19L 3s

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

┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║║│║║║║║║│║║║║║║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLLLLLLsLLLLLLsLLLLLLs sLLLLLLsLLLLLLsLLLLLLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	15\22 to 13\19 (818.2¢ to 821.1¢)
Dark	6\19 to 7\22 (378.9¢ to 381.8¢)
TAMNAMS information
Descends from	3L 7s (sephiroid)
Ancestor's step ratio range	4:1 to 5:1
Related MOS scales
Parent	3L 16s
Sister	3L 19s
Daughters	22L 19s, 19L 22s
Neutralized	16L 6s
2-Flought	41L 3s, 19L 25s
Equal tunings
Equalized (L:s = 1:1)	15\22 (818.2¢)
Supersoft (L:s = 4:3)	58\85 (818.8¢)
Soft (L:s = 3:2)	43\63 (819.0¢)
Semisoft (L:s = 5:3)	71\104 (819.2¢)
Basic (L:s = 2:1)	28\41 (819.5¢)
Semihard (L:s = 5:2)	69\101 (819.8¢)
Hard (L:s = 3:1)	41\60 (820.0¢)
Superhard (L:s = 4:1)	54\79 (820.3¢)
Collapsed (L:s = 1:0)	13\19 (821.1¢)

19L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 3 small steps, repeating every octave. 19L 3s is related to 3L 7s, expanding it by 12 tones. Generators that produce this scale range from 818.2¢ to 821.1¢, or from 378.9¢ to 381.8¢.

It is notable for supporting Magic temperament.

Modes

Modes of 19L 3s

UDP	Cyclic order	Step pattern
21|0	1	LLLLLLLsLLLLLLsLLLLLLs
20|1	16	LLLLLLsLLLLLLLsLLLLLLs
19|2	9	LLLLLLsLLLLLLsLLLLLLLs
18|3	2	LLLLLLsLLLLLLsLLLLLLsL
17|4	17	LLLLLsLLLLLLLsLLLLLLsL
16|5	10	LLLLLsLLLLLLsLLLLLLLsL
15|6	3	LLLLLsLLLLLLsLLLLLLsLL
14|7	18	LLLLsLLLLLLLsLLLLLLsLL
13|8	11	LLLLsLLLLLLsLLLLLLLsLL
12|9	4	LLLLsLLLLLLsLLLLLLsLLL
11|10	19	LLLsLLLLLLLsLLLLLLsLLL
10|11	12	LLLsLLLLLLsLLLLLLLsLLL
9|12	5	LLLsLLLLLLsLLLLLLsLLLL
8|13	20	LLsLLLLLLLsLLLLLLsLLLL
7|14	13	LLsLLLLLLsLLLLLLLsLLLL
6|15	6	LLsLLLLLLsLLLLLLsLLLLL
5|16	21	LsLLLLLLLsLLLLLLsLLLLL
4|17	14	LsLLLLLLsLLLLLLLsLLLLL
3|18	7	LsLLLLLLsLLLLLLsLLLLLL
2|19	22	sLLLLLLLsLLLLLLsLLLLLL
1|20	15	sLLLLLLsLLLLLLLsLLLLLL
0|21	8	sLLLLLLsLLLLLLsLLLLLLL

