19L 6s

↖ 18L 5s	↑ 19L 5s	20L 5s ↗
← 18L 6s	19L 6s	20L 6s →
↙ 18L 7s	↓ 19L 7s	20L 7s ↘

Scale structure
Step pattern	LLLLsLLLsLLLsLLLsLLLsLLLs sLLLsLLLsLLLsLLLsLLLsLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	21\25 to 16\19 (1008.0 ¢ to 1010.5 ¢)
Dark	3\19 to 4\25 (189.5 ¢ to 192.0 ¢)
TAMNAMS information
Related to	6L 1s (archaeotonic)
With tunings	3:1 to 4:1 (parahard)
Related MOS scales
Parent	6L 13s
Sister	6L 19s
Daughters	25L 19s, 19L 25s
Neutralized	13L 12s
2-Flought	44L 6s, 19L 31s
Equal tunings
Equalized (L:s = 1:1)	21\25 (1008.0 ¢)
Supersoft (L:s = 4:3)	79\94 (1008.5 ¢)
Soft (L:s = 3:2)	58\69 (1008.7 ¢)
Semisoft (L:s = 5:3)	95\113 (1008.8 ¢)
Basic (L:s = 2:1)	37\44 (1009.1 ¢)
Semihard (L:s = 5:2)	90\107 (1009.3 ¢)
Hard (L:s = 3:1)	53\63 (1009.5 ¢)
Superhard (L:s = 4:1)	69\82 (1009.8 ¢)
Collapsed (L:s = 1:0)	16\19 (1010.5 ¢)
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19L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 6 small steps, repeating every octave. 19L 6s is a great-grandchild scale of 6L 1s, expanding it by 18 tones. Generators that produce this scale range from 1008 ¢ to 1010.5 ¢, or from 189.5 ¢ to 192 ¢.

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 6s

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 48.0 ¢
	Major 1-mosstep	M1ms	L	48.0 ¢ to 63.2 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	63.2 ¢ to 96.0 ¢
	Major 2-mosstep	M2ms	2L	96.0 ¢ to 126.3 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	126.3 ¢ to 144.0 ¢
	Major 3-mosstep	M3ms	3L	144.0 ¢ to 189.5 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	189.5 ¢ to 192.0 ¢
	Augmented 4-mosstep	A4ms	4L	192.0 ¢ to 252.6 ¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	189.5 ¢ to 240.0 ¢
	Major 5-mosstep	M5ms	4L + s	240.0 ¢ to 252.6 ¢
6-mosstep	Minor 6-mosstep	m6ms	4L + 2s	252.6 ¢ to 288.0 ¢
	Major 6-mosstep	M6ms	5L + s	288.0 ¢ to 315.8 ¢
7-mosstep	Minor 7-mosstep	m7ms	5L + 2s	315.8 ¢ to 336.0 ¢
	Major 7-mosstep	M7ms	6L + s	336.0 ¢ to 378.9 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	378.9 ¢ to 384.0 ¢
	Major 8-mosstep	M8ms	7L + s	384.0 ¢ to 442.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	6L + 3s	378.9 ¢ to 432.0 ¢
	Major 9-mosstep	M9ms	7L + 2s	432.0 ¢ to 442.1 ¢
10-mosstep	Minor 10-mosstep	m10ms	7L + 3s	442.1 ¢ to 480.0 ¢
	Major 10-mosstep	M10ms	8L + 2s	480.0 ¢ to 505.3 ¢
11-mosstep	Minor 11-mosstep	m11ms	8L + 3s	505.3 ¢ to 528.0 ¢
	Major 11-mosstep	M11ms	9L + 2s	528.0 ¢ to 568.4 ¢
12-mosstep	Minor 12-mosstep	m12ms	9L + 3s	568.4 ¢ to 576.0 ¢
	Major 12-mosstep	M12ms	10L + 2s	576.0 ¢ to 631.6 ¢
13-mosstep	Minor 13-mosstep	m13ms	9L + 4s	568.4 ¢ to 624.0 ¢
	Major 13-mosstep	M13ms	10L + 3s	624.0 ¢ to 631.6 ¢
14-mosstep	Minor 14-mosstep	m14ms	10L + 4s	631.6 ¢ to 672.0 ¢
	Major 14-mosstep	M14ms	11L + 3s	672.0 ¢ to 694.7 ¢
15-mosstep	Minor 15-mosstep	m15ms	11L + 4s	694.7 ¢ to 720.0 ¢
	Major 15-mosstep	M15ms	12L + 3s	720.0 ¢ to 757.9 ¢
16-mosstep	Minor 16-mosstep	m16ms	12L + 4s	757.9 ¢ to 768.0 ¢
	Major 16-mosstep	M16ms	13L + 3s	768.0 ¢ to 821.1 ¢
17-mosstep	Minor 17-mosstep	m17ms	12L + 5s	757.9 ¢ to 816.0 ¢
	Major 17-mosstep	M17ms	13L + 4s	816.0 ¢ to 821.1 ¢
18-mosstep	Minor 18-mosstep	m18ms	13L + 5s	821.1 ¢ to 864.0 ¢
	Major 18-mosstep	M18ms	14L + 4s	864.0 ¢ to 884.2 ¢
19-mosstep	Minor 19-mosstep	m19ms	14L + 5s	884.2 ¢ to 912.0 ¢
	Major 19-mosstep	M19ms	15L + 4s	912.0 ¢ to 947.4 ¢
20-mosstep	Minor 20-mosstep	m20ms	15L + 5s	947.4 ¢ to 960.0 ¢
	Major 20-mosstep	M20ms	16L + 4s	960.0 ¢ to 1010.5 ¢
21-mosstep	Diminished 21-mosstep	d21ms	15L + 6s	947.4 ¢ to 1008.0 ¢
	Perfect 21-mosstep	P21ms	16L + 5s	1008.0 ¢ to 1010.5 ¢
22-mosstep	Minor 22-mosstep	m22ms	16L + 6s	1010.5 ¢ to 1056.0 ¢
	Major 22-mosstep	M22ms	17L + 5s	1056.0 ¢ to 1073.7 ¢
23-mosstep	Minor 23-mosstep	m23ms	17L + 6s	1073.7 ¢ to 1104.0 ¢
	Major 23-mosstep	M23ms	18L + 5s	1104.0 ¢ to 1136.8 ¢
24-mosstep	Minor 24-mosstep	m24ms	18L + 6s	1136.8 ¢ to 1152.0 ¢
	Major 24-mosstep	M24ms	19L + 5s	1152.0 ¢ to 1200.0 ¢
25-mosstep	Perfect 25-mosstep	P25ms	19L + 6s	1200.0 ¢

