176/175

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Interval information
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