3L 19s

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↙ 2L 20s	↓ 3L 20s	4L 20s ↘

┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐ │║││││││║││││││║││││││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssssLssssssLsssssss sssssssLssssssLssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
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
Ancestor's step ratio range	5:1 to 1:0
Related MOS scales
Parent	3L 16s
Sister	19L 3s
Daughters	22L 3s, 3L 22s
Neutralized	6L 16s
2-Flought	25L 19s, 3L 41s
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	Cyclic 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

Intervals

Intervals of 3L 19s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0¢ to 54.5¢
	Major 1-mosstep	M1ms	L	54.5¢ to 400.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 109.1¢
	Major 2-mosstep	M2ms	L + s	109.1¢ to 400.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 163.6¢
	Major 3-mosstep	M3ms	L + 2s	163.6¢ to 400.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 218.2¢
	Major 4-mosstep	M4ms	L + 3s	218.2¢ to 400.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 272.7¢
	Major 5-mosstep	M5ms	L + 4s	272.7¢ to 400.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 327.3¢
	Major 6-mosstep	M6ms	L + 5s	327.3¢ to 400.0¢
7-mosstep	Diminished 7-mosstep	d7ms	7s	0.0¢ to 381.8¢
	Perfect 7-mosstep	P7ms	L + 6s	381.8¢ to 400.0¢
8-mosstep	Minor 8-mosstep	m8ms	L + 7s	400.0¢ to 436.4¢
	Major 8-mosstep	M8ms	2L + 6s	436.4¢ to 800.0¢
9-mosstep	Minor 9-mosstep	m9ms	L + 8s	400.0¢ to 490.9¢
	Major 9-mosstep	M9ms	2L + 7s	490.9¢ to 800.0¢
10-mosstep	Minor 10-mosstep	m10ms	L + 9s	400.0¢ to 545.5¢
	Major 10-mosstep	M10ms	2L + 8s	545.5¢ to 800.0¢
11-mosstep	Minor 11-mosstep	m11ms	L + 10s	400.0¢ to 600.0¢
	Major 11-mosstep	M11ms	2L + 9s	600.0¢ to 800.0¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	400.0¢ to 654.5¢
	Major 12-mosstep	M12ms	2L + 10s	654.5¢ to 800.0¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	400.0¢ to 709.1¢
	Major 13-mosstep	M13ms	2L + 11s	709.1¢ to 800.0¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	400.0¢ to 763.6¢
	Major 14-mosstep	M14ms	2L + 12s	763.6¢ to 800.0¢
15-mosstep	Perfect 15-mosstep	P15ms	2L + 13s	800.0¢ to 818.2¢
	Augmented 15-mosstep	A15ms	3L + 12s	818.2¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	2L + 14s	800.0¢ to 872.7¢
	Major 16-mosstep	M16ms	3L + 13s	872.7¢ to 1200.0¢
17-mosstep	Minor 17-mosstep	m17ms	2L + 15s	800.0¢ to 927.3¢
	Major 17-mosstep	M17ms	3L + 14s	927.3¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	2L + 16s	800.0¢ to 981.8¢
	Major 18-mosstep	M18ms	3L + 15s	981.8¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	2L + 17s	800.0¢ to 1036.4¢
	Major 19-mosstep	M19ms	3L + 16s	1036.4¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	2L + 18s	800.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	3L + 17s	1090.9¢ to 1200.0¢
21-mosstep	Minor 21-mosstep	m21ms	2L + 19s	800.0¢ to 1145.5¢
	Major 21-mosstep	M21ms	3L + 18s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	3L + 19s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 3L 19s

Generator(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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