15L 3s
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Scale structure
Step pattern
LLLLLsLLLLLsLLLLLs
sLLLLLsLLLLLsLLLLL
Equave
2/1 (1200.0¢)
Period
1\3 (400.0¢)
Generator size
Bright
1\18 to 1\15 (66.7¢ to 80.0¢)
Dark
4\15 to 5\18 (320.0¢ to 333.3¢)
TAMNAMS information
Descends from
3L 6s (tcherepnin)
Ancestor's step ratio range
3:1 to 4:1 (parahard)
Related MOS scales
Parent
3L 12s
Sister
3L 15s
Daughters
18L 15s, 15L 18s
Neutralized
12L 6s
2-Flought
33L 3s, 15L 21s
Equal tunings
Equalized (L:s = 1:1)
1\18 (66.7¢)
Supersoft (L:s = 4:3)
4\69 (69.6¢)
Soft (L:s = 3:2)
3\51 (70.6¢)
Semisoft (L:s = 5:3)
5\84 (71.4¢)
Basic (L:s = 2:1)
2\33 (72.7¢)
Semihard (L:s = 5:2)
5\81 (74.1¢)
Hard (L:s = 3:1)
3\48 (75.0¢)
Superhard (L:s = 4:1)
4\63 (76.2¢)
Collapsed (L:s = 1:0)
1\15 (80.0¢)
| ↖ 14L 2s | ↑ 15L 2s | 16L 2s ↗ |
| ← 14L 3s | 15L 3s | 16L 3s → |
| ↙ 14L 4s | ↓ 15L 4s | 16L 4s ↘ |
┌╥╥╥╥╥┬╥╥╥╥╥┬╥╥╥╥╥┬┐ │║║║║║│║║║║║│║║║║║││ ││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLsLLLLLsLLLLL
15L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 3 small steps, with a period of 5 large steps and 1 small step that repeats every 400.0¢, or 3 times every octave. 15L 3s is a great-grandchild scale of 3L 6s, expanding it by 9 tones. Generators that produce this scale range from 66.7¢ to 80¢, or from 320¢ to 333.3¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 15|0(3) | 1 | LLLLLsLLLLLsLLLLLs |
| 12|3(3) | 2 | LLLLsLLLLLsLLLLLsL |
| 9|6(3) | 3 | LLLsLLLLLsLLLLLsLL |
| 6|9(3) | 4 | LLsLLLLLsLLLLLsLLL |
| 3|12(3) | 5 | LsLLLLLsLLLLLsLLLL |
| 0|15(3) | 6 | sLLLLLsLLLLLsLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0¢ to 66.7¢ |
| Perfect 1-mosstep | P1ms | L | 66.7¢ to 80.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 80.0¢ to 133.3¢ |
| Major 2-mosstep | M2ms | 2L | 133.3¢ to 160.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 160.0¢ to 200.0¢ |
| Major 3-mosstep | M3ms | 3L | 200.0¢ to 240.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 240.0¢ to 266.7¢ |
| Major 4-mosstep | M4ms | 4L | 266.7¢ to 320.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 4L + s | 320.0¢ to 333.3¢ |
| Augmented 5-mosstep | A5ms | 5L | 333.3¢ to 400.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | 5L + s | 400.0¢ |
| 7-mosstep | Diminished 7-mosstep | d7ms | 5L + 2s | 400.0¢ to 466.7¢ |
| Perfect 7-mosstep | P7ms | 6L + s | 466.7¢ to 480.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 6L + 2s | 480.0¢ to 533.3¢ |
| Major 8-mosstep | M8ms | 7L + s | 533.3¢ to 560.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 560.0¢ to 600.0¢ |
| Major 9-mosstep | M9ms | 8L + s | 600.0¢ to 640.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 640.0¢ to 666.7¢ |
| Major 10-mosstep | M10ms | 9L + s | 666.7¢ to 720.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 9L + 2s | 720.0¢ to 733.3¢ |
