords. See Valinorsmic clan for the clan of rank-3 temperaments where it is tempered out.