Intervals

Intervals of 19L 3s

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 63.2¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	63.2¢ to 109.1¢
	Major 2-mosstep	M2ms	2L	109.1¢ to 126.3¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	126.3¢ to 163.6¢
	Major 3-mosstep	M3ms	3L	163.6¢ to 189.5¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	189.5¢ to 218.2¢
	Major 4-mosstep	M4ms	4L	218.2¢ to 252.6¢
5-mosstep	Minor 5-mosstep	m5ms	4L + s	252.6¢ to 272.7¢
	Major 5-mosstep	M5ms	5L	272.7¢ to 315.8¢
6-mosstep	Minor 6-mosstep	m6ms	5L + s	315.8¢ to 327.3¢
	Major 6-mosstep	M6ms	6L	327.3¢ to 378.9¢
7-mosstep	Perfect 7-mosstep	P7ms	6L + s	378.9¢ to 381.8¢
	Augmented 7-mosstep	A7ms	7L	381.8¢ to 442.1¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	378.9¢ to 436.4¢
	Major 8-mosstep	M8ms	7L + s	436.4¢ to 442.1¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	442.1¢ to 490.9¢
	Major 9-mosstep	M9ms	8L + s	490.9¢ to 505.3¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	505.3¢ to 545.5¢
	Major 10-mosstep	M10ms	9L + s	545.5¢ to 568.4¢
11-mosstep	Minor 11-mosstep	m11ms	9L + 2s	568.4¢ to 600.0¢
	Major 11-mosstep	M11ms	10L + s	600.0¢ to 631.6¢
12-mosstep	Minor 12-mosstep	m12ms	10L + 2s	631.6¢ to 654.5¢
	Major 12-mosstep	M12ms	11L + s	654.5¢ to 694.7¢
13-mosstep	Minor 13-mosstep	m13ms	11L + 2s	694.7¢ to 709.1¢
	Major 13-mosstep	M13ms	12L + s	709.1¢ to 757.9¢
14-mosstep	Minor 14-mosstep	m14ms	12L + 2s	757.9¢ to 763.6¢
	Major 14-mosstep	M14ms	13L + s	763.6¢ to 821.1¢
15-mosstep	Diminished 15-mosstep	d15ms	12L + 3s	757.9¢ to 818.2¢
	Perfect 15-mosstep	P15ms	13L + 2s	818.2¢ to 821.1¢
16-mosstep	Minor 16-mosstep	m16ms	13L + 3s	821.1¢ to 872.7¢
	Major 16-mosstep	M16ms	14L + 2s	872.7¢ to 884.2¢
17-mosstep	Minor 17-mosstep	m17ms	14L + 3s	884.2¢ to 927.3¢
	Major 17-mosstep	M17ms	15L + 2s	927.3¢ to 947.4¢
18-mosstep	Minor 18-mosstep	m18ms	15L + 3s	947.4¢ to 981.8¢
	Major 18-mosstep	M18ms	16L + 2s	981.8¢ to 1010.5¢
19-mosstep	Minor 19-mosstep	m19ms	16L + 3s	1010.5¢ to 1036.4¢
	Major 19-mosstep	M19ms	17L + 2s	1036.4¢ to 1073.7¢
20-mosstep	Minor 20-mosstep	m20ms	17L + 3s	1073.7¢ to 1090.9¢
	Major 20-mosstep	M20ms	18L + 2s	1090.9¢ to 1136.8¢
21-mosstep	Minor 21-mosstep	m21ms	18L + 3s	1136.8¢ to 1145.5¢
	Major 21-mosstep	M21ms	19L + 2s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	19L + 3s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 19L 3s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
15\22						818.182	381.818	1:1	1.000	Equalized 19L 3s
					88\129	818.605	381.395	6:5	1.200
				73\107		818.692	381.308	5:4	1.250
					131\192	818.750	381.250	9:7	1.286
			58\85			818.824	381.176	4:3	1.333	Supersoft 19L 3s
					159\233	818.884	381.116	11:8	1.375
				101\148		818.919	381.081	7:5	1.400
					144\211	818.957	381.043	10:7	1.429
		43\63				819.048	380.952	3:2	1.500	Soft 19L 3s
					157\230	819.130	380.870	11:7	1.571
				114\167		819.162	380.838	8:5	1.600
					185\271	819.188	380.812	13:8	1.625
			71\104			819.231	380.769	5:3	1.667	Semisoft 19L 3s
					170\249	819.277	380.723	12:7	1.714
				99\145		819.310	380.690	7:4	1.750
					127\186	819.355	380.645	9:5	1.800
	28\41					819.512	380.488	2:1	2.000	Basic 19L 3s Scales with tunings softer than this are proper Simplest tuning for Magic[22]
					125\183	819.672	380.328	9:4	2.250
				97\142		819.718	380.282	7:3	2.333
					166\243	819.753	380.247	12:5	2.400
			69\101			819.802	380.198	5:2	2.500	Semihard 19L 3s
					179\262	819.847	380.153	13:5	2.600
				110\161		819.876	380.124	8:3	2.667
					151\221	819.910	380.090	11:4	2.750
		41\60				820.000	380.000	3:1	3.000	Hard 19L 3s
					136\199	820.101	379.899	10:3	3.333
				95\139		820.144	379.856	7:2	3.500
					149\218	820.183	379.817	11:3	3.667
			54\79			820.253	379.747	4:1	4.000	Superhard 19L 3s
					121\177	820.339	379.661	9:2	4.500
				67\98		820.408	379.592	5:1	5.000
					80\117	820.513	379.487	6:1	6.000
13\19						821.053	378.947	1:0	→ ∞	Collapsed 19L 3s

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