22L 1s: Difference between revisions
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== Scale tree == | == Scale tree == | ||
{ | {{Scale tree}} | ||
==See also== | ==See also== | ||
* [[33/32]] | * [[33/32]] | ||
* [[33/32 equal step tuning]] | * [[33/32 equal step tuning]] | ||
Revision as of 00:27, 3 March 2024
| ← 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 |