10L 21s
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Scale structure
Step pattern
LssLssLssLssLssLssLssLssLssLsss
sssLssLssLssLssLssLssLssLssLssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Step size ranges
Large
1\31 to 1\10 (38.7¢ to 120.0¢)
Small
0\10 to 1\31 (0.0¢ to 38.7¢)
Generator size
Bright
3\31 to 1\10 (116.1¢ to 120.0¢)
Dark
9\10 to 28\31 (1080.0¢ to 1083.9¢)
TAMNAMS information
Descends from
1L 9s (antisinatonic)
Related MOS scales
Parent
10L 11s
Sister
21L 10s
Daughters
31L 10s
10L 31s
Equal tunings
Equalized (L:s = 1:1)
3\31 (116.1¢)
Supersoft (L:s = 4:3)
10\103 (116.5¢)
Soft (L:s = 3:2)
7\72 (116.7¢)
Semisoft (L:s = 5:3)
11\113 (116.8¢)
Basic (L:s = 2:1)
4\41 (117.1¢)
Semihard (L:s = 5:2)
9\92 (117.4¢)
Hard (L:s = 3:1)
5\51 (117.6¢)
Superhard (L:s = 4:1)
6\61 (118.0¢)
Collapsed (L:s = 1:0)
1\10 (120.0¢)
| ↖9L 20s | ↑10L 20s | 11L 20s↗ |
| ←9L 21s | 10L 21s | 11L 21s→ |
| ↙9L 22s | ↓10L 22s | 11L 22s↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┬┐ │║││║││║││║││║││║││║││║││║││║││││ │││││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLssLssLssLssLssLssLssLssLssL
10L 31s
10L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 21 small steps, repeating every octave. 10L 21s is a great-grandchild scale of 1L 9s, expanding it by 21 tones. Generators that produce this scale range from 116.1¢ to 120¢, or from 1080¢ to 1083.9¢.
Modes
| UDP | Rotational order | Step pattern |
|---|---|---|
| 30|0 | 1 | LssLssLssLssLssLssLssLssLssLsss |
| 29|1 | 4 | LssLssLssLssLssLssLssLssLsssLss |
| 28|2 | 7 | LssLssLssLssLssLssLssLsssLssLss |
| 27|3 | 10 | LssLssLssLssLssLssLsssLssLssLss |
| 26|4 | 13 | LssLssLssLssLssLsssLssLssLssLss |
| 25|5 | 16 | LssLssLssLssLsssLssLssLssLssLss |
| 24|6 | 19 | LssLssLssLsssLssLssLssLssLssLss |
| 23|7 | 22 | LssLssLsssLssLssLssLssLssLssLss |
| 22|8 | 25 | LssLsssLssLssLssLssLssLssLssLss |
| 21|9 | 28 | LsssLssLssLssLssLssLssLssLssLss |
| 20|10 | 31 | sLssLssLssLssLssLssLssLssLssLss |
| 19|11 | 3 | sLssLssLssLssLssLssLssLssLsssLs |
| 18|12 | 6 | sLssLssLssLssLssLssLssLsssLssLs |
| 17|13 | 9 | sLssLssLssLssLssLssLsssLssLssLs |
| 16|14 | 12 | sLssLssLssLssLssLsssLssLssLssLs |
| 15|15 | 15 | sLssLssLssLssLsssLssLssLssLssLs |
| 14|16 | 18 | sLssLssLssLsssLssLssLssLssLssLs |
| 13|17 | 21 | sLssLssLsssLssLssLssLssLssLssLs |
| 12|18 | 24 | sLssLsssLssLssLssLssLssLssLssLs |
| 11|19 | 27 | sLsssLssLssLssLssLssLssLssLssLs |
| 10|20 | 30 | ssLssLssLssLssLssLssLssLssLssLs |
| 9|21 | 2 | ssLssLssLssLssLssLssLssLssLsssL |
