10L 12s

10L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 12 small steps, with a period of 5 large steps and 6 small steps that repeats every 600.0 ¢, or twice every octave. 10L 12s is a grandchild scale of 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 109.1 ¢ to 120 ¢, or from 480 ¢ to 490.9 ¢.

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

Scale structure
Step pattern	LsLsLsLsLssLsLsLsLsLss ssLsLsLsLsLssLsLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	2\22 to 1\10 (109.1 ¢ to 120.0 ¢)
Dark	4\10 to 9\22 (480.0 ¢ to 490.9 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	10L 2s
Sister	12L 10s
Daughters	22L 10s, 10L 22s
Neutralized	20L 2s
2-Flought	32L 12s, 10L 34s
Equal tunings
Equalized (L:s = 1:1)	2\22 (109.1 ¢)
Supersoft (L:s = 4:3)	7\76 (110.5 ¢)
Soft (L:s = 3:2)	5\54 (111.1 ¢)
Semisoft (L:s = 5:3)	8\86 (111.6 ¢)
Basic (L:s = 2:1)	3\32 (112.5 ¢)
Semihard (L:s = 5:2)	7\74 (113.5 ¢)
Hard (L:s = 3:1)	4\42 (114.3 ¢)
Superhard (L:s = 4:1)	5\52 (115.4 ¢)
Collapsed (L:s = 1:0)	1\10 (120.0 ¢)
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Modes

Scale degrees of the modes of 10L 12s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22
20|0(2)	1	LsLsLsLsLssLsLsLsLsLss	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Maj.	Perf.
18|2(2)	3	LsLsLsLssLsLsLsLsLssLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
16|4(2)	5	LsLsLssLsLsLsLsLssLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
14|6(2)	7	LsLssLsLsLsLsLssLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
12|8(2)	9	LssLsLsLsLsLssLsLsLsLs	Perf.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.	Maj.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
10|10(2)	11	sLsLsLsLsLssLsLsLsLsLs	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Maj.	Perf.
8|12(2)	2	sLsLsLsLssLsLsLsLsLssL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Perf.	Min.	Perf.
6|14(2)	4	sLsLsLssLsLsLsLsLssLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Maj.	Min.	Maj.	Min.	Min.	Perf.	Min.	Perf.
4|16(2)	6	sLsLssLsLsLsLsLssLsLsL	Perf.	Min.	Perf.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Maj.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
2|18(2)	8	sLssLsLsLsLsLssLsLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
0|20(2)	10	ssLsLsLsLsLssLsLsLsLsL	Perf.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.	Min.	Dim.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.

