2L 13s

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↖ 1L 12s↑ 2L 12s 3L 12s ↗
← 1L 13s2L 13s3L 13s →
↙ 1L 14s↓ 2L 14s 3L 14s ↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Descends from 2L 7s (balzano)
Ancestor's step ratio range 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¢)

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.

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