| Augmented 11-mosstep | A11ms | 10L + s | 733.3¢ to 800.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 10L + 2s | 800.0¢ |
| 13-mosstep | Diminished 13-mosstep | d13ms | 10L + 3s | 800.0¢ to 866.7¢ |
| Perfect 13-mosstep | P13ms | 11L + 2s | 866.7¢ to 880.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 11L + 3s | 880.0¢ to 933.3¢ |
| Major 14-mosstep | M14ms | 12L + 2s | 933.3¢ to 960.0¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 12L + 3s | 960.0¢ to 1000.0¢ |
| Major 15-mosstep | M15ms | 13L + 2s | 1000.0¢ to 1040.0¢ | |
| 16-mosstep | Minor 16-mosstep | m16ms | 13L + 3s | 1040.0¢ to 1066.7¢ |
| Major 16-mosstep | M16ms | 14L + 2s | 1066.7¢ to 1120.0¢ | |
| 17-mosstep | Perfect 17-mosstep | P17ms | 14L + 3s | 1120.0¢ to 1133.3¢ |
| Augmented 17-mosstep | A17ms | 15L + 2s | 1133.3¢ to 1200.0¢ | |
| 18-mosstep | Perfect 18-mosstep | P18ms | 15L + 3s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\18 | 66.667 | 333.333 | 1:1 | 1.000 | Equalized 15L 3s | |||||
| 6\105 | 68.571 | 331.429 | 6:5 | 1.200 | ||||||
| 5\87 | 68.966 | 331.034 | 5:4 | 1.250 | ||||||
| 9\156 | 69.231 | 330.769 | 9:7 | 1.286 | ||||||
| 4\69 | 69.565 | 330.435 | 4:3 | 1.333 | Supersoft 15L 3s | |||||
| 11\189 | 69.841 | 330.159 | 11:8 | 1.375 | ||||||
| 7\120 | 70.000 | 330.000 | 7:5 | 1.400 | ||||||
| 10\171 | 70.175 | 329.825 | 10:7 | 1.429 | ||||||
| 3\51 | 70.588 | 329.412 | 3:2 | 1.500 | Soft 15L 3s | |||||
| 11\186 | 70.968 | 329.032 | 11:7 | 1.571 | ||||||
| 8\135 | 71.111 | 328.889 | 8:5 | 1.600 | ||||||
| 13\219 | 71.233 | 328.767 | 13:8 | 1.625 | ||||||
| 5\84 | 71.429 | 328.571 | 5:3 | 1.667 | Semisoft 15L 3s | |||||
| 12\201 | 71.642 | 328.358 | 12:7 | 1.714 | ||||||
| 7\117 | 71.795 | 328.205 | 7:4 | 1.750 | ||||||
| 9\150 | 72.000 | 328.000 | 9:5 | 1.800 | ||||||
| 2\33 | 72.727 | 327.273 | 2:1 | 2.000 | Basic 15L 3s | |||||
| 9\147 | 73.469 | 326.531 | 9:4 | 2.250 | ||||||
| 7\114 | 73.684 | 326.316 | 7:3 | 2.333 | ||||||
| 12\195 | 73.846 | 326.154 | 12:5 | 2.400 | ||||||
| 5\81 | 74.074 | 325.926 | 5:2 | 2.500 | Semihard 15L 3s | |||||
| 13\210 | 74.286 | 325.714 | 13:5 | 2.600 | ||||||
| 8\129 | 74.419 | 325.581 | 8:3 | 2.667 | ||||||
| 11\177 | 74.576 | 325.424 | 11:4 | 2.750 | ||||||
| 3\48 | 75.000 | 325.000 | 3:1 | 3.000 | Hard 15L 3s | |||||
| 10\159 | 75.472 | 324.528 | 10:3 | 3.333 | ||||||
| 7\111 | 75.676 | 324.324 | 7:2 | 3.500 | ||||||
| 11\174 | 75.862 | 324.138 | 11:3 | 3.667 | ||||||
| 4\63 | 76.190 | 323.810 | 4:1 | 4.000 | Superhard 15L 3s | |||||
| 9\141 | 76.596 | 323.404 | 9:2 | 4.500 | ||||||
| 5\78 | 76.923 | 323.077 | 5:1 | 5.000 | ||||||
| 6\93 | 77.419 | 322.581 | 6:1 | 6.000 | ||||||
| 1\15 | 80.000 | 320.000 | 1:0 | → ∞ | Collapsed 15L 3s | |||||
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