176/175: Difference between revisions

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 norm (log2 nd)	14.9106
Weil norm (log2 max(n, d))	14.9189
Wilson norm (sopfr(nd))	36
Comma size	small
S-expressions	S8/S10,; S22⋅S23⋅S24
	Open this interval in xen-calc

Revision as of 14:02, 13 April 2025

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).

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.

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-'''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''', 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]].
 /175 factors neatly into two [[13-limit]] [[superparticular]] commas: ([[352/351]])([[351/350]]).