13L 5s

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↖ 12L 4s ↑13L 4s 14L 4s ↗
← 12L 5s13L 5s 14L 5s →
↙ 12L 6s ↓13L 6s 14L 6s ↘
┌╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║║│║║│║║║│║║││
││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLsLLLsLLs
sLLsLLLsLLsLLLsLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 11\18 to 8\13 (733.3¢ to 738.5¢)
Dark 5\13 to 7\18 (461.5¢ to 466.7¢)
TAMNAMS information
Descends from 5L 3s (oneirotonic)
Required step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 5L 8s
Sister 5L 13s
Daughters 18L 13s, 13L 18s
Neutralized 8L 10s
2-Flought 31L 5s, 13L 23s
Equal tunings
Equalized (L:s = 1:1) 11\18 (733.3¢)
Supersoft (L:s = 4:3) 41\67 (734.3¢)
Soft (L:s = 3:2) 30\49 (734.7¢)
Semisoft (L:s = 5:3) 49\80 (735.0¢)
Basic (L:s = 2:1) 19\31 (735.5¢)
Semihard (L:s = 5:2) 46\75 (736.0¢)
Hard (L:s = 3:1) 27\44 (736.4¢)
Superhard (L:s = 4:1) 35\57 (736.8¢)
Collapsed (L:s = 1:0) 8\13 (738.5¢)

13L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 5 small steps, repeating every octave. 13L 5s is a grandchild scale of 5L 3s, expanding it by 10 tones. Generators that produce this scale range from 733.3¢ to 738.5¢, or from 461.5¢ to 466.7¢.

Modes

Modes of 13L 5s
UDP Rotational order Step pattern
17|0 1 LLLsLLLsLLsLLLsLLs
16|1 12 LLLsLLsLLLsLLLsLLs
15|2 5 LLLsLLsLLLsLLsLLLs
14|3 16 LLsLLLsLLLsLLsLLLs
13|4 9 LLsLLLsLLsLLLsLLLs
12|5 2 LLsLLLsLLsLLLsLLsL
11|6 13 LLsLLsLLLsLLLsLLsL
10|7 6 LLsLLsLLLsLLsLLLsL
9|8 17 LsLLLsLLLsLLsLLLsL
8|9 10 LsLLLsLLsLLLsLLLsL
7|10 3 LsLLLsLLsLLLsLLsLL
6|11 14 LsLLsLLLsLLLsLLsLL
5|12 7 LsLLsLLLsLLsLLLsLL
4|13 18 sLLLsLLLsLLsLLLsLL
3|14 11 sLLLsLLsLLLsLLLsLL
2|15 4 sLLLsLLsLLLsLLsLLL
1|16 15 sLLsLLLsLLLsLLsLLL
0|17 8 sLLsLLLsLLsLLLsLLL

Scale tree

Scale Tree and Tuning Spectrum of 13L 5s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
11\18 733.333 466.667 1:1 1.000 Equalized 13L 5s
63\103 733.981 466.019 6:5 1.200
52\85 734.118 465.882 5:4 1.250
93\152 734.211 465.789 9:7 1.286
41\67 734.328 465.672 4:3 1.333 Supersoft 13L 5s
112\183 734.426 465.574 11:8 1.375
71\116 734.483 465.517 7:5 1.400
101\165 734.545 465.455 10:7 1.429
30\49 734.694 465.306 3:2 1.500 Soft 13L 5s
109\178 734.831 465.169 11:7 1.571
79\129 734.884 465.116 8:5 1.600
128\209 734.928 465.072 13:8 1.625
49\80 735.000 465.000 5:3 1.667 Semisoft 13L 5s
117\191 735.079 464.921 12:7 1.714
68\111 735.135 464.865 7:4 1.750
87\142 735.211 464.789 9:5 1.800
19\31 735.484 464.516 2:1 2.000 Basic 13L 5s
Scales with tunings softer than this are proper
84\137 735.766 464.234 9:4 2.250
65\106 735.849 464.151 7:3 2.333
111\181 735.912 464.088 12:5 2.400
46\75 736.000 464.000 5:2 2.500 Semihard 13L 5s
119\194 736.082 463.918 13:5 2.600
73\119 736.134 463.866 8:3 2.667
100\163 736.196 463.804 11:4 2.750
27\44 736.364 463.636 3:1 3.000 Hard 13L 5s
89\145 736.552 463.448 10:3 3.333
62\101 736.634 463.366 7:2 3.500
97\158 736.709 463.291 11:3 3.667
35\57 736.842 463.158 4:1 4.000 Superhard 13L 5s
78\127 737.008 462.992 9:2 4.500
43\70 737.143 462.857 5:1 5.000
51\83 737.349 462.651 6:1 6.000
8\13 738.462 461.538 1:0 → ∞ Collapsed 13L 5s
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