8L 21s
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Scale structure
Step pattern
LssLsssLssLsssLsssLssLsssLsss
sssLsssLssLsssLsssLssLsssLssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
18\29 to 5\8 (744.8¢ to 750.0¢)
Dark
3\8 to 11\29 (450.0¢ to 455.2¢)
TAMNAMS information
Descends from
5L 3s (oneirotonic)
Ancestor's step ratio range
1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent
8L 13s
Sister
21L 8s
Daughters
29L 8s, 8L 29s
Neutralized
16L 13s
2-Flought
37L 21s, 8L 50s
Equal tunings
Equalized (L:s = 1:1)
18\29 (744.8¢)
Supersoft (L:s = 4:3)
59\95 (745.3¢)
Soft (L:s = 3:2)
41\66 (745.5¢)
Semisoft (L:s = 5:3)
64\103 (745.6¢)
Basic (L:s = 2:1)
23\37 (745.9¢)
Semihard (L:s = 5:2)
51\82 (746.3¢)
Hard (L:s = 3:1)
28\45 (746.7¢)
Superhard (L:s = 4:1)
33\53 (747.2¢)
Collapsed (L:s = 1:0)
5\8 (750.0¢)
| ↖ 7L 20s | ↑ 8L 20s | 9L 20s ↗ |
| ← 7L 21s | 8L 21s | 9L 21s → |
| ↙ 7L 22s | ↓ 8L 22s | 9L 22s ↘ |
┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬┬╥┬┬╥┬┬┬╥┬┬┬┐ │║││║│││║││║│││║│││║││║│││║││││ │││││││││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLssLsssLsssLssLsssLssL
8L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 21 small steps, repeating every octave. 8L 21s is a great-grandchild scale of 5L 3s, expanding it by 21 tones. Generators that produce this scale range from 744.8¢ to 750¢, or from 450¢ to 455.2¢.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 28|0 | 1 | LssLsssLssLsssLsssLssLsssLsss |
| 27|1 | 19 | LssLsssLsssLssLsssLssLsssLsss |
| 26|2 | 8 | LssLsssLsssLssLsssLsssLssLsss |
| 25|3 | 26 | LsssLssLsssLssLsssLsssLssLsss |
| 24|4 | 15 | LsssLssLsssLsssLssLsssLssLsss |
| 23|5 | 4 | LsssLssLsssLsssLssLsssLsssLss |
| 22|6 | 22 | LsssLsssLssLsssLssLsssLsssLss |
| 21|7 | 11 | LsssLsssLssLsssLsssLssLsssLss |
| 20|8 | 29 | sLssLsssLssLsssLsssLssLsssLss |
| 19|9 | 18 | sLssLsssLsssLssLsssLssLsssLss |
| 18|10 | 7 | sLssLsssLsssLssLsssLsssLssLss |
| 17|11 | 25 | sLsssLssLsssLssLsssLsssLssLss |
| 16|12 | 14 | sLsssLssLsssLsssLssLsssLssLss |
| 15|13 | 3 | sLsssLssLsssLsssLssLsssLsssLs |
| 14|14 | 21 | sLsssLsssLssLsssLssLsssLsssLs |
| 13|15 | 10 | sLsssLsssLssLsssLsssLssLsssLs |
| 12|16 | 28 | ssLssLsssLssLsssLsssLssLsssLs |
| 11|17 | 17 | ssLssLsssLsssLssLsssLssLsssLs |
| 10|18 | 6 | ssLssLsssLsssLssLsssLsssLssLs |
| 9|19 | 24 | ssLsssLssLsssLssLsssLsssLssLs |
| 8|20 | 13 | ssLsssLssLsssLsssLssLsssLssLs |
| 7|21 | 2 | ssLsssLssLsssLsssLssLsssLsssL |
| 6|22 | 20 | ssLsssLsssLssLsssLssLsssLsssL |
| 5|23 | 9 | ssLsssLsssLssLsssLsssLssLsssL |
| 4|24 | 27 | sssLssLsssLssLsssLsssLssLsssL |
| 3|25 | 16 | sssLssLsssLsssLssLsssLssLsssL |
| 2|26 | 5 | sssLssLsssLsssLssLsssLsssLssL |
| 1|27 | 23 | sssLsssLssLsssLssLsssLsssLssL |
| 0|28 | 12 | sssLsssLssLsssLsssLssLsssLssL |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 18\29 | 744.828 | 455.172 | 1:1 | 1.000 | Equalized 8L 21s | |||||
| 95\153 | 745.098 | 454.902 | 6:5 | 1.200 | ||||||
| 77\124 | 745.161 | 454.839 | 5:4 | 1.250 | ||||||
| 136\219 | 745.205 | 454.795 | 9:7 | 1.286 | ||||||
| 59\95 | 745.263 | 454.737 | 4:3 | 1.333 | Supersoft 8L 21s | |||||
| 159\256 | 745.312 | 454.688 | 11:8 | 1.375 | ||||||
| 100\161 | 745.342 | 454.658 | 7:5 | 1.400 | ||||||
| 141\227 | 745.374 | 454.626 | 10:7 | 1.429 | ||||||
| 41\66 | 745.455 | 454.545 | 3:2 | 1.500 | Soft 8L 21s | |||||
| 146\235 | 745.532 | 454.468 | 11:7 | 1.571 | ||||||
| 105\169 | 745.562 | 454.438 | 8:5 | 1.600 | ||||||
| 169\272 | 745.588 | 454.412 | 13:8 | 1.625 | ||||||
| 64\103 | 745.631 | 454.369 | 5:3 | 1.667 | Semisoft 8L 21s | |||||
| 151\243 | 745.679 | 454.321 | 12:7 | 1.714 | ||||||
| 87\140 | 745.714 | 454.286 | 7:4 | 1.750 | ||||||
| 110\177 | 745.763 | 454.237 | 9:5 | 1.800 | ||||||
| 23\37 | 745.946 | 454.054 | 2:1 | 2.000 | Basic 8L 21s Scales with tunings softer than this are proper | |||||
| 97\156 | 746.154 | 453.846 | 9:4 | 2.250 | ||||||
| 74\119 | 746.218 | 453.782 | 7:3 | 2.333 | ||||||
| 125\201 | 746.269 | 453.731 | 12:5 | 2.400 | ||||||
| 51\82 | 746.341 | 453.659 | 5:2 | 2.500 | Semihard 8L 21s | |||||
| 130\209 | 746.411 | 453.589 | 13:5 | 2.600 | ||||||
| 79\127 | 746.457 | 453.543 | 8:3 | 2.667 | ||||||
| 107\172 | 746.512 | 453.488 | 11:4 | 2.750 | ||||||
| 28\45 | 746.667 | 453.333 | 3:1 | 3.000 | Hard 8L 21s | |||||
| 89\143 | 746.853 | 453.147 | 10:3 | 3.333 | ||||||
| 61\98 | 746.939 | 453.061 | 7:2 | 3.500 | ||||||
| 94\151 | 747.020 | 452.980 | 11:3 | 3.667 | ||||||
| 33\53 | 747.170 | 452.830 | 4:1 | 4.000 | Superhard 8L 21s | |||||
| 71\114 | 747.368 | 452.632 | 9:2 | 4.500 | ||||||
| 38\61 | 747.541 | 452.459 | 5:1 | 5.000 | ||||||
| 43\69 | 747.826 | 452.174 | 6:1 | 6.000 | ||||||
| 5\8 | 750.000 | 450.000 | 1:0 | → ∞ | Collapsed 8L 21s | |||||
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