15L 5s
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Scale structure
Step pattern
LLLsLLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLLsLLL
Equave
2/1 (1200.0¢)
Period
1\5 (240.0¢)
Generator size
Bright
1\20 to 1\15 (60.0¢ to 80.0¢)
Dark
2\15 to 3\20 (160.0¢ to 180.0¢)
TAMNAMS information
Descends from
5L 5s (pentawood)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
5L 10s
Sister
5L 15s
Daughters
20L 15s, 15L 20s
Neutralized
10L 10s
2-Flought
35L 5s, 15L 25s
Equal tunings
Equalized (L:s = 1:1)
1\20 (60.0¢)
Supersoft (L:s = 4:3)
4\75 (64.0¢)
Soft (L:s = 3:2)
3\55 (65.5¢)
Semisoft (L:s = 5:3)
5\90 (66.7¢)
Basic (L:s = 2:1)
2\35 (68.6¢)
Semihard (L:s = 5:2)
5\85 (70.6¢)
Hard (L:s = 3:1)
3\50 (72.0¢)
Superhard (L:s = 4:1)
4\65 (73.8¢)
Collapsed (L:s = 1:0)
1\15 (80.0¢)
| ↖ 14L 4s | ↑ 15L 4s | 16L 4s ↗ |
| ← 14L 5s | 15L 5s | 16L 5s → |
| ↙ 14L 6s | ↓ 15L 6s | 16L 6s ↘ |
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬╥╥╥┬┐ │║║║│║║║│║║║│║║║│║║║││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLsLLLsLLLsLLL
15L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 5 small steps, with a period of 3 large steps and 1 small step that repeats every 240.0¢, or 5 times every octave. 15L 5s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 60¢ to 80¢, or from 160¢ to 180¢. 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(5) | 1 | LLLsLLLsLLLsLLLsLLLs |
| 10|5(5) | 2 | LLsLLLsLLLsLLLsLLLsL |
| 5|10(5) | 3 | LsLLLsLLLsLLLsLLLsLL |
| 0|15(5) | 4 | sLLLsLLLsLLLsLLLsLLL |
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 60.0¢ |
| Perfect 1-mosstep | P1ms | L | 60.0¢ to 80.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 80.0¢ to 120.0¢ |
| Major 2-mosstep | M2ms | 2L | 120.0¢ to 160.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 160.0¢ to 180.0¢ |
| Augmented 3-mosstep | A3ms | 3L | 180.0¢ to 240.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | 3L + s | 240.0¢ |
| 5-mosstep | Diminished 5-mosstep | d5ms | 3L + 2s | 240.0¢ to 300.0¢ |
| Perfect 5-mosstep | P5ms | 4L + s | 300.0¢ to 320.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 320.0¢ to 360.0¢ |
| Major 6-mosstep | M6ms | 5L + s | 360.0¢ to 400.0¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 5L + 2s | 400.0¢ to 420.0¢ |
| Augmented 7-mosstep | A7ms | 6L + s | 420.0¢ to 480.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 6L + 2s | 480.0¢ |
| 9-mosstep | Diminished 9-mosstep | d9ms | 6L + 3s | 480.0¢ to 540.0¢ |
| Perfect 9-mosstep | P9ms | 7L + 2s | 540.0¢ to 560.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 7L + 3s | 560.0¢ to 600.0¢ |
| Major 10-mosstep | M10ms | 8L + 2s | 600.0¢ to 640.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 8L + 3s | 640.0¢ to 660.0¢ |
| Augmented 11-mosstep | A11ms | 9L + 2s | 660.0¢ to 720.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 9L + 3s | 720.0¢ |
