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 cents). Since its generator is a tritone, it harmonic entropy minimum is where the generator is 7/5.

1/2					600
				11/23	573.913
			10/21		571.429
				19/40	570
					568.885
		9/19			568.421
					567.446
				26/55	567.273
					567.098
			17/36		566.667
				25/53	566.038
	8/17				564.706
				31/66	563.818
					563.557
			23/49		563.265
					563.045
				38/81	562.963
					562,829
		15/32			562.5
				37/79	562.025
			22/47		561.702
				29/62	561.290
7/15					560