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
						Bright	Dark	L:s	Hardness
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 Sephiroth
					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	Golden sephiroth
			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	Unnamed golden tuning
				17\54		377.778	822.222	8:3	2.667	Muggles
					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	Magic / witchcraft
				13\41		380.488	819.512	7:2	3.500	Magic
					20\63	380.952	819.048	11:3	3.667	Magic / necromancy
			7\22			381.818	818.182	4:1	4.000	Superhard 3L 10s
					15\47	382.979	817.021	9:2	4.500	Marveltri
				8\25		384.000	816.000	5:1	5.000
					9\28	385.714	814.286	6:1	6.000	Würschmidt ↓
1\3						400.000	800.000	1:0	→ ∞	Collapsed 3L 10s