13L 5s
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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)
Related MOS scales
Parent
5L 8s
Sister
5L 13s
Daughters
18L 13s
13L 18s
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¢)
| ↖12L 4s | ↑13L 4s | 14L 4s↗ |
| ←12L 5s | 13L 5s | 14L 5s→ |
| ↙12L 6s | ↓13L 6s | 14L 6s↘ |
┌╥╥╥┬╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║║│║║│║║║│║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLLsLLsLLLsLLL
13L 18s
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
| 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
| Generator (in steps of 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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