1L 13s
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Scale structure
Step pattern
Lsssssssssssss
sssssssssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
13\14 to 1\1 (1114.3¢ to 1200.0¢)
Dark
0\1 to 1\14 (0.0¢ to 85.7¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Ancestor's step ratio range
5:1 to 1:0
Related MOS scales
Parent
1L 12s
Sister
13L 1s
Daughters
14L 1s, 1L 14s
Neutralized
2L 12s
2-Flought
15L 13s, 1L 27s
Equal tunings
Equalized (L:s = 1:1)
13\14 (1114.3¢)
Supersoft (L:s = 4:3)
40\43 (1116.3¢)
Soft (L:s = 3:2)
27\29 (1117.2¢)
Semisoft (L:s = 5:3)
41\44 (1118.2¢)
Basic (L:s = 2:1)
14\15 (1120.0¢)
Semihard (L:s = 5:2)
29\31 (1122.6¢)
Hard (L:s = 3:1)
15\16 (1125.0¢)
Superhard (L:s = 4:1)
16\17 (1129.4¢)
Collapsed (L:s = 1:0)
1\1 (1200.0¢)
| ↑ 1L 12s | 2L 12s ↗ | |
| 1L 13s | 2L 13s → | |
| ↓ 1L 14s | 2L 14s ↘ |
┌╥┬┬┬┬┬┬┬┬┬┬┬┬┬┐ │║││││││││││││││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssssssssssL
1L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 13 small steps, repeating every octave. 1L 13s is related to 1L 9s, expanding it by 4 tones. Generators that produce this scale range from 1114.3¢ to 1200¢, or from 0¢ to 85.7¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 13|0 | 1 | Lsssssssssssss |
| 12|1 | 14 | sLssssssssssss |
| 11|2 | 13 | ssLsssssssssss |
| 10|3 | 12 | sssLssssssssss |
| 9|4 | 11 | ssssLsssssssss |
| 8|5 | 10 | sssssLssssssss |
| 7|6 | 9 | ssssssLsssssss |
| 6|7 | 8 | sssssssLssssss |
| 5|8 | 7 | ssssssssLsssss |
| 4|9 | 6 | sssssssssLssss |
| 3|10 | 5 | ssssssssssLsss |
| 2|11 | 4 | sssssssssssLss |
| 1|12 | 3 | ssssssssssssLs |
| 0|13 | 2 | sssssssssssssL |
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 85.7¢ |
| Augmented 1-mosstep | A1ms | L | 85.7¢ to 1200.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 171.4¢ |
| Major 2-mosstep | M2ms | L + s | 171.4¢ to 1200.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 257.1¢ |
| Major 3-mosstep | M3ms | L + 2s | 257.1¢ to 1200.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 342.9¢ |
| Major 4-mosstep | M4ms | L + 3s | 342.9¢ to 1200.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 5s | 0.0¢ to 428.6¢ |
| Major 5-mosstep | M5ms | L + 4s | 428.6¢ to 1200.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 6s | 0.0¢ to 514.3¢ |
| Major 6-mosstep | M6ms | L + 5s | 514.3¢ to 1200.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 7s | 0.0¢ to 600.0¢ |
| Major 7-mosstep | M7ms | L + 6s | 600.0¢ to 1200.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 8s | 0.0¢ to 685.7¢ |
| Major 8-mosstep | M8ms | L + 7s | 685.7¢ to 1200.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 9s | 0.0¢ to 771.4¢ |
| Major 9-mosstep | M9ms | L + 8s | 771.4¢ to 1200.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 10s | 0.0¢ to 857.1¢ |
| Major 10-mosstep | M10ms | L + 9s | 857.1¢ to 1200.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 11s | 0.0¢ to 942.9¢ |
| Major 11-mosstep | M11ms | L + 10s | 942.9¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 12s | 0.0¢ to 1028.6¢ |
| Major 12-mosstep | M12ms | L + 11s | 1028.6¢ to 1200.0¢ | |
| 13-mosstep | Diminished 13-mosstep | d13ms | 13s | 0.0¢ to 1114.3¢ |
| Perfect 13-mosstep | P13ms | L + 12s | 1114.3¢ to 1200.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | L + 13s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 13\14 | 1114.286 | 85.714 | 1:1 | 1.000 | Equalized 1L 13s | |||||
| 66\71 | 1115.493 | 84.507 | 6:5 | 1.200 | ||||||
| 53\57 | 1115.789 | 84.211 | 5:4 | 1.250 | ||||||
| 93\100 | 1116.000 | 84.000 | 9:7 | 1.286 | ||||||
| 40\43 | 1116.279 | 83.721 | 4:3 | 1.333 | Supersoft 1L 13s | |||||
| 107\115 | 1116.522 | 83.478 | 11:8 | 1.375 | ||||||
| 67\72 | 1116.667 | 83.333 | 7:5 | 1.400 | Marvolo | |||||
| 94\101 | 1116.832 | 83.168 | 10:7 | 1.429 | ||||||
| 27\29 | 1117.241 | 82.759 | 3:2 | 1.500 | Soft 1L 13s Nautilus | |||||
| 95\102 | 1117.647 | 82.353 | 11:7 | 1.571 | ||||||
| 68\73 | 1117.808 | 82.192 | 8:5 | 1.600 | ||||||
| 109\117 | 1117.949 | 82.051 | 13:8 | 1.625 | Unnamed golden tuning | |||||
| 41\44 | 1118.182 | 81.818 | 5:3 | 1.667 | Semisoft 1L 13s | |||||
| 96\103 | 1118.447 | 81.553 | 12:7 | 1.714 | ||||||
| 55\59 | 1118.644 | 81.356 | 7:4 | 1.750 | ||||||
| 69\74 | 1118.919 | 81.081 | 9:5 | 1.800 | ||||||
| 14\15 | 1120.000 | 80.000 | 2:1 | 2.000 | Basic 1L 13s Scales with tunings softer than this are proper | |||||
| 57\61 | 1121.311 | 78.689 | 9:4 | 2.250 | ||||||
| 43\46 | 1121.739 | 78.261 | 7:3 | 2.333 | ||||||
| 72\77 | 1122.078 | 77.922 | 12:5 | 2.400 | Valentine | |||||
| 29\31 | 1122.581 | 77.419 | 5:2 | 2.500 | Semihard 1L 13s | |||||
| 73\78 | 1123.077 | 76.923 | 13:5 | 2.600 | Unnamed golden tuning | |||||
| 44\47 | 1123.404 | 76.596 | 8:3 | 2.667 | ||||||
| 59\63 | 1123.810 | 76.190 | 11:4 | 2.750 | ||||||
| 15\16 | 1125.000 | 75.000 | 3:1 | 3.000 | Hard 1L 13s | |||||
| 46\49 | 1126.531 | 73.469 | 10:3 | 3.333 | ||||||
| 31\33 | 1127.273 | 72.727 | 7:2 | 3.500 | ||||||
| 47\50 | 1128.000 | 72.000 | 11:3 | 3.667 | ||||||
| 16\17 | 1129.412 | 70.588 | 4:1 | 4.000 | Superhard 1L 13s | |||||
| 33\35 | 1131.429 | 68.571 | 9:2 | 4.500 | ||||||
| 17\18 | 1133.333 | 66.667 | 5:1 | 5.000 | ||||||
| 18\19 | 1136.842 | 63.158 | 6:1 | 6.000 | Sycamore, unicorn | |||||
| 1\1 | 1200.000 | 0.000 | 1:0 | → ∞ | Collapsed 1L 13s | |||||
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