3L 19s

↖2L 18s	↑3L 18s	4L 18s↗
←2L 19s	3L 19s	4L 19s→
↙2L 20s	↓3L 20s	4L 20s↘

┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐ │║││││││║││││││║││││││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssssLssssssLsssssss sssssssLssssssLssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Step size
Large	1\22 to 1\3 (54.5¢ to 400.0¢)
Small	0\3 to 1\22 (0.0¢ to 54.5¢)
Generator size
Bright	7\22 to 1\3 (381.8¢ to 400.0¢)
Dark	2\3 to 15\22 (800.0¢ to 818.2¢)
TAMNAMS information
Descends from	3L 7s (sephiroid)
Related MOS scales
Parent	3L 16s
Sister	19L 3s
Daughters	22L 3s 3L 22s
Equal tunings
Equalized (L:s = 1:1)	7\22 (381.8¢)
Supersoft (L:s = 4:3)	22\69 (382.6¢)
Soft (L:s = 3:2)	15\47 (383.0¢)
Semisoft (L:s = 5:3)	23\72 (383.3¢)
Basic (L:s = 2:1)	8\25 (384.0¢)
Semihard (L:s = 5:2)	17\53 (384.9¢)
Hard (L:s = 3:1)	9\28 (385.7¢)
Superhard (L:s = 4:1)	10\31 (387.1¢)
Collapsed (L:s = 1:0)	1\3 (400.0¢)

3L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 19 small steps, repeating every octave. 3L 19s is related to 3L 7s, expanding it by 12 tones. Generators that produce this scale range from 381.8¢ to 400¢, or from 800¢ to 818.2¢.

Modes

Modes of 3L 19s

UDP	Rotational order	Step pattern
21|0	1	LssssssLssssssLsssssss
20|1	8	LssssssLsssssssLssssss
19|2	15	LsssssssLssssssLssssss
18|3	22	sLssssssLssssssLssssss
17|4	7	sLssssssLsssssssLsssss
16|5	14	sLsssssssLssssssLsssss
15|6	21	ssLssssssLssssssLsssss
14|7	6	ssLssssssLsssssssLssss
13|8	13	ssLsssssssLssssssLssss
12|9	20	sssLssssssLssssssLssss
11|10	5	sssLssssssLsssssssLsss
10|11	12	sssLsssssssLssssssLsss
9|12	19	ssssLssssssLssssssLsss
8|13	4	ssssLssssssLsssssssLss
7|14	11	ssssLsssssssLssssssLss
6|15	18	sssssLssssssLssssssLss
5|16	3	sssssLssssssLsssssssLs
4|17	10	sssssLsssssssLssssssLs
3|18	17	ssssssLssssssLssssssLs
2|19	2	ssssssLssssssLsssssssL
1|20	9	ssssssLsssssssLssssssL
0|21	16	sssssssLssssssLssssssL

Scale tree

Scale tree and tuning spectrum of 3L 19s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\22						381.818	818.182	1:1	1.000	Equalized 3L 19s
					36\113	382.301	817.699	6:5	1.200
				29\91		382.418	817.582	5:4	1.250
					51\160	382.500	817.500	9:7	1.286
			22\69			382.609	817.391	4:3	1.333	Supersoft 3L 19s
					59\185	382.703	817.297	11:8	1.375
				37\116		382.759	817.241	7:5	1.400
					52\163	382.822	817.178	10:7	1.429
		15\47				382.979	817.021	3:2	1.500	Soft 3L 19s
					53\166	383.133	816.867	11:7	1.571
				38\119		383.193	816.807	8:5	1.600
					61\191	383.246	816.754	13:8	1.625
			23\72			383.333	816.667	5:3	1.667	Semisoft 3L 19s
					54\169	383.432	816.568	12:7	1.714
				31\97		383.505	816.495	7:4	1.750
					39\122	383.607	816.393	9:5	1.800
	8\25					384.000	816.000	2:1	2.000	Basic 3L 19s Scales with tunings softer than this are proper
					33\103	384.466	815.534	9:4	2.250
				25\78		384.615	815.385	7:3	2.333
					42\131	384.733	815.267	12:5	2.400
			17\53			384.906	815.094	5:2	2.500	Semihard 3L 19s
					43\134	385.075	814.925	13:5	2.600
				26\81		385.185	814.815	8:3	2.667
					35\109	385.321	814.679	11:4	2.750
		9\28				385.714	814.286	3:1	3.000	Hard 3L 19s
					28\87	386.207	813.793	10:3	3.333
				19\59		386.441	813.559	7:2	3.500
					29\90	386.667	813.333	11:3	3.667
			10\31			387.097	812.903	4:1	4.000	Superhard 3L 19s
					21\65	387.692	812.308	9:2	4.500
				11\34		388.235	811.765	5:1	5.000
					12\37	389.189	810.811	6:1	6.000
1\3						400.000	800.000	1:0	→ ∞	Collapsed 3L 19s

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