21L 1s
21L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 21 large steps and 1 small step, repeating every octave. 21L 1s is related to 1L 9s, expanding it by 12 tones. Generators that produce this scale range from 54.5 ¢ to 57.1 ¢, or from 1142.9 ¢ to 1145.5 ¢. Scales of this form are always proper because there is only one small step. 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.
| ← 20L 1s | 21L 1s | 22L 1s → |
| ↙ 20L 2s | ↓ 21L 2s | 22L 2s ↘ |
sLLLLLLLLLLLLLLLLLLLLL
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
The scale's approach to standard harmony can be considered based on the mode.
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.
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.
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
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 | Inverting the scale yields a 700 cent fifth | |||||
| 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 | ||||||