2L 13s
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Scale structure
Step pattern
LssssssLsssssss
sssssssLssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
7\15 to 1\2 (560.0¢ to 600.0¢)
Dark
1\2 to 8\15 (600.0¢ to 640.0¢)
TAMNAMS information
Descends from
2L 7s (balzano)
Ancestor's step ratio range
4:1 to 1:0 (ultrahard)
Related MOS scales
Parent
2L 11s
Sister
13L 2s
Daughters
15L 2s, 2L 15s
Neutralized
4L 11s
2-Flought
17L 13s, 2L 28s
Equal tunings
Equalized (L:s = 1:1)
7\15 (560.0¢)
Supersoft (L:s = 4:3)
22\47 (561.7¢)
Soft (L:s = 3:2)
15\32 (562.5¢)
Semisoft (L:s = 5:3)
23\49 (563.3¢)
Basic (L:s = 2:1)
8\17 (564.7¢)
Semihard (L:s = 5:2)
17\36 (566.7¢)
Hard (L:s = 3:1)
9\19 (568.4¢)
Superhard (L:s = 4:1)
10\21 (571.4¢)
Collapsed (L:s = 1:0)
1\2 (600.0¢)
| ↖ 1L 12s | ↑ 2L 12s | 3L 12s ↗ |
| ← 1L 13s | 2L 13s | 3L 13s → |
| ↙ 1L 14s | ↓ 2L 14s | 3L 14s ↘ |
┌╥┬┬┬┬┬┬╥┬┬┬┬┬┬┬┐ │║││││││║││││││││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssssssLssssssL
2L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 13 small steps, repeating every octave. 2L 13s is a great-grandchild scale of 2L 7s, expanding it by 6 tones. Generators that produce this scale range from 560¢ to 600¢, or from 600¢ to 640¢.
This MOS is the simplest that has a tritone as the only possible size of a generator, since the smallest size for a tritone is defined to be 7/15edo (560 cents). Since its generator is a tritone, its harmonic entropy minimum is where the generator is 7/5.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 14|0 | 1 | LssssssLsssssss |
| 13|1 | 8 | LsssssssLssssss |
| 12|2 | 15 | sLssssssLssssss |
| 11|3 | 7 | sLsssssssLsssss |
| 10|4 | 14 | ssLssssssLsssss |
| 9|5 | 6 | ssLsssssssLssss |
| 8|6 | 13 | sssLssssssLssss |
| 7|7 | 5 | sssLsssssssLsss |
| 6|8 | 12 | ssssLssssssLsss |
| 5|9 | 4 | ssssLsssssssLss |
| 4|10 | 11 | sssssLssssssLss |
| 3|11 | 3 | sssssLsssssssLs |
| 2|12 | 10 | ssssssLssssssLs |
| 1|13 | 2 | ssssssLsssssssL |
| 0|14 | 9 | sssssssLssssssL |
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 80.0¢ |
| Major 1-mosstep | M1ms | L | 80.0¢ to 600.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 160.0¢ |
| Major 2-mosstep | M2ms | L + s | 160.0¢ to 600.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 240.0¢ |
| Major 3-mosstep | M3ms | L + 2s | 240.0¢ to 600.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 320.0¢ |
| Major 4-mosstep | M4ms | L + 3s | 320.0¢ to 600.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 5s | 0.0¢ to 400.0¢ |
| Major 5-mosstep | M5ms | L + 4s | 400.0¢ to 600.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 6s | 0.0¢ to 480.0¢ |
| Major 6-mosstep | M6ms | L + 5s | 480.0¢ to 600.0¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | 7s | 0.0¢ to 560.0¢ |
| Perfect 7-mosstep | P7ms | L + 6s | 560.0¢ to 600.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | L + 7s | 600.0¢ to 640.0¢ |
