19L 3s

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 ¢.

↖ 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
Related to	3L 7s (sephiroid)
With tunings	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 ¢)
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It is notable for supporting Magic temperament.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 19L 3s

Bright gens	Scale degree	Abbrev.
40	Augmented 6-mosdegree	A6md
39	Augmented 13-mosdegree	A13md
38	Augmented 20-mosdegree	A20md
37	Augmented 5-mosdegree	A5md
36	Augmented 12-mosdegree	A12md
35	Augmented 19-mosdegree	A19md
34	Augmented 4-mosdegree	A4md
33	Augmented 11-mosdegree	A11md
32	Augmented 18-mosdegree	A18md
31	Augmented 3-mosdegree	A3md
30	Augmented 10-mosdegree	A10md
29	Augmented 17-mosdegree	A17md
28	Augmented 2-mosdegree	A2md
27	Augmented 9-mosdegree	A9md
26	Augmented 16-mosdegree	A16md
25	Augmented 1-mosdegree	A1md
24	Augmented 8-mosdegree	A8md
23	Augmented 15-mosdegree	A15md
22	Augmented 0-mosdegree	A0md
21	Augmented 7-mosdegree	A7md
20	Major 14-mosdegree	M14md
19	Major 21-mosdegree	M21md
18	Major 6-mosdegree	M6md
17	Major 13-mosdegree	M13md
16	Major 20-mosdegree	M20md
15	Major 5-mosdegree	M5md
14	Major 12-mosdegree	M12md
13	Major 19-mosdegree	M19md
12	Major 4-mosdegree	M4md
11	Major 11-mosdegree	M11md
10	Major 18-mosdegree	M18md
9	Major 3-mosdegree	M3md
8	Major 10-mosdegree	M10md
7	Major 17-mosdegree	M17md
6	Major 2-mosdegree	M2md
5	Major 9-mosdegree	M9md
4	Major 16-mosdegree	M16md
3	Major 1-mosdegree	M1md
2	Major 8-mosdegree	M8md
1	Perfect 15-mosdegree	P15md
0	Perfect 0-mosdegree Perfect 22-mosdegree	P0md P22md
−1	Perfect 7-mosdegree	P7md
−2	Minor 14-mosdegree	m14md
−3	Minor 21-mosdegree	m21md
−4	Minor 6-mosdegree	m6md
−5	Minor 13-mosdegree	m13md
−6	Minor 20-mosdegree	m20md
−7	Minor 5-mosdegree	m5md
−8	Minor 12-mosdegree	m12md
−9	Minor 19-mosdegree	m19md
−10	Minor 4-mosdegree	m4md
−11	Minor 11-mosdegree	m11md
−12	Minor 18-mosdegree	m18md
−13	Minor 3-mosdegree	m3md
−14	Minor 10-mosdegree	m10md
−15	Minor 17-mosdegree	m17md
−16	Minor 2-mosdegree	m2md
−17	Minor 9-mosdegree	m9md
−18	Minor 16-mosdegree	m16md
−19	Minor 1-mosdegree	m1md
−20	Minor 8-mosdegree	m8md
−21	Diminished 15-mosdegree	d15md
−22	Diminished 22-mosdegree	d22md
−23	Diminished 7-mosdegree	d7md
−24	Diminished 14-mosdegree	d14md
−25	Diminished 21-mosdegree	d21md
−26	Diminished 6-mosdegree	d6md
−27	Diminished 13-mosdegree	d13md
−28	Diminished 20-mosdegree	d20md
−29	Diminished 5-mosdegree	d5md
−30	Diminished 12-mosdegree	d12md
−31	Diminished 19-mosdegree	d19md
−32	Diminished 4-mosdegree	d4md
−33	Diminished 11-mosdegree	d11md
−34	Diminished 18-mosdegree	d18md
−35	Diminished 3-mosdegree	d3md
−36	Diminished 10-mosdegree	d10md
−37	Diminished 17-mosdegree	d17md
−38	Diminished 2-mosdegree	d2md
−39	Diminished 9-mosdegree	d9md
−40	Diminished 16-mosdegree	d16md

Modes

Scale degrees of the modes of 19L 3s

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

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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