10L 5s

10L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 5 small steps, with a period of 2 large steps and 1 small step that repeats every 240.0 ¢, or 5 times every octave. 10L 5s is a child scale of 5L 5s, expanding it by 5 tones. Generators that produce this scale range from 80 ¢ to 120 ¢, or from 120 ¢ to 160 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

↖ 9L 4s	↑ 10L 4s	11L 4s ↗
← 9L 5s	10L 5s	11L 5s →
↙ 9L 6s	↓ 10L 6s	11L 6s ↘

Scale structure
Step pattern	LLsLLsLLsLLsLLs sLLsLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	1\5 (240.0 ¢)
Generator size
Bright	1\15 to 1\10 (80.0 ¢ to 120.0 ¢)
Dark	1\10 to 2\15 (120.0 ¢ to 160.0 ¢)
TAMNAMS information
Related to	5L 5s (pentawood)
With tunings	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	5L 5s
Sister	5L 10s
Daughters	15L 10s, 10L 15s
Neutralized	5L 10s
2-Flought	25L 5s, 10L 20s
Equal tunings
Equalized (L:s = 1:1)	1\15 (80.0 ¢)
Supersoft (L:s = 4:3)	4\55 (87.3 ¢)
Soft (L:s = 3:2)	3\40 (90.0 ¢)
Semisoft (L:s = 5:3)	5\65 (92.3 ¢)
Basic (L:s = 2:1)	2\25 (96.0 ¢)
Semihard (L:s = 5:2)	5\60 (100.0 ¢)
Hard (L:s = 3:1)	3\35 (102.9 ¢)
Superhard (L:s = 4:1)	4\45 (106.7 ¢)
Collapsed (L:s = 1:0)	1\10 (120.0 ¢)
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Modes

Modes of 10L 5s

UDP	Cyclic order	Step pattern
10|0(5)	1	LLsLLsLLsLLsLLs
5|5(5)	2	LsLLsLLsLLsLLsL
0|10(5)	3	sLLsLLsLLsLLsLL

Intervals

Intervals of 10L 5s

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 80.0 ¢
	Perfect 1-mosstep	P1ms	L	80.0 ¢ to 120.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	120.0 ¢ to 160.0 ¢
	Augmented 2-mosstep	A2ms	2L	160.0 ¢ to 240.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	240.0 ¢
4-mosstep	Diminished 4-mosstep	d4ms	2L + 2s	240.0 ¢ to 320.0 ¢
	Perfect 4-mosstep	P4ms	3L + s	320.0 ¢ to 360.0 ¢
5-mosstep	Perfect 5-mosstep	P5ms	3L + 2s	360.0 ¢ to 400.0 ¢
	Augmented 5-mosstep	A5ms	4L + s	400.0 ¢ to 480.0 ¢
6-mosstep	Perfect 6-mosstep	P6ms	4L + 2s	480.0 ¢
7-mosstep	Diminished 7-mosstep	d7ms	4L + 3s	480.0 ¢ to 560.0 ¢
	Perfect 7-mosstep	P7ms	5L + 2s	560.0 ¢ to 600.0 ¢
8-mosstep	Perfect 8-mosstep	P8ms	5L + 3s	600.0 ¢ to 640.0 ¢
	Augmented 8-mosstep	A8ms	6L + 2s	640.0 ¢ to 720.0 ¢
9-mosstep	Perfect 9-mosstep	P9ms	6L + 3s	720.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	6L + 4s	720.0 ¢ to 800.0 ¢
	Perfect 10-mosstep	P10ms	7L + 3s	800.0 ¢ to 840.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	7L + 4s	840.0 ¢ to 880.0 ¢
	Augmented 11-mosstep	A11ms	8L + 3s	880.0 ¢ to 960.0 ¢
12-mosstep	Perfect 12-mosstep	P12ms	8L + 4s	960.0 ¢
13-mosstep	Diminished 13-mosstep	d13ms	8L + 5s	960.0 ¢ to 1040.0 ¢
	Perfect 13-mosstep	P13ms	9L + 4s	1040.0 ¢ to 1080.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	9L + 5s	1080.0 ¢ to 1120.0 ¢
	Augmented 14-mosstep	A14ms	10L + 4s	1120.0 ¢ to 1200.0 ¢
15-mosstep	Perfect 15-mosstep	P15ms	10L + 5s	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 10L 5s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\15						80.000	160.000	1:1	1.000	Equalized 10L 5s
					6\85	84.706	155.294	6:5	1.200
				5\70		85.714	154.286	5:4	1.250
					9\125	86.400	153.600	9:7	1.286
			4\55			87.273	152.727	4:3	1.333	Supersoft 10L 5s
					11\150	88.000	152.000	11:8	1.375
				7\95		88.421	151.579	7:5	1.400
					10\135	88.889	151.111	10:7	1.429
		3\40				90.000	150.000	3:2	1.500	Soft 10L 5s
					11\145	91.034	148.966	11:7	1.571
				8\105		91.429	148.571	8:5	1.600
					13\170	91.765	148.235	13:8	1.625
			5\65			92.308	147.692	5:3	1.667	Semisoft 10L 5s
					12\155	92.903	147.097	12:7	1.714
				7\90		93.333	146.667	7:4	1.750
					9\115	93.913	146.087	9:5	1.800
	2\25					96.000	144.000	2:1	2.000	Basic 10L 5s
					9\110	98.182	141.818	9:4	2.250
				7\85		98.824	141.176	7:3	2.333
					12\145	99.310	140.690	12:5	2.400
			5\60			100.000	140.000	5:2	2.500	Semihard 10L 5s
					13\155	100.645	139.355	13:5	2.600
				8\95		101.053	138.947	8:3	2.667
					11\130	101.538	138.462	11:4	2.750
		3\35				102.857	137.143	3:1	3.000	Hard 10L 5s
					10\115	104.348	135.652	10:3	3.333
				7\80		105.000	135.000	7:2	3.500
					11\125	105.600	134.400	11:3	3.667
			4\45			106.667	133.333	4:1	4.000	Superhard 10L 5s
					9\100	108.000	132.000	9:2	4.500
				5\55		109.091	130.909	5:1	5.000
					6\65	110.769	129.231	6:1	6.000
1\10						120.000	120.000	1:0	→ ∞	Collapsed 10L 5s

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