21L 1s
| ← 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
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 tricesimoprimal quartertonic | |||||
| 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 | ||||||