21L 1s: Difference between revisions
Created page with "{{Infobox MOS | Periods = 1 | nLargeSteps = 21 | nSmallSteps = 1 | Equalized = 1 | Collapsed = 1 | Pattern = LLL...21x...LLLs | Other names = tricesimoprimal quartertonic }} 2..." |
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== 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. | ||
== Modes == | == Modes == | ||
Revision as of 06:25, 14 January 2023
| ← 20L 1s | 21L 1s | 22L 1s → |
| ↙ 20L 2s | ↓ 21L 2s | 22L 2s ↘ |
sLLLLLLLLLLLLLLLLLLLLL
21L 1s is the scale that is most commonly produced by stacking the interval of 32/31 or 31/30.
A name tricesimoprimal quartertonic is proposed 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
Eliora proposes naming the brightest mode Alpharabian, after the fact that 33/32 is called Al-Farabi quarter-tone, and the rest after Tarot Major Arcana adjectivals based on how many generators down there is.
| Mode | Name |
|---|---|
| 22|0 | Alpharabian |
| 21|1 | Magical |
| 20|2 | High Priestess's |
| 19|3 | Empress's |
| ... | ... |
| 2|20 | Judgemental |
| 1|21 | Worldwide |
| 0|22 | Foolish |
Scale tree
| Generator | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|
| 1\23 | 1 | 1 | 1.000 | ||||||
| 6\137 | 6 | 5 | 1.200 | ||||||
| 5\114 | 5 | 4 | 1.250 | ||||||
| 9\205 | 9 | 7 | 1.286 | ||||||
| 4\91 | 4 | 3 | 1.333 | 13 steps adding to lower bound of diatonic fifths (685.71c) is here | |||||
| 11\250 | 11 | 8 | 1.375 | ||||||
| 7\159 | 7 | 5 | 1.400 | ||||||
| 10\227 | 10 | 7 | 1.428 | ||||||
| 3\68 | 3 | 2 | 1.500 | Stretched 23edo is in this range | |||||
| 11\249 | 11 | 7 | 1.571 | ||||||
| 8\181 | 8 | 5 | 1.600 | ||||||
| 13\294 | 13 | 8 | 1.625 | ||||||
| 5\113 | 5 | 3 | 1.667 | ||||||
| 12\271 | 12 | 7 | 1.714 | ||||||
| 7\158 | 7 | 4 | 1.750 | ||||||
| 9\203 | 9 | 5 | 1.800 | ||||||
| 2\45 | 2 | 1 | 2.000 | Basic quartismoid | |||||
| 9\202 | 9 | 4 | 2.250 | ||||||
| 7\157 | 7 | 3 | 2.333 | ||||||
| 12\269 | 12 | 5 | 2.400 | ||||||
| 5\112 | 5 | 2 | 2.500 | 13 steps adding to 1/4 comma meantone fifth is around here | |||||
| 13\291 | 13 | 5 | 2.600 | ||||||
| 8\179 | 8 | 3 | 2.667 | ||||||
| 11\246 | 11 | 4 | 2.750 | ||||||
| 3\67 | 3 | 1 | 3.000 | ||||||
| 10\223 | 10 | 3 | 3.333 | ||||||
| 7\156 | 7 | 2 | 3.500 | 13 steps adding to a 700 cent fifth is here | |||||
| 11\245 | 11 | 3 | 3.667 | ||||||
| 4\89 | 4 | 1 | 4.000 | ||||||
| 9\200 | 9 | 2 | 4.500 | 13 steps adding to 3/2 perfect fifth is around here | |||||
| 5\111 | 5 | 1 | 5.000 | ||||||
| 6\133 | 6 | 1 | 6.000 | ||||||
| 1\22 | 1 | 0 | → inf | ||||||