9L 3s
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Step pattern
LLLsLLLsLLLs
sLLLsLLLsLLL
Equave
2/1 (1200.0 ¢)
Period
1\3 (400.0 ¢)
Bright
1\12 to 1\9 (100.0 ¢ to 133.3 ¢)
Dark
2\9 to 3\12 (266.7 ¢ to 300.0 ¢)
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Parent
3L 6s
Sister
3L 9s
Daughters
12L 9s, 9L 12s
Neutralized
6L 6s
2-Flought
21L 3s, 9L 15s
Equalized (L:s = 1:1)
1\12 (100.0 ¢)
Supersoft (L:s = 4:3)
4\45 (106.7 ¢)
Soft (L:s = 3:2)
3\33 (109.1 ¢)
Semisoft (L:s = 5:3)
5\54 (111.1 ¢)
Basic (L:s = 2:1)
2\21 (114.3 ¢)
Semihard (L:s = 5:2)
5\51 (117.6 ¢)
Hard (L:s = 3:1)
3\30 (120.0 ¢)
Superhard (L:s = 4:1)
4\39 (123.1 ¢)
Collapsed (L:s = 1:0)
1\9 (133.3 ¢)
| ↖ 8L 2s | ↑ 9L 2s | 10L 2s ↗ |
| ← 8L 3s | 9L 3s | 10L 3s → |
| ↙ 8L 4s | ↓ 9L 4s | 10L 4s ↘ |
┌╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLLsLLLsLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
9L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 3 small steps, with a period of 3 large steps and 1 small step that repeats every 400.0 ¢, or 3 times every octave. 9L 3s is a child scale of 3L 6s, expanding it by 3 tones. Generators that produce this scale range from 100 ¢ to 133.3 ¢, or from 266.7 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
9L 3s represents the chromatic scale of August temperament and its higher-limit extensions.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
{{subst:MOS data temporary}}
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\12 | 100.000 | 300.000 | 1:1 | 1.000 | Equalized 9L 3s | |||||
| 6\69 | 104.348 | 295.652 | 6:5 | 1.200 | ||||||
| 5\57 | 105.263 | 294.737 | 5:4 | 1.250 | ||||||
| 9\102 | 105.882 | 294.118 | 9:7 | 1.286 | ||||||
| 4\45 | 106.667 | 293.333 | 4:3 | 1.333 | Supersoft 9L 3s | |||||
| 11\123 | 107.317 | 292.683 | 11:8 | 1.375 | ||||||
| 7\78 | 107.692 | 292.308 | 7:5 | 1.400 | August | |||||
| 10\111 | 108.108 | 291.892 | 10:7 | 1.429 | ||||||
| 3\33 | 109.091 | 290.909 | 3:2 | 1.500 | Soft 9L 3s | |||||
| 11\120 | 110.000 | 290.000 | 11:7 | 1.571 | ||||||
| 8\87 | 110.345 | 289.655 | 8:5 | 1.600 | ||||||
| 13\141 | 110.638 | 289.362 | 13:8 | 1.625 | ||||||
| 5\54 | 111.111 | 288.889 | 5:3 | 1.667 | Semisoft 9L 3s | |||||
| 12\129 | 111.628 | 288.372 | 12:7 | 1.714 | ||||||
| 7\75 | 112.000 | 288.000 | 7:4 | 1.750 | ||||||
| 9\96 | 112.500 | 287.500 | 9:5 | 1.800 | 11-limit August | |||||
| 2\21 | 114.286 | 285.714 | 2:1 | 2.000 | Basic 9L 3s 13-limit August | |||||
| 9\93 | 116.129 | 283.871 | 9:4 | 2.250 | ||||||
| 7\72 | 116.667 | 283.333 | 7:3 | 2.333 | ||||||
| 12\123 | 117.073 | 282.927 | 12:5 | 2.400 | ||||||
| 5\51 | 117.647 | 282.353 | 5:2 | 2.500 | Semihard 9L 3s | |||||
| 13\132 | 118.182 | 281.818 | 13:5 | 2.600 | ||||||
| 8\81 | 118.519 | 281.481 | 8:3 | 2.667 | ||||||
| 11\111 | 118.919 | 281.081 | 11:4 | 2.750 | ||||||
| 3\30 | 120.000 | 280.000 | 3:1 | 3.000 | Hard 9L 3s | |||||
| 10\99 | 121.212 | 278.788 | 10:3 | 3.333 | ||||||
| 7\69 | 121.739 | 278.261 | 7:2 | 3.500 | ||||||
| 11\108 | 122.222 | 277.778 | 11:3 | 3.667 | ||||||
| 4\39 | 123.077 | 276.923 | 4:1 | 4.000 | Superhard 9L 3s | |||||
| 9\87 | 124.138 | 275.862 | 9:2 | 4.500 | ||||||
| 5\48 | 125.000 | 275.000 | 5:1 | 5.000 | ||||||
| 6\57 | 126.316 | 273.684 | 6:1 | 6.000 | ||||||
| 1\9 | 133.333 | 266.667 | 1:0 | → ∞ | Collapsed 9L 3s | |||||
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