3L 9s
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Scale structure
Step pattern
LsssLsssLsss
sssLsssLsssL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
3\12 to 1\3 (300.0¢ to 400.0¢)
Dark
0\3 to 1\12 (0.0¢ to 100.0¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Required step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
3L 6s
Sister
9L 3s
Daughters
12L 3s
3L 12s
Equal tunings
Equalized (L:s = 1:1)
3\12 (300.0¢)
Supersoft (L:s = 4:3)
10\39 (307.7¢)
Soft (L:s = 3:2)
7\27 (311.1¢)
Semisoft (L:s = 5:3)
11\42 (314.3¢)
Basic (L:s = 2:1)
4\15 (320.0¢)
Semihard (L:s = 5:2)
9\33 (327.3¢)
Hard (L:s = 3:1)
5\18 (333.3¢)
Superhard (L:s = 4:1)
6\21 (342.9¢)
Collapsed (L:s = 1:0)
1\3 (400.0¢)
Todo: review
Adopt scale tree template, review entries
| ↖2L 8s | ↑3L 8s | 4L 8s↗ |
| ←2L 9s | 3L 9s | 4L 9s→ |
| ↙2L 10s | ↓3L 10s | 4L 10s↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬┐ │║│││║│││║││││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLsssL
3L 12s
3L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 9 small steps, with a period of 1 large step and 3 small steps that repeats every 400.0¢, or 3 times every octave. 3L 9s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 300¢ to 400¢, or from 0¢ to 100¢.
This MOS represents, among other chromatic scales, that of the Augene temperament.
Modes
- 9|0(3) LsssLsssLsss
- 6|3(3) sLsssLsssLss
- 3|6(3) ssLsssLsssLs
- 0|9(3) sssLsssLsssL
Scale tree
Generator ranges:
- Chroma-positive generator: 300 cents (3\12) to 400 cents (1\3)
- Chroma-negative generator: 0 cents (0\3) to 100 cents (1\12)
| Small step (chroma-negative generator) |
Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1\12 | 100.000 | 1 | 1 | 1.000 | ||||||
| 5\63 | 95.238 | 6 | 5 | 1.200 | Misty/fog | |||||
| 4\51 | 94.118 | 5 | 4 | 1.250 | ||||||
| 7\90 | 93.333 | 9 | 7 | 1.286 | ||||||
| 3\39 | 92.308 | 4 | 3 | 1.333 | ||||||
| 8\105 | 91.429 | 11 | 8 | 1.375 | ||||||
| 5\66 | 90.909 | 7 | 5 | 1.400 | ||||||
| 7\93 | 90.323 | 10 | 7 | 1.429 | ||||||
| 2\27 | 88.889 | 3 | 2 | 1.500 | Augene is around here | |||||
| 7\96 | 87.500 | 11 | 7 | 1.571 | ||||||
| 5\69 | 86.957 | 8 | 5 | 1.600 | ||||||
| 8\111 | 86.486 | 13 | 8 | 1.625 | Golden augene (86.6169¢) | |||||
| 3\42 | 85.714 | 5 | 3 | 1.667 | ||||||
| 7\99 | 84.848 | 12 | 7 | 1.714 | ||||||
| 4\57 | 84.211 | 7 | 4 | 1.750 | ||||||
| 5\72 | 83.333 | 9 | 5 | 1.800 | ||||||
| 1\15 | 80.000 | 2 | 1 | 2.000 | Basic 3L 9s (Generators larger than this are proper) | |||||
| 4\63 | 76.190 | 9 | 4 | 2.250 | ||||||
| 3\48 | 75.000 | 7 | 3 | 2.333 | ||||||
| 5\81 | 74.074 | 12 | 5 | 2.400 | ||||||
| 2\33 | 72.727 | 5 | 2 | 2.500 | Inflated is around here | |||||
| 5\84 | 71.429 | 13 | 5 | 2.600 | Golden inflated (71.1993¢) | |||||
| 3\51 | 70.588 | 8 | 3 | 2.667 | ||||||
| 4\69 | 69.565 | 11 | 4 | 2.750 | ||||||
| 1\18 | 66.667 | 3 | 1 | 3.000 | ||||||
| 3\57 | 63.158 | 10 | 3 | 3.333 | ||||||
| 2\39 | 61.538 | 7 | 2 | 3.500 | ||||||
| 3\60 | 60.000 | 11 | 3 | 3.667 | ||||||
| 1\21 | 57.143 | 4 | 1 | 4.000 | ||||||
| 2\45 | 53.333 | 9 | 2 | 4.500 | ||||||
| 1\24 | 50.000 | 5 | 1 | 5.000 | ||||||
| 1\27 | 44.444 | 6 | 1 | 6.000 | Hemiaug | |||||
| 0\3 | 0 | 1 | 0 | → inf | ||||||