176/175: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 176/175~~

~~| Monzo = 4 0 -2 -1 1~~

~~| Cents = 9.86461~~

| Name = Valinorsma

| Color name =

| Color name = 1orgg1, lorugugu 1sn,<br>Lorugugu comma

~~| FJS name = d1<sup>11</sup><sub>25~~,7<~~/sub~~>

| Comma = yes

| ~~Sound~~ =

}}

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

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 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 ==

* [[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:11-limit]]~~

~~[[Category:Small commas]]~~

~~[[Category:Superparticular]]~~

[[Category:Valinorsmic]]

[[Category:Commas with unknown etymology]]

[[Category:~~Todo:add color name~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 176/175
-| Monzo = 4 0 -2 -1 1
-| Cents = 9.86461
 | Name = Valinorsma
-| Color name =
+| Color name = 1orgg1, lorugugu 1sn,<br>Lorugugu comma
-| FJS name = d1<sup>11</sup><sub>25,7</sub>
+| Comma = yes
-| Sound =
 }}
+'''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]]. Tempering it out leads to the rank-4 valinorsmic temperament.
+/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 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 ==
-* [[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:11-limit]]
-[[Category:Small commas]]
-[[Category:Superparticular]]
 [[Category:Valinorsmic]]
+[[Category:Commas with unknown etymology]]
-[[Category:Todo:add color name]]