22L 1s is the scale that is most commonly produced by stacking the interval of 33/32.
A 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.
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.
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.
|4\91||4||3||1.333||13 steps adding to lower bound of diatonic fifths (685.71c) is here|
|3\68||3||2||1.500||Stretched 23edo is in this range|
|5\112||5||2||2.500||13 steps adding to 1/4 comma meantone fifth is around here|
|7\156||7||2||3.500||13 steps adding to a 700 cent fifth is here|
|9\200||9||2||4.500||13 steps adding to 3/2 perfect fifth is around here|