19L 12s

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

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Scale structure
Step pattern	LLsLLsLsLLsLsLLsLLsLsLLsLsLLsLs sLsLLsLsLLsLsLLsLLsLsLLsLsLLsLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\31 to 8\19 (503.2¢ to 505.3¢)
Dark	11\19 to 18\31 (694.7¢ to 696.8¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Ancestor's step ratio range	3:2 to 5:3 (quasisoft)
Related MOS scales
Parent	12L 7s
Sister	12L 19s
Daughters	31L 19s, 19L 31s
Neutralized	7L 24s
2-Flought	50L 12s, 19L 43s
Equal tunings
Equalized (L:s = 1:1)	13\31 (503.2¢)
Supersoft (L:s = 4:3)	47\112 (503.6¢)
Soft (L:s = 3:2)	34\81 (503.7¢)
Semisoft (L:s = 5:3)	55\131 (503.8¢)
Basic (L:s = 2:1)	21\50 (504.0¢)
Semihard (L:s = 5:2)	50\119 (504.2¢)
Hard (L:s = 3:1)	29\69 (504.3¢)
Superhard (L:s = 4:1)	37\88 (504.5¢)
Collapsed (L:s = 1:0)	8\19 (505.3¢)

19L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 19 large steps and 12 small steps, repeating every octave. 19L 12s is a great-grandchild scale of 5L 2s, expanding it by 24 tones. Generators that produce this scale range from 503.2¢ to 505.3¢, or from 694.7¢ to 696.8¢. It is associated with flatter meantone temperaments.

Intervals

Intervals of 19L 12s

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 63.2¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	63.2¢ to 77.4¢
	Major 2-mosstep	M2ms	2L	77.4¢ to 126.3¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	63.2¢ to 116.1¢
	Major 3-mosstep	M3ms	2L + s	116.1¢ to 126.3¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	126.3¢ to 154.8¢
	Major 4-mosstep	M4ms	3L + s	154.8¢ to 189.5¢
5-mosstep	Minor 5-mosstep	m5ms	3L + 2s	189.5¢ to 193.5¢
	Major 5-mosstep	M5ms	4L + s	193.5¢ to 252.6¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	189.5¢ to 232.3¢
	Major 6-mosstep	M6ms	4L + 2s	232.3¢ to 252.6¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	252.6¢ to 271.0¢
	Major 7-mosstep	M7ms	5L + 2s	271.0¢ to 315.8¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	252.6¢ to 309.7¢
	Major 8-mosstep	M8ms	5L + 3s	309.7¢ to 315.8¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	315.8¢ to 348.4¢
	Major 9-mosstep	M9ms	6L + 3s	348.4¢ to 378.9¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	378.9¢ to 387.1¢
	Major 10-mosstep	M10ms	7L + 3s	387.1¢ to 442.1¢
11-mosstep	Minor 11-mosstep	m11ms	6L + 5s	378.9¢ to 425.8¢
	Major 11-mosstep	M11ms	7L + 4s	425.8¢ to 442.1¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	442.1¢ to 464.5¢
	Major 12-mosstep	M12ms	8L + 4s	464.5¢ to 505.3¢
13-mosstep	Diminished 13-mosstep	d13ms	7L + 6s	442.1¢ to 503.2¢
	Perfect 13-mosstep	P13ms	8L + 5s	503.2¢ to 505.3¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	505.3¢ to 541.9¢
	Major 14-mosstep	M14ms	9L + 5s	541.9¢ to 568.4¢
15-mosstep	Minor 15-mosstep	m15ms	9L + 6s	568.4¢ to 580.6¢
	Major 15-mosstep	M15ms	10L + 5s	580.6¢ to 631.6¢
16-mosstep	Minor 16-mosstep	m16ms	9L + 7s	568.4¢ to 619.4¢
	Major 16-mosstep	M16ms	10L + 6s	619.4¢ to 631.6¢
17-mosstep	Minor 17-mosstep	m17ms	10L + 7s	631.6¢ to 658.1¢
	Major 17-mosstep	M17ms	11L + 6s	658.1¢ to 694.7¢
18-mosstep	Perfect 18-mosstep	P18ms	11L + 7s	694.7¢ to 696.8¢
	Augmented 18-mosstep	A18ms	12L + 6s	696.8¢ to 757.9¢
19-mosstep	Minor 19-mosstep	m19ms	11L + 8s	694.7¢ to 735.5¢
	Major 19-mosstep	M19ms	12L + 7s	735.5¢ to 757.9¢
20-mosstep	Minor 20-mosstep	m20ms	12L + 8s	757.9¢ to 774.2¢
	Major 20-mosstep	M20ms	13L + 7s	774.2¢ to 821.1¢
21-mosstep	Minor 21-mosstep	m21ms	12L + 9s	757.9¢ to 812.9¢
	Major 21-mosstep	M21ms	13L + 8s	812.9¢ to 821.1¢
22-mosstep	Minor 22-mosstep	m22ms	13L + 9s	821.1¢ to 851.6¢
	Major 22-mosstep	M22ms	14L + 8s	851.6¢ to 884.2¢
23-mosstep	Minor 23-mosstep	m23ms	14L + 9s	884.2¢ to 890.3¢
	Major 23-mosstep	M23ms	15L + 8s	890.3¢ to 947.4¢
24-mosstep	Minor 24-mosstep	m24ms	14L + 10s	884.2¢ to 929.0¢
	Major 24-mosstep	M24ms	15L + 9s	929.0¢ to 947.4¢
25-mosstep	Minor 25-mosstep	m25ms	15L + 10s	947.4¢ to 967.7¢
	Major 25-mosstep	M25ms	16L + 9s	967.7¢ to 1010.5¢
26-mosstep	Minor 26-mosstep	m26ms	15L + 11s	947.4¢ to 1006.5¢
	Major 26-mosstep	M26ms	16L + 10s	1006.5¢ to 1010.5¢
27-mosstep	Minor 27-mosstep	m27ms	16L + 11s	1010.5¢ to 1045.2¢
	Major 27-mosstep	M27ms	17L + 10s	1045.2¢ to 1073.7¢
28-mosstep	Minor 28-mosstep	m28ms	17L + 11s	1073.7¢ to 1083.9¢
	Major 28-mosstep	M28ms	18L + 10s	1083.9¢ to 1136.8¢
29-mosstep	Minor 29-mosstep	m29ms	17L + 12s	1073.7¢ to 1122.6¢
	Major 29-mosstep	M29ms	18L + 11s	1122.6¢ to 1136.8¢
30-mosstep	Minor 30-mosstep	m30ms	18L + 12s	1136.8¢ to 1161.3¢
	Major 30-mosstep	M30ms	19L + 11s	1161.3¢ to 1200.0¢
31-mosstep	Perfect 31-mosstep	P31ms	19L + 12s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 19L 12s

