8L 3s
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Scale structure
Step pattern
LLLsLLLsLLs
sLLsLLLsLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
4\11 to 3\8 (436.4¢ to 450.0¢)
Dark
5\8 to 7\11 (750.0¢ to 763.6¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Required step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
3L 5s
Sister
3L 8s
Daughters
11L 8s
8L 11s
Equal tunings
Equalized (L:s = 1:1)
4\11 (436.4¢)
Supersoft (L:s = 4:3)
15\41 (439.0¢)
Soft (L:s = 3:2)
11\30 (440.0¢)
Semisoft (L:s = 5:3)
18\49 (440.8¢)
Basic (L:s = 2:1)
7\19 (442.1¢)
Semihard (L:s = 5:2)
17\46 (443.5¢)
Hard (L:s = 3:1)
10\27 (444.4¢)
Superhard (L:s = 4:1)
13\35 (445.7¢)
Collapsed (L:s = 1:0)
3\8 (450.0¢)
Todo: review
Adopt scale tree template, review entries, make pentachordal analysis its own section?
| ↖7L 2s | ↑8L 2s | 9L 2s↗ |
| ←7L 3s | 8L 3s | 9L 3s→ |
| ↙7L 4s | ↓8L 4s | 9L 4s↘ |
┌╥╥╥┬╥╥╥┬╥╥┬┐ │║║║│║║║│║║││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLLsLLL
8L 11s
8L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 3 small steps, repeating every octave. 8L 3s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 436.4¢ to 450¢, or from 750¢ to 763.6¢.
The only significant harmonic entropy minimum with this MOS pattern is sensi, in which the generator is 9/7 and two of them make a 5/3.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 10|0 | 1 | LLLsLLLsLLs |
| 9|1 | 5 | LLLsLLsLLLs |
| 8|2 | 9 | LLsLLLsLLLs |
| 7|3 | 2 | LLsLLLsLLsL |
| 6|4 | 6 | LLsLLsLLLsL |
| 5|5 | 10 | LsLLLsLLLsL |
| 4|6 | 3 | LsLLLsLLsLL |
| 3|7 | 7 | LsLLsLLLsLL |
| 2|8 | 11 | sLLLsLLLsLL |
| 1|9 | 4 | sLLLsLLsLLL |
| 0|10 | 8 | sLLsLLLsLLL |
Scale tree
| Generator | Cents | Pentachord steps | Comments | |||||
|---|---|---|---|---|---|---|---|---|
| 4\11 | 436.364 | 1 1 1 1 | ||||||
| 23\63 | 438.095 | 6 6 6 5 | ||||||
| 19\52 | 438.462 | 5 5 5 4 | ||||||
| 15\41 | 439.024 | 4 4 4 3 | ||||||
| 11\30 | 440 | 3 3 3 2 | Optimum rank range (L/s=3/2) | |||||
| 440.364 | pi pi pi 2 | |||||||
| 29\79 | 440.506 | 8 8 8 5 | ||||||
| 440.592 | phi phi phi 1 | |||||||
| 47\128 | 440.625 | 13 13 13 8 | Unnamed golden temperament | |||||
| 18\49 | 440.816 | 5 5 5 3 | ||||||
| 441.101 | √3 √3 √3 1 | |||||||
| 25\68 | 441.176 | 7 7 7 4 | ||||||
| 7\19 | 442.105 | 2 2 2 1 | Boundary of propriety: generators smaller than this are proper | |||||
| 24\65 | 443.077 | 7 7 7 3 | ||||||
| 17\46 | 443.478 | 5 5 5 2 | Sensi is about here | |||||
| 44\119 | 443.6975 | 13 13 13 5 | Golden Sensi | |||||
| 443.7355 | phi+1 phi+1 phi+1 1 | |||||||
| 27\73 | 443.836 | 8 8 8 3 | ||||||
| 443.9385 | e e e 1 | |||||||
| 10\27 | 444.444 | 3 3 3 1 | ||||||
| 444.668 | pi pi pi 1 | |||||||
| 13\35 | 445.714 | 4 4 4 1 | ||||||
| 16\43 | 446.512 | 5 5 5 1 | ||||||
| 19\51 | 447.059 | 6 6 6 1 | ||||||
| 3\8 | 450 | 1 1 1 0 | ||||||