176/175: Difference between revisions
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Make valinor explicit |
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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 == | == 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 likely derives from "Valinor" (a location in J. R. R. Tolkien's Middle-earth), but what association Valinor has to this comma is unknown. | ||
== See also == | == See also == | ||
Revision as of 13:25, 20 October 2025
| Interval information |
Lorugugu comma
reduced
S22⋅S23⋅S24
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).
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.