3L 11s
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Scale structure
Step pattern
LsssLssssLssss
ssssLssssLsssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
9\14 to 2\3 (771.4¢ to 800.0¢)
Dark
1\3 to 5\14 (400.0¢ to 428.6¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Ancestor's step ratio range
3:1 to 1:0 (hard)
Related MOS scales
Parent
3L 8s
Sister
11L 3s
Daughters
14L 3s, 3L 14s
Neutralized
6L 8s
2-Flought
17L 11s, 3L 25s
Equal tunings
Equalized (L:s = 1:1)
9\14 (771.4¢)
Supersoft (L:s = 4:3)
29\45 (773.3¢)
Soft (L:s = 3:2)
20\31 (774.2¢)
Semisoft (L:s = 5:3)
31\48 (775.0¢)
Basic (L:s = 2:1)
11\17 (776.5¢)
Semihard (L:s = 5:2)
24\37 (778.4¢)
Hard (L:s = 3:1)
13\20 (780.0¢)
Superhard (L:s = 4:1)
15\23 (782.6¢)
Collapsed (L:s = 1:0)
2\3 (800.0¢)
| ↖ 2L 10s | ↑ 3L 10s | 4L 10s ↗ |
| ← 2L 11s | 3L 11s | 4L 11s → |
| ↙ 2L 12s | ↓ 3L 12s | 4L 12s ↘ |
┌╥┬┬┬╥┬┬┬┬╥┬┬┬┬┐ │║│││║││││║│││││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
ssssLssssLsssL
3L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 11 small steps, repeating every octave. 3L 11s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 771.4¢ to 800¢, or from 400¢ to 428.6¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 13|0 | 1 | LsssLssssLssss |
| 12|1 | 10 | LssssLsssLssss |
| 11|2 | 5 | LssssLssssLsss |
| 10|3 | 14 | sLsssLssssLsss |
| 9|4 | 9 | sLssssLsssLsss |
| 8|5 | 4 | sLssssLssssLss |
| 7|6 | 13 | ssLsssLssssLss |
| 6|7 | 8 | ssLssssLsssLss |
| 5|8 | 3 | ssLssssLssssLs |
| 4|9 | 12 | sssLsssLssssLs |
| 3|10 | 7 | sssLssssLsssLs |
| 2|11 | 2 | sssLssssLssssL |
| 1|12 | 11 | ssssLsssLssssL |
| 0|13 | 6 | ssssLssssLsssL |
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 85.7¢ |
| Major 1-mosstep | M1ms | L | 85.7¢ to 400.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 171.4¢ |
| Major 2-mosstep | M2ms | L + s | 171.4¢ to 400.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 257.1¢ |
| Major 3-mosstep | M3ms | L + 2s | 257.1¢ to 400.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 342.9¢ |
| Major 4-mosstep | M4ms | L + 3s | 342.9¢ to 400.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | L + 4s | 400.0¢ to 428.6¢ |
| Augmented 5-mosstep | A5ms | 2L + 3s | 428.6¢ to 800.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 400.0¢ to 514.3¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 514.3¢ to 800.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 400.0¢ to 600.0¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 600.0¢ to 800.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 400.0¢ to 685.7¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 685.7¢ to 800.0¢ | |
| 9-mosstep | Diminished 9-mosstep | d9ms | L + 8s | 400.0¢ to 771.4¢ |
| Perfect 9-mosstep | P9ms | 2L + 7s | 771.4¢ to 800.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 800.0¢ to 857.1¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 857.1¢ to 1200.0¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 2L + 9s | 800.0¢ to 942.9¢ |
| Major 11-mosstep | M11ms | 3L + 8s | 942.9¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 2L + 10s | 800.0¢ to 1028.6¢ |
| Major 12-mosstep | M12ms | 3L + 9s | 1028.6¢ to 1200.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 2L + 11s | 800.0¢ to 1114.3¢ |
| Major 13-mosstep | M13ms | 3L + 10s | 1114.3¢ to 1200.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 3L + 11s | 1200.0¢ |
Tuning spectrum
 |
Todo: review Review entries from past page revision and enter them into the scale tree. |
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 9\14 | 771.429 | 428.571 | 1:1 | 1.000 | Equalized 3L 11s | |||||
| 47\73 | 772.603 | 427.397 | 6:5 | 1.200 | ||||||
| 38\59 | 772.881 | 427.119 | 5:4 | 1.250 | ||||||
| 67\104 | 773.077 | 426.923 | 9:7 | 1.286 | ||||||
| 29\45 | 773.333 | 426.667 | 4:3 | 1.333 | Supersoft 3L 11s | |||||
| 78\121 | 773.554 | 426.446 | 11:8 | 1.375 | ||||||
| 49\76 | 773.684 | 426.316 | 7:5 | 1.400 | ||||||
| 69\107 | 773.832 | 426.168 | 10:7 | 1.429 | ||||||
| 20\31 | 774.194 | 425.806 | 3:2 | 1.500 | Soft 3L 11s | |||||
| 71\110 | 774.545 | 425.455 | 11:7 | 1.571 | ||||||
| 51\79 | 774.684 | 425.316 | 8:5 | 1.600 | ||||||
| 82\127 | 774.803 | 425.197 | 13:8 | 1.625 | ||||||
| 31\48 | 775.000 | 425.000 | 5:3 | 1.667 | Semisoft 3L 11s | |||||
| 73\113 | 775.221 | 424.779 | 12:7 | 1.714 | ||||||
| 42\65 | 775.385 | 424.615 | 7:4 | 1.750 | ||||||
| 53\82 | 775.610 | 424.390 | 9:5 | 1.800 | ||||||
| 11\17 | 776.471 | 423.529 | 2:1 | 2.000 | Basic 3L 11s Scales with tunings softer than this are proper | |||||
| 46\71 | 777.465 | 422.535 | 9:4 | 2.250 | ||||||
| 35\54 | 777.778 | 422.222 | 7:3 | 2.333 | ||||||
| 59\91 | 778.022 | 421.978 | 12:5 | 2.400 | ||||||
| 24\37 | 778.378 | 421.622 | 5:2 | 2.500 | Semihard 3L 11s | |||||
| 61\94 | 778.723 | 421.277 | 13:5 | 2.600 | ||||||
| 37\57 | 778.947 | 421.053 | 8:3 | 2.667 | ||||||
| 50\77 | 779.221 | 420.779 | 11:4 | 2.750 | ||||||
| 13\20 | 780.000 | 420.000 | 3:1 | 3.000 | Hard 3L 11s | |||||
| 41\63 | 780.952 | 419.048 | 10:3 | 3.333 | ||||||
| 28\43 | 781.395 | 418.605 | 7:2 | 3.500 | ||||||
| 43\66 | 781.818 | 418.182 | 11:3 | 3.667 | ||||||
| 15\23 | 782.609 | 417.391 | 4:1 | 4.000 | Superhard 3L 11s | |||||
| 32\49 | 783.673 | 416.327 | 9:2 | 4.500 | ||||||
| 17\26 | 784.615 | 415.385 | 5:1 | 5.000 | ||||||
| 19\29 | 786.207 | 413.793 | 6:1 | 6.000 | ||||||
| 2\3 | 800.000 | 400.000 | 1:0 | → ∞ | Collapsed 3L 11s | |||||
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