21L 1s


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

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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

Descends from

1L 9s (antisinatonic)

Ancestor's step ratio range

12:1 to 13:1

Other names

Name(s)

escapist,
tricesimoprimal quartertonic

Related MOS scales

Equal tunings

Equalized (L:s = 1:1)

1\22 (54.5¢)

Supersoft (L:s = 4:3)

4\87 (55.2¢)

3\65 (55.4¢)

5\108 (55.6¢)

2\43 (55.8¢)

5\107 (56.1¢)

3\64 (56.2¢)

Superhard (L:s = 4:1)

4\85 (56.5¢)

Collapsed (L:s = 1:0)

1\21 (57.1¢)

21L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 21 large steps and 1 small step, repeating every octave. 21L 1s is related to 1L 9s, expanding it by 12 tones. Generators that produce this scale range from 54.5¢ to 57.1¢, or from 1142.9¢ to 1145.5¢. Scales of this form are always proper because there is only one small step. Eliora proposes the name escapist for this pattern, referencing the escapade temperament which is supported by both 21edo and 22edo, thus covering the entire tuning spectrum.

Moremajorthanmajor proposes the name tricesimoprimal quartertonic 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

The scale's approach to standard harmony can be considered based on the mode.

Brighter modes

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.

Darker modes

If instead the small step is stacked down, this enables the scale to approximate the standard 4:5:6 and 10:12:15 triads, as the escapade temperament does.

The escapade temperament reaches 4/3 in 9 gensteps, meaning that modes from Hermit (12|9) onward support a perfect fifth from the tonic. This also enables the modes from Hermit through Temperance (7|14) to support the major triad, 4:5:6, and from Devil (6|15) onward to support the minor triad, 10:12:15. The 700 cent fifth is supported in 108edo, stacking steps of 5\108 downward.

