21L 1s: Difference between revisions
not super sure what to do with the mode names and everything given how the page is written off 22L 1s but I see the valuability of this MOS in the context of an escapade-like temperament |
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==Tuning ranges== | ==Tuning ranges== | ||
The scale's approach to standard harmony can be considered based on the mode. | |||
=== Diatonic fifth and 65edo (Ultrasoft and supersoft) === | === Brighter modes === | ||
==== Diatonic fifth and 65edo (Ultrasoft and supersoft) ==== | |||
Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth. | Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In [[65edo]], the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of [[5edo]], and thus is the exact boundary between a fifth proper and a fifth-sixth. | ||
If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth. | If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth. | ||
=== Fifth-sixth (hard of supersoft) === | ==== Fifth-sixth (hard of supersoft) ==== | ||
From 1\21 to 3\65, 13 steps amount to a fifth-sixth. | From 1\21 to 3\65, 13 steps amount to a fifth-sixth. | ||
If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora. | If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora. | ||
=== Darker modes === | |||
If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the [[escapade]] temperament does. | |||
The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7|14) to support the major triad, 4:5:6, and from Devil (6|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in [[108edo]], stacking steps of 5\108 downward. | |||
== Relation to other equal divisions == | == Relation to other equal divisions == | ||
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| || || ||5\108|| || ||5||3||1.667 | | || || ||5\108|| || ||5||3||1.667 | ||
| | |Inverting the scale yields a 700 cent fifth | ||
|- | |- | ||
| || || || || ||12\259||12||7||1.714 | | || || || || ||12\259||12||7||1.714 | ||