3L 16s
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Scale structure
Step pattern
LsssssLsssssLssssss
ssssssLsssssLsssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\19 to 1\3 (378.9¢ to 400.0¢)
Dark
2\3 to 13\19 (800.0¢ to 821.1¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Required step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
3L 13s
Sister
16L 3s
Daughters
19L 3s
3L 19s
Equal tunings
Equalized (L:s = 1:1)
6\19 (378.9¢)
Supersoft (L:s = 4:3)
19\60 (380.0¢)
Soft (L:s = 3:2)
13\41 (380.5¢)
Semisoft (L:s = 5:3)
20\63 (381.0¢)
Basic (L:s = 2:1)
7\22 (381.8¢)
Semihard (L:s = 5:2)
15\47 (383.0¢)
Hard (L:s = 3:1)
8\25 (384.0¢)
Superhard (L:s = 4:1)
9\28 (385.7¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
Todo: review
Adopt scale tree template, review entries
| ↖2L 15s | ↑3L 15s | 4L 15s↗ |
| ←2L 16s | 3L 16s | 4L 16s→ |
| ↙2L 17s | ↓3L 17s | 4L 17s↘ |
┌╥┬┬┬┬┬╥┬┬┬┬┬╥┬┬┬┬┬┬┐ │║│││││║│││││║│││││││ │││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssssLsssssLsssssL
3L 19s
3L 16s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 16 small steps, repeating every octave. 3L 16s is a great-grandchild scale of 3L 7s, expanding it by 9 tones. Generators that produce this scale range from 378.9¢ to 400¢, or from 800¢ to 821.1¢.
This scale is associated with magic temperament, where 5 bright generators maps to 3/1, and würschmidt temperament, where the generator is 5/4.
Modes
- 18|0 LsssssLsssssLssssss
- 17|1 LsssssLssssssLsssss
- 16|2 LssssssLsssssLsssss
- 15|3 sLsssssLsssssLsssss
- 14|4 sLsssssLssssssLssss
- 13|5 sLssssssLsssssLssss
- 12|6 ssLsssssLsssssLssss
- 11|7 ssLsssssLssssssLsss
- 10|8 ssLssssssLsssssLsss
- 9|9 sssLsssssLsssssLsss
- 8|10 sssLsssssLssssssLss
- 7|11 sssLssssssLsssssLss
- 6|12 ssssLsssssLsssssLss
- 5|13 ssssLsssssLssssssLs
- 4|14 ssssLssssssLsssssLs
- 3|15 sssssLsssssLsssssLs
- 2|16 sssssLsssssLssssssL
- 1|17 sssssLssssssLsssssL
- 0|18 ssssssLsssssLsssssL
Scales tree
Generator ranges:
- Bright generator: 378.9474 cents (6\19) to 400 cents (1\3)
- Dark generator: 800 cents (2\3) to 821.0526 cents (13\19)
| Bright generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 6\19 | 378.947 | 1 | 1 | 1.000 | ||||||
| 31\98 | 379.592 | 6 | 5 | 1.200 | ||||||
| 25\79 | 379.747 | 5 | 4 | 1.250 | ||||||
| 44\139 | 379.856 | 9 | 7 | 1.286 | ||||||
| 19\60 | 380.000 | 4 | 3 | 1.333 | ||||||
| 51\161 | 380.124 | 11 | 8 | 1.375 | Witchcraft | |||||
| 32\101 | 380.198 | 7 | 5 | 1.400 | ||||||
| 45\142 | 380.282 | 10 | 7 | 1.429 | ||||||
| 13\41 | 380.488 | 3 | 2 | 1.500 | Magic is around here | |||||
| 46\145 | 380.690 | 11 | 7 | 1.571 | ||||||
| 33\104 | 380.769 | 8 | 5 | 1.600 | ||||||
| 53\167 | 380.838 | 13 | 8 | 1.625 | Necromancy Golden magic (380.8191¢) | |||||
| 20\63 | 380.952 | 5 | 3 | 1.667 | ||||||
| 47\148 | 381.081 | 12 | 7 | 1.714 | ||||||
| 27\85 | 381.176 | 7 | 4 | 1.750 | ||||||
| 34\107 | 381.308 | 9 | 5 | 1.800 | ||||||
| 7\22 | 381.818 | 2 | 1 | 2.000 | Basic 3L 16s (Generators smaller than this are proper) | |||||
| 29\91 | 382.418 | 9 | 4 | 2.250 | ||||||
| 22\69 | 382.609 | 7 | 3 | 2.333 | Marveltri | |||||
| 37\116 | 382.759 | 12 | 5 | 2.400 | Marveltri | |||||
| 15\47 | 382.979 | 5 | 2 | 2.500 | Marveltri | |||||
| 38\119 | 383.193 | 13 | 5 | 2.600 | Unnamed golden tuning (383.2314¢) | |||||
| 23\72 | 383.333 | 8 | 3 | 2.667 | ||||||
| 31\97 | 383.505 | 11 | 4 | 2.750 | ||||||
| 8\25 | 384.000 | 3 | 1 | 3.000 | ||||||
| 25\78 | 384.615 | 10 | 3 | 3.333 | ||||||
| 17\53 | 384.906 | 7 | 2 | 3.500 | ||||||
| 26\81 | 385.185 | 11 | 3 | 3.667 | ||||||
| 9\28 | 385.714 | 4 | 1 | 4.000 | ||||||
| 19\59 | 386.441 | 9 | 2 | 4.500 | Sulis | |||||
| 10\31 | 387.097 | 5 | 1 | 5.000 | Grendel/Würschmidt | |||||
| 11\34 | 388.235 | 6 | 1 | 6.000 | ||||||
| 1\3 | 400.000 | 1 | 0 | → inf | ||||||