8L 5s
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Scale structure
Step pattern
LLsLLsLsLLsLs
sLsLLsLsLLsLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
8\13 to 5\8 (738.5¢ to 750.0¢)
Dark
3\8 to 5\13 (450.0¢ to 461.5¢)
TAMNAMS information
Descends from
5L 3s (oneirotonic)
Related MOS scales
Parent
5L 3s
Sister
5L 8s
Daughters
13L 8s
8L 13s
Equal tunings
Equalized (L:s = 1:1)
8\13 (738.5¢)
Supersoft (L:s = 4:3)
29\47 (740.4¢)
Soft (L:s = 3:2)
21\34 (741.2¢)
Semisoft (L:s = 5:3)
34\55 (741.8¢)
Basic (L:s = 2:1)
13\21 (742.9¢)
Semihard (L:s = 5:2)
31\50 (744.0¢)
Hard (L:s = 3:1)
18\29 (744.8¢)
Superhard (L:s = 4:1)
23\37 (745.9¢)
Collapsed (L:s = 1:0)
5\8 (750.0¢)
| ↖7L 4s | ↑8L 4s | 9L 4s↗ |
| ←7L 5s | 8L 5s | 9L 5s→ |
| ↙7L 6s | ↓8L 6s | 9L 6s↘ |
┌╥╥┬╥╥┬╥┬╥╥┬╥┬┐ │║║│║║│║│║║│║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLsLLsLsLLsLL
8L 13s
8L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 5 small steps, repeating every octave. 8L 5s is a child scale of 5L 3s, expanding it by 5 tones. Generators that produce this scale range from 738.5¢ to 750¢, or from 450¢ to 461.5¢.
8L 5s represents the chromatic scale of Semidim, Tridec, Ammonite and Petrtri temperaments. It represents tempered chains of the 13:10 or 17:13 semisixth, thus rendering 10:13:17 as an equidistant triad and tempering out 170:169. Also, the ratio between the generator of this MOS and its inverse is close to logarithmic phi, or even logarithmic phi itself.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 12|0 | 1 | LLsLLsLsLLsLs |
| 11|1 | 9 | LLsLsLLsLLsLs |
| 10|2 | 4 | LLsLsLLsLsLLs |
| 9|3 | 12 | LsLLsLLsLsLLs |
| 8|4 | 7 | LsLLsLsLLsLLs |
| 7|5 | 2 | LsLLsLsLLsLsL |
| 6|6 | 10 | LsLsLLsLLsLsL |
| 5|7 | 5 | LsLsLLsLsLLsL |
| 4|8 | 13 | sLLsLLsLsLLsL |
| 3|9 | 8 | sLLsLsLLsLLsL |
| 2|10 | 3 | sLLsLsLLsLsLL |
| 1|11 | 11 | sLsLLsLLsLsLL |
| 0|12 | 6 | sLsLLsLsLLsLL |
Scale tree
| Generator (in steps of edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 8\13 | 738.462 | 461.538 | 1:1 | 1.000 | Equalized 8L 5s | |||||
| 45\73 | 739.726 | 460.274 | 6:5 | 1.200 | ||||||
| 37\60 | 740.000 | 460.000 | 5:4 | 1.250 | ||||||
| 66\107 | 740.187 | 459.813 | 9:7 | 1.286 | ||||||
| 29\47 | 740.426 | 459.574 | 4:3 | 1.333 | Supersoft 8L 5s | |||||
| 79\128 | 740.625 | 459.375 | 11:8 | 1.375 | ||||||
| 50\81 | 740.741 | 459.259 | 7:5 | 1.400 | ||||||
| 71\115 | 740.870 | 459.130 | 10:7 | 1.429 | ||||||
| 21\34 | 741.176 | 458.824 | 3:2 | 1.500 | Soft 8L 5s | |||||
| 76\123 | 741.463 | 458.537 | 11:7 | 1.571 | ||||||
| 55\89 | 741.573 | 458.427 | 8:5 | 1.600 | ||||||
| 89\144 | 741.667 | 458.333 | 13:8 | 1.625 | ||||||
| 34\55 | 741.818 | 458.182 | 5:3 | 1.667 | Semisoft 8L 5s | |||||
| 81\131 | 741.985 | 458.015 | 12:7 | 1.714 | ||||||
| 47\76 | 742.105 | 457.895 | 7:4 | 1.750 | ||||||
| 60\97 | 742.268 | 457.732 | 9:5 | 1.800 | ||||||
| 13\21 | 742.857 | 457.143 | 2:1 | 2.000 | Basic 8L 5s Scales with tunings softer than this are proper | |||||
| 57\92 | 743.478 | 456.522 | 9:4 | 2.250 | ||||||
| 44\71 | 743.662 | 456.338 | 7:3 | 2.333 | ||||||
| 75\121 | 743.802 | 456.198 | 12:5 | 2.400 | ||||||
| 31\50 | 744.000 | 456.000 | 5:2 | 2.500 | Semihard 8L 5s | |||||
| 80\129 | 744.186 | 455.814 | 13:5 | 2.600 | ||||||
| 49\79 | 744.304 | 455.696 | 8:3 | 2.667 | ||||||
| 67\108 | 744.444 | 455.556 | 11:4 | 2.750 | ||||||
| 18\29 | 744.828 | 455.172 | 3:1 | 3.000 | Hard 8L 5s | |||||
| 59\95 | 745.263 | 454.737 | 10:3 | 3.333 | ||||||
| 41\66 | 745.455 | 454.545 | 7:2 | 3.500 | ||||||
| 64\103 | 745.631 | 454.369 | 11:3 | 3.667 | ||||||
| 23\37 | 745.946 | 454.054 | 4:1 | 4.000 | Superhard 8L 5s | |||||
| 51\82 | 746.341 | 453.659 | 9:2 | 4.500 | ||||||
| 28\45 | 746.667 | 453.333 | 5:1 | 5.000 | ||||||
| 33\53 | 747.170 | 452.830 | 6:1 | 6.000 | ||||||
| 5\8 | 750.000 | 450.000 | 1:0 | → ∞ | Collapsed 8L 5s | |||||