13L 8s

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↖ 12L 7s ↑ 13L 7s 14L 7s ↗
← 12L 8s 13L 8s 14L 8s →
↙ 12L 9s ↓ 13L 9s 14L 9s ↘ 
┌╥╥┬╥╥┬╥┬╥╥┬╥╥┬╥┬╥╥┬╥┬┐
│║║│║║│║│║║│║║│║│║║│║││
│││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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

Intervals

Intervals of 13L 8s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 57.1¢
Major 1-mosstep M1ms L 57.1¢ to 92.3¢
2-mosstep Minor 2-mosstep m2ms L + s 92.3¢ to 114.3¢
Major 2-mosstep M2ms 2L 114.3¢ to 184.6¢
3-mosstep Minor 3-mosstep m3ms L + 2s 92.3¢ to 171.4¢
Major 3-mosstep M3ms 2L + s 171.4¢ to 184.6¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 184.6¢ to 228.6¢
Major 4-mosstep M4ms 3L + s 228.6¢ to 276.9¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 276.9¢ to 285.7¢
Major 5-mosstep M5ms 4L + s 285.7¢ to 369.2¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 276.9¢ to 342.9¢
Major 6-mosstep M6ms 4L + 2s 342.9¢ to 369.2¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 369.2¢ to 400.0¢
Major 7-mosstep M7ms 5L + 2s 400.0¢ to 461.5¢
8-mosstep Diminished 8-mosstep d8ms 4L + 4s 369.2¢ to 457.1¢
Perfect 8-mosstep P8ms 5L + 3s 457.1¢ to 461.5¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 461.5¢ to 514.3¢
Major 9-mosstep M9ms 6L + 3s 514.3¢ to 553.8¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 553.8¢ to 571.4¢
Major 10-mosstep M10ms 7L + 3s 571.4¢ to 646.2¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 553.8¢ to 628.6¢
Major 11-mosstep M11ms 7L + 4s 628.6¢ to 646.2¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 646.2¢ to 685.7¢
Major 12-mosstep M12ms 8L + 4s 685.7¢ to 738.5¢
13-mosstep Perfect 13-mosstep P13ms 8L + 5s 738.5¢ to 742.9¢
Augmented 13-mosstep A13ms 9L + 4s 742.9¢ to 830.8¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 738.5¢ to 800.0¢
Major 14-mosstep M14ms 9L + 5s 800.0¢ to 830.8¢
15-mosstep Minor 15-mosstep m15ms 9L + 6s 830.8¢ to 857.1¢
Major 15-mosstep M15ms 10L + 5s 857.1¢ to 923.1¢
16-mosstep Minor 16-mosstep m16ms 9L + 7s 830.8¢ to 914.3¢
Major 16-mosstep M16ms 10L + 6s 914.3¢ to 923.1¢
17-mosstep Minor 17-mosstep m17ms 10L + 7s 923.1¢ to 971.4¢
Major 17-mosstep M17ms 11L + 6s 971.4¢ to 1015.4¢
18-mosstep Minor 18-mosstep m18ms 11L + 7s 1015.4¢ to 1028.6¢
Major 18-mosstep M18ms 12L + 6s 1028.6¢ to 1107.7¢
19-mosstep Minor 19-mosstep m19ms 11L + 8s 1015.4¢ to 1085.7¢
Major 19-mosstep M19ms 12L + 7s 1085.7¢ to 1107.7¢
20-mosstep Minor 20-mosstep m20ms 12L + 8s 1107.7¢ to 1142.9¢
Major 20-mosstep M20ms 13L + 7s 1142.9¢ to 1200.0¢
21-mosstep Perfect 21-mosstep P21ms 13L + 8s 1200.0¢

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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