Generator(edo)							Cents		Step ratio		Comments
							Bright	Dark	L:s	Hardness
13\31							503.226	696.774	1:1	1.000	Equalized 19L 12s
						86\205	503.415	696.585	7:6	1.167
					73\174		503.448	696.552	6:5	1.200
						133\317	503.470	696.530	11:9	1.222
				60\143			503.497	696.503	5:4	1.250
						167\398	503.518	696.482	14:11	1.273
					107\255		503.529	696.471	9:7	1.286
						154\367	503.542	696.458	13:10	1.300
			47\112				503.571	696.429	4:3	1.333	Supersoft 19L 12s
						175\417	503.597	696.403	15:11	1.364
					128\305		503.607	696.393	11:8	1.375
						209\498	503.614	696.386	18:13	1.385
				81\193			503.627	696.373	7:5	1.400
						196\467	503.640	696.360	17:12	1.417
					115\274		503.650	696.350	10:7	1.429
						149\355	503.662	696.338	13:9	1.444
		34\81					503.704	696.296	3:2	1.500	Soft 19L 12s
						157\374	503.743	696.257	14:9	1.556
					123\293		503.754	696.246	11:7	1.571
						212\505	503.762	696.238	19:12	1.583
				89\212			503.774	696.226	8:5	1.600
						233\555	503.784	696.216	21:13	1.615
					144\343		503.790	696.210	13:8	1.625
						199\474	503.797	696.203	18:11	1.636
			55\131				503.817	696.183	5:3	1.667	Semisoft 19L 12s
						186\443	503.837	696.163	17:10	1.700
					131\312		503.846	696.154	12:7	1.714
						207\493	503.854	696.146	19:11	1.727
				76\181			503.867	696.133	7:4	1.750
						173\412	503.883	696.117	16:9	1.778
					97\231		503.896	696.104	9:5	1.800
						118\281	503.915	696.085	11:6	1.833
	21\50						504.000	696.000	2:1	2.000	Basic 19L 12s Scales with tunings softer than this are proper
						113\269	504.089	695.911	11:5	2.200
					92\219		504.110	695.890	9:4	2.250
						163\388	504.124	695.876	16:7	2.286
				71\169			504.142	695.858	7:3	2.333
						192\457	504.158	695.842	19:8	2.375
					121\288		504.167	695.833	12:5	2.400
						171\407	504.177	695.823	17:7	2.429
			50\119				504.202	695.798	5:2	2.500	Semihard 19L 12s
						179\426	504.225	695.775	18:7	2.571
					129\307		504.235	695.765	13:5	2.600
						208\495	504.242	695.758	21:8	2.625
				79\188			504.255	695.745	8:3	2.667
						187\445	504.270	695.730	19:7	2.714
					108\257		504.280	695.720	11:4	2.750
						137\326	504.294	695.706	14:5	2.800
		29\69					504.348	695.652	3:1	3.000	Hard 19L 12s
						124\295	504.407	695.593	13:4	3.250
					95\226		504.425	695.575	10:3	3.333
						161\383	504.439	695.561	17:5	3.400
				66\157			504.459	695.541	7:2	3.500
						169\402	504.478	695.522	18:5	3.600
					103\245		504.490	695.510	11:3	3.667
						140\333	504.505	695.495	15:4	3.750
			37\88				504.545	695.455	4:1	4.000	Superhard 19L 12s
						119\283	504.594	695.406	13:3	4.333
					82\195		504.615	695.385	9:2	4.500
						127\302	504.636	695.364	14:3	4.667
				45\107			504.673	695.327	5:1	5.000
						98\233	504.721	695.279	11:2	5.500
					53\126		504.762	695.238	6:1	6.000
						61\145	504.828	695.172	7:1	7.000
8\19							505.263	694.737	1:0	→ ∞	Collapsed 19L 12s

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