21L 1s

← 20L 1s	21L 1s	22L 1s →
↙ 20L 2s	↓ 21L 2s	22L 2s ↘

Scale structure
Step pattern	LLLLLLLLLLLLLLLLLLLLLs sLLLLLLLLLLLLLLLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\22 to 1\21 (54.5 ¢ to 57.1 ¢)
Dark	20\21 to 21\22 (1142.9 ¢ to 1145.5 ¢)
TAMNAMS information
Related to	1L 9s (antisinatonic)
With tunings	12:1 to 13:1
Related MOS scales
Parent	1L 20s
Sister	1L 21s
Daughters	22L 21s, 21L 22s
Neutralized	20L 2s
2-Flought	43L 1s, 21L 23s
Equal tunings
Equalized (L:s = 1:1)	1\22 (54.5 ¢)
Supersoft (L:s = 4:3)	4\87 (55.2 ¢)
Soft (L:s = 3:2)	3\65 (55.4 ¢)
Semisoft (L:s = 5:3)	5\108 (55.6 ¢)
Basic (L:s = 2:1)	2\43 (55.8 ¢)
Semihard (L:s = 5:2)	5\107 (56.1 ¢)
Hard (L:s = 3:1)	3\64 (56.2 ¢)
Superhard (L:s = 4:1)	4\85 (56.5 ¢)
Collapsed (L:s = 1:0)	1\21 (57.1 ¢)
View • Talk • Edit

21L 1s is the scale that is most commonly produced by stacking the interval of 32/31 or 31/30.

A name tricesimoprimal quartertonic is proposed for this pattern since its harmonic entropy minimum corresponds to tempering out the unnamed comma 961/960 - the tricesimoprimal quartertones being equated with each other. In addition, both 21edo and 22edo, extreme ranges of the MOS do not temper out this comma, while EDOs up to 100-200 which have this scale do.

Tuning ranges

Diatonic fifth and 65edo (Ultrasoft and supersoft)

Between 3\65 and 1\22, 13 steps amount to a diatonic fifth, which corresponds to the ultrasoft step ratio range. In 65edo, the fifth produced by 13 steps of the tricesimoprimal quartertonic scale is the same as 3 steps of 5edo, and thus is the exact boundary between a fifth proper and a fifth-sixth.

If the pure 32/31 is used as a generator, the resulting fifth is 714.53756 cents, which puts it in the category around Ultrapyth.

Fifth-sixth (hard of supersoft)

From 1\21 to 3\65, 13 steps amount to a fifth-sixth.

If the pure 31/30 is used as a generator, the resulting fifth-sixth is 737.96915 cents, which puts it in the category around father/petritri/aurora.

Relation to other equal divisions

2 steps act as a pseudo-16/15, and when they actually act as 16/15, 961/960 is tempered out.

Modes

The author proposes naming the modes after Tarot Major Arcana adjectivals based on how many generators down there is since there are 22 of them.

Mode	Name
21|0	Foolish
20|1	Magical
19|2	High Priestess's
18|3	Empress's
...	...
3|19	Lunar
2|19	Solar
1|20	Judgemental
0|21	Worldwide

Scale tree

Generator						L	s	L/s	Comments
1\22						1	1	1.000
					6\131	6	5	1.200
				5\109		5	4	1.250
					9\196	9	7	1.286
			4\87			4	3	1.333
					11\239	11	8	1.375
				7\152		7	5	1.400
					10\217	10	7	1.428
		3\65				3	2	1.500	13 steps adding to upper bound of diatonic fifths (720¢) is here
					11\238	11	7	1.571
				8\173		8	5	1.600
					13\281	13	8	1.625
			5\108			5	3	1.667
					12\259	12	7	1.714
				7\151		7	4	1.750
					9\194	9	5	1.800
	2\43					2	1	2.000	Basic tricesimoprimal quartertonic
					9\193	9	4	2.250
				7\150		7	3	2.333
					12\257	12	5	2.400
			5\107			5	2	2.500
					13\278	13	5	2.600
				8\171		8	3	2.667
					11\235	11	4	2.750
		3\64				3	1	3.000
					10\213	10	3	3.333
				7\149		7	2	3.500
					11\234	11	3	3.667
			4\85			4	1	4.000
					9\191	9	2	4.500
				5\106		5	1	5.000
					6\127	6	1	6.000
1\21						1	0	→ inf

See also

• 32/31
• 31/30