5L 12s

↖ 4L 11s	↑ 5L 11s	6L 11s ↗
← 4L 12s	5L 12s	6L 12s →
↙ 4L 13s	↓ 5L 13s	6L 13s ↘

┌╥┬┬╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║││║│││║││║││││ │││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssLssLsssLssLsss sssLssLsssLssLssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	10\17 to 3\5 (705.9¢ to 720.0¢)
Dark	2\5 to 7\17 (480.0¢ to 494.1¢)
TAMNAMS information
Descends from	5L 2s (diatonic)
Ancestor's step ratio range	3:1 to 1:0 (hard)
Related MOS scales
Parent	5L 7s
Sister	12L 5s
Daughters	17L 5s, 5L 17s
Neutralized	10L 7s
2-Flought	22L 12s, 5L 29s
Equal tunings
Equalized (L:s = 1:1)	10\17 (705.9¢)
Supersoft (L:s = 4:3)	33\56 (707.1¢)
Soft (L:s = 3:2)	23\39 (707.7¢)
Semisoft (L:s = 5:3)	36\61 (708.2¢)
Basic (L:s = 2:1)	13\22 (709.1¢)
Semihard (L:s = 5:2)	29\49 (710.2¢)
Hard (L:s = 3:1)	16\27 (711.1¢)
Superhard (L:s = 4:1)	19\32 (712.5¢)
Collapsed (L:s = 1:0)	3\5 (720.0¢)

5L 12s, also called s-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 12 small steps, repeating every octave. 5L 12s is a grandchild scale of 5L 2s, expanding it by 10 tones. Generators that produce this scale range from 705.9¢ to 720¢, or from 480¢ to 494.1¢. This scale is characterized by having a diesis (the difference between a large step and two small steps) that is larger than the chroma.

The supra/quasisuper version is proper, but the superpyth/ultrapyth version is improper (it does not become proper until you add 5 more notes to form the superpyth 22-note scale).

Modes

Modes of 5L 12s

UDP	Cyclic Order	Step Pattern
16|0	1	LssLssLsssLssLsss
15|1	11	LssLsssLssLssLsss
14|2	4	LssLsssLssLsssLss
13|3	14	LsssLssLssLsssLss
12|4	7	LsssLssLsssLssLss
11|5	17	sLssLssLsssLssLss
10|6	10	sLssLsssLssLssLss
9|7	3	sLssLsssLssLsssLs
8|8	13	sLsssLssLssLsssLs
7|9	6	sLsssLssLsssLssLs
6|10	16	ssLssLssLsssLssLs
5|11	9	ssLssLsssLssLssLs
4|12	2	ssLssLsssLssLsssL
3|13	12	ssLsssLssLssLsssL
2|14	5	ssLsssLssLsssLssL
1|15	15	sssLssLssLsssLssL
0|16	8	sssLssLsssLssLssL

Scale tree

Scale Tree and Tuning Spectrum of 5L 12s

Generator(edo)						Cents		Step Ratio		Comments
						Bright	Dark	L:s	Hardness
10\17						705.882	494.118	1:1	1.000	Equalized 5L 12s
					53\90	706.667	493.333	6:5	1.200
				43\73		706.849	493.151	5:4	1.250
					76\129	706.977	493.023	9:7	1.286
			33\56			707.143	492.857	4:3	1.333	Supersoft 5L 12s Supra
					89\151	707.285	492.715	11:8	1.375
				56\95		707.368	492.632	7:5	1.400
					79\134	707.463	492.537	10:7	1.429
		23\39				707.692	492.308	3:2	1.500	Soft 5L 12s
					82\139	707.914	492.086	11:7	1.571
				59\100		708.000	492.000	8:5	1.600
					95\161	708.075	491.925	13:8	1.625	Golden supra (708.0539¢)
			36\61			708.197	491.803	5:3	1.667	Semisoft 5L 12s Quasisuper / quasisupra
					85\144	708.333	491.667	12:7	1.714
				49\83		708.434	491.566	7:4	1.750
					62\105	708.571	491.429	9:5	1.800
	13\22					709.091	490.909	2:1	2.000	Basic 5L 12s Scales with tunings softer than this are proper
					55\93	709.677	490.323	9:4	2.250
				42\71		709.859	490.141	7:3	2.333
					71\120	710.000	490.000	12:5	2.400
			29\49			710.204	489.796	5:2	2.500	Semihard 5L 12s Superpyth
					74\125	710.400	489.600	13:5	2.600	Golden superpyth (710.4345¢)
				45\76		710.526	489.474	8:3	2.667
					61\103	710.680	489.320	11:4	2.750
		16\27				711.111	488.889	3:1	3.000	Hard 5L 12s
					51\86	711.628	488.372	10:3	3.333
				35\59		711.864	488.136	7:2	3.500	Quasiultra
					54\91	712.088	487.912	11:3	3.667
			19\32			712.500	487.500	4:1	4.000	Superhard 5L 12s
					41\69	713.043	486.957	9:2	4.500
				22\37		713.514	486.486	5:1	5.000	Oceanfront / ultrapyth
					25\42	714.286	485.714	6:1	6.000	↓ Hemiseven
3\5						720.000	480.000	1:0	→ ∞	Collapsed 5L 12s