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 ¢, 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 ¢ 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.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
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MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\23 | 52.174 | 1147.826 | 1:1 | 1.000 | Equalized 22L 1s | |||||
| 6\137 | 52.555 | 1147.445 | 6:5 | 1.200 | ||||||
| 5\114 | 52.632 | 1147.368 | 5:4 | 1.250 | ||||||
| 9\205 | 52.683 | 1147.317 | 9:7 | 1.286 | ||||||
| 4\91 | 52.747 | 1147.253 | 4:3 | 1.333 | Supersoft 22L 1s | |||||
| 11\250 | 52.800 | 1147.200 | 11:8 | 1.375 | ||||||
| 7\159 | 52.830 | 1147.170 | 7:5 | 1.400 | ||||||
| 10\227 | 52.863 | 1147.137 | 10:7 | 1.429 | ||||||
| 3\68 | 52.941 | 1147.059 | 3:2 | 1.500 | Soft 22L 1s | |||||
| 11\249 | 53.012 | 1146.988 | 11:7 | 1.571 | ||||||
| 8\181 | 53.039 | 1146.961 | 8:5 | 1.600 | ||||||
| 13\294 | 53.061 | 1146.939 | 13:8 | 1.625 | ||||||
| 5\113 | 53.097 | 1146.903 | 5:3 | 1.667 | Semisoft 22L 1s | |||||
| 12\271 | 53.137 | 1146.863 | 12:7 | 1.714 | ||||||
| 7\158 | 53.165 | 1146.835 | 7:4 | 1.750 | ||||||
| 9\203 | 53.202 | 1146.798 | 9:5 | 1.800 | ||||||
| 2\45 | 53.333 | 1146.667 | 2:1 | 2.000 | Basic 22L 1s | |||||
| 9\202 | 53.465 | 1146.535 | 9:4 | 2.250 | ||||||
| 7\157 | 53.503 | 1146.497 | 7:3 | 2.333 | ||||||
| 12\269 | 53.532 | 1146.468 | 12:5 | 2.400 | ||||||
| 5\112 | 53.571 | 1146.429 | 5:2 | 2.500 | Semihard 22L 1s | |||||
| 13\291 | 53.608 | 1146.392 | 13:5 | 2.600 | ||||||
| 8\179 | 53.631 | 1146.369 | 8:3 | 2.667 | ||||||
| 11\246 | 53.659 | 1146.341 | 11:4 | 2.750 | ||||||
| 3\67 | 53.731 | 1146.269 | 3:1 | 3.000 | Hard 22L 1s | |||||
| 10\223 | 53.812 | 1146.188 | 10:3 | 3.333 | ||||||
| 7\156 | 53.846 | 1146.154 | 7:2 | 3.500 | ||||||
| 11\245 | 53.878 | 1146.122 | 11:3 | 3.667 | ||||||
| 4\89 | 53.933 | 1146.067 | 4:1 | 4.000 | Superhard 22L 1s | |||||
| 9\200 | 54.000 | 1146.000 | 9:2 | 4.500 | ||||||
| 5\111 | 54.054 | 1145.946 | 5:1 | 5.000 | ||||||
| 6\133 | 54.135 | 1145.865 | 6:1 | 6.000 | ||||||
| 1\22 | 54.545 | 1145.455 | 1:0 | → ∞ | Collapsed 22L 1s | |||||