22L 1s

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Scale structure
Step pattern	LLLLLLLLLLLLLLLLLLLLLLs sLLLLLLLLLLLLLLLLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\23 to 1\22 (52.2 ¢ to 54.5 ¢)
Dark	21\22 to 22\23 (1145.5 ¢ to 1147.8 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	13:1 to 14:1
Related MOS scales
Parent	1L 21s
Sister	1L 22s
Daughters	23L 22s, 22L 23s
Neutralized	21L 2s
2-Flought	45L 1s, 22L 24s
Equal tunings
Equalized (L:s = 1:1)	1\23 (52.2 ¢)
Supersoft (L:s = 4:3)	4\91 (52.7 ¢)
Soft (L:s = 3:2)	3\68 (52.9 ¢)
Semisoft (L:s = 5:3)	5\113 (53.1 ¢)
Basic (L:s = 2:1)	2\45 (53.3 ¢)
Semihard (L:s = 5:2)	5\112 (53.6 ¢)
Hard (L:s = 3:1)	3\67 (53.7 ¢)
Superhard (L:s = 4:1)	4\89 (53.9 ¢)
Collapsed (L:s = 1:0)	1\22 (54.5 ¢)

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 of 22L 1s

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 ¢

See also

• 33/32
• 33/32 equal step tuning