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

Intervals

Intervals of 21L 1s
Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.	Steps subtended	Range in cents
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0¢ to 54.5¢
1-mosstep	Perfect 1-mosstep	P1ms	L	54.5¢ to 57.1¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	57.1¢ to 109.1¢
2-mosstep	Major 2-mosstep	M2ms	2L	109.1¢ to 114.3¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	114.3¢ to 163.6¢
3-mosstep	Major 3-mosstep	M3ms	3L	163.6¢ to 171.4¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	171.4¢ to 218.2¢
4-mosstep	Major 4-mosstep	M4ms	4L	218.2¢ to 228.6¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	228.6¢ to 272.7¢
5-mosstep	Major 5-mosstep	M5ms	5L	272.7¢ to 285.7¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	285.7¢ to 327.3¢
6-mosstep	Major 6-mosstep	M6ms	6L	327.3¢ to 342.9¢
7-mosstep	Minor 7-mosstep	m7ms	6L + s	342.9¢ to 381.8¢
7-mosstep	Major 7-mosstep	M7ms	7L	381.8¢ to 400.0¢
8-mosstep	Minor 8-mosstep	m8ms	7L + s	400.0¢ to 436.4¢
8-mosstep	Major 8-mosstep	M8ms	8L	436.4¢ to 457.1¢
9-mosstep	Minor 9-mosstep	m9ms	8L + s	457.1¢ to 490.9¢
9-mosstep	Major 9-mosstep	M9ms	9L	490.9¢ to 514.3¢
10-mosstep	Minor 10-mosstep	m10ms	9L + s	514.3¢ to 545.5¢
10-mosstep	Major 10-mosstep	M10ms	10L	545.5¢ to 571.4¢
11-mosstep	Minor 11-mosstep	m11ms	10L + s	571.4¢ to 600.0¢
11-mosstep	Major 11-mosstep	M11ms	11L	600.0¢ to 628.6¢
12-mosstep	Minor 12-mosstep	m12ms	11L + s	628.6¢ to 654.5¢
12-mosstep	Major 12-mosstep	M12ms	12L	654.5¢ to 685.7¢
13-mosstep	Minor 13-mosstep	m13ms	12L + s	685.7¢ to 709.1¢
13-mosstep	Major 13-mosstep	M13ms	13L	709.1¢ to 742.9¢
14-mosstep	Minor 14-mosstep	m14ms	13L + s	742.9¢ to 763.6¢
14-mosstep	Major 14-mosstep	M14ms	14L	763.6¢ to 800.0¢
15-mosstep	Minor 15-mosstep	m15ms	14L + s	800.0¢ to 818.2¢
15-mosstep	Major 15-mosstep	M15ms	15L	818.2¢ to 857.1¢
16-mosstep	Minor 16-mosstep	m16ms	15L + s	857.1¢ to 872.7¢
16-mosstep	Major 16-mosstep	M16ms	16L	872.7¢ to 914.3¢
17-mosstep	Minor 17-mosstep	m17ms	16L + s	914.3¢ to 927.3¢
17-mosstep	Major 17-mosstep	M17ms	17L	927.3¢ to 971.4¢
18-mosstep	Minor 18-mosstep	m18ms	17L + s	971.4¢ to 981.8¢
18-mosstep	Major 18-mosstep	M18ms	18L	981.8¢ to 1028.6¢
19-mosstep	Minor 19-mosstep	m19ms	18L + s	1028.6¢ to 1036.4¢
19-mosstep	Major 19-mosstep	M19ms	19L	1036.4¢ to 1085.7¢
20-mosstep	Minor 20-mosstep	m20ms	19L + s	1085.7¢ to 1090.9¢
20-mosstep	Major 20-mosstep	M20ms	20L	1090.9¢ to 1142.9¢
21-mosstep	Perfect 21-mosstep	P21ms	20L + s	1142.9¢ to 1145.5¢
21-mosstep	Augmented 21-mosstep	A21ms	21L	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	21L + s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 21L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
1\22						54.545	1145.455	1:1	1.000	Equalized 21L 1s
					6\131	54.962	1145.038	6:5	1.200
				5\109		55.046	1144.954	5:4	1.250
					9\196	55.102	1144.898	9:7	1.286
			4\87			55.172	1144.828	4:3	1.333	Supersoft 21L 1s
					11\239	55.230	1144.770	11:8	1.375
				7\152		55.263	1144.737	7:5	1.400
					10\217	55.300	1144.700	10:7	1.429
		3\65				55.385	1144.615	3:2	1.500	Soft 21L 1s
					11\238	55.462	1144.538	11:7	1.571
				8\173		55.491	1144.509	8:5	1.600
					13\281	55.516	1144.484	13:8	1.625
			5\108			55.556	1144.444	5:3	1.667	Semisoft 21L 1s
					12\259	55.598	1144.402	12:7	1.714
				7\151		55.629	1144.371	7:4	1.750
					9\194	55.670	1144.330	9:5	1.800
	2\43					55.814	1144.186	2:1	2.000	Basic 21L 1s
					9\193	55.959	1144.041	9:4	2.250
				7\150		56.000	1144.000	7:3	2.333
					12\257	56.031	1143.969	12:5	2.400
			5\107			56.075	1143.925	5:2	2.500	Semihard 21L 1s
					13\278	56.115	1143.885	13:5	2.600
				8\171		56.140	1143.860	8:3	2.667
					11\235	56.170	1143.830	11:4	2.750
		3\64				56.250	1143.750	3:1	3.000	Hard 21L 1s
					10\213	56.338	1143.662	10:3	3.333
				7\149		56.376	1143.624	7:2	3.500
					11\234	56.410	1143.590	11:3	3.667
			4\85			56.471	1143.529	4:1	4.000	Superhard 21L 1s
					9\191	56.545	1143.455	9:2	4.500
				5\106		56.604	1143.396	5:1	5.000
					6\127	56.693	1143.307	6:1	6.000
1\21						57.143	1142.857	1:0	→ ∞	Collapsed 21L 1s