Generator chain

Generator chain of 19L 6s

Bright gens	Scale degree	Abbrev.
43	Augmented 3-mosdegree	A3md
42	Augmented 7-mosdegree	A7md
41	Augmented 11-mosdegree	A11md
40	Augmented 15-mosdegree	A15md
39	Augmented 19-mosdegree	A19md
38	Augmented 23-mosdegree	A23md
37	Augmented 2-mosdegree	A2md
36	Augmented 6-mosdegree	A6md
35	Augmented 10-mosdegree	A10md
34	Augmented 14-mosdegree	A14md
33	Augmented 18-mosdegree	A18md
32	Augmented 22-mosdegree	A22md
31	Augmented 1-mosdegree	A1md
30	Augmented 5-mosdegree	A5md
29	Augmented 9-mosdegree	A9md
28	Augmented 13-mosdegree	A13md
27	Augmented 17-mosdegree	A17md
26	Augmented 21-mosdegree	A21md
25	Augmented 0-mosdegree	A0md
24	Augmented 4-mosdegree	A4md
23	Major 8-mosdegree	M8md
22	Major 12-mosdegree	M12md
21	Major 16-mosdegree	M16md
20	Major 20-mosdegree	M20md
19	Major 24-mosdegree	M24md
18	Major 3-mosdegree	M3md
17	Major 7-mosdegree	M7md
16	Major 11-mosdegree	M11md
15	Major 15-mosdegree	M15md
14	Major 19-mosdegree	M19md
13	Major 23-mosdegree	M23md
12	Major 2-mosdegree	M2md
11	Major 6-mosdegree	M6md
10	Major 10-mosdegree	M10md
9	Major 14-mosdegree	M14md
8	Major 18-mosdegree	M18md
7	Major 22-mosdegree	M22md
6	Major 1-mosdegree	M1md
5	Major 5-mosdegree	M5md
4	Major 9-mosdegree	M9md
3	Major 13-mosdegree	M13md
2	Major 17-mosdegree	M17md
1	Perfect 21-mosdegree	P21md
0	Perfect 0-mosdegree Perfect 25-mosdegree	P0md P25md
−1	Perfect 4-mosdegree	P4md
−2	Minor 8-mosdegree	m8md
−3	Minor 12-mosdegree	m12md
−4	Minor 16-mosdegree	m16md
−5	Minor 20-mosdegree	m20md
−6	Minor 24-mosdegree	m24md
−7	Minor 3-mosdegree	m3md
−8	Minor 7-mosdegree	m7md
−9	Minor 11-mosdegree	m11md
−10	Minor 15-mosdegree	m15md
−11	Minor 19-mosdegree	m19md
−12	Minor 23-mosdegree	m23md
−13	Minor 2-mosdegree	m2md
−14	Minor 6-mosdegree	m6md
−15	Minor 10-mosdegree	m10md
−16	Minor 14-mosdegree	m14md
−17	Minor 18-mosdegree	m18md
−18	Minor 22-mosdegree	m22md
−19	Minor 1-mosdegree	m1md
−20	Minor 5-mosdegree	m5md
−21	Minor 9-mosdegree	m9md
−22	Minor 13-mosdegree	m13md
−23	Minor 17-mosdegree	m17md
−24	Diminished 21-mosdegree	d21md
−25	Diminished 25-mosdegree	d25md
−26	Diminished 4-mosdegree	d4md
−27	Diminished 8-mosdegree	d8md
−28	Diminished 12-mosdegree	d12md
−29	Diminished 16-mosdegree	d16md
−30	Diminished 20-mosdegree	d20md
−31	Diminished 24-mosdegree	d24md
−32	Diminished 3-mosdegree	d3md
−33	Diminished 7-mosdegree	d7md
−34	Diminished 11-mosdegree	d11md
−35	Diminished 15-mosdegree	d15md
−36	Diminished 19-mosdegree	d19md
−37	Diminished 23-mosdegree	d23md
−38	Diminished 2-mosdegree	d2md
−39	Diminished 6-mosdegree	d6md
−40	Diminished 10-mosdegree	d10md
−41	Diminished 14-mosdegree	d14md
−42	Diminished 18-mosdegree	d18md
−43	Diminished 22-mosdegree	d22md

