176/175: Difference between revisions

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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]]~~. Tempering it out leads to the rank-4 valinorsmic temperament~~.

'''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]].

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.

== 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]]

[[Category:Valinorsmic]]

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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]]. Tempering it out leads to the rank-4 valinorsmic temperament.
+'''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]].
-/175 factors neatly into two [[13-limit]] [[superparticular]] commas: [[352/351]] × [[351/350]].
+/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.
 == 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]]
 [[Category:Valinorsmic]]