Intervals

Intervals of 10L 12s

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 120.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 109.1 ¢
	Perfect 2-mosstep	P2ms	L + s	109.1 ¢ to 120.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	120.0 ¢ to 163.6 ¢
	Major 3-mosstep	M3ms	2L + s	163.6 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	120.0 ¢ to 218.2 ¢
	Major 4-mosstep	M4ms	2L + 2s	218.2 ¢ to 240.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	240.0 ¢ to 272.7 ¢
	Major 5-mosstep	M5ms	3L + 2s	272.7 ¢ to 360.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	240.0 ¢ to 327.3 ¢
	Major 6-mosstep	M6ms	3L + 3s	327.3 ¢ to 360.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	360.0 ¢ to 381.8 ¢
	Major 7-mosstep	M7ms	4L + 3s	381.8 ¢ to 480.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	3L + 5s	360.0 ¢ to 436.4 ¢
	Major 8-mosstep	M8ms	4L + 4s	436.4 ¢ to 480.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	4L + 5s	480.0 ¢ to 490.9 ¢
	Augmented 9-mosstep	A9ms	5L + 4s	490.9 ¢ to 600.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	4L + 6s	480.0 ¢ to 545.5 ¢
	Major 10-mosstep	M10ms	5L + 5s	545.5 ¢ to 600.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	5L + 6s	600.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	5L + 7s	600.0 ¢ to 654.5 ¢
	Major 12-mosstep	M12ms	6L + 6s	654.5 ¢ to 720.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	5L + 8s	600.0 ¢ to 709.1 ¢
	Perfect 13-mosstep	P13ms	6L + 7s	709.1 ¢ to 720.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	6L + 8s	720.0 ¢ to 763.6 ¢
	Major 14-mosstep	M14ms	7L + 7s	763.6 ¢ to 840.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	6L + 9s	720.0 ¢ to 818.2 ¢
	Major 15-mosstep	M15ms	7L + 8s	818.2 ¢ to 840.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	7L + 9s	840.0 ¢ to 872.7 ¢
	Major 16-mosstep	M16ms	8L + 8s	872.7 ¢ to 960.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	7L + 10s	840.0 ¢ to 927.3 ¢
	Major 17-mosstep	M17ms	8L + 9s	927.3 ¢ to 960.0 ¢
18-mosstep	Minor 18-mosstep	m18ms	8L + 10s	960.0 ¢ to 981.8 ¢
	Major 18-mosstep	M18ms	9L + 9s	981.8 ¢ to 1080.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	8L + 11s	960.0 ¢ to 1036.4 ¢
	Major 19-mosstep	M19ms	9L + 10s	1036.4 ¢ to 1080.0 ¢
20-mosstep	Perfect 20-mosstep	P20ms	9L + 11s	1080.0 ¢ to 1090.9 ¢
	Augmented 20-mosstep	A20ms	10L + 10s	1090.9 ¢ to 1200.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	9L + 12s	1080.0 ¢ to 1145.5 ¢
	Major 21-mosstep	M21ms	10L + 11s	1145.5 ¢ to 1200.0 ¢
22-mosstep	Perfect 22-mosstep	P22ms	10L + 12s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 12s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\22						109.091	490.909	1:1	1.000	Equalized 10L 12s
					11\120	110.000	490.000	6:5	1.200
				9\98		110.204	489.796	5:4	1.250
					16\174	110.345	489.655	9:7	1.286
			7\76			110.526	489.474	4:3	1.333	Supersoft 10L 12s
					19\206	110.680	489.320	11:8	1.375
				12\130		110.769	489.231	7:5	1.400
					17\184	110.870	489.130	10:7	1.429
		5\54				111.111	488.889	3:2	1.500	Soft 10L 12s
					18\194	111.340	488.660	11:7	1.571
				13\140		111.429	488.571	8:5	1.600
					21\226	111.504	488.496	13:8	1.625
			8\86			111.628	488.372	5:3	1.667	Semisoft 10L 12s
					19\204	111.765	488.235	12:7	1.714
				11\118		111.864	488.136	7:4	1.750
					14\150	112.000	488.000	9:5	1.800
	3\32					112.500	487.500	2:1	2.000	Basic 10L 12s Scales with tunings softer than this are proper
					13\138	113.043	486.957	9:4	2.250
				10\106		113.208	486.792	7:3	2.333
					17\180	113.333	486.667	12:5	2.400
			7\74			113.514	486.486	5:2	2.500	Semihard 10L 12s
					18\190	113.684	486.316	13:5	2.600
				11\116		113.793	486.207	8:3	2.667
					15\158	113.924	486.076	11:4	2.750
		4\42				114.286	485.714	3:1	3.000	Hard 10L 12s
					13\136	114.706	485.294	10:3	3.333
				9\94		114.894	485.106	7:2	3.500
					14\146	115.068	484.932	11:3	3.667
			5\52			115.385	484.615	4:1	4.000	Superhard 10L 12s
					11\114	115.789	484.211	9:2	4.500
				6\62		116.129	483.871	5:1	5.000
					7\72	116.667	483.333	6:1	6.000
1\10						120.000	480.000	1:0	→ ∞	Collapsed 10L 12s

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