5L 15s
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Scale structure
Step pattern
LsssLsssLsssLsssLsss
sssLsssLsssLsssLsssL
Equave
2/1 (1200.0¢)
Period
1\5 (240.0¢)
Generator size
Bright
3\20 to 1\5 (180.0¢ to 240.0¢)
Dark
0\5 to 1\20 (0.0¢ to 60.0¢)
TAMNAMS information
Descends from
5L 5s (pentawood)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
5L 10s
Sister
15L 5s
Daughters
20L 5s, 5L 20s
Neutralized
10L 10s
2-Flought
25L 15s, 5L 35s
Equal tunings
Equalized (L:s = 1:1)
3\20 (180.0¢)
Supersoft (L:s = 4:3)
10\65 (184.6¢)
Soft (L:s = 3:2)
7\45 (186.7¢)
Semisoft (L:s = 5:3)
11\70 (188.6¢)
Basic (L:s = 2:1)
4\25 (192.0¢)
Semihard (L:s = 5:2)
9\55 (196.4¢)
Hard (L:s = 3:1)
5\30 (200.0¢)
Superhard (L:s = 4:1)
6\35 (205.7¢)
Collapsed (L:s = 1:0)
1\5 (240.0¢)
| ↖ 4L 14s | ↑ 5L 14s | 6L 14s ↗ |
| ← 4L 15s | 5L 15s | 6L 15s → |
| ↙ 4L 16s | ↓ 5L 16s | 6L 16s ↘ |
┌╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬╥┬┬┬┐ │║│││║│││║│││║│││║││││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLsssLsssLsssL
5L 15s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 15 small steps, with a period of 1 large step and 3 small steps that repeats every 240.0¢, or 5 times every octave. 5L 15s is a grandchild scale of 5L 5s, expanding it by 10 tones. Generators that produce this scale range from 180¢ to 240¢, or from 0¢ to 60¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 15|0(5) | 1 | LsssLsssLsssLsssLsss |
| 10|5(5) | 4 | sLsssLsssLsssLsssLss |
| 5|10(5) | 3 | ssLsssLsssLsssLsssLs |
| 0|15(5) | 2 | sssLsssLsssLsssLsssL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0¢ to 60.0¢ |
| Augmented 1-mosstep | A1ms | L | 60.0¢ to 240.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 120.0¢ |
| Major 2-mosstep | M2ms | L + s | 120.0¢ to 240.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0¢ to 180.0¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 180.0¢ to 240.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 240.0¢ |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 240.0¢ to 300.0¢ |
| Augmented 5-mosstep | A5ms | 2L + 3s | 300.0¢ to 480.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 240.0¢ to 360.0¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 360.0¢ to 480.0¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | L + 6s | 240.0¢ to 420.0¢ |
| Perfect 7-mosstep | P7ms | 2L + 5s | 420.0¢ to 480.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 2L + 6s | 480.0¢ |
| 9-mosstep | Perfect 9-mosstep | P9ms | 2L + 7s | 480.0¢ to 540.0¢ |
| Augmented 9-mosstep | A9ms | 3L + 6s | 540.0¢ to 720.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 480.0¢ to 600.0¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 600.0¢ to 720.0¢ | |
| 11-mosstep | Diminished 11-mosstep | d11ms | 2L + 9s | 480.0¢ to 660.0¢ |
| Perfect 11-mosstep | P11ms | 3L + 8s | 660.0¢ to 720.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 3L + 9s | 720.0¢ |
