176/175: Difference between revisions

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'''176/175''', the '''valinorsma''', is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 9.9 [[cent]]s. 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''', 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.

Tempering out this comma leads to the rank-4 '''valinorsmic temperament''' (→ [[Rank-4 temperament #Valinorsmic (176/175)]]), or in the 2.5.7.11 subgroup, the [[valinor]] temperament, enabling [[valinorsmic chords]]. See [[Valinorsmic clan]] for the clan of rank-3 temperaments where it is tempered out.

== Etymology ==

The name seems to originally have been a portmanteau of "[[valentine]]", "[[orwell]]", and possibly an additional temperament, all of which temper out this comma in the 11-limit, as was a common custom for naming commas. However, the name has been re-interpreted as referring to "Valinor", a location in J. R. R. Tolkien's Middle-earth, and various temperaments in the valinorsmic clan have been named after the Valar, that realm's inhabitants.

== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

[[Category:Valinorsmic]]

[[Category:Commas with unknown etymology]]

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+'''176/175''', the '''valinorsma''', is a [[small comma|small]] [[11-limit]] [[comma]] measuring about 9.9 [[cent]]s. 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''', 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]]).
 == 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.
+Tempering out this comma leads to the rank-4 '''valinorsmic temperament''' (→ [[Rank-4 temperament #Valinorsmic (176/175)]]), or in the 2.5.7.11 subgroup, the [[valinor]] temperament, enabling [[valinorsmic chords]]. See [[Valinorsmic clan]] for the clan of rank-3 temperaments where it is tempered out.
+== Etymology ==
+The name seems to originally have been a portmanteau of "[[valentine]]", "[[orwell]]", and possibly an additional temperament, all of which temper out this comma in the 11-limit, as was a common custom for naming commas. However, the name has been re-interpreted as referring to "Valinor", a location in J. R. R. Tolkien's Middle-earth, and various temperaments in the valinorsmic clan have been named after the Valar, that realm's inhabitants.
 == See also ==
-* [[Small comma]]
 * [[List of superparticular intervals]]
 [[Category:Valinorsmic]]
+[[Category:Commas with unknown etymology]]