12L 19s

↖ 11L 18s	↑ 12L 18s	13L 18s ↗
← 11L 19s	12L 19s	13L 19s →
↙ 11L 20s	↓ 12L 20s	13L 20s ↘

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Scale structure
Step pattern	LsLssLsLssLsLssLssLsLssLsLssLss ssLssLsLssLsLssLssLsLssLsLssLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	18\31 to 7\12 (696.8¢ to 700.0¢)
Dark	5\12 to 13\31 (500.0¢ to 503.2¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Ancestor's step ratio range	5:3 to 2:1 (minisoft)
Related MOS scales
Parent	12L 7s
Sister	19L 12s
Daughters	31L 12s, 12L 31s
Neutralized	24L 7s
2-Flought	43L 19s, 12L 50s
Equal tunings
Equalized (L:s = 1:1)	18\31 (696.8¢)
Supersoft (L:s = 4:3)	61\105 (697.1¢)
Soft (L:s = 3:2)	43\74 (697.3¢)
Semisoft (L:s = 5:3)	68\117 (697.4¢)
Basic (L:s = 2:1)	25\43 (697.7¢)
Semihard (L:s = 5:2)	57\98 (698.0¢)
Hard (L:s = 3:1)	32\55 (698.2¢)
Superhard (L:s = 4:1)	39\67 (698.5¢)
Collapsed (L:s = 1:0)	7\12 (700.0¢)

12L 19s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 19 small steps, repeating every octave. 12L 19s is a great-grandchild scale of 5L 2s, expanding it by 24 tones. Generators that produce this scale range from 696.8¢ to 700¢, or from 500¢ to 503.2¢. It is associated with sharper meantone temperaments.

Intervals

Intervals of 12L 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 38.7¢
	Major 1-mosstep	M1ms	L	38.7¢ to 100.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 77.4¢
	Major 2-mosstep	M2ms	L + s	77.4¢ to 100.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	100.0¢ to 116.1¢
	Major 3-mosstep	M3ms	2L + s	116.1¢ to 200.0¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	100.0¢ to 154.8¢
	Major 4-mosstep	M4ms	2L + 2s	154.8¢ to 200.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	100.0¢ to 193.5¢
	Major 5-mosstep	M5ms	2L + 3s	193.5¢ to 200.0¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	200.0¢ to 232.3¢
	Major 6-mosstep	M6ms	3L + 3s	232.3¢ to 300.0¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	200.0¢ to 271.0¢
	Major 7-mosstep	M7ms	3L + 4s	271.0¢ to 300.0¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	300.0¢ to 309.7¢
	Major 8-mosstep	M8ms	4L + 4s	309.7¢ to 400.0¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	300.0¢ to 348.4¢
	Major 9-mosstep	M9ms	4L + 5s	348.4¢ to 400.0¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	300.0¢ to 387.1¢
	Major 10-mosstep	M10ms	4L + 6s	387.1¢ to 400.0¢
11-mosstep	Minor 11-mosstep	m11ms	4L + 7s	400.0¢ to 425.8¢
	Major 11-mosstep	M11ms	5L + 6s	425.8¢ to 500.0¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	400.0¢ to 464.5¢
	Major 12-mosstep	M12ms	5L + 7s	464.5¢ to 500.0¢
13-mosstep	Perfect 13-mosstep	P13ms	5L + 8s	500.0¢ to 503.2¢
	Augmented 13-mosstep	A13ms	6L + 7s	503.2¢ to 600.0¢
14-mosstep	Minor 14-mosstep	m14ms	5L + 9s	500.0¢ to 541.9¢
	Major 14-mosstep	M14ms	6L + 8s	541.9¢ to 600.0¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	500.0¢ to 580.6¢
	Major 15-mosstep	M15ms	6L + 9s	580.6¢ to 600.0¢
16-mosstep	Minor 16-mosstep	m16ms	6L + 10s	600.0¢ to 619.4¢
	Major 16-mosstep	M16ms	7L + 9s	619.4¢ to 700.0¢
17-mosstep	Minor 17-mosstep	m17ms	6L + 11s	600.0¢ to 658.1¢
	Major 17-mosstep	M17ms	7L + 10s	658.1¢ to 700.0¢
18-mosstep	Diminished 18-mosstep	d18ms	6L + 12s	600.0¢ to 696.8¢
	Perfect 18-mosstep	P18ms	7L + 11s	696.8¢ to 700.0¢
19-mosstep	Minor 19-mosstep	m19ms	7L + 12s	700.0¢ to 735.5¢
	Major 19-mosstep	M19ms	8L + 11s	735.5¢ to 800.0¢
20-mosstep	Minor 20-mosstep	m20ms	7L + 13s	700.0¢ to 774.2¢
	Major 20-mosstep	M20ms	8L + 12s	774.2¢ to 800.0¢
21-mosstep	Minor 21-mosstep	m21ms	8L + 13s	800.0¢ to 812.9¢
	Major 21-mosstep	M21ms	9L + 12s	812.9¢ to 900.0¢
22-mosstep	Minor 22-mosstep	m22ms	8L + 14s	800.0¢ to 851.6¢
	Major 22-mosstep	M22ms	9L + 13s	851.6¢ to 900.0¢
23-mosstep	Minor 23-mosstep	m23ms	8L + 15s	800.0¢ to 890.3¢
	Major 23-mosstep	M23ms	9L + 14s	890.3¢ to 900.0¢
24-mosstep	Minor 24-mosstep	m24ms	9L + 15s	900.0¢ to 929.0¢
	Major 24-mosstep	M24ms	10L + 14s	929.0¢ to 1000.0¢
25-mosstep	Minor 25-mosstep	m25ms	9L + 16s	900.0¢ to 967.7¢
	Major 25-mosstep	M25ms	10L + 15s	967.7¢ to 1000.0¢
26-mosstep	Minor 26-mosstep	m26ms	10L + 16s	1000.0¢ to 1006.5¢
	Major 26-mosstep	M26ms	11L + 15s	1006.5¢ to 1100.0¢
27-mosstep	Minor 27-mosstep	m27ms	10L + 17s	1000.0¢ to 1045.2¢
	Major 27-mosstep	M27ms	11L + 16s	1045.2¢ to 1100.0¢
28-mosstep	Minor 28-mosstep	m28ms	10L + 18s	1000.0¢ to 1083.9¢
	Major 28-mosstep	M28ms	11L + 17s	1083.9¢ to 1100.0¢
29-mosstep	Minor 29-mosstep	m29ms	11L + 18s	1100.0¢ to 1122.6¢
	Major 29-mosstep	M29ms	12L + 17s	1122.6¢ to 1200.0¢
30-mosstep	Minor 30-mosstep	m30ms	11L + 19s	1100.0¢ to 1161.3¢
	Major 30-mosstep	M30ms	12L + 18s	1161.3¢ to 1200.0¢
31-mosstep	Perfect 31-mosstep	P31ms	12L + 19s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 12L 19s

