13L 2s
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Scale structure
Step pattern
LLLLLLLsLLLLLLs
sLLLLLLsLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Step size
Large
1\15 to 1\13 (80.0¢ to 92.3¢)
Small
0\13 to 1\15 (0.0¢ to 80.0¢)
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)
Related MOS scales
Parent
2L 11s
Sister
2L 13s
Daughters
15L 13s
13L 15s
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¢)
| ↖12L 1s | ↑13L 1s | 14L 1s↗ |
| ←12L 2s | 13L 2s | 14L 2s→ |
| ↙12L 3s | ↓13L 3s | 14L 3s↘ |
┌╥╥╥╥╥╥╥┬╥╥╥╥╥╥┬┐ │║║║║║║║│║║║║║║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLsLLLLLLL
13L 15s
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.
| Generator (in steps of 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 | |||||