2L 13s

↖ 1L 12s	↑ 2L 12s	3L 12s ↗
← 1L 13s	2L 13s	3L 13s →
↙ 1L 14s	↓ 2L 14s	3L 14s ↘

Scale structure
Step pattern	LssssssLsssssss sssssssLssssssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	7\15 to 1\2 (560.0 ¢ to 600.0 ¢)
Dark	1\2 to 8\15 (600.0 ¢ to 640.0 ¢)
TAMNAMS information
Related to	2L 7s (balzano)
With tunings	4:1 to 1:0 (ultrahard)
Related MOS scales
Parent	2L 11s
Sister	13L 2s
Daughters	15L 2s, 2L 15s
Neutralized	4L 11s
2-Flought	17L 13s, 2L 28s
Equal tunings
Equalized (L:s = 1:1)	7\15 (560.0 ¢)
Supersoft (L:s = 4:3)	22\47 (561.7 ¢)
Soft (L:s = 3:2)	15\32 (562.5 ¢)
Semisoft (L:s = 5:3)	23\49 (563.3 ¢)
Basic (L:s = 2:1)	8\17 (564.7 ¢)
Semihard (L:s = 5:2)	17\36 (566.7 ¢)
Hard (L:s = 3:1)	9\19 (568.4 ¢)
Superhard (L:s = 4:1)	10\21 (571.4 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)
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2L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 13 small steps, repeating every octave. 2L 13s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 560 ¢ to 600 ¢, or from 600 ¢ to 640 ¢.

This MOS is the simplest that has a tritone as the only possible size of a generator, since the smallest size for a tritone is defined to be 7/15edo (560 ¢). Since its generator is a tritone, its harmonic entropy minimum is where the generator is 7/5.

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 2L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
7\15						560.000	640.000	1:1	1.000	Equalized 2L 13s
					36\77	561.039	638.961	6:5	1.200
				29\62		561.290	638.710	5:4	1.250
					51\109	561.468	638.532	9:7	1.286
			22\47			561.702	638.298	4:3	1.333	Supersoft 2L 13s
					59\126	561.905	638.095	11:8	1.375
				37\79		562.025	637.975	7:5	1.400
					52\111	562.162	637.838	10:7	1.429
		15\32				562.500	637.500	3:2	1.500	Soft 2L 13s
					53\113	562.832	637.168	11:7	1.571
				38\81		562.963	637.037	8:5	1.600
					61\130	563.077	636.923	13:8	1.625
			23\49			563.265	636.735	5:3	1.667	Semisoft 2L 13s
					54\115	563.478	636.522	12:7	1.714
				31\66		563.636	636.364	7:4	1.750
					39\83	563.855	636.145	9:5	1.800
	8\17					564.706	635.294	2:1	2.000	Basic 2L 13s Scales with tunings softer than this are proper
					33\70	565.714	634.286	9:4	2.250
				25\53		566.038	633.962	7:3	2.333
					42\89	566.292	633.708	12:5	2.400
			17\36			566.667	633.333	5:2	2.500	Semihard 2L 13s
					43\91	567.033	632.967	13:5	2.600
				26\55		567.273	632.727	8:3	2.667
					35\74	567.568	632.432	11:4	2.750
		9\19				568.421	631.579	3:1	3.000	Hard 2L 13s
					28\59	569.492	630.508	10:3	3.333
				19\40		570.000	630.000	7:2	3.500
					29\61	570.492	629.508	11:3	3.667
			10\21			571.429	628.571	4:1	4.000	Superhard 2L 13s
					21\44	572.727	627.273	9:2	4.500
				11\23		573.913	626.087	5:1	5.000
					12\25	576.000	624.000	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 13s