13L 8s

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↖ 12L 7s↑ 13L 7s 14L 7s ↗
← 12L 8s13L 8s14L 8s →
↙ 12L 9s↓ 13L 9s 14L 9s ↘
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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¢)

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

Modes of 13L 8s
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

Scale Tree and Tuning Spectrum of 13L 8s
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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