22L 1s
| ← 21L 1s | 22L 1s | 23L 1s → |
| ↙ 21L 2s | ↓ 22L 2s | 23L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║║║║║║║║││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLLLLLLLLLLLLL
22L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 22 large steps and 1 small step, repeating every octave. 22L 1s is related to 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 52.2 ¢ to 54.5 ¢, or from 1145.5 ¢ to 1147.8 ¢. Scales of this form are always proper because there is only one small step. This scale is produced by stacking the interval of 33/32 (around 53¢).
The name quartismoid is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the quartisma - five 33/32s being equated with 7/6. In addition, both 22edo and 23edo, extreme ranges of the MOS temper out the quartisma, as well as a large portion of EDOs up to 100-200 which have this scale.
Tuning ranges
Mavila fifth and 91edo (Ultrasoft and supersoft)
Between 4\91 and 1\23, 13 steps amount to a pelog / mavila fifth, which corresponds to the ultrasoft step ratio range. In 91edo, the fifth produced by 13 steps of the quartismoid scale is the same as 4 steps of 7edo, and thus is the exact boundary between mavila and diatonic.
Diatonic fifth (hard of supersoft)
From 1\22 to 4\91, 13 steps amount to a diatonic fifth.
If the pure 33/32 is used as a generator, the resulting fifth is 692.54826 cents, which puts it in the category around flattone.
700-cent, just, and superpyth fifths (step ratio 7:2 and harder)
In 156edo, the fifth becomes the 12edo 700-cent fifth. In 200edo, the fifth comes incredibly close to just, as the number 200 is a semiconvergent denominator to the approximation of log2(3/2).
When the step ratio is greater than 4.472, then 13 generators amount to a superpyth fifth and the tuning approaches 22edo.
Relation to other equal divisions
6 steps act as a pseudo-6/5, and when they actually act as 6/5 along with 5 steps being equal to 7/6, 385/384 is tempered out. If one were to instead tune in favour of 6/5 instead of 7/6, the resulting hardness would be around 1.233. 114edo and 137edo represent this the best.
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 |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0 ¢ to 52.2 ¢ |
| Perfect 1-mosstep | P1ms | L | 52.2 ¢ to 54.5 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 54.5 ¢ to 104.3 ¢ |
| Major 2-mosstep | M2ms | 2L | 104.3 ¢ to 109.1 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 109.1 ¢ to 156.5 ¢ |
| Major 3-mosstep | M3ms | 3L | 156.5 ¢ to 163.6 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 163.6 ¢ to 208.7 ¢ |
| Major 4-mosstep | M4ms | 4L | 208.7 ¢ to 218.2 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 218.2 ¢ to 260.9 ¢ |
| Major 5-mosstep | M5ms | 5L | 260.9 ¢ to 272.7 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 272.7 ¢ to 313.0 ¢ |
| Major 6-mosstep | M6ms | 6L | 313.0 ¢ to 327.3 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 327.3 ¢ to 365.2 ¢ |
| Major 7-mosstep | M7ms | 7L | 365.2 ¢ to 381.8 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 381.8 ¢ to 417.4 ¢ |
| Major 8-mosstep | M8ms | 8L | 417.4 ¢ to 436.4 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 436.4 ¢ to 469.6 ¢ |
| Major 9-mosstep | M9ms | 9L | 469.6 ¢ to 490.9 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 490.9 ¢ to 521.7 ¢ |
| Major 10-mosstep | M10ms | 10L | 521.7 ¢ to 545.5 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 545.5 ¢ to 573.9 ¢ |
| Major 11-mosstep | M11ms | 11L | 573.9 ¢ to 600.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 11L + s | 600.0 ¢ to 626.1 ¢ |
| Major 12-mosstep | M12ms | 12L | 626.1 ¢ to 654.5 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 12L + s | 654.5 ¢ to 678.3 ¢ |
| Major 13-mosstep | M13ms | 13L | 678.3 ¢ to 709.1 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 13L + s | 709.1 ¢ to 730.4 ¢ |
| Major 14-mosstep | M14ms | 14L | 730.4 ¢ to 763.6 ¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 14L + s | 763.6 ¢ to 782.6 ¢ |
| Major 15-mosstep | M15ms | 15L | 782.6 ¢ to 818.2 ¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 15L + s | 818.2 ¢ to 834.8 ¢ |
| Major 16-mosstep | M16ms | 16L | 834.8 ¢ to 872.7 ¢ | |
| 17-mosstep | Minor 17-mosstep | m17ms | 16L + s | 872.7 ¢ to 887.0 ¢ |
| Major 17-mosstep | M17ms | 17L | 887.0 ¢ to 927.3 ¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 17L + s | 927.3 ¢ to 939.1 ¢ |
| Major 18-mosstep | M18ms | 18L | 939.1 ¢ to 981.8 ¢ | |
| 19-mosstep | Minor 19-mosstep | m19ms | 18L + s | 981.8 ¢ to 991.3 ¢ |
| Major 19-mosstep | M19ms | 19L | 991.3 ¢ to 1036.4 ¢ | |
| 20-mosstep | Minor 20-mosstep | m20ms | 19L + s | 1036.4 ¢ to 1043.5 ¢ |
| Major 20-mosstep | M20ms | 20L | 1043.5 ¢ to 1090.9 ¢ | |
| 21-mosstep | Minor 21-mosstep | m21ms | 20L + s | 1090.9 ¢ to 1095.7 ¢ |
| Major 21-mosstep | M21ms | 21L | 1095.7 ¢ to 1145.5 ¢ | |
| 22-mosstep | Perfect 22-mosstep | P22ms | 21L + s | 1145.5 ¢ to 1147.8 ¢ |
| Augmented 22-mosstep | A22ms | 22L | 1147.8 ¢ to 1200.0 ¢ | |
| 23-mosstep | Perfect 23-mosstep | P23ms | 22L + s | 1200.0 ¢ |