3L 20s
| ↖ 2L 19s | ↑ 3L 19s | 4L 19s ↗ |
| ← 2L 20s | 3L 20s | 4L 20s → |
| ↙ 2L 21s | ↓ 3L 21s | 4L 21s ↘ |
Scale structure
sssssssLsssssssLssssssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
3L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 20 small steps, repeating every octave. 3L 20s is related to 3L 5s, expanding it by 15 tones. Generators that produce this scale range from 782.6 ¢ to 800 ¢, or from 400 ¢ to 417.4 ¢.
This is the MOS where the small steps split 7-7-6 among the large steps. Its generator is a supermajor third no larger than 8/23edo (417.391 cents), which is almost exactly 14/11.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 22|0 | 1 | LssssssLsssssssLsssssss |
| 21|1 | 16 | LsssssssLssssssLsssssss |
| 20|2 | 8 | LsssssssLsssssssLssssss |
| 19|3 | 23 | sLssssssLsssssssLssssss |
| 18|4 | 15 | sLsssssssLssssssLssssss |
| 17|5 | 7 | sLsssssssLsssssssLsssss |
| 16|6 | 22 | ssLssssssLsssssssLsssss |
| 15|7 | 14 | ssLsssssssLssssssLsssss |
| 14|8 | 6 | ssLsssssssLsssssssLssss |
| 13|9 | 21 | sssLssssssLsssssssLssss |
| 12|10 | 13 | sssLsssssssLssssssLssss |
| 11|11 | 5 | sssLsssssssLsssssssLsss |
| 10|12 | 20 | ssssLssssssLsssssssLsss |
| 9|13 | 12 | ssssLsssssssLssssssLsss |
| 8|14 | 4 | ssssLsssssssLsssssssLss |
| 7|15 | 19 | sssssLssssssLsssssssLss |
| 6|16 | 11 | sssssLsssssssLssssssLss |
| 5|17 | 3 | sssssLsssssssLsssssssLs |
| 4|18 | 18 | ssssssLssssssLsssssssLs |
| 3|19 | 10 | ssssssLsssssssLssssssLs |
| 2|20 | 2 | ssssssLsssssssLsssssssL |
| 1|21 | 17 | sssssssLssssssLsssssssL |
| 0|22 | 9 | sssssssLsssssssLssssssL |
Scale tree
|
Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead.
Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}
|
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 15\23 | 782.609 | 417.391 | 1:1 | 1.000 | Equalized 3L 20s | |||||
| 77\118 | 783.051 | 416.949 | 6:5 | 1.200 | ||||||
| 62\95 | 783.158 | 416.842 | 5:4 | 1.250 | ||||||
| 109\167 | 783.234 | 416.766 | 9:7 | 1.286 | ||||||
| 47\72 | 783.333 | 416.667 | 4:3 | 1.333 | Supersoft 3L 20s | |||||
| 126\193 | 783.420 | 416.580 | 11:8 | 1.375 | ||||||
| 79\121 | 783.471 | 416.529 | 7:5 | 1.400 | ||||||
| 111\170 | 783.529 | 416.471 | 10:7 | 1.429 | ||||||
| 32\49 | 783.673 | 416.327 | 3:2 | 1.500 | Soft 3L 20s | |||||
| 113\173 | 783.815 | 416.185 | 11:7 | 1.571 | ||||||
| 81\124 | 783.871 | 416.129 | 8:5 | 1.600 | ||||||
| 130\199 | 783.920 | 416.080 | 13:8 | 1.625 | ||||||
| 49\75 | 784.000 | 416.000 | 5:3 | 1.667 | Semisoft 3L 20s | |||||
| 115\176 | 784.091 | 415.909 | 12:7 | 1.714 | ||||||
| 66\101 | 784.158 | 415.842 | 7:4 | 1.750 | ||||||
| 83\127 | 784.252 | 415.748 | 9:5 | 1.800 | ||||||
| 17\26 | 784.615 | 415.385 | 2:1 | 2.000 | Basic 3L 20s Scales with tunings softer than this are proper | |||||
| 70\107 | 785.047 | 414.953 | 9:4 | 2.250 | ||||||
| 53\81 | 785.185 | 414.815 | 7:3 | 2.333 | ||||||
| 89\136 | 785.294 | 414.706 | 12:5 | 2.400 | ||||||
| 36\55 | 785.455 | 414.545 | 5:2 | 2.500 | Semihard 3L 20s | |||||
| 91\139 | 785.612 | 414.388 | 13:5 | 2.600 | ||||||
| 55\84 | 785.714 | 414.286 | 8:3 | 2.667 | ||||||
| 74\113 | 785.841 | 414.159 | 11:4 | 2.750 | ||||||
| 19\29 | 786.207 | 413.793 | 3:1 | 3.000 | Hard 3L 20s | |||||
| 59\90 | 786.667 | 413.333 | 10:3 | 3.333 | ||||||
| 40\61 | 786.885 | 413.115 | 7:2 | 3.500 | ||||||
| 61\93 | 787.097 | 412.903 | 11:3 | 3.667 | ||||||
| 21\32 | 787.500 | 412.500 | 4:1 | 4.000 | Superhard 3L 20s | |||||
| 44\67 | 788.060 | 411.940 | 9:2 | 4.500 | ||||||
| 23\35 | 788.571 | 411.429 | 5:1 | 5.000 | ||||||
| 25\38 | 789.474 | 410.526 | 6:1 | 6.000 | ||||||
| 2\3 | 800.000 | 400.000 | 1:0 | → ∞ | Collapsed 3L 20s | |||||