2L 19s

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↙ 1L 20s	↓ 2L 20s	3L 20s ↘

Scale structure
Step pattern	LsssssssssLssssssssss ssssssssssLsssssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	10\21 to 1\2 (571.4 ¢ to 600.0 ¢)
Dark	1\2 to 11\21 (600.0 ¢ to 628.6 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	7:1 to 1:0
Related MOS scales
Parent	2L 17s
Sister	19L 2s
Daughters	21L 2s, 2L 21s
Neutralized	4L 17s
2-Flought	23L 19s, 2L 40s
Equal tunings
Equalized (L:s = 1:1)	10\21 (571.4 ¢)
Supersoft (L:s = 4:3)	31\65 (572.3 ¢)
Soft (L:s = 3:2)	21\44 (572.7 ¢)
Semisoft (L:s = 5:3)	32\67 (573.1 ¢)
Basic (L:s = 2:1)	11\23 (573.9 ¢)
Semihard (L:s = 5:2)	23\48 (575.0 ¢)
Hard (L:s = 3:1)	12\25 (576.0 ¢)
Superhard (L:s = 4:1)	13\27 (577.8 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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2L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 19 small steps, repeating every octave. 2L 19s is related to 2L 7s, expanding it by 12 tones. Generators that produce this scale range from 571.4 ¢ to 600 ¢, or from 600 ¢ to 628.6 ¢.

This is the MOS where the small steps split 10-9 between the large steps. With a generator no smaller than 10/21edo (571.429 cents), it achieves a harmonic entropy minimum at generator = 7/5 (almost exactly 17/35edo).

Modes

Modes of 2L 19s

UDP	Cyclic order	Step pattern
20|0	1	LsssssssssLssssssssss
19|1	11	LssssssssssLsssssssss
18|2	21	sLsssssssssLsssssssss
17|3	10	sLssssssssssLssssssss
16|4	20	ssLsssssssssLssssssss
15|5	9	ssLssssssssssLsssssss
14|6	19	sssLsssssssssLsssssss
13|7	8	sssLssssssssssLssssss
12|8	18	ssssLsssssssssLssssss
11|9	7	ssssLssssssssssLsssss
10|10	17	sssssLsssssssssLsssss
9|11	6	sssssLssssssssssLssss
8|12	16	ssssssLsssssssssLssss
7|13	5	ssssssLssssssssssLsss
6|14	15	sssssssLsssssssssLsss
5|15	4	sssssssLssssssssssLss
4|16	14	ssssssssLsssssssssLss
3|17	3	ssssssssLssssssssssLs
2|18	13	sssssssssLsssssssssLs
1|19	2	sssssssssLssssssssssL
0|20	12	ssssssssssLsssssssssL

Intervals

Intervals of 2L 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 57.1 ¢
	Major 1-mosstep	M1ms	L	57.1 ¢ to 600.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 114.3 ¢
	Major 2-mosstep	M2ms	L + s	114.3 ¢ to 600.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 171.4 ¢
	Major 3-mosstep	M3ms	L + 2s	171.4 ¢ to 600.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0 ¢ to 228.6 ¢
	Major 4-mosstep	M4ms	L + 3s	228.6 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0 ¢ to 285.7 ¢
	Major 5-mosstep	M5ms	L + 4s	285.7 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0 ¢ to 342.9 ¢
	Major 6-mosstep	M6ms	L + 5s	342.9 ¢ to 600.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0 ¢ to 400.0 ¢
	Major 7-mosstep	M7ms	L + 6s	400.0 ¢ to 600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0 ¢ to 457.1 ¢
	Major 8-mosstep	M8ms	L + 7s	457.1 ¢ to 600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0 ¢ to 514.3 ¢
	Major 9-mosstep	M9ms	L + 8s	514.3 ¢ to 600.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	10s	0.0 ¢ to 571.4 ¢
	Perfect 10-mosstep	P10ms	L + 9s	571.4 ¢ to 600.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	L + 10s	600.0 ¢ to 628.6 ¢
	Augmented 11-mosstep	A11ms	2L + 9s	628.6 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	L + 11s	600.0 ¢ to 685.7 ¢
	Major 12-mosstep	M12ms	2L + 10s	685.7 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0 ¢ to 742.9 ¢
	Major 13-mosstep	M13ms	2L + 11s	742.9 ¢ to 1200.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0 ¢ to 800.0 ¢
	Major 14-mosstep	M14ms	2L + 12s	800.0 ¢ to 1200.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	600.0 ¢ to 857.1 ¢
	Major 15-mosstep	M15ms	2L + 13s	857.1 ¢ to 1200.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	600.0 ¢ to 914.3 ¢
	Major 16-mosstep	M16ms	2L + 14s	914.3 ¢ to 1200.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	L + 16s	600.0 ¢ to 971.4 ¢
	Major 17-mosstep	M17ms	2L + 15s	971.4 ¢ to 1200.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	L + 17s	600.0 ¢ to 1028.6 ¢
	Major 18-mosstep	M18ms	2L + 16s	1028.6 ¢ to 1200.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	L + 18s	600.0 ¢ to 1085.7 ¢
	Major 19-mosstep	M19ms	2L + 17s	1085.7 ¢ to 1200.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	L + 19s	600.0 ¢ to 1142.9 ¢
	Major 20-mosstep	M20ms	2L + 18s	1142.9 ¢ to 1200.0 ¢
21-mosstep	Perfect 21-mosstep	P21ms	2L + 19s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 2L 19s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
10\21						571.429	628.571	1:1	1.000	Equalized 2L 19s
					51\107	571.963	628.037	6:5	1.200
				41\86		572.093	627.907	5:4	1.250
					72\151	572.185	627.815	9:7	1.286
			31\65			572.308	627.692	4:3	1.333	Supersoft 2L 19s
					83\174	572.414	627.586	11:8	1.375
				52\109		572.477	627.523	7:5	1.400
					73\153	572.549	627.451	10:7	1.429
		21\44				572.727	627.273	3:2	1.500	Soft 2L 19s
					74\155	572.903	627.097	11:7	1.571
				53\111		572.973	627.027	8:5	1.600
					85\178	573.034	626.966	13:8	1.625
			32\67			573.134	626.866	5:3	1.667	Semisoft 2L 19s
					75\157	573.248	626.752	12:7	1.714
				43\90		573.333	626.667	7:4	1.750
					54\113	573.451	626.549	9:5	1.800
	11\23					573.913	626.087	2:1	2.000	Basic 2L 19s Scales with tunings softer than this are proper
					45\94	574.468	625.532	9:4	2.250
				34\71		574.648	625.352	7:3	2.333
					57\119	574.790	625.210	12:5	2.400
			23\48			575.000	625.000	5:2	2.500	Semihard 2L 19s
					58\121	575.207	624.793	13:5	2.600
				35\73		575.342	624.658	8:3	2.667
					47\98	575.510	624.490	11:4	2.750
		12\25				576.000	624.000	3:1	3.000	Hard 2L 19s
					37\77	576.623	623.377	10:3	3.333
				25\52		576.923	623.077	7:2	3.500
					38\79	577.215	622.785	11:3	3.667
			13\27			577.778	622.222	4:1	4.000	Superhard 2L 19s
					27\56	578.571	621.429	9:2	4.500
				14\29		579.310	620.690	5:1	5.000
					15\31	580.645	619.355	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 19s