| 13-mosstep | Perfect 13-mosstep | P13ms | 3L + 10s | 720.0¢ to 780.0¢ |
| Augmented 13-mosstep | A13ms | 4L + 9s | 780.0¢ to 960.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 3L + 11s | 720.0¢ to 840.0¢ |
| Major 14-mosstep | M14ms | 4L + 10s | 840.0¢ to 960.0¢ | |
| 15-mosstep | Diminished 15-mosstep | d15ms | 3L + 12s | 720.0¢ to 900.0¢ |
| Perfect 15-mosstep | P15ms | 4L + 11s | 900.0¢ to 960.0¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 4L + 12s | 960.0¢ |
| 17-mosstep | Perfect 17-mosstep | P17ms | 4L + 13s | 960.0¢ to 1020.0¢ |
| Augmented 17-mosstep | A17ms | 5L + 12s | 1020.0¢ to 1200.0¢ | |
| 18-mosstep | Minor 18-mosstep | m18ms | 4L + 14s | 960.0¢ to 1080.0¢ |
| Major 18-mosstep | M18ms | 5L + 13s | 1080.0¢ to 1200.0¢ | |
| 19-mosstep | Diminished 19-mosstep | d19ms | 4L + 15s | 960.0¢ to 1140.0¢ |
| Perfect 19-mosstep | P19ms | 5L + 14s | 1140.0¢ to 1200.0¢ | |
| 20-mosstep | Perfect 20-mosstep | P20ms | 5L + 15s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\20 | 180.000 | 60.000 | 1:1 | 1.000 | Equalized 5L 15s | |||||
| 16\105 | 182.857 | 57.143 | 6:5 | 1.200 | ||||||
| 13\85 | 183.529 | 56.471 | 5:4 | 1.250 | ||||||
| 23\150 | 184.000 | 56.000 | 9:7 | 1.286 | ||||||
| 10\65 | 184.615 | 55.385 | 4:3 | 1.333 | Supersoft 5L 15s | |||||
| 27\175 | 185.143 | 54.857 | 11:8 | 1.375 | ||||||
| 17\110 | 185.455 | 54.545 | 7:5 | 1.400 | ||||||
| 24\155 | 185.806 | 54.194 | 10:7 | 1.429 | ||||||
| 7\45 | 186.667 | 53.333 | 3:2 | 1.500 | Soft 5L 15s | |||||
| 25\160 | 187.500 | 52.500 | 11:7 | 1.571 | ||||||
| 18\115 | 187.826 | 52.174 | 8:5 | 1.600 | ||||||
| 29\185 | 188.108 | 51.892 | 13:8 | 1.625 | ||||||
| 11\70 | 188.571 | 51.429 | 5:3 | 1.667 | Semisoft 5L 15s | |||||
| 26\165 | 189.091 | 50.909 | 12:7 | 1.714 | ||||||
| 15\95 | 189.474 | 50.526 | 7:4 | 1.750 | ||||||
| 19\120 | 190.000 | 50.000 | 9:5 | 1.800 | ||||||
| 4\25 | 192.000 | 48.000 | 2:1 | 2.000 | Basic 5L 15s Scales with tunings softer than this are proper | |||||
| 17\105 | 194.286 | 45.714 | 9:4 | 2.250 | ||||||
| 13\80 | 195.000 | 45.000 | 7:3 | 2.333 | ||||||
| 22\135 | 195.556 | 44.444 | 12:5 | 2.400 | ||||||
| 9\55 | 196.364 | 43.636 | 5:2 | 2.500 | Semihard 5L 15s | |||||
| 23\140 | 197.143 | 42.857 | 13:5 | 2.600 | ||||||
| 14\85 | 197.647 | 42.353 | 8:3 | 2.667 | ||||||
| 19\115 | 198.261 | 41.739 | 11:4 | 2.750 | ||||||
| 5\30 | 200.000 | 40.000 | 3:1 | 3.000 | Hard 5L 15s | |||||
| 16\95 | 202.105 | 37.895 | 10:3 | 3.333 | ||||||
| 11\65 | 203.077 | 36.923 | 7:2 | 3.500 | ||||||
| 17\100 | 204.000 | 36.000 | 11:3 | 3.667 | ||||||
| 6\35 | 205.714 | 34.286 | 4:1 | 4.000 | Superhard 5L 15s | |||||
| 13\75 | 208.000 | 32.000 | 9:2 | 4.500 | ||||||
| 7\40 | 210.000 | 30.000 | 5:1 | 5.000 | ||||||
| 8\45 | 213.333 | 26.667 | 6:1 | 6.000 | ||||||
| 1\5 | 240.000 | 0.000 | 1:0 | → ∞ | Collapsed 5L 15s | |||||
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