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 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]]).

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

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.

~~== 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]]

[[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 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]]).
-/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)]]), 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 likely derives from "Valinor" (a location in J. R. R. Tolkien's Middle-earth), but what association Valinor has to this comma is unknown.
+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.
-== 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]]
 [[Category:Valinorsmic]]
 [[Category:Commas with unknown etymology]]