15L 1s
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Scale structure
Step pattern
LLLLLLLLLLLLLLLs
sLLLLLLLLLLLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
1\16 to 1\15 (75.0¢ to 80.0¢)
Dark
14\15 to 15\16 (1120.0¢ to 1125.0¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
6:1 to 7:1
Related MOS scales
Parent
1L 14s
Sister
1L 15s
Daughters
16L 15s, 15L 16s
Neutralized
14L 2s
2-Flought
31L 1s, 15L 17s
Equal tunings
Equalized (L:s = 1:1)
1\16 (75.0¢)
Supersoft (L:s = 4:3)
4\63 (76.2¢)
Soft (L:s = 3:2)
3\47 (76.6¢)
Semisoft (L:s = 5:3)
5\78 (76.9¢)
Basic (L:s = 2:1)
2\31 (77.4¢)
Semihard (L:s = 5:2)
5\77 (77.9¢)
Hard (L:s = 3:1)
3\46 (78.3¢)
Superhard (L:s = 4:1)
4\61 (78.7¢)
Collapsed (L:s = 1:0)
1\15 (80.0¢)
← 14L 1s | 15L 1s | 16L 1s → |
↙ 14L 2s | ↓ 15L 2s | 16L 2s ↘ |
┌╥╥╥╥╥╥╥╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║║║║║║║║││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLLLLLLLLLLLL
15L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 15 large steps and 1 small step, repeating every octave. 15L 1s is related to 1L 9s, expanding it by 6 tones. Generators that produce this scale range from 75¢ to 80¢, or from 1120¢ to 1125¢. Scales of this form are always proper because there is only one small step.
It is notable for corresponding to valentine[16].
Modes
UDP | Cyclic order |
Step pattern |
---|---|---|
15|0 | 1 | LLLLLLLLLLLLLLLs |
14|1 | 2 | LLLLLLLLLLLLLLsL |
13|2 | 3 | LLLLLLLLLLLLLsLL |
12|3 | 4 | LLLLLLLLLLLLsLLL |
11|4 | 5 | LLLLLLLLLLLsLLLL |
10|5 | 6 | LLLLLLLLLLsLLLLL |
9|6 | 7 | LLLLLLLLLsLLLLLL |
8|7 | 8 | LLLLLLLLsLLLLLLL |
7|8 | 9 | LLLLLLLsLLLLLLLL |
6|9 | 10 | LLLLLLsLLLLLLLLL |
5|10 | 11 | LLLLLsLLLLLLLLLL |
4|11 | 12 | LLLLsLLLLLLLLLLL |
3|12 | 13 | LLLsLLLLLLLLLLLL |
2|13 | 14 | LLsLLLLLLLLLLLLL |
1|14 | 15 | LsLLLLLLLLLLLLLL |
0|15 | 16 | sLLLLLLLLLLLLLLL |
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 75.0¢ |
Perfect 1-mosstep | P1ms | L | 75.0¢ to 80.0¢ | |
2-mosstep | Minor 2-mosstep | m2ms | L + s | 80.0¢ to 150.0¢ |
Major 2-mosstep | M2ms | 2L | 150.0¢ to 160.0¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 160.0¢ to 225.0¢ |
Major 3-mosstep | M3ms | 3L | 225.0¢ to 240.0¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 240.0¢ to 300.0¢ |
Major 4-mosstep | M4ms | 4L | 300.0¢ to 320.0¢ | |
5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 320.0¢ to 375.0¢ |
Major 5-mosstep | M5ms | 5L | 375.0¢ to 400.0¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 400.0¢ to 450.0¢ |
Major 6-mosstep | M6ms | 6L | 450.0¢ to 480.0¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 480.0¢ to 525.0¢ |
Major 7-mosstep | M7ms | 7L | 525.0¢ to 560.0¢ | |
8-mosstep | Minor 8-mosstep | m8ms | 7L + s | 560.0¢ to 600.0¢ |
Major 8-mosstep | M8ms | 8L | 600.0¢ to 640.0¢ | |
