8L 13s

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↖7L 12s↑8L 12s 9L 12s↗
←7L 13s8L 13s9L 13s→
↙7L 14s↓8L 14s 9L 14s↘
Brightest mode LsLssLsLssLssLsLssLss
Period 2/1
Range for bright generator 13\21 (742.9¢) to 5\8 (750¢)
Range for dark generator 3\8 (450¢) to 8\21 (457.1¢)
Parent MOS 8L 5s
Sister MOS 13L 8s
Daughter MOSes 21L 8s, 8L 21s
Equal tunings
Supersoft (L:s = 4:3) 44\71 (743.7¢)
Soft (L:s = 3:2) 31\50 (744¢)
Semisoft (L:s = 5:3) 49\79 (744.3¢)
Basic (L:s = 2:1) 18\29 (744.8¢)
Semihard (L:s = 5:2) 41\66 (745.5¢)
Hard (L:s = 3:1) 23\37 (745.9¢)
Superhard (L:s = 4:1) 28\45 (746.7¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

8L 13s is an octave-equivalent moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9¢ to 750¢, or from 450¢ to 457.1¢.

Modes

Modes of 8L 13s
UDP Rotational order Step pattern
20|0 1 LsLssLsLssLssLsLssLss
19|1 14 LsLssLssLsLssLsLssLss
18|2 6 LsLssLssLsLssLssLsLss
17|3 19 LssLsLssLsLssLssLsLss
16|4 11 LssLsLssLssLsLssLsLss
15|5 3 LssLsLssLssLsLssLssLs
14|6 16 LssLssLsLssLsLssLssLs
13|7 8 LssLssLsLssLssLsLssLs
12|8 21 sLsLssLsLssLssLsLssLs
11|9 13 sLsLssLssLsLssLsLssLs
10|10 5 sLsLssLssLsLssLssLsLs
9|11 18 sLssLsLssLsLssLssLsLs
8|12 10 sLssLsLssLssLsLssLsLs
7|13 2 sLssLsLssLssLsLssLssL
6|14 15 sLssLssLsLssLsLssLssL
5|15 7 sLssLssLsLssLssLsLssL
4|16 20 ssLsLssLsLssLssLsLssL
3|17 12 ssLsLssLssLsLssLsLssL
2|18 4 ssLsLssLssLsLssLssLsL
1|19 17 ssLssLsLssLsLssLssLsL
0|20 9 ssLssLsLssLssLsLssLsL

Scale tree

generator L s L/s gen (cents) comment
3\8 1 0 450.000
29\77 8 1 8.000 451.948
26\69 7 1 7.000 452.174
49\130 13 2 6.500 452.308
23\61 6 1 6.000 452.459
43\114 11 2 5.500 452.632
20\53 5 1 5.000 452.830
37\98 9 2 4.500 453.061
54\143 13 3 4.333 453.147
17\45 4 1 4.000 453.333
48\127 11 3 3.667 453.543
31\82 7 2 3.500 453.659
45\119 10 3 3.333 453.782
14\37 3 1 3.000 454.054
53\140 11 4 2.750 454.286
39\103 8 3 2.667 454.369
25\66 5 2 2.500 454.545
36\95 7 3 2.333 454.737
47\124 9 4 2.250 454.839
11\29 2 1 2.000 455.172
52\137 9 5 1.800 455.474
41\108 7 4 1.750 455.556
30\79 5 3 1.667 455.696
49\129 8 5 1.600 455.814
19\50 3 2 1.500 456.000
46\121 7 5 1.400 456.198
27\71 4 3 1.333 456.338
35\92 5 4 1.250 456.522
43\113 6 5 1.200 456.637
51\134 7 6 1.167 456.716
59\155 8 7 1.143 456.774
8\21 1 1 1.000 457.143