12L 7s

Todo: review Adopt scale tree, review entries

↖ 11L 6s	↑ 12L 6s	13L 6s ↗
← 11L 7s	12L 7s	13L 7s →
↙ 11L 8s	↓ 12L 8s	13L 8s ↘

┌╥╥┬╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬┐ │║║│║║│║║│║│║║│║║│║││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLLsLLsLsLLsLLsLs sLsLLsLLsLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\19 to 7\12 (694.7 ¢ to 700.0 ¢)
Dark	5\12 to 8\19 (500.0 ¢ to 505.3 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	7L 5s
Sister	7L 12s
Daughters	19L 12s, 12L 19s
Neutralized	5L 14s
2-Flought	31L 7s, 12L 26s
Equal tunings
Equalized (L:s = 1:1)	11\19 (694.7 ¢)
Supersoft (L:s = 4:3)	40\69 (695.7 ¢)
Soft (L:s = 3:2)	29\50 (696.0 ¢)
Semisoft (L:s = 5:3)	47\81 (696.3 ¢)
Basic (L:s = 2:1)	18\31 (696.8 ¢)
Semihard (L:s = 5:2)	43\74 (697.3 ¢)
Hard (L:s = 3:1)	25\43 (697.7 ¢)
Superhard (L:s = 4:1)	32\55 (698.2 ¢)
Collapsed (L:s = 1:0)	7\12 (700.0 ¢)

12L 7s, also called m-enharmonic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 7 small steps, repeating every octave. 12L 7s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 694.7 ¢ to 700 ¢, or from 500 ¢ to 505.3 ¢. Temperaments associated with this scale include meantone, as the meantone enharmonic scale.

Modes

Modes of 12L 7s

UDP	Cyclic order	Step pattern
18|0	1	LLsLLsLLsLsLLsLLsLs
17|1	12	LLsLLsLsLLsLLsLLsLs
16|2	4	LLsLLsLsLLsLLsLsLLs
15|3	15	LLsLsLLsLLsLLsLsLLs
14|4	7	LLsLsLLsLLsLsLLsLLs
13|5	18	LsLLsLLsLLsLsLLsLLs
12|6	10	LsLLsLLsLsLLsLLsLLs
11|7	2	LsLLsLLsLsLLsLLsLsL
10|8	13	LsLLsLsLLsLLsLLsLsL
9|9	5	LsLLsLsLLsLLsLsLLsL
8|10	16	LsLsLLsLLsLLsLsLLsL
7|11	8	LsLsLLsLLsLsLLsLLsL
6|12	19	sLLsLLsLLsLsLLsLLsL
5|13	11	sLLsLLsLsLLsLLsLLsL
4|14	3	sLLsLLsLsLLsLLsLsLL
3|15	14	sLLsLsLLsLLsLLsLsLL
2|16	6	sLLsLsLLsLLsLsLLsLL
1|17	17	sLsLLsLLsLLsLsLLsLL
0|18	9	sLsLLsLLsLsLLsLLsLL

Scale tree

Generator ranges:

• Chroma-positive generator: 694.7368 cents (11\19) to 700 cents (7\12)
• Chroma-negative generator: 500 cents (5\12) to 505.2632 cents (8\19)

Generator						Cents	L	s	L/s	Comments
11\19						694.737	1	1	1.000
					62\107	695.327	6	5	1.200
				51\88		695.455	5	4	1.250
					91\157	695.541	9	7	1.286
			40\69			695.652	4	3	1.333
					109\188	695.745	11	8	1.375
				69\119		695.798	7	5	1.400
					98\169	695.858	10	7	1.428
		29\50				696.000	3	2	1.500	Meantone / Meanpop
					105\181	696.133	11	7	1.571
				76\131		696.183	8	5	1.600
					123\212	696.226	13	8	1.625	Golden meantone (696.2145¢)
			47\81			696.296	5	3	1.667	Meantone / Meanpop
					112\193	696.373	12	7	1.714
				65\112		696.429	7	4	1.750
					83\143	696.503	9	5	1.800
	18\31					696.774	2	1	2.000	Basic 12L 7s (Generators smaller than this are proper)
					79\136	697.059	9	4	2.250
				61\105		697.143	7	3	2.333	Meantone / Huygens
					104\179	697.207	12	5	2.400
			43\74			697.297	5	2	2.500	Meantone / Huygens / Grosstone
					111\191	697.382	13	5	2.600	Golden grosstone (697.3969¢)
				68\117		697.436	8	3	2.667
					93\160	697.500	11	4	2.750
		25\43				697.674	3	1	3.000	Meantone / Meridetone
					82\141	697.872	10	3	3.333
				57\98		697.959	7	2	3.500
					89\153	698.039	11	3	3.667
			32\55			698.182	4	1	4.000
					71\122	698.361	9	2	4.500
				39\67		698.507	5	1	5.000
					46\79	698.734	6	1	6.000
7\12						700.000	1	0	→ inf