13L 8s
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Scale structure
Step pattern
LLsLLsLsLLsLLsLsLLsLs
sLsLLsLsLLsLLsLsLLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
8\21 to 5\13 (457.1¢ to 461.5¢)
Dark
8\13 to 13\21 (738.5¢ to 742.9¢)
TAMNAMS information
Descends from
5L 3s (oneirotonic)
Ancestor's step ratio range
3:2 to 2:1 (hyposoft)
Related MOS scales
Parent
8L 5s
Sister
8L 13s
Daughters
21L 13s, 13L 21s
Neutralized
5L 16s
2-Flought
34L 8s, 13L 29s
Equal tunings
Equalized (L:s = 1:1)
8\21 (457.1¢)
Supersoft (L:s = 4:3)
29\76 (457.9¢)
Soft (L:s = 3:2)
21\55 (458.2¢)
Semisoft (L:s = 5:3)
34\89 (458.4¢)
Basic (L:s = 2:1)
13\34 (458.8¢)
Semihard (L:s = 5:2)
31\81 (459.3¢)
Hard (L:s = 3:1)
18\47 (459.6¢)
Superhard (L:s = 4:1)
23\60 (460.0¢)
Collapsed (L:s = 1:0)
5\13 (461.5¢)
↖ 12L 7s | ↑ 13L 7s | 14L 7s ↗ |
← 12L 8s | 13L 8s | 14L 8s → |
↙ 12L 9s | ↓ 13L 9s | 14L 9s ↘ |
┌╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║║│║│║║│║║│║│║║│║││ │││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLsLLsLLsLsLLsLL
13L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 8 small steps, repeating every octave. 13L 8s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 457.1¢ to 461.5¢, or from 738.5¢ to 742.9¢.
Modes
UDP | Cyclic Order |
Step Pattern |
---|---|---|
20|0 | 1 | LLsLLsLsLLsLLsLsLLsLs |
19|1 | 9 | LLsLLsLsLLsLsLLsLLsLs |
18|2 | 17 | LLsLsLLsLLsLsLLsLLsLs |
17|3 | 4 | LLsLsLLsLLsLsLLsLsLLs |
16|4 | 12 | LLsLsLLsLsLLsLLsLsLLs |
15|5 | 20 | LsLLsLLsLsLLsLLsLsLLs |
14|6 | 7 | LsLLsLLsLsLLsLsLLsLLs |
13|7 | 15 | LsLLsLsLLsLLsLsLLsLLs |
12|8 | 2 | LsLLsLsLLsLLsLsLLsLsL |
11|9 | 10 | LsLLsLsLLsLsLLsLLsLsL |
10|10 | 18 | LsLsLLsLLsLsLLsLLsLsL |
9|11 | 5 | LsLsLLsLLsLsLLsLsLLsL |
8|12 | 13 | LsLsLLsLsLLsLLsLsLLsL |
7|13 | 21 | sLLsLLsLsLLsLLsLsLLsL |
6|14 | 8 | sLLsLLsLsLLsLsLLsLLsL |
5|15 | 16 | sLLsLsLLsLLsLsLLsLLsL |
4|16 | 3 | sLLsLsLLsLLsLsLLsLsLL |
3|17 | 11 | sLLsLsLLsLsLLsLLsLsLL |
2|18 | 19 | sLsLLsLLsLsLLsLLsLsLL |
1|19 | 6 | sLsLLsLLsLsLLsLsLLsLL |
0|20 | 14 | sLsLLsLsLLsLLsLsLLsLL |
Scale tree
Generator(edo) | Cents | Step Ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
8\21 | 457.143 | 742.857 | 1:1 | 1.000 | Equalized 13L 8s | |||||
45\118 | 457.627 | 742.373 | 6:5 | 1.200 | ||||||
37\97 | 457.732 | 742.268 | 5:4 | 1.250 | ||||||
66\173 | 457.803 | 742.197 | 9:7 | 1.286 | ||||||
29\76 | 457.895 | 742.105 | 4:3 | 1.333 | Supersoft 13L 8s | |||||
79\207 | 457.971 | 742.029 | 11:8 | 1.375 | ||||||
50\131 | 458.015 | 741.985 | 7:5 | 1.400 | ||||||
71\186 | 458.065 | 741.935 | 10:7 | 1.429 | ||||||
21\55 | 458.182 | 741.818 | 3:2 | 1.500 | Soft 13L 8s | |||||
76\199 | 458.291 | 741.709 | 11:7 | 1.571 | ||||||
55\144 | 458.333 | 741.667 | 8:5 | 1.600 | ||||||
89\233 | 458.369 | 741.631 | 13:8 | 1.625 | ||||||
34\89 | 458.427 | 741.573 | 5:3 | 1.667 | Semisoft 13L 8s | |||||
81\212 | 458.491 | 741.509 | 12:7 | 1.714 | ||||||
47\123 | 458.537 | 741.463 | 7:4 | 1.750 | ||||||
60\157 | 458.599 | 741.401 | 9:5 | 1.800 | ||||||
13\34 | 458.824 | 741.176 | 2:1 | 2.000 | Basic 13L 8s Scales with tunings softer than this are proper | |||||
57\149 | 459.060 | 740.940 | 9:4 | 2.250 | ||||||
44\115 | 459.130 | 740.870 | 7:3 | 2.333 | ||||||
75\196 | 459.184 | 740.816 | 12:5 | 2.400 | ||||||
31\81 | 459.259 | 740.741 | 5:2 | 2.500 | Semihard 13L 8s | |||||
80\209 | 459.330 | 740.670 | 13:5 | 2.600 | ||||||
49\128 | 459.375 | 740.625 | 8:3 | 2.667 | ||||||
67\175 | 459.429 | 740.571 | 11:4 | 2.750 | ||||||
18\47 | 459.574 | 740.426 | 3:1 | 3.000 | Hard 13L 8s | |||||
59\154 | 459.740 | 740.260 | 10:3 | 3.333 | ||||||
41\107 | 459.813 | 740.187 | 7:2 | 3.500 | ||||||
64\167 | 459.880 | 740.120 | 11:3 | 3.667 | ||||||
23\60 | 460.000 | 740.000 | 4:1 | 4.000 | Superhard 13L 8s | |||||
51\133 | 460.150 | 739.850 | 9:2 | 4.500 | ||||||
28\73 | 460.274 | 739.726 | 5:1 | 5.000 | ||||||
33\86 | 460.465 | 739.535 | 6:1 | 6.000 | ||||||
5\13 | 461.538 | 738.462 | 1:0 | → ∞ | Collapsed 13L 8s |
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