10L 6s

10L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 6 small steps, with a period of 5 large steps and 3 small steps that repeats every 600.0 ¢, or twice every octave. 10L 6s is a child scale of 6L 4s, expanding it by 6 tones. Generators that produce this scale range from 225 ¢ to 240 ¢, or from 360 ¢ to 375 ¢. This scale is notable for supporting Lemba temperament; the entire range is suitable, with a generator range of about 229 to 232 ¢ being optimal.

↖ 9L 5s	↑ 10L 5s	11L 5s ↗
← 9L 6s	10L 6s	11L 6s →
↙ 9L 7s	↓ 10L 7s	11L 7s ↘

Scale structure
Step pattern	LLsLLsLsLLsLLsLs sLsLLsLLsLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	3\16 to 2\10 (225.0 ¢ to 240.0 ¢)
Dark	3\10 to 5\16 (360.0 ¢ to 375.0 ¢)
TAMNAMS information
Related to	6L 4s (lemon)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	6L 4s
Sister	6L 10s
Daughters	16L 10s, 10L 16s
Neutralized	4L 12s
2-Flought	26L 6s, 10L 22s
Equal tunings
Equalized (L:s = 1:1)	3\16 (225.0 ¢)
Supersoft (L:s = 4:3)	11\58 (227.6 ¢)
Soft (L:s = 3:2)	8\42 (228.6 ¢)
Semisoft (L:s = 5:3)	13\68 (229.4 ¢)
Basic (L:s = 2:1)	5\26 (230.8 ¢)
Semihard (L:s = 5:2)	12\62 (232.3 ¢)
Hard (L:s = 3:1)	7\36 (233.3 ¢)
Superhard (L:s = 4:1)	9\46 (234.8 ¢)
Collapsed (L:s = 1:0)	2\10 (240.0 ¢)
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Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 10L 6s

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 75.0 ¢
	Major 1-mosstep	M1ms	L	75.0 ¢ to 120.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	120.0 ¢ to 150.0 ¢
	Major 2-mosstep	M2ms	2L	150.0 ¢ to 240.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	L + 2s	120.0 ¢ to 225.0 ¢
	Perfect 3-mosstep	P3ms	2L + s	225.0 ¢ to 240.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	240.0 ¢ to 300.0 ¢
	Major 4-mosstep	M4ms	3L + s	300.0 ¢ to 360.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	360.0 ¢ to 375.0 ¢
	Augmented 5-mosstep	A5ms	4L + s	375.0 ¢ to 480.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	360.0 ¢ to 450.0 ¢
	Major 6-mosstep	M6ms	4L + 2s	450.0 ¢ to 480.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	4L + 3s	480.0 ¢ to 525.0 ¢
	Major 7-mosstep	M7ms	5L + 2s	525.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	600.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	5L + 4s	600.0 ¢ to 675.0 ¢
	Major 9-mosstep	M9ms	6L + 3s	675.0 ¢ to 720.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	6L + 4s	720.0 ¢ to 750.0 ¢
	Major 10-mosstep	M10ms	7L + 3s	750.0 ¢ to 840.0 ¢
11-mosstep	Diminished 11-mosstep	d11ms	6L + 5s	720.0 ¢ to 825.0 ¢
	Perfect 11-mosstep	P11ms	7L + 4s	825.0 ¢ to 840.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	7L + 5s	840.0 ¢ to 900.0 ¢
	Major 12-mosstep	M12ms	8L + 4s	900.0 ¢ to 960.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	8L + 5s	960.0 ¢ to 975.0 ¢
	Augmented 13-mosstep	A13ms	9L + 4s	975.0 ¢ to 1080.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	8L + 6s	960.0 ¢ to 1050.0 ¢
	Major 14-mosstep	M14ms	9L + 5s	1050.0 ¢ to 1080.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	9L + 6s	1080.0 ¢ to 1125.0 ¢
	Major 15-mosstep	M15ms	10L + 5s	1125.0 ¢ to 1200.0 ¢
16-mosstep	Perfect 16-mosstep	P16ms	10L + 6s	1200.0 ¢

