10L 13s

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↖ 9L 12s ↑10L 12s 11L 12s ↗
← 9L 13s10L 13s 11L 13s →
↙ 9L 14s ↓10L 14s 11L 14s ↘
┌╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬╥┬╥┬╥┬┬┐
│║│║│║│║││║│║│║││║│║│║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLssLsLsLssLsLsLss
ssLsLsLssLsLsLssLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 16\23 to 7\10 (834.8¢ to 840.0¢)
Dark 3\10 to 7\23 (360.0¢ to 365.2¢)
TAMNAMS information
Descends from 3L 7s (sephiroid)
Ancestor's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 10L 3s
Sister 13L 10s
Daughters 23L 10s, 10L 23s
Neutralized 20L 3s
2-Flought 33L 13s, 10L 36s
Equal tunings
Equalized (L:s = 1:1) 16\23 (834.8¢)
Supersoft (L:s = 4:3) 55\79 (835.4¢)
Soft (L:s = 3:2) 39\56 (835.7¢)
Semisoft (L:s = 5:3) 62\89 (836.0¢)
Basic (L:s = 2:1) 23\33 (836.4¢)
Semihard (L:s = 5:2) 53\76 (836.8¢)
Hard (L:s = 3:1) 30\43 (837.2¢)
Superhard (L:s = 4:1) 37\53 (837.7¢)
Collapsed (L:s = 1:0) 7\10 (840.0¢)

10L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 13 small steps, repeating every octave. 10L 13s is a grandchild scale of 3L 7s, expanding it by 13 tones. Generators that produce this scale range from 834.8¢ to 840¢, or from 360¢ to 365.2¢.

Modes

Modes of 10L 13s
UDP Rotational order Step pattern
22|0 1 LsLsLsLssLsLsLssLsLsLss
21|1 17 LsLsLssLsLsLsLssLsLsLss
20|2 10 LsLsLssLsLsLssLsLsLsLss
19|3 3 LsLsLssLsLsLssLsLsLssLs
18|4 19 LsLssLsLsLsLssLsLsLssLs
17|5 12 LsLssLsLsLssLsLsLsLssLs
16|6 5 LsLssLsLsLssLsLsLssLsLs
15|7 21 LssLsLsLsLssLsLsLssLsLs
14|8 14 LssLsLsLssLsLsLsLssLsLs
13|9 7 LssLsLsLssLsLsLssLsLsLs
12|10 23 sLsLsLsLssLsLsLssLsLsLs
11|11 16 sLsLsLssLsLsLsLssLsLsLs
10|12 9 sLsLsLssLsLsLssLsLsLsLs
9|13 2 sLsLsLssLsLsLssLsLsLssL
8|14 18 sLsLssLsLsLsLssLsLsLssL
7|15 11 sLsLssLsLsLssLsLsLsLssL
6|16 4 sLsLssLsLsLssLsLsLssLsL
5|17 20 sLssLsLsLsLssLsLsLssLsL
4|18 13 sLssLsLsLssLsLsLsLssLsL
3|19 6 sLssLsLsLssLsLsLssLsLsL
2|20 22 ssLsLsLsLssLsLsLssLsLsL
1|21 15 ssLsLsLssLsLsLsLssLsLsL
0|22 8 ssLsLsLssLsLsLssLsLsLsL

Scale tree

Scale Tree and Tuning Spectrum of 10L 13s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
16\23 834.783 365.217 1:1 1.000 Equalized 10L 13s
87\125 835.200 364.800 6:5 1.200
71\102 835.294 364.706 5:4 1.250
126\181 835.359 364.641 9:7 1.286
55\79 835.443 364.557 4:3 1.333 Supersoft 10L 13s
149\214 835.514 364.486 11:8 1.375
94\135 835.556 364.444 7:5 1.400
133\191 835.602 364.398 10:7 1.429
39\56 835.714 364.286 3:2 1.500 Soft 10L 13s
140\201 835.821 364.179 11:7 1.571
101\145 835.862 364.138 8:5 1.600
163\234 835.897 364.103 13:8 1.625
62\89 835.955 364.045 5:3 1.667 Semisoft 10L 13s
147\211 836.019 363.981 12:7 1.714
85\122 836.066 363.934 7:4 1.750
108\155 836.129 363.871 9:5 1.800
23\33 836.364 363.636 2:1 2.000 Basic 10L 13s
Scales with tunings softer than this are proper
99\142 836.620 363.380 9:4 2.250
76\109 836.697 363.303 7:3 2.333
129\185 836.757 363.243 12:5 2.400
53\76 836.842 363.158 5:2 2.500 Semihard 10L 13s
136\195 836.923 363.077 13:5 2.600
83\119 836.975 363.025 8:3 2.667
113\162 837.037 362.963 11:4 2.750
30\43 837.209 362.791 3:1 3.000 Hard 10L 13s
97\139 837.410 362.590 10:3 3.333
67\96 837.500 362.500 7:2 3.500
104\149 837.584 362.416 11:3 3.667
37\53 837.736 362.264 4:1 4.000 Superhard 10L 13s
81\116 837.931 362.069 9:2 4.500
44\63 838.095 361.905 5:1 5.000
51\73 838.356 361.644 6:1 6.000
7\10 840.000 360.000 1:0 → ∞ Collapsed 10L 13s
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