21L 1s: Difference between revisions
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| Collapsed = 1 | | Collapsed = 1 | ||
| Pattern = LLL...21x...LLLs | | Pattern = LLL...21x...LLLs | ||
| Other names = tricesimoprimal quartertonic | | Other names = escapist,<br> tricesimoprimal quartertonic | ||
}} | }} | ||
{{MOS intro}} | |||
[[Eliora]] proposes the name '''escapist''' for this pattern, referencing the [[escapade]] temperament which is supported by both [[21edo]] and [[22edo]], thus covering the entire tuning spectrum; [[User:Lériendil|Lériendil]] proposes '''noletic''' for similar reasons, as 9 generators reach a diatonic [[4/3]], supporting the scale [[9ed4/3]] known also as "noleta". | |||
[[User:Moremajorthanmajor|Moremajorthanmajor]] proposes the name ''tricesimoprimal quartertonic'' for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960—the tricesimoprimal quartertones being equated with each other. In addition, both [[21edo]] and [[22edo]], extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do. | |||
==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 == | ||
2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out. | 2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out. | ||
== Scale properties == | |||
{{TAMNAMS use}} | |||
=== Intervals === | |||
{{MOS intervals}} | |||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
== Proposed mode names === | |||
The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| | ! Mode | ||
| | ! Name | ||
|- | |||
| 21{{pipe}}0 | |||
| Foolish | |||
|- | |||
| 20{{pipe}}1 | |||
| Magical | |||
|- | |- | ||
| | | 19{{pipe}}2 | ||
| | | High Priestess's | ||
|- | |- | ||
| | | 18{{pipe}}3 | ||
| | | Empress's | ||
|- | |- | ||
| | | … | ||
| | | … | ||
|- | |- | ||
| | | 3{{pipe}}19 | ||
| | | Lunar | ||
|- | |- | ||
| | | 2{{pipe}}19 | ||
| | | Solar | ||
|- | |- | ||
| | | 1{{pipe}}20 | ||
| | | Judgemental | ||
|- | |- | ||
| | | 0{{pipe}}21 | ||
| | | Worldwide | ||
|} | |} | ||
== Intervals == | |||
{{MOS intervals}} | |||
== Scale tree == | == Scale tree == | ||
{ | {{MOS tuning spectrum}} | ||
== See also == | |||
* [[32/31]] | |||
* [[31/30]] | |||
* [[Escapade]] | |||
==See also== | |||
* [[ | |||
* [[ | |||