9-mosstep | Minor 9-mosstep | m9ms | 8L + s | 640.0¢ to 675.0¢ |
Major 9-mosstep | M9ms | 9L | 675.0¢ to 720.0¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 9L + s | 720.0¢ to 750.0¢ |
Major 10-mosstep | M10ms | 10L | 750.0¢ to 800.0¢ | |
11-mosstep | Minor 11-mosstep | m11ms | 10L + s | 800.0¢ to 825.0¢ |
Major 11-mosstep | M11ms | 11L | 825.0¢ to 880.0¢ | |
12-mosstep | Minor 12-mosstep | m12ms | 11L + s | 880.0¢ to 900.0¢ |
Major 12-mosstep | M12ms | 12L | 900.0¢ to 960.0¢ | |
13-mosstep | Minor 13-mosstep | m13ms | 12L + s | 960.0¢ to 975.0¢ |
Major 13-mosstep | M13ms | 13L | 975.0¢ to 1040.0¢ | |
14-mosstep | Minor 14-mosstep | m14ms | 13L + s | 1040.0¢ to 1050.0¢ |
Major 14-mosstep | M14ms | 14L | 1050.0¢ to 1120.0¢ | |
15-mosstep | Perfect 15-mosstep | P15ms | 14L + s | 1120.0¢ to 1125.0¢ |
Augmented 15-mosstep | A15ms | 15L | 1125.0¢ to 1200.0¢ | |
16-mosstep | Perfect 16-mosstep | P16ms | 15L + s | 1200.0¢ |
Scale tree
Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
1\16 | 75.000 | 1125.000 | 1:1 | 1.000 | Equalized 15L 1s | |||||
6\95 | 75.789 | 1124.211 | 6:5 | 1.200 | ||||||
5\79 | 75.949 | 1124.051 | 5:4 | 1.250 | ||||||
9\142 | 76.056 | 1123.944 | 9:7 | 1.286 | ||||||
4\63 | 76.190 | 1123.810 | 4:3 | 1.333 | Supersoft 15L 1s | |||||
11\173 | 76.301 | 1123.699 | 11:8 | 1.375 | ||||||
7\110 | 76.364 | 1123.636 | 7:5 | 1.400 | ||||||
10\157 | 76.433 | 1123.567 | 10:7 | 1.429 | ||||||
3\47 | 76.596 | 1123.404 | 3:2 | 1.500 | Soft 15L 1s | |||||
11\172 | 76.744 | 1123.256 | 11:7 | 1.571 | ||||||
8\125 | 76.800 | 1123.200 | 8:5 | 1.600 | ||||||
13\203 | 76.847 | 1123.153 | 13:8 | 1.625 | ||||||
5\78 | 76.923 | 1123.077 | 5:3 | 1.667 | Semisoft 15L 1s | |||||
12\187 | 77.005 | 1122.995 | 12:7 | 1.714 | ||||||
7\109 | 77.064 | 1122.936 | 7:4 | 1.750 | ||||||
9\140 | 77.143 | 1122.857 | 9:5 | 1.800 | Tertia / Tertiaseptal | |||||
2\31 | 77.419 | 1122.581 | 2:1 | 2.000 | Basic 15L 1s | |||||
9\139 | 77.698 | 1122.302 | 9:4 | 2.250 | ||||||
7\108 | 77.778 | 1122.222 | 7:3 | 2.333 | ||||||
12\185 | 77.838 | 1122.162 | 12:5 | 2.400 | ||||||
5\77 | 77.922 | 1122.078 | 5:2 | 2.500 | Semihard 15L 1s | |||||
13\200 | 78.000 | 1122.000 | 13:5 | 2.600 | ||||||
8\123 | 78.049 | 1121.951 | 8:3 | 2.667 | Valentine | |||||
11\169 | 78.107 | 1121.893 | 11:4 | 2.750 | ||||||
3\46 | 78.261 | 1121.739 | 3:1 | 3.000 | Hard 15L 1s | |||||
10\153 | 78.431 | 1121.569 | 10:3 | 3.333 | ||||||
7\107 | 78.505 | 1121.495 | 7:2 | 3.500 | ||||||
11\168 | 78.571 | 1121.429 | 11:3 | 3.667 | ||||||
4\61 | 78.689 | 1121.311 | 4:1 | 4.000 | Superhard 15L 1s | |||||
9\137 | 78.832 | 1121.168 | 9:2 | 4.500 | ||||||
5\76 | 78.947 | 1121.053 | 5:1 | 5.000 | ||||||
6\91 | 79.121 | 1120.879 | 6:1 | 6.000 | ||||||
1\15 | 80.000 | 1120.000 | 1:0 | → ∞ | Collapsed 15L 1s |
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