13L 3s
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Scale structure
Step pattern
LLLLLsLLLLsLLLLs
sLLLLsLLLLsLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
11\16 to 9\13 (825.0¢ to 830.8¢)
Dark
4\13 to 5\16 (369.2¢ to 375.0¢)
TAMNAMS information
Descends from
3L 7s (sephiroid)
Ancestor's step ratio range
2:1 to 3:1 (hypohard)
Related MOS scales
Parent
3L 10s
Sister
3L 13s
Daughters
16L 13s, 13L 16s
Neutralized
10L 6s
2-Flought
29L 3s, 13L 19s
Equal tunings
Equalized (L:s = 1:1)
11\16 (825.0¢)
Supersoft (L:s = 4:3)
42\61 (826.2¢)
Soft (L:s = 3:2)
31\45 (826.7¢)
Semisoft (L:s = 5:3)
51\74 (827.0¢)
Basic (L:s = 2:1)
20\29 (827.6¢)
Semihard (L:s = 5:2)
49\71 (828.2¢)
Hard (L:s = 3:1)
29\42 (828.6¢)
Superhard (L:s = 4:1)
38\55 (829.1¢)
Collapsed (L:s = 1:0)
9\13 (830.8¢)
| ↖ 12L 2s | ↑ 13L 2s | 14L 2s ↗ |
| ← 12L 3s | 13L 3s | 14L 3s → |
| ↙ 12L 4s | ↓ 13L 4s | 14L 4s ↘ |
┌╥╥╥╥╥┬╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║│║║║║││ ││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLsLLLLL
13L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 3 small steps, repeating every octave. 13L 3s is a grandchild scale of 3L 7s, expanding it by 6 tones. Generators that produce this scale range from 825¢ to 830.8¢, or from 369.2¢ to 375¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 15|0 | 1 | LLLLLsLLLLsLLLLs |
| 14|1 | 12 | LLLLsLLLLLsLLLLs |
| 13|2 | 7 | LLLLsLLLLsLLLLLs |
| 12|3 | 2 | LLLLsLLLLsLLLLsL |
| 11|4 | 13 | LLLsLLLLLsLLLLsL |
| 10|5 | 8 | LLLsLLLLsLLLLLsL |
| 9|6 | 3 | LLLsLLLLsLLLLsLL |
| 8|7 | 14 | LLsLLLLLsLLLLsLL |
| 7|8 | 9 | LLsLLLLsLLLLLsLL |
| 6|9 | 4 | LLsLLLLsLLLLsLLL |
| 5|10 | 15 | LsLLLLLsLLLLsLLL |
| 4|11 | 10 | LsLLLLsLLLLLsLLL |
| 3|12 | 5 | LsLLLLsLLLLsLLLL |
| 2|13 | 16 | sLLLLLsLLLLsLLLL |
| 1|14 | 11 | sLLLLsLLLLLsLLLL |
| 0|15 | 6 | sLLLLsLLLLsLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 75.0¢ |
| Major 1-mosstep | M1ms | L | 75.0¢ to 92.3¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 92.3¢ to 150.0¢ |
| Major 2-mosstep | M2ms | 2L | 150.0¢ to 184.6¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 184.6¢ to 225.0¢ |
| Major 3-mosstep | M3ms | 3L | 225.0¢ to 276.9¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 276.9¢ to 300.0¢ |
| Major 4-mosstep | M4ms | 4L | 300.0¢ to 369.2¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 4L + s | 369.2¢ to 375.0¢ |
| Augmented 5-mosstep | A5ms | 5L | 375.0¢ to 461.5¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 369.2¢ to 450.0¢ |
| Major 6-mosstep | M6ms | 5L + s | 450.0¢ to 461.5¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 5L + 2s | 461.5¢ to 525.0¢ |
| Major 7-mosstep | M7ms | 6L + s | 525.0¢ to 553.8¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 6L + 2s | 553.8¢ to 600.0¢ |
| Major 8-mosstep | M8ms | 7L + s | 600.0¢ to 646.2¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 646.2¢ to 675.0¢ |
