176/175

Interval information

Ratio	176/175
Factorization	24 × 5-2 × 7-1 × 11
Monzo	[4 0 -2 -1 1⟩
Size in cents	9.864608¢
Name	Valinorsma
Color name	1orgg1, lorugugu 1sn, Lorugugu comma
FJS name	[math]\displaystyle{ \text{d1}^{11}_{5,5,7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	14.9106
Weil height (log2 max(n, d))	14.9189
Wilson height (sopfr(nd))	36
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~2.05691 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 the 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).

Etymology

The name likely derives from "Valinor" (a location in J. R. R. Tolkien's Middle-earth), but what association Valinor has to this comma is unknown.

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.

See also

• Small comma
• List of superparticular intervals