7L 12s

Todo: review Adopt scale tree template, review entries

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

┌╥┬╥┬┬╥┬┬╥┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║│║││║││║│││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLssLsLssLssLss ssLssLssLsLssLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	8\19 to 3\7 (505.3 ¢ to 514.3 ¢)
Dark	4\7 to 11\19 (685.7 ¢ to 694.7 ¢)
TAMNAMS information
Related to	5L 2s (diatonic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	7L 5s
Sister	12L 7s
Daughters	19L 7s, 7L 19s
Neutralized	14L 5s
2-Flought	26L 12s, 7L 31s
Equal tunings
Equalized (L:s = 1:1)	8\19 (505.3 ¢)
Supersoft (L:s = 4:3)	27\64 (506.2 ¢)
Soft (L:s = 3:2)	19\45 (506.7 ¢)
Semisoft (L:s = 5:3)	30\71 (507.0 ¢)
Basic (L:s = 2:1)	11\26 (507.7 ¢)
Semihard (L:s = 5:2)	25\59 (508.5 ¢)
Hard (L:s = 3:1)	14\33 (509.1 ¢)
Superhard (L:s = 4:1)	17\40 (510.0 ¢)
Collapsed (L:s = 1:0)	3\7 (514.3 ¢)

7L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 12 small steps, repeating every octave. 7L 12s is a grandchild scale of 5L 2s, expanding it by 12 tones. Generators that produce this scale range from 505.3 ¢ to 514.3 ¢, or from 685.7 ¢ to 694.7 ¢. Temperaments associated with this scale include flattone, as the flattone enharmonic scale.

Modes

Modes of 7L 12s

UDP	Cyclic order	Step pattern
18|0	1	LsLssLssLsLssLssLss
17|1	9	LsLssLssLssLsLssLss
16|2	17	LssLsLssLssLsLssLss
15|3	6	LssLsLssLssLssLsLss
14|4	14	LssLssLsLssLssLsLss
13|5	3	LssLssLsLssLssLssLs
12|6	11	LssLssLssLsLssLssLs
11|7	19	sLsLssLssLsLssLssLs
10|8	8	sLsLssLssLssLsLssLs
9|9	16	sLssLsLssLssLsLssLs
8|10	5	sLssLsLssLssLssLsLs
7|11	13	sLssLssLsLssLssLsLs
6|12	2	sLssLssLsLssLssLssL
5|13	10	sLssLssLssLsLssLssL
4|14	18	ssLsLssLssLsLssLssL
3|15	7	ssLsLssLssLssLsLssL
2|16	15	ssLssLsLssLssLsLssL
1|17	4	ssLssLsLssLssLssLsL
0|18	12	ssLssLssLsLssLssLsL

Scale tree

Generator ranges:

• Chroma-positive generator: 505.2632 cents (8\19) to 514.2857 cents (3\7)
• Chroma-negative generator: 685.7143 cents (4\7) to 694.7368 cents (11\19)

Generator						Cents	L	s	L/s	Comments
8\19						505.263	1	1	1.000
					43\102	505.882	6	5	1.200
				35\83		506.024	5	4	1.250
					62\147	506.122	9	7	1.286
			27\64			506.250	4	3	1.333
					73\173	506.358	11	8	1.375
				46\109		506.422	7	5	1.400
					65\154	506.494	10	7	1.428
		19\45				506.667	3	2	1.500	Flattone
					68\161	506.832	11	7	1.571
				49\116		506.897	8	5	1.600
					79\187	506.952	13	8	1.625	Golden flattone (506.9365¢)
			30\71			507.042	5	3	1.667
					71\168	507.143	12	7	1.714
				41\97		507.216	7	4	1.750
					52\123	507.317	9	5	1.800
	11\26					507.692	2	1	2.000	Basic 7L 12s (Generators smaller than this are proper)
					47\111	508.108	9	4	2.250
				36\85		508.235	7	3	2.333
					61\144	508.333	12	5	2.400
			25\59			508.475	5	2	2.500
					64\151	508.609	13	5	2.600	Unnamed golden tuning (508.6329¢)
				39\92		508.696	8	3	2.667
					53\125	508.800	11	4	2.750
		14\33				509.091	3	1	3.000
					45\106	509.434	10	3	3.333
				31\73		509.589	7	2	3.500
					48\113	509.735	11	3	3.667
			17\40			510.000	4	1	4.000
					37\87	510.345	9	2	4.500
				20\47		510.638	5	1	5.000
					23\54	511.111	6	1	6.000
3\7						514.286	1	0	→ inf