| Major 9-mosstep | M9ms | 8L + s | 675.0¢ to 738.5¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 738.5¢ to 750.0¢ |
| Major 10-mosstep | M10ms | 9L + s | 750.0¢ to 830.8¢ | |
| 11-mosstep | Diminished 11-mosstep | d11ms | 8L + 3s | 738.5¢ to 825.0¢ |
| Perfect 11-mosstep | P11ms | 9L + 2s | 825.0¢ to 830.8¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 9L + 3s | 830.8¢ to 900.0¢ |
| Major 12-mosstep | M12ms | 10L + 2s | 900.0¢ to 923.1¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 10L + 3s | 923.1¢ to 975.0¢ |
| Major 13-mosstep | M13ms | 11L + 2s | 975.0¢ to 1015.4¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 11L + 3s | 1015.4¢ to 1050.0¢ |
| Major 14-mosstep | M14ms | 12L + 2s | 1050.0¢ to 1107.7¢ | |
| 15-mosstep | Minor 15-mosstep | m15ms | 12L + 3s | 1107.7¢ to 1125.0¢ |
| Major 15-mosstep | M15ms | 13L + 2s | 1125.0¢ to 1200.0¢ | |
| 16-mosstep | Perfect 16-mosstep | P16ms | 13L + 3s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 11\16 | 825.000 | 375.000 | 1:1 | 1.000 | Equalized 13L 3s | |||||
| 64\93 | 825.806 | 374.194 | 6:5 | 1.200 | ||||||
| 53\77 | 825.974 | 374.026 | 5:4 | 1.250 | ||||||
| 95\138 | 826.087 | 373.913 | 9:7 | 1.286 | ||||||
| 42\61 | 826.230 | 373.770 | 4:3 | 1.333 | Supersoft 13L 3s | |||||
| 115\167 | 826.347 | 373.653 | 11:8 | 1.375 | ||||||
| 73\106 | 826.415 | 373.585 | 7:5 | 1.400 | ||||||
| 104\151 | 826.490 | 373.510 | 10:7 | 1.429 | ||||||
| 31\45 | 826.667 | 373.333 | 3:2 | 1.500 | Soft 13L 3s | |||||
| 113\164 | 826.829 | 373.171 | 11:7 | 1.571 | ||||||
| 82\119 | 826.891 | 373.109 | 8:5 | 1.600 | ||||||
| 133\193 | 826.943 | 373.057 | 13:8 | 1.625 | ||||||
| 51\74 | 827.027 | 372.973 | 5:3 | 1.667 | Semisoft 13L 3s | |||||
| 122\177 | 827.119 | 372.881 | 12:7 | 1.714 | ||||||
| 71\103 | 827.184 | 372.816 | 7:4 | 1.750 | ||||||
| 91\132 | 827.273 | 372.727 | 9:5 | 1.800 | ||||||
| 20\29 | 827.586 | 372.414 | 2:1 | 2.000 | Basic 13L 3s Scales with tunings softer than this are proper | |||||
| 89\129 | 827.907 | 372.093 | 9:4 | 2.250 | ||||||
| 69\100 | 828.000 | 372.000 | 7:3 | 2.333 | ||||||
| 118\171 | 828.070 | 371.930 | 12:5 | 2.400 | ||||||
| 49\71 | 828.169 | 371.831 | 5:2 | 2.500 | Semihard 13L 3s | |||||
| 127\184 | 828.261 | 371.739 | 13:5 | 2.600 | ||||||
| 78\113 | 828.319 | 371.681 | 8:3 | 2.667 | ||||||
| 107\155 | 828.387 | 371.613 | 11:4 | 2.750 | ||||||
| 29\42 | 828.571 | 371.429 | 3:1 | 3.000 | Hard 13L 3s | |||||
| 96\139 | 828.777 | 371.223 | 10:3 | 3.333 | ||||||
| 67\97 | 828.866 | 371.134 | 7:2 | 3.500 | ||||||
| 105\152 | 828.947 | 371.053 | 11:3 | 3.667 | ||||||
| 38\55 | 829.091 | 370.909 | 4:1 | 4.000 | Superhard 13L 3s | |||||
| 85\123 | 829.268 | 370.732 | 9:2 | 4.500 | ||||||
| 47\68 | 829.412 | 370.588 | 5:1 | 5.000 | ||||||
| 56\81 | 829.630 | 370.370 | 6:1 | 6.000 | ||||||
| 9\13 | 830.769 | 369.231 | 1:0 | → ∞ | Collapsed 13L 3s | |||||
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