Generator(edo)							Cents		Step ratio		Comments
							Bright	Dark	L:s	Hardness
18\31							696.774	503.226	1:1	1.000	Equalized 12L 19s
						115\198	696.970	503.030	7:6	1.167
					97\167		697.006	502.994	6:5	1.200
						176\303	697.030	502.970	11:9	1.222
				79\136			697.059	502.941	5:4	1.250
						219\377	697.082	502.918	14:11	1.273
					140\241		697.095	502.905	9:7	1.286
						201\346	697.110	502.890	13:10	1.300
			61\105				697.143	502.857	4:3	1.333	Supersoft 12L 19s
						226\389	697.172	502.828	15:11	1.364
					165\284		697.183	502.817	11:8	1.375
						269\463	697.192	502.808	18:13	1.385
				104\179			697.207	502.793	7:5	1.400
						251\432	697.222	502.778	17:12	1.417
					147\253		697.233	502.767	10:7	1.429
						190\327	697.248	502.752	13:9	1.444
		43\74					697.297	502.703	3:2	1.500	Soft 12L 19s
						197\339	697.345	502.655	14:9	1.556
					154\265		697.358	502.642	11:7	1.571
						265\456	697.368	502.632	19:12	1.583
				111\191			697.382	502.618	8:5	1.600
						290\499	697.395	502.605	21:13	1.615
					179\308		697.403	502.597	13:8	1.625
						247\425	697.412	502.588	18:11	1.636
			68\117				697.436	502.564	5:3	1.667	Semisoft 12L 19s
						229\394	697.462	502.538	17:10	1.700
					161\277		697.473	502.527	12:7	1.714
						254\437	697.483	502.517	19:11	1.727
				93\160			697.500	502.500	7:4	1.750
						211\363	697.521	502.479	16:9	1.778
					118\203		697.537	502.463	9:5	1.800
						143\246	697.561	502.439	11:6	1.833
	25\43						697.674	502.326	2:1	2.000	Basic 12L 19s Scales with tunings softer than this are proper
						132\227	697.797	502.203	11:5	2.200
					107\184		697.826	502.174	9:4	2.250
						189\325	697.846	502.154	16:7	2.286
				82\141			697.872	502.128	7:3	2.333
						221\380	697.895	502.105	19:8	2.375
					139\239		697.908	502.092	12:5	2.400
						196\337	697.923	502.077	17:7	2.429
			57\98				697.959	502.041	5:2	2.500	Semihard 12L 19s
						203\349	697.994	502.006	18:7	2.571
					146\251		698.008	501.992	13:5	2.600
						235\404	698.020	501.980	21:8	2.625
				89\153			698.039	501.961	8:3	2.667
						210\361	698.061	501.939	19:7	2.714
					121\208		698.077	501.923	11:4	2.750
						153\263	698.099	501.901	14:5	2.800
		32\55					698.182	501.818	3:1	3.000	Hard 12L 19s
						135\232	698.276	501.724	13:4	3.250
					103\177		698.305	501.695	10:3	3.333
						174\299	698.328	501.672	17:5	3.400
				71\122			698.361	501.639	7:2	3.500
						181\311	698.392	501.608	18:5	3.600
					110\189		698.413	501.587	11:3	3.667
						149\256	698.438	501.562	15:4	3.750
			39\67				698.507	501.493	4:1	4.000	Superhard 12L 19s
						124\213	698.592	501.408	13:3	4.333
					85\146		698.630	501.370	9:2	4.500
						131\225	698.667	501.333	14:3	4.667
				46\79			698.734	501.266	5:1	5.000
						99\170	698.824	501.176	11:2	5.500
					53\91		698.901	501.099	6:1	6.000
						60\103	699.029	500.971	7:1	7.000
7\12							700.000	500.000	1:0	→ ∞	Collapsed 12L 19s

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