12L 10s

↖11L 9s	↑12L 9s	13L 9s↗
←11L 10s	12L 10s	13L 10s→
↙11L 11s	↓12L 11s	13L 11s↘

┌╥╥┬╥┬╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║│║║│║│║│║│║││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLsLsLsLLsLsLsLsLs sLsLsLsLsLLsLsLsLsLsLL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	9\22 to 5\12 (490.9¢ to 500.0¢)
Dark	1\12 to 2\22 (100.0¢ to 109.1¢)
TAMNAMS information
Descends from	2L 8s (jaric)
Related MOS scales
Parent	10L 2s
Sister	10L 12s
Daughters	22L 12s 12L 22s
Equal tunings
Equalized (L:s = 1:1)	9\22 (490.9¢)
Supersoft (L:s = 4:3)	32\78 (492.3¢)
Soft (L:s = 3:2)	23\56 (492.9¢)
Semisoft (L:s = 5:3)	37\90 (493.3¢)
Basic (L:s = 2:1)	14\34 (494.1¢)
Semihard (L:s = 5:2)	33\80 (495.0¢)
Hard (L:s = 3:1)	19\46 (495.7¢)
Superhard (L:s = 4:1)	24\58 (496.6¢)
Collapsed (L:s = 1:0)	5\12 (500.0¢)

12L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 10 small steps, with a period of 6 large steps and 5 small steps that repeats every 600.0¢, or twice every octave. 12L 10s is a grandchild scale of 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 490.9¢ to 500¢, or from 100¢ to 109.1¢.

This scale is the quartertone scale of diaschismic temperament with dark generators above 100¢ (around the upper range of a diatonic semitone). This maps 5/4 (386¢) to one period (600¢) minus two dark generators.

Modes

Modes of 12L 10s

UDP	Rotational order	Step pattern
20|0(2)	1	LLsLsLsLsLsLLsLsLsLsLs
18|2(2)	10	LsLLsLsLsLsLsLLsLsLsLs
16|4(2)	8	LsLsLLsLsLsLsLsLLsLsLs
14|6(2)	6	LsLsLsLLsLsLsLsLsLLsLs
12|8(2)	4	LsLsLsLsLLsLsLsLsLsLLs
10|10(2)	2	LsLsLsLsLsLLsLsLsLsLsL
8|12(2)	11	sLLsLsLsLsLsLLsLsLsLsL
6|14(2)	9	sLsLLsLsLsLsLsLLsLsLsL
4|16(2)	7	sLsLsLLsLsLsLsLsLLsLsL
2|18(2)	5	sLsLsLsLLsLsLsLsLsLLsL
0|20(2)	3	sLsLsLsLsLLsLsLsLsLsLL

Scale tree

Scale tree and tuning spectrum of 12L 10s

Generator (in steps of edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
9\22						490.909	109.091	1:1	1.000	Equalized 12L 10s
					50\122	491.803	108.197	6:5	1.200
				41\100		492.000	108.000	5:4	1.250
					73\178	492.135	107.865	9:7	1.286
			32\78			492.308	107.692	4:3	1.333	Supersoft 12L 10s
					87\212	492.453	107.547	11:8	1.375
				55\134		492.537	107.463	7:5	1.400
					78\190	492.632	107.368	10:7	1.429
		23\56				492.857	107.143	3:2	1.500	Soft 12L 10s
					83\202	493.069	106.931	11:7	1.571
				60\146		493.151	106.849	8:5	1.600
					97\236	493.220	106.780	13:8	1.625
			37\90			493.333	106.667	5:3	1.667	Semisoft 12L 10s
					88\214	493.458	106.542	12:7	1.714
				51\124		493.548	106.452	7:4	1.750
					65\158	493.671	106.329	9:5	1.800
	14\34					494.118	105.882	2:1	2.000	Basic 12L 10s Scales with tunings softer than this are proper
					61\148	494.595	105.405	9:4	2.250
				47\114		494.737	105.263	7:3	2.333
					80\194	494.845	105.155	12:5	2.400
			33\80			495.000	105.000	5:2	2.500	Semihard 12L 10s
					85\206	495.146	104.854	13:5	2.600
				52\126		495.238	104.762	8:3	2.667
					71\172	495.349	104.651	11:4	2.750
		19\46				495.652	104.348	3:1	3.000	Hard 12L 10s
					62\150	496.000	104.000	10:3	3.333
				43\104		496.154	103.846	7:2	3.500	Diaschismic
					67\162	496.296	103.704	11:3	3.667
			24\58			496.552	103.448	4:1	4.000	Superhard 12L 10s
					53\128	496.875	103.125	9:2	4.500
				29\70		497.143	102.857	5:1	5.000
					34\82	497.561	102.439	6:1	6.000
5\12						500.000	100.000	1:0	→ ∞	Collapsed 12L 10s