| Augmented 8-mosstep | A8ms | 2L + 6s | 640.0¢ to 1200.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 600.0¢ to 720.0¢ |
| Major 9-mosstep | M9ms | 2L + 7s | 720.0¢ to 1200.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | L + 9s | 600.0¢ to 800.0¢ |
| Major 10-mosstep | M10ms | 2L + 8s | 800.0¢ to 1200.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | L + 10s | 600.0¢ to 880.0¢ |
| Major 11-mosstep | M11ms | 2L + 9s | 880.0¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | L + 11s | 600.0¢ to 960.0¢ |
| Major 12-mosstep | M12ms | 2L + 10s | 960.0¢ to 1200.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | L + 12s | 600.0¢ to 1040.0¢ |
| Major 13-mosstep | M13ms | 2L + 11s | 1040.0¢ to 1200.0¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | L + 13s | 600.0¢ to 1120.0¢ |
| Major 14-mosstep | M14ms | 2L + 12s | 1120.0¢ to 1200.0¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 2L + 13s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\15 | 560.000 | 640.000 | 1:1 | 1.000 | Equalized 2L 13s | |||||
| 36\77 | 561.039 | 638.961 | 6:5 | 1.200 | ||||||
| 29\62 | 561.290 | 638.710 | 5:4 | 1.250 | ||||||
| 51\109 | 561.468 | 638.532 | 9:7 | 1.286 | ||||||
| 22\47 | 561.702 | 638.298 | 4:3 | 1.333 | Supersoft 2L 13s | |||||
| 59\126 | 561.905 | 638.095 | 11:8 | 1.375 | ||||||
| 37\79 | 562.025 | 637.975 | 7:5 | 1.400 | ||||||
| 52\111 | 562.162 | 637.838 | 10:7 | 1.429 | ||||||
| 15\32 | 562.500 | 637.500 | 3:2 | 1.500 | Soft 2L 13s | |||||
| 53\113 | 562.832 | 637.168 | 11:7 | 1.571 | ||||||
| 38\81 | 562.963 | 637.037 | 8:5 | 1.600 | ||||||
| 61\130 | 563.077 | 636.923 | 13:8 | 1.625 | ||||||
| 23\49 | 563.265 | 636.735 | 5:3 | 1.667 | Semisoft 2L 13s | |||||
| 54\115 | 563.478 | 636.522 | 12:7 | 1.714 | ||||||
| 31\66 | 563.636 | 636.364 | 7:4 | 1.750 | ||||||
| 39\83 | 563.855 | 636.145 | 9:5 | 1.800 | ||||||
| 8\17 | 564.706 | 635.294 | 2:1 | 2.000 | Basic 2L 13s Scales with tunings softer than this are proper | |||||
| 33\70 | 565.714 | 634.286 | 9:4 | 2.250 | ||||||
| 25\53 | 566.038 | 633.962 | 7:3 | 2.333 | ||||||
| 42\89 | 566.292 | 633.708 | 12:5 | 2.400 | ||||||
| 17\36 | 566.667 | 633.333 | 5:2 | 2.500 | Semihard 2L 13s | |||||
| 43\91 | 567.033 | 632.967 | 13:5 | 2.600 | ||||||
| 26\55 | 567.273 | 632.727 | 8:3 | 2.667 | ||||||
| 35\74 | 567.568 | 632.432 | 11:4 | 2.750 | ||||||
| 9\19 | 568.421 | 631.579 | 3:1 | 3.000 | Hard 2L 13s | |||||
| 28\59 | 569.492 | 630.508 | 10:3 | 3.333 | ||||||
| 19\40 | 570.000 | 630.000 | 7:2 | 3.500 | ||||||
| 29\61 | 570.492 | 629.508 | 11:3 | 3.667 | ||||||
| 10\21 | 571.429 | 628.571 | 4:1 | 4.000 | Superhard 2L 13s | |||||
| 21\44 | 572.727 | 627.273 | 9:2 | 4.500 | ||||||
| 11\23 | 573.913 | 626.087 | 5:1 | 5.000 | ||||||
| 12\25 | 576.000 | 624.000 | 6:1 | 6.000 | ||||||
| 1\2 | 600.000 | 600.000 | 1:0 | → ∞ | Collapsed 2L 13s | |||||