3L 10s

↖ 2L 9s ↑ 3L 9s 4L 9s ↗

← 2L 10s 3L 10s 4L 10s →

↙ 2L 11s ↓ 3L 11s 4L 11s ↘
	Scale structure
Step pattern	LsssLsssLssss; ssssLsssLsssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
	Generator size
Bright	4\13 to 1\3 (369.2 ¢ to 400.0 ¢)
Dark	2\3 to 9\13 (800.0 ¢ to 830.8 ¢)
	TAMNAMS information
Related to	3L 7s (sephiroid)
With tunings	2:1 to 1:0 (hard-of-basic)
	Related MOS scales
Parent	3L 7s
Sister	10L 3s
Daughters	13L 3s, 3L 13s
Neutralized	6L 7s
2-Flought	16L 10s, 3L 23s
	Equal tunings
Equalized (L:s = 1:1)	4\13 (369.2 ¢)
Supersoft (L:s = 4:3)	13\42 (371.4 ¢)
Soft (L:s = 3:2)	9\29 (372.4 ¢)
Semisoft (L:s = 5:3)	14\45 (373.3 ¢)
Basic (L:s = 2:1)	5\16 (375.0 ¢)
Semihard (L:s = 5:2)	11\35 (377.1 ¢)
Hard (L:s = 3:1)	6\19 (378.9 ¢)
Superhard (L:s = 4:1)	7\22 (381.8 ¢)
Collapsed (L:s = 1:0)	1\3 (400.0 ¢)
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3L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 10 small steps, repeating every octave. 3L 10s is a child scale of 3L 7s, expanding it by 3 tones. Generators that produce this scale range from 369.2 ¢ to 400 ¢, or from 800 ¢ to 830.8 ¢.

Some notable temperaments that form a MOS with this pattern are magic and würschmidt. Of course, magic[13] is still slightly improper and würschmidt[13] is almost totally lopsided (L:s = 6:1 to 8:1). Even so, the excellence of magic temperament as a fit for 13 tone per octave melodic scales and its close affinity to strongly harmonic fifth temperaments make up for the roughness of the major third that 13 tone circles favor multiple times over.

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.

Template:MOS data is deprecated.

Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees

Scale tree

Scale tree and tuning spectrum of 3L 10s
Generator^(edo)						Cents		Step ratio		Comments
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments
4\13						369.231	830.769	1:1	1.000	Equalized 3L 10s
					21\68	370.588	829.412	6:5	1.200
				17\55		370.909	829.091	5:4	1.250
					30\97	371.134	828.866	9:7	1.286
			13\42			371.429	828.571	4:3	1.333	Supersoft 3L 10s
					35\113	371.681	828.319	11:8	1.375
				22\71		371.831	828.169	7:5	1.400
					31\100	372.000	828.000	10:7	1.429
		9\29				372.414	827.586	3:2	1.500	Soft 3L 10s
					32\103	372.816	827.184	11:7	1.571
				23\74		372.973	827.027	8:5	1.600
					37\119	373.109	826.891	13:8	1.625
			14\45			373.333	826.667	5:3	1.667	Semisoft 3L 10s
					33\106	373.585	826.415	12:7	1.714
				19\61		373.770	826.230	7:4	1.750
					24\77	374.026	825.974	9:5	1.800
	5\16					375.000	825.000	2:1	2.000	Basic 3L 10s Scales with tunings softer than this are proper
					21\67	376.119	823.881	9:4	2.250
				16\51		376.471	823.529	7:3	2.333
					27\86	376.744	823.256	12:5	2.400
			11\35			377.143	822.857	5:2	2.500	Semihard 3L 10s
					28\89	377.528	822.472	13:5	2.600
				17\54		377.778	822.222	8:3	2.667
					23\73	378.082	821.918	11:4	2.750
		6\19				378.947	821.053	3:1	3.000	Hard 3L 10s
					19\60	380.000	820.000	10:3	3.333
				13\41		380.488	819.512	7:2	3.500
					20\63	380.952	819.048	11:3	3.667
			7\22			381.818	818.182	4:1	4.000	Superhard 3L 10s
					15\47	382.979	817.021	9:2	4.500
				8\25		384.000	816.000	5:1	5.000
					9\28	385.714	814.286	6:1	6.000
1\3						400.000	800.000	1:0	→ ∞	Collapsed 3L 10s