Modes

Scale degrees of the modes of 19L 6s

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	23	24	25
24|0	1	LLLLsLLLsLLLsLLLsLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
23|1	22	LLLsLLLLsLLLsLLLsLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
22|2	18	LLLsLLLsLLLLsLLLsLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
21|3	14	LLLsLLLsLLLsLLLLsLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
20|4	10	LLLsLLLsLLLsLLLsLLLLsLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Perf.
19|5	6	LLLsLLLsLLLsLLLsLLLsLLLLs	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Perf.
18|6	2	LLLsLLLsLLLsLLLsLLLsLLLsL	Perf.	Maj.	Maj.	Maj.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
17|7	23	LLsLLLLsLLLsLLLsLLLsLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
16|8	19	LLsLLLsLLLLsLLLsLLLsLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
15|9	15	LLsLLLsLLLsLLLLsLLLsLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
14|10	11	LLsLLLsLLLsLLLsLLLLsLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
13|11	7	LLsLLLsLLLsLLLsLLLsLLLLsL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Perf.
12|12	3	LLsLLLsLLLsLLLsLLLsLLLsLL	Perf.	Maj.	Maj.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
11|13	24	LsLLLLsLLLsLLLsLLLsLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
10|14	20	LsLLLsLLLLsLLLsLLLsLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
9|15	16	LsLLLsLLLsLLLLsLLLsLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
8|16	12	LsLLLsLLLsLLLsLLLLsLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
7|17	8	LsLLLsLLLsLLLsLLLsLLLLsLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Perf.
6|18	4	LsLLLsLLLsLLLsLLLsLLLsLLL	Perf.	Maj.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
5|19	25	sLLLLsLLLsLLLsLLLsLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
4|20	21	sLLLsLLLLsLLLsLLLsLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
3|21	17	sLLLsLLLsLLLLsLLLsLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
2|22	13	sLLLsLLLsLLLsLLLLsLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
1|23	9	sLLLsLLLsLLLsLLLsLLLLsLLL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Perf.
0|24	5	sLLLsLLLsLLLsLLLsLLLsLLLL	Perf.	Min.	Min.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 19L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
21\25						1008.000	192.000	1:1	1.000	Equalized 19L 6s
					121\144	1008.333	191.667	6:5	1.200
				100\119		1008.403	191.597	5:4	1.250
					179\213	1008.451	191.549	9:7	1.286
			79\94			1008.511	191.489	4:3	1.333	Supersoft 19L 6s
					216\257	1008.560	191.440	11:8	1.375
				137\163		1008.589	191.411	7:5	1.400
					195\232	1008.621	191.379	10:7	1.429
		58\69				1008.696	191.304	3:2	1.500	Soft 19L 6s
					211\251	1008.765	191.235	11:7	1.571
				153\182		1008.791	191.209	8:5	1.600
					248\295	1008.814	191.186	13:8	1.625
			95\113			1008.850	191.150	5:3	1.667	Semisoft 19L 6s
					227\270	1008.889	191.111	12:7	1.714
				132\157		1008.917	191.083	7:4	1.750
					169\201	1008.955	191.045	9:5	1.800
	37\44					1009.091	190.909	2:1	2.000	Basic 19L 6s Scales with tunings softer than this are proper
					164\195	1009.231	190.769	9:4	2.250
				127\151		1009.272	190.728	7:3	2.333
					217\258	1009.302	190.698	12:5	2.400
			90\107			1009.346	190.654	5:2	2.500	Semihard 19L 6s
					233\277	1009.386	190.614	13:5	2.600
				143\170		1009.412	190.588	8:3	2.667
					196\233	1009.442	190.558	11:4	2.750
		53\63				1009.524	190.476	3:1	3.000	Hard 19L 6s
					175\208	1009.615	190.385	10:3	3.333
				122\145		1009.655	190.345	7:2	3.500
					191\227	1009.692	190.308	11:3	3.667
			69\82			1009.756	190.244	4:1	4.000	Superhard 19L 6s
					154\183	1009.836	190.164	9:2	4.500
				85\101		1009.901	190.099	5:1	5.000
					101\120	1010.000	190.000	6:1	6.000
16\19						1010.526	189.474	1:0	→ ∞	Collapsed 19L 6s

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