10L 2s

10L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 2 small steps, with a period of 5 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. 10L 2s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 100 ¢ to 120 ¢, or from 480 ¢ to 500 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. The only significant harmonic entropy minimum with this MOS pattern is srutal/pajara, which appears as a 12-note scale of srutal/pajara[12].

↖ 9L 1s	↑ 10L 1s	11L 1s ↗
← 9L 2s	10L 2s	11L 2s →
↙ 9L 3s	↓ 10L 3s	11L 3s ↘

Scale structure
Step pattern	LLLLLsLLLLLs sLLLLLsLLLLL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	1\12 to 1\10 (100.0 ¢ to 120.0 ¢)
Dark	4\10 to 5\12 (480.0 ¢ to 500.0 ¢)
TAMNAMS information
Related to	2L 8s (jaric)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	2L 8s
Sister	2L 10s
Daughters	12L 10s, 10L 12s
Neutralized	8L 4s
2-Flought	22L 2s, 10L 14s
Equal tunings
Equalized (L:s = 1:1)	1\12 (100.0 ¢)
Supersoft (L:s = 4:3)	4\46 (104.3 ¢)
Soft (L:s = 3:2)	3\34 (105.9 ¢)
Semisoft (L:s = 5:3)	5\56 (107.1 ¢)
Basic (L:s = 2:1)	2\22 (109.1 ¢)
Semihard (L:s = 5:2)	5\54 (111.1 ¢)
Hard (L:s = 3:1)	3\32 (112.5 ¢)
Superhard (L:s = 4:1)	4\42 (114.3 ¢)
Collapsed (L:s = 1:0)	1\10 (120.0 ¢)
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Modes

Modes of 10L 2s

UDP	Cyclic order	Step pattern
10|0(2)	1	LLLLLsLLLLLs
8|2(2)	2	LLLLsLLLLLsL
6|4(2)	3	LLLsLLLLLsLL
4|6(2)	4	LLsLLLLLsLLL
2|8(2)	5	LsLLLLLsLLLL
0|10(2)	6	sLLLLLsLLLLL

Intervals

Intervals of 10L 2s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 100.0 ¢
	Perfect 1-mosstep	P1ms	L	100.0 ¢ to 120.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	120.0 ¢ to 200.0 ¢
	Major 2-mosstep	M2ms	2L	200.0 ¢ to 240.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	2L + s	240.0 ¢ to 300.0 ¢
	Major 3-mosstep	M3ms	3L	300.0 ¢ to 360.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	3L + s	360.0 ¢ to 400.0 ¢
	Major 4-mosstep	M4ms	4L	400.0 ¢ to 480.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	4L + s	480.0 ¢ to 500.0 ¢
	Augmented 5-mosstep	A5ms	5L	500.0 ¢ to 600.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	5L + s	600.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	5L + 2s	600.0 ¢ to 700.0 ¢
	Perfect 7-mosstep	P7ms	6L + s	700.0 ¢ to 720.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	6L + 2s	720.0 ¢ to 800.0 ¢
	Major 8-mosstep	M8ms	7L + s	800.0 ¢ to 840.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	7L + 2s	840.0 ¢ to 900.0 ¢
	Major 9-mosstep	M9ms	8L + s	900.0 ¢ to 960.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	8L + 2s	960.0 ¢ to 1000.0 ¢
	Major 10-mosstep	M10ms	9L + s	1000.0 ¢ to 1080.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	9L + 2s	1080.0 ¢ to 1100.0 ¢
	Augmented 11-mosstep	A11ms	10L + s	1100.0 ¢ to 1200.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	10L + 2s	1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 10L 2s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\12						100.000	500.000	1:1	1.000	Equalized 10L 2s
					6\70	102.857	497.143	6:5	1.200
				5\58		103.448	496.552	5:4	1.250
					9\104	103.846	496.154	9:7	1.286
			4\46			104.348	495.652	4:3	1.333	Supersoft 10L 2s
					11\126	104.762	495.238	11:8	1.375
				7\80		105.000	495.000	7:5	1.400
					10\114	105.263	494.737	10:7	1.429
		3\34				105.882	494.118	3:2	1.500	Soft 10L 2s ↕ Srutal / pajara
					11\124	106.452	493.548	11:7	1.571
				8\90		106.667	493.333	8:5	1.600
					13\146	106.849	493.151	13:8	1.625
			5\56			107.143	492.857	5:3	1.667	Semisoft 10L 2s
					12\134	107.463	492.537	12:7	1.714
				7\78		107.692	492.308	7:4	1.750
					9\100	108.000	492.000	9:5	1.800
	2\22					109.091	490.909	2:1	2.000	Basic 10L 2s
					9\98	110.204	489.796	9:4	2.250
				7\76		110.526	489.474	7:3	2.333
					12\130	110.769	489.231	12:5	2.400
			5\54			111.111	488.889	5:2	2.500	Semihard 10L 2s
					13\140	111.429	488.571	13:5	2.600
				8\86		111.628	488.372	8:3	2.667
					11\118	111.864	488.136	11:4	2.750
		3\32				112.500	487.500	3:1	3.000	Hard 10L 2s
					10\106	113.208	486.792	10:3	3.333
				7\74		113.514	486.486	7:2	3.500
					11\116	113.793	486.207	11:3	3.667
			4\42			114.286	485.714	4:1	4.000	Superhard 10L 2s
					9\94	114.894	485.106	9:2	4.500
				5\52		115.385	484.615	5:1	5.000
					6\62	116.129	483.871	6:1	6.000
1\10						120.000	480.000	1:0	→ ∞	Collapsed 10L 2s