4L 10s

4L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 10 small steps, with a period of 2 large steps and 5 small steps that repeats every 600.0 ¢, or twice every octave. 4L 10s is a child scale of 4L 6s, expanding it by 4 tones. Generators that produce this scale range from 257.1 ¢ to 300 ¢, or from 300 ¢ to 342.9 ¢.

↖ 3L 9s	↑ 4L 9s	5L 9s ↗
← 3L 10s	4L 10s	5L 10s →
↙ 3L 11s	↓ 4L 11s	5L 11s ↘

Scale structure
Step pattern	LssLsssLssLsss sssLssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	1\2 (600.0 ¢)
Generator size
Bright	3\14 to 1\4 (257.1 ¢ to 300.0 ¢)
Dark	1\4 to 4\14 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Related to	4L 6s (lime)
With tunings	2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent	4L 6s
Sister	10L 4s
Daughters	14L 4s, 4L 14s
Neutralized	8L 6s
2-Flought	18L 10s, 4L 24s
Equal tunings
Equalized (L:s = 1:1)	3\14 (257.1 ¢)
Supersoft (L:s = 4:3)	10\46 (260.9 ¢)
Soft (L:s = 3:2)	7\32 (262.5 ¢)
Semisoft (L:s = 5:3)	11\50 (264.0 ¢)
Basic (L:s = 2:1)	4\18 (266.7 ¢)
Semihard (L:s = 5:2)	9\40 (270.0 ¢)
Hard (L:s = 3:1)	5\22 (272.7 ¢)
Superhard (L:s = 4:1)	6\26 (276.9 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)
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The generator range puts a minor third (300 to 342.857 cents) -1 generator away from the period and 38edo almost exactly at the harmonic entropy minimum for its pattern.

Modes

Modes of 4L 10s

UDP	Cyclic order	Step pattern
12|0(2)	1	LssLsssLssLsss
10|2(2)	4	LsssLssLsssLss
8|4(2)	7	sLssLsssLssLss
6|6(2)	3	sLsssLssLsssLs
4|8(2)	6	ssLssLsssLssLs
2|10(2)	2	ssLsssLssLsssL
0|12(2)	5	sssLssLsssLssL

Intervals

Intervals of 4L 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 85.7 ¢
	Major 1-mosstep	M1ms	L	85.7 ¢ to 300.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 171.4 ¢
	Major 2-mosstep	M2ms	L + s	171.4 ¢ to 300.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 257.1 ¢
	Perfect 3-mosstep	P3ms	L + 2s	257.1 ¢ to 300.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	300.0 ¢ to 342.9 ¢
	Augmented 4-mosstep	A4ms	2L + 2s	342.9 ¢ to 600.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	300.0 ¢ to 428.6 ¢
	Major 5-mosstep	M5ms	2L + 3s	428.6 ¢ to 600.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	300.0 ¢ to 514.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	514.3 ¢ to 600.0 ¢
7-mosstep	Perfect 7-mosstep	P7ms	2L + 5s	600.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	600.0 ¢ to 685.7 ¢
	Major 8-mosstep	M8ms	3L + 5s	685.7 ¢ to 900.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	600.0 ¢ to 771.4 ¢
	Major 9-mosstep	M9ms	3L + 6s	771.4 ¢ to 900.0 ¢
10-mosstep	Diminished 10-mosstep	d10ms	2L + 8s	600.0 ¢ to 857.1 ¢
	Perfect 10-mosstep	P10ms	3L + 7s	857.1 ¢ to 900.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	900.0 ¢ to 942.9 ¢
	Augmented 11-mosstep	A11ms	4L + 7s	942.9 ¢ to 1200.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	900.0 ¢ to 1028.6 ¢
	Major 12-mosstep	M12ms	4L + 8s	1028.6 ¢ to 1200.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	900.0 ¢ to 1114.3 ¢
	Major 13-mosstep	M13ms	4L + 9s	1114.3 ¢ to 1200.0 ¢
14-mosstep	Perfect 14-mosstep	P14ms	4L + 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 4L 10s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\14						257.143	342.857	1:1	1.000	Equalized 4L 10s
					16\74	259.459	340.541	6:5	1.200
				13\60		260.000	340.000	5:4	1.250
					23\106	260.377	339.623	9:7	1.286
			10\46			260.870	339.130	4:3	1.333	Supersoft 4L 10s
					27\124	261.290	338.710	11:8	1.375
				17\78		261.538	338.462	7:5	1.400
					24\110	261.818	338.182	10:7	1.429
		7\32				262.500	337.500	3:2	1.500	Soft 4L 10s
					25\114	263.158	336.842	11:7	1.571
				18\82		263.415	336.585	8:5	1.600
					29\132	263.636	336.364	13:8	1.625
			11\50			264.000	336.000	5:3	1.667	Semisoft 4L 10s
					26\118	264.407	335.593	12:7	1.714
				15\68		264.706	335.294	7:4	1.750
					19\86	265.116	334.884	9:5	1.800
	4\18					266.667	333.333	2:1	2.000	Basic 4L 10s Scales with tunings softer than this are proper
					17\76	268.421	331.579	9:4	2.250
				13\58		268.966	331.034	7:3	2.333
					22\98	269.388	330.612	12:5	2.400
			9\40			270.000	330.000	5:2	2.500	Semihard 4L 10s
					23\102	270.588	329.412	13:5	2.600
				14\62		270.968	329.032	8:3	2.667
					19\84	271.429	328.571	11:4	2.750
		5\22				272.727	327.273	3:1	3.000	Hard 4L 10s
					16\70	274.286	325.714	10:3	3.333
				11\48		275.000	325.000	7:2	3.500
					17\74	275.676	324.324	11:3	3.667
			6\26			276.923	323.077	4:1	4.000	Superhard 4L 10s
					13\56	278.571	321.429	9:2	4.500
				7\30		280.000	320.000	5:1	5.000
					8\34	282.353	317.647	6:1	6.000
1\4						300.000	300.000	1:0	→ ∞	Collapsed 4L 10s