13L 2s

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↖ 12L 1s ↑13L 1s 14L 1s ↗
← 12L 2s13L 2s 14L 2s →
↙ 12L 3s ↓13L 3s 14L 3s ↘
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐
│║║║║║║║│║║║║║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLsLLLLLLs
sLLLLLLsLLLLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 8\15 to 7\13 (640.0¢ to 646.2¢)
Dark 6\13 to 7\15 (553.8¢ to 560.0¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Required step ratio range 3:1 to 4:1 (parahard)
Related MOS scales
Parent 2L 11s
Sister 2L 13s
Daughters 15L 13s, 13L 15s
Neutralized 11L 4s
2-Flought 28L 2s, 13L 17s
Equal tunings
Equalized (L:s = 1:1) 8\15 (640.0¢)
Supersoft (L:s = 4:3) 31\58 (641.4¢)
Soft (L:s = 3:2) 23\43 (641.9¢)
Semisoft (L:s = 5:3) 38\71 (642.3¢)
Basic (L:s = 2:1) 15\28 (642.9¢)
Semihard (L:s = 5:2) 37\69 (643.5¢)
Hard (L:s = 3:1) 22\41 (643.9¢)
Superhard (L:s = 4:1) 29\54 (644.4¢)
Collapsed (L:s = 1:0) 7\13 (646.2¢)

13L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every octave. 13L 2s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 640¢ to 646.2¢, or from 553.8¢ to 560¢. The dark generator for this scale corresponds to a superfourth, intervals sharper than 4/3. This generator has almost no sensible interpretation except to be taken as 11/8, meaning the MOS is an 11+-limit scale.

Scale Tree and Tuning Spectrum of 13L 2s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
8\15 640.000 560.000 1:1 1.000 Equalized 13L 2s
47\88 640.909 559.091 6:5 1.200
39\73 641.096 558.904 5:4 1.250
70\131 641.221 558.779 9:7 1.286
31\58 641.379 558.621 4:3 1.333 Supersoft 13L 2s
85\159 641.509 558.491 11:8 1.375
54\101 641.584 558.416 7:5 1.400
77\144 641.667 558.333 10:7 1.429
23\43 641.860 558.140 3:2 1.500 Soft 13L 2s
84\157 642.038 557.962 11:7 1.571
61\114 642.105 557.895 8:5 1.600
99\185 642.162 557.838 13:8 1.625
38\71 642.254 557.746 5:3 1.667 Semisoft 13L 2s
91\170 642.353 557.647 12:7 1.714
53\99 642.424 557.576 7:4 1.750
68\127 642.520 557.480 9:5 1.800
15\28 642.857 557.143 2:1 2.000 Basic 13L 2s
Scales with tunings softer than this are proper
67\125 643.200 556.800 9:4 2.250
52\97 643.299 556.701 7:3 2.333
89\166 643.373 556.627 12:5 2.400
37\69 643.478 556.522 5:2 2.500 Semihard 13L 2s
96\179 643.575 556.425 13:5 2.600
59\110 643.636 556.364 8:3 2.667
81\151 643.709 556.291 11:4 2.750
22\41 643.902 556.098 3:1 3.000 Hard 13L 2s
73\136 644.118 555.882 10:3 3.333
51\95 644.211 555.789 7:2 3.500
80\149 644.295 555.705 11:3 3.667
29\54 644.444 555.556 4:1 4.000 Superhard 13L 2s
65\121 644.628 555.372 9:2 4.500
36\67 644.776 555.224 5:1 5.000
43\80 645.000 555.000 6:1 6.000
7\13 646.154 553.846 1:0 → ∞ Collapsed 13L 2s