| 8|22 | 5 | ssLssLssLssLssLssLssLssLsssLssL |
| 7|23 | 8 | ssLssLssLssLssLssLssLsssLssLssL |
| 6|24 | 11 | ssLssLssLssLssLssLsssLssLssLssL |
| 5|25 | 14 | ssLssLssLssLssLsssLssLssLssLssL |
| 4|26 | 17 | ssLssLssLssLsssLssLssLssLssLssL |
| 3|27 | 20 | ssLssLssLsssLssLssLssLssLssLssL |
| 2|28 | 23 | ssLssLsssLssLssLssLssLssLssLssL |
| 1|29 | 26 | ssLsssLssLssLssLssLssLssLssLssL |
| 0|30 | 29 | sssLssLssLssLssLssLssLssLssLssL |
Scale tree
| Generator (in steps of edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\31 | 116.129 | 1083.871 | 1:1 | 1.000 | Equalized 10L 21s | |||||
| 16\165 | 116.364 | 1083.636 | 6:5 | 1.200 | ||||||
| 13\134 | 116.418 | 1083.582 | 5:4 | 1.250 | ||||||
| 23\237 | 116.456 | 1083.544 | 9:7 | 1.286 | ||||||
| 10\103 | 116.505 | 1083.495 | 4:3 | 1.333 | Supersoft 10L 21s | |||||
| 27\278 | 116.547 | 1083.453 | 11:8 | 1.375 | ||||||
| 17\175 | 116.571 | 1083.429 | 7:5 | 1.400 | ||||||
| 24\247 | 116.599 | 1083.401 | 10:7 | 1.429 | ||||||
| 7\72 | 116.667 | 1083.333 | 3:2 | 1.500 | Soft 10L 21s | |||||
| 25\257 | 116.732 | 1083.268 | 11:7 | 1.571 | ||||||
| 18\185 | 116.757 | 1083.243 | 8:5 | 1.600 | ||||||
| 29\298 | 116.779 | 1083.221 | 13:8 | 1.625 | ||||||
| 11\113 | 116.814 | 1083.186 | 5:3 | 1.667 | Semisoft 10L 21s | |||||
| 26\267 | 116.854 | 1083.146 | 12:7 | 1.714 | ||||||
| 15\154 | 116.883 | 1083.117 | 7:4 | 1.750 | ||||||
| 19\195 | 116.923 | 1083.077 | 9:5 | 1.800 | ||||||
| 4\41 | 117.073 | 1082.927 | 2:1 | 2.000 | Basic 10L 21s Scales with tunings softer than this are proper | |||||
| 17\174 | 117.241 | 1082.759 | 9:4 | 2.250 | ||||||
| 13\133 | 117.293 | 1082.707 | 7:3 | 2.333 | ||||||
| 22\225 | 117.333 | 1082.667 | 12:5 | 2.400 | ||||||
| 9\92 | 117.391 | 1082.609 | 5:2 | 2.500 | Semihard 10L 21s | |||||
| 23\235 | 117.447 | 1082.553 | 13:5 | 2.600 | ||||||
| 14\143 | 117.483 | 1082.517 | 8:3 | 2.667 | ||||||
| 19\194 | 117.526 | 1082.474 | 11:4 | 2.750 | ||||||
| 5\51 | 117.647 | 1082.353 | 3:1 | 3.000 | Hard 10L 21s | |||||
| 16\163 | 117.791 | 1082.209 | 10:3 | 3.333 | ||||||
| 11\112 | 117.857 | 1082.143 | 7:2 | 3.500 | ||||||
| 17\173 | 117.919 | 1082.081 | 11:3 | 3.667 | ||||||
| 6\61 | 118.033 | 1081.967 | 4:1 | 4.000 | Superhard 10L 21s | |||||
| 13\132 | 118.182 | 1081.818 | 9:2 | 4.500 | ||||||
| 7\71 | 118.310 | 1081.690 | 5:1 | 5.000 | ||||||
| 8\81 | 118.519 | 1081.481 | 6:1 | 6.000 | ||||||
| 1\10 | 120.000 | 1080.000 | 1:0 | → ∞ | Collapsed 10L 21s | |||||
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