21L 1s: Difference between revisions
31-limit is a bit too complex for scales of this size, refer to the escapade temperament |
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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21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]]. | 21L 1s is the scale which has a generator step between one step of [[21edo]] and one step of [[22edo]]. | ||
[[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. | [[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: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. | [[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. | ||
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|- | |- | ||
| ||2\43|| || || || ||2||1||2.000 | | ||2\43|| || || || ||2||1||2.000 | ||
|Basic | |Basic escapist | ||
|- | |- | ||
| || || || || ||9\193||9||4||2.250 | | || || || || ||9\193||9||4||2.250 | ||
Revision as of 13:09, 19 February 2023
| ← 20L 1s | 21L 1s | 22L 1s → |
| ↙ 20L 2s | ↓ 21L 2s | 22L 2s ↘ |
sLLLLLLLLLLLLLLLLLLLLL
21L 1s is the scale which has a generator step between one step of 21edo and one step of 22edo.
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.
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
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.
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)
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.
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.
Modes
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.
| Mode | Name |
|---|---|
| 21|0 | Foolish |
| 20|1 | Magical |
| 19|2 | High Priestess's |
| 18|3 | Empress's |
| ... | ... |
| 3|19 | Lunar |
| 2|19 | Solar |
| 1|20 | Judgemental |
| 0|21 | Worldwide |
Scale tree
| Generator | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|
| 1\22 | 1 | 1 | 1.000 | ||||||
| 6\131 | 6 | 5 | 1.200 | ||||||
| 5\109 | 5 | 4 | 1.250 | ||||||
| 9\196 | 9 | 7 | 1.286 | ||||||
| 4\87 | 4 | 3 | 1.333 | ||||||
| 11\239 | 11 | 8 | 1.375 | ||||||
| 7\152 | 7 | 5 | 1.400 | ||||||
| 10\217 | 10 | 7 | 1.428 | ||||||
| 3\65 | 3 | 2 | 1.500 | 13 steps adding to upper bound of diatonic fifths (720¢) is here | |||||
| 11\238 | 11 | 7 | 1.571 | ||||||
| 8\173 | 8 | 5 | 1.600 | ||||||
| 13\281 | 13 | 8 | 1.625 | ||||||
| 5\108 | 5 | 3 | 1.667 | ||||||
| 12\259 | 12 | 7 | 1.714 | ||||||
| 7\151 | 7 | 4 | 1.750 | ||||||
| 9\194 | 9 | 5 | 1.800 | ||||||
| 2\43 | 2 | 1 | 2.000 | Basic escapist | |||||
| 9\193 | 9 | 4 | 2.250 | ||||||
| 7\150 | 7 | 3 | 2.333 | ||||||
| 12\257 | 12 | 5 | 2.400 | ||||||
| 5\107 | 5 | 2 | 2.500 | ||||||
| 13\278 | 13 | 5 | 2.600 | ||||||
| 8\171 | 8 | 3 | 2.667 | ||||||
| 11\235 | 11 | 4 | 2.750 | ||||||
| 3\64 | 3 | 1 | 3.000 | ||||||
| 10\213 | 10 | 3 | 3.333 | ||||||
| 7\149 | 7 | 2 | 3.500 | ||||||
| 11\234 | 11 | 3 | 3.667 | ||||||
| 4\85 | 4 | 1 | 4.000 | ||||||
| 9\191 | 9 | 2 | 4.500 | ||||||
| 5\106 | 5 | 1 | 5.000 | ||||||
| 6\127 | 6 | 1 | 6.000 | ||||||
| 1\21 | 1 | 0 | → inf | ||||||