5L 12s

Todo: review Adopt scale tree template, review entries

5L 12s 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.

↖ 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
Related to	5L 2s (diatonic)
With tunings	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 ¢)
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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

Generator ranges:

• Chroma-positive generator: 705.8824 cents (10\17) to 720 cents (3\5)
• Chroma-negative generator: 480 cents (2\5) to 494.1176 cents (7\17)

Generator						Cents	L	s	L/s	Comments
10\17						705.882	1	1	1.000
					53\90	706.667	6	5	1.200
				43\73		706.849	5	4	1.250
					76\129	706.977	9	7	1.286
			33\56			707.143	4	3	1.333	Supra
					89\151	707.285	11	8	1.375
				56\95		707.368	7	5	1.400
					79\134	707.463	10	7	1.428
		23\39				707.692	3	2	1.500
					82\139	707.914	11	7	1.571
				59\100		708.000	8	5	1.600
					95\161	708.075	13	8	1.625	Golden supra (708.0539¢)
			36\61			708.197	5	3	1.667	Quasisuper / quasisupra
					85\144	708.333	12	7	1.714
				49\83		708.434	7	4	1.750
					62\105	708.571	9	5	1.800
	13\22					709.091	2	1	2.000	Basic 5L 12s (Generators smaller than this are proper)
					55\93	709.677	9	4	2.250
				42\71		709.859	7	3	2.333
					71\120	710.000	12	5	2.400
			29\49			710.204	5	2	2.500	Superpyth
					74\125	710.400	13	5	2.600	Golden superpyth (710.4345¢)
				45\76		710.526	8	3	2.667
					61\103	710.680	11	4	2.750
		16\27				711.111	3	1	3.000
					51\86	711.628	10	3	3.333
				35\59		711.864	7	2	3.500
					54\91	712.088	11	3	3.667
			19\32			712.500	4	1	4.000
					41\69	713.043	9	2	4.500
				22\37		713.514	5	1	5.000	Oceanfront / Ultrapyth
					25\42	714.286	6	1	6.000	Hemiseven↓
3\5						720.000	1	0	→ inf