| 13-mosstep | Diminished 13-mosstep | d13ms | 9L + 4s | 720.0¢ to 780.0¢ |
| Perfect 13-mosstep | P13ms | 10L + 3s | 780.0¢ to 800.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 10L + 4s | 800.0¢ to 840.0¢ |
| Major 14-mosstep | M14ms | 11L + 3s | 840.0¢ to 880.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 11L + 4s | 880.0¢ to 900.0¢ |
| Augmented 15-mosstep | A15ms | 12L + 3s | 900.0¢ to 960.0¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 12L + 4s | 960.0¢ |
| 17-mosstep | Diminished 17-mosstep | d17ms | 12L + 5s | 960.0¢ to 1020.0¢ |
| Perfect 17-mosstep | P17ms | 13L + 4s | 1020.0¢ to 1040.0¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 13L + 5s | 1040.0¢ to 1080.0¢ |
| Major 18-mosstep | M18ms | 14L + 4s | 1080.0¢ to 1120.0¢ | |
| 19-mosstep | Perfect 19-mosstep | P19ms | 14L + 5s | 1120.0¢ to 1140.0¢ |
| Augmented 19-mosstep | A19ms | 15L + 4s | 1140.0¢ to 1200.0¢ | |
| 20-mosstep | Perfect 20-mosstep | P20ms | 15L + 5s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\20 | 60.000 | 180.000 | 1:1 | 1.000 | Equalized 15L 5s | |||||
| 6\115 | 62.609 | 177.391 | 6:5 | 1.200 | ||||||
| 5\95 | 63.158 | 176.842 | 5:4 | 1.250 | ||||||
| 9\170 | 63.529 | 176.471 | 9:7 | 1.286 | ||||||
| 4\75 | 64.000 | 176.000 | 4:3 | 1.333 | Supersoft 15L 5s | |||||
| 11\205 | 64.390 | 175.610 | 11:8 | 1.375 | ||||||
| 7\130 | 64.615 | 175.385 | 7:5 | 1.400 | ||||||
| 10\185 | 64.865 | 175.135 | 10:7 | 1.429 | ||||||
| 3\55 | 65.455 | 174.545 | 3:2 | 1.500 | Soft 15L 5s | |||||
| 11\200 | 66.000 | 174.000 | 11:7 | 1.571 | ||||||
| 8\145 | 66.207 | 173.793 | 8:5 | 1.600 | ||||||
| 13\235 | 66.383 | 173.617 | 13:8 | 1.625 | ||||||
| 5\90 | 66.667 | 173.333 | 5:3 | 1.667 | Semisoft 15L 5s | |||||
| 12\215 | 66.977 | 173.023 | 12:7 | 1.714 | ||||||
| 7\125 | 67.200 | 172.800 | 7:4 | 1.750 | ||||||
| 9\160 | 67.500 | 172.500 | 9:5 | 1.800 | ||||||
| 2\35 | 68.571 | 171.429 | 2:1 | 2.000 | Basic 15L 5s | |||||
| 9\155 | 69.677 | 170.323 | 9:4 | 2.250 | ||||||
| 7\120 | 70.000 | 170.000 | 7:3 | 2.333 | ||||||
| 12\205 | 70.244 | 169.756 | 12:5 | 2.400 | ||||||
| 5\85 | 70.588 | 169.412 | 5:2 | 2.500 | Semihard 15L 5s | |||||
| 13\220 | 70.909 | 169.091 | 13:5 | 2.600 | ||||||
| 8\135 | 71.111 | 168.889 | 8:3 | 2.667 | ||||||
| 11\185 | 71.351 | 168.649 | 11:4 | 2.750 | ||||||
| 3\50 | 72.000 | 168.000 | 3:1 | 3.000 | Hard 15L 5s | |||||
| 10\165 | 72.727 | 167.273 | 10:3 | 3.333 | ||||||
| 7\115 | 73.043 | 166.957 | 7:2 | 3.500 | ||||||
| 11\180 | 73.333 | 166.667 | 11:3 | 3.667 | ||||||
| 4\65 | 73.846 | 166.154 | 4:1 | 4.000 | Superhard 15L 5s | |||||
| 9\145 | 74.483 | 165.517 | 9:2 | 4.500 | ||||||
| 5\80 | 75.000 | 165.000 | 5:1 | 5.000 | ||||||
| 6\95 | 75.789 | 164.211 | 6:1 | 6.000 | ||||||
| 1\15 | 80.000 | 160.000 | 1:0 | → ∞ | Collapsed 15L 5s | |||||
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