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
Related to	2L 8s (jaric)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	10L 2s
Sister	10L 12s
Daughters	22L 12s, 12L 22s
Neutralized	2L 20s
2-Flought	34L 10s, 12L 32s
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 ¢)
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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	Cyclic 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

Intervals

Intervals of 12L 10s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0 ¢ to 54.5 ¢
	Major 1-mosstep	M1ms	L	54.5 ¢ to 100.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	100.0 ¢ to 109.1 ¢
	Augmented 2-mosstep	A2ms	2L	109.1 ¢ to 200.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	100.0 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	2L + s	163.6 ¢ to 200.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	200.0 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	3L + s	218.2 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	200.0 ¢ to 272.7 ¢
	Major 5-mosstep	M5ms	3L + 2s	272.7 ¢ to 300.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	300.0 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	4L + 2s	327.3 ¢ to 400.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	300.0 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	4L + 3s	381.8 ¢ to 400.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	400.0 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	5L + 3s	436.4 ¢ to 500.0 ¢
9-mosstep	Diminished 9-mosstep	d9ms	4L + 5s	400.0 ¢ to 490.9 ¢
	Perfect 9-mosstep	P9ms	5L + 4s	490.9 ¢ to 500.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	500.0 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	6L + 4s	545.5 ¢ to 600.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	6L + 5s	600.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	600.0 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	7L + 5s	654.5 ¢ to 700.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	7L + 6s	700.0 ¢ to 709.1 ¢
	Augmented 13-mosstep	A13ms	8L + 5s	709.1 ¢ to 800.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	7L + 7s	700.0 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	8L + 6s	763.6 ¢ to 800.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	8L + 7s	800.0 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	9L + 6s	818.2 ¢ to 900.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	8L + 8s	800.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	9L + 7s	872.7 ¢ to 900.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	9L + 8s	900.0 ¢ to 927.3 ¢
	Major 17-mosstep	M17ms	10L + 7s	927.3 ¢ to 1000.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	9L + 9s	900.0 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	10L + 8s	981.8 ¢ to 1000.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	10L + 9s	1000.0 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	11L + 8s	1036.4 ¢ to 1100.0 ¢
20-mosstep	Diminished 20-mosstep	d20ms	10L + 10s	1000.0 ¢ to 1090.9 ¢
	Perfect 20-mosstep	P20ms	11L + 9s	1090.9 ¢ to 1100.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	11L + 10s	1100.0 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	12L + 9s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	12L + 10s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 12L 10s

Generator(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