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 ¢)
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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.