13L 10s
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Scale structure
Step pattern
LLsLsLsLLsLsLsLLsLsLsLs
sLsLsLsLLsLsLsLLsLsLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
7\23 to 4\13 (365.2¢ to 369.2¢)
Dark
9\13 to 16\23 (830.8¢ to 834.8¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Required step ratio range
3:2 to 2:1 (hyposoft)
Related MOS scales
Parent
10L 3s
Sister
10L 13s
Daughters
23L 13s
13L 23s
Equal tunings
Equalized (L:s = 1:1)
7\23 (365.2¢)
Supersoft (L:s = 4:3)
25\82 (365.9¢)
Soft (L:s = 3:2)
18\59 (366.1¢)
Semisoft (L:s = 5:3)
29\95 (366.3¢)
Basic (L:s = 2:1)
11\36 (366.7¢)
Semihard (L:s = 5:2)
26\85 (367.1¢)
Hard (L:s = 3:1)
15\49 (367.3¢)
Superhard (L:s = 4:1)
19\62 (367.7¢)
Collapsed (L:s = 1:0)
4\13 (369.2¢)
Todo: confirm
Confirm temperaments that correspond with this mos
| ↖12L 9s | ↑13L 9s | 14L 9s↗ |
| ←12L 10s | 13L 10s | 14L 10s→ |
| ↙12L 11s | ↓13L 11s | 14L 11s↘ |
┌╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬┐ │║║│║│║│║║│║│║│║║│║│║│║││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLsLsLLsLsLsLLsLsLsLL
13L 23s
13L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 10 small steps, repeating every octave. 13L 10s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 365.2¢ to 369.2¢, or from 830.8¢ to 834.8¢.
This scale is the quartertone scale of unidec temperament.
Scale tree
| Generator (edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\23 | 365.217 | 834.783 | 1:1 | 1.000 | Equalized 13L 10s | |||||
| 39\128 | 365.625 | 834.375 | 6:5 | 1.200 | ||||||
| 32\105 | 365.714 | 834.286 | 5:4 | 1.250 | ||||||
| 57\187 | 365.775 | 834.225 | 9:7 | 1.286 | ||||||
| 25\82 | 365.854 | 834.146 | 4:3 | 1.333 | Supersoft 13L 10s | |||||
| 68\223 | 365.919 | 834.081 | 11:8 | 1.375 | ||||||
| 43\141 | 365.957 | 834.043 | 7:5 | 1.400 | ||||||
| 61\200 | 366.000 | 834.000 | 10:7 | 1.429 | ||||||
| 18\59 | 366.102 | 833.898 | 3:2 | 1.500 | Soft 13L 10s | |||||
| 65\213 | 366.197 | 833.803 | 11:7 | 1.571 | ||||||
| 47\154 | 366.234 | 833.766 | 8:5 | 1.600 | ||||||
| 76\249 | 366.265 | 833.735 | 13:8 | 1.625 | ||||||
| 29\95 | 366.316 | 833.684 | 5:3 | 1.667 | Semisoft 13L 10s | |||||
| 69\226 | 366.372 | 833.628 | 12:7 | 1.714 | ||||||
| 40\131 | 366.412 | 833.588 | 7:4 | 1.750 | ||||||
| 51\167 | 366.467 | 833.533 | 9:5 | 1.800 | ||||||
| 11\36 | 366.667 | 833.333 | 2:1 | 2.000 | Basic 13L 10s Scales with tunings softer than this are proper | |||||
| 48\157 | 366.879 | 833.121 | 9:4 | 2.250 | ||||||
| 37\121 | 366.942 | 833.058 | 7:3 | 2.333 | ||||||
| 63\206 | 366.990 | 833.010 | 12:5 | 2.400 | ||||||
| 26\85 | 367.059 | 832.941 | 5:2 | 2.500 | Semihard 13L 10s | |||||
| 67\219 | 367.123 | 832.877 | 13:5 | 2.600 | ||||||
| 41\134 | 367.164 | 832.836 | 8:3 | 2.667 | ||||||
| 56\183 | 367.213 | 832.787 | 11:4 | 2.750 | ||||||
| 15\49 | 367.347 | 832.653 | 3:1 | 3.000 | Hard 13L 10s | |||||
| 49\160 | 367.500 | 832.500 | 10:3 | 3.333 | ||||||
| 34\111 | 367.568 | 832.432 | 7:2 | 3.500 | ||||||
| 53\173 | 367.630 | 832.370 | 11:3 | 3.667 | ||||||
| 19\62 | 367.742 | 832.258 | 4:1 | 4.000 | Superhard 13L 10s | |||||
| 42\137 | 367.883 | 832.117 | 9:2 | 4.500 | ||||||
| 23\75 | 368.000 | 832.000 | 5:1 | 5.000 | ||||||
| 27\88 | 368.182 | 831.818 | 6:1 | 6.000 | ||||||
| 4\13 | 369.231 | 830.769 | 1:0 | → ∞ | Collapsed 13L 10s | |||||