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]] [[ | |||
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 == | == Temperaments == | ||
Tempering out this comma leads to the rank-4 '''valinorsmic temperament''' (→ [[Rank-4 temperament #Valinorsmic (176/175)]]), | 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 == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Valinorsmic]] | [[Category:Valinorsmic]] | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] | ||
Latest revision as of 22:15, 8 January 2026
| Interval information |
Lorugugu comma
reduced
S22⋅S23⋅S24
176/175, the valinorsma, is a small 11-limit 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).
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.