Generator chain

Generator chain of 10L 6s

Bright gens	Scale degree	Abbrev.	Scale degree	Abbrev.
12	Augmented 4-mosdegree	A4md	Augmented 12-mosdegree	A12md
11	Augmented 1-mosdegree	A1md	Augmented 9-mosdegree	A9md
10	Augmented 6-mosdegree	A6md	Augmented 14-mosdegree	A14md
9	Augmented 3-mosdegree	A3md	Augmented 11-mosdegree	A11md
8	Augmented 0-mosdegree	A0md	Augmented 8-mosdegree	A8md
7	Augmented 5-mosdegree	A5md	Augmented 13-mosdegree	A13md
6	Major 2-mosdegree	M2md	Major 10-mosdegree	M10md
5	Major 7-mosdegree	M7md	Major 15-mosdegree	M15md
4	Major 4-mosdegree	M4md	Major 12-mosdegree	M12md
3	Major 1-mosdegree	M1md	Major 9-mosdegree	M9md
2	Major 6-mosdegree	M6md	Major 14-mosdegree	M14md
1	Perfect 3-mosdegree	P3md	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 8-mosdegree	P0md P8md	Perfect 8-mosdegree Perfect 16-mosdegree	P8md P16md
−1	Perfect 5-mosdegree	P5md	Perfect 13-mosdegree	P13md
−2	Minor 2-mosdegree	m2md	Minor 10-mosdegree	m10md
−3	Minor 7-mosdegree	m7md	Minor 15-mosdegree	m15md
−4	Minor 4-mosdegree	m4md	Minor 12-mosdegree	m12md
−5	Minor 1-mosdegree	m1md	Minor 9-mosdegree	m9md
−6	Minor 6-mosdegree	m6md	Minor 14-mosdegree	m14md
−7	Diminished 3-mosdegree	d3md	Diminished 11-mosdegree	d11md
−8	Diminished 8-mosdegree	d8md	Diminished 16-mosdegree	d16md
−9	Diminished 5-mosdegree	d5md	Diminished 13-mosdegree	d13md
−10	Diminished 2-mosdegree	d2md	Diminished 10-mosdegree	d10md
−11	Diminished 7-mosdegree	d7md	Diminished 15-mosdegree	d15md
−12	Diminished 4-mosdegree	d4md	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 10L 6s

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
14|0(2)	1	LLsLLsLsLLsLLsLs	Perf.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Aug.	Maj.	Maj.	Perf.
12|2(2)	4	LLsLsLLsLLsLsLLs	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.
10|4(2)	7	LsLLsLLsLsLLsLLs	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Maj.	Perf.
8|6(2)	2	LsLLsLsLLsLLsLsL	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Perf.	Maj.	Min.	Perf.
6|8(2)	5	LsLsLLsLLsLsLLsL	Perf.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.
4|10(2)	8	sLLsLLsLsLLsLLsL	Perf.	Min.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.	Min.	Min.	Perf.	Min.	Perf.	Maj.	Min.	Perf.
2|12(2)	3	sLLsLsLLsLLsLsLL	Perf.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Perf.	Min.	Perf.	Min.	Min.	Perf.
0|14(2)	6	sLsLLsLLsLsLLsLL	Perf.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Perf.	Min.	Min.	Dim.	Min.	Perf.	Min.	Min.	Perf.

Scale tree

Scale tree and tuning spectrum of 10L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\16						225.000	375.000	1:1	1.000	Equalized 10L 6s
					17\90	226.667	373.333	6:5	1.200
				14\74		227.027	372.973	5:4	1.250
					25\132	227.273	372.727	9:7	1.286
			11\58			227.586	372.414	4:3	1.333	Supersoft 10L 6s
					30\158	227.848	372.152	11:8	1.375
				19\100		228.000	372.000	7:5	1.400
					27\142	228.169	371.831	10:7	1.429
		8\42				228.571	371.429	3:2	1.500	Soft 10L 6s
					29\152	228.947	371.053	11:7	1.571
				21\110		229.091	370.909	8:5	1.600
					34\178	229.213	370.787	13:8	1.625
			13\68			229.412	370.588	5:3	1.667	Semisoft 10L 6s
					31\162	229.630	370.370	12:7	1.714
				18\94		229.787	370.213	7:4	1.750
					23\120	230.000	370.000	9:5	1.800
	5\26					230.769	369.231	2:1	2.000	Basic 10L 6s Scales with tunings softer than this are proper Optimal Lemba
					22\114	231.579	368.421	9:4	2.250
				17\88		231.818	368.182	7:3	2.333
					29\150	232.000	368.000	12:5	2.400
			12\62			232.258	367.742	5:2	2.500	Semihard 10L 6s
					31\160	232.500	367.500	13:5	2.600
				19\98		232.653	367.347	8:3	2.667
					26\134	232.836	367.164	11:4	2.750
		7\36				233.333	366.667	3:1	3.000	Hard 10L 6s
					23\118	233.898	366.102	10:3	3.333
				16\82		234.146	365.854	7:2	3.500
					25\128	234.375	365.625	11:3	3.667
			9\46			234.783	365.217	4:1	4.000	Superhard 10L 6s Echidnic
					20\102	235.294	364.706	9:2	4.500
				11\56		235.714	364.286	5:1	5.000
					13\66	236.364	363.636	6:1	6.000
2\10						240.000	360.000	1:0	→ ∞	Collapsed 10L 6s