8L 1s (3/1-equivalent)
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Scale structure
Step pattern
LLLLLLLLs
sLLLLLLLL
Equave
3/1 (1902.0¢)
Period
3/1 (1902.0¢)
Generator size(edt)
Bright
1\9 to 1\8 (211.3¢ to 237.7¢)
Dark
7\8 to 8\9 (1664.2¢ to 1690.6¢)
Related MOS scales
Parent
1L 7s⟨3/1⟩
Sister
1L 8s⟨3/1⟩
Daughters
9L 8s⟨3/1⟩, 8L 9s⟨3/1⟩
Neutralized
7L 2s⟨3/1⟩
2-Flought
17L 1s⟨3/1⟩, 8L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)
1\9 (211.3¢)
Supersoft (L:s = 4:3)
4\35 (217.4¢)
Soft (L:s = 3:2)
3\26 (219.5¢)
Semisoft (L:s = 5:3)
5\43 (221.2¢)
Basic (L:s = 2:1)
2\17 (223.8¢)
Semihard (L:s = 5:2)
5\42 (226.4¢)
Hard (L:s = 3:1)
3\25 (228.2¢)
Superhard (L:s = 4:1)
4\33 (230.5¢)
Collapsed (L:s = 1:0)
1\8 (237.7¢)
← 7L 1s⟨3/1⟩ | 8L 1s (3/1-equivalent) | 9L 1s⟨3/1⟩ → |
↙ 7L 2s⟨3/1⟩ | ↓ 8L 2s⟨3/1⟩ | 9L 2s⟨3/1⟩ ↘ |
┌╥╥╥╥╥╥╥╥┬┐ │║║║║║║║║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLLLLLLLL
8L 1s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 8 large steps and 1 small step, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 211.3¢ to 237.7¢, or from 1664.2¢ to 1690.6¢. Scales of this form are always proper because there is only one small step.
Theory
Temperament interpretations
Modes
UDP | Cyclic Order |
Step Pattern |
---|---|---|
8|0 | 1 | LLLLLLLLs |
7|1 | 2 | LLLLLLLsL |
6|2 | 3 | LLLLLLsLL |
5|3 | 4 | LLLLLsLLL |
4|4 | 5 | LLLLsLLLL |
3|5 | 6 | LLLsLLLLL |
2|6 | 7 | LLsLLLLLL |
1|7 | 8 | LsLLLLLLL |
0|8 | 9 | sLLLLLLLL |
Scale degrees
UDP | Cyclic Order |
Step Pattern |
Scale Degree (mosdegree) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||
8|0 | 1 | LLLLLLLLs | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Perf. |
7|1 | 2 | LLLLLLLsL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
6|2 | 3 | LLLLLLsLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. |
5|3 | 4 | LLLLLsLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. | Perf. |
4|4 | 5 | LLLLsLLLL | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. | Perf. |
3|5 | 6 | LLLsLLLLL | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. | Perf. |
2|6 | 7 | LLsLLLLLL | Perf. | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
1|7 | 8 | LsLLLLLLL | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
0|8 | 9 | sLLLLLLLL | Perf. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
Scale tree
Generator(edt) | Cents | Step Ratio | Comments(always proper) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
1\9 | 211.328 | 1690.627 | 1:1 | 1.000 | Equalized 8L 1s⟨3/1⟩ | |||||
6\53 | 215.316 | 1686.639 | 6:5 | 1.200 | ||||||
5\44 | 216.131 | 1685.824 | 5:4 | 1.250 | ||||||
9\79 | 216.678 | 1685.277 | 9:7 | 1.286 | Just 17/15 generator | |||||
4\35 | 217.366 | 1684.589 | 4:3 | 1.333 | Supersoft 8L 1s⟨3/1⟩ | |||||
11\96 | 217.932 | 1684.023 | 11:8 | 1.375 | ||||||
7\61 | 218.257 | 1683.698 | 7:5 | 1.400 | ||||||
10\87 | 218.616 | 1683.339 | 10:7 | 1.429 | ||||||
3\26 | 219.456 | 1682.499 | 3:2 | 1.500 | Soft 8L 1s⟨3/1⟩ | |||||
11\95 | 220.226 | 1681.729 | 11:7 | 1.571 | Dubhe is around here | |||||
8\69 | 220.517 | 1681.438 | 8:5 | 1.600 | ||||||
13\112 | 220.763 | 1681.192 | 13:8 | 1.625 | ||||||
5\43 | 221.158 | 1680.797 | 5:3 | 1.667 | Semisoft 8L 1s⟨3/1⟩ | |||||
12\103 | 221.587 | 1680.368 | 12:7 | 1.714 | ||||||
7\60 | 221.895 | 1680.060 | 7:4 | 1.750 | ||||||
9\77 | 222.306 | 1679.649 | 9:5 | 1.800 | ||||||
2\17 | 223.759 | 1678.196 | 2:1 | 2.000 | Basic 8L 1s⟨3/1⟩ | |||||
9\76 | 225.232 | 1676.723 | 9:4 | 2.250 | ||||||
7\59 | 225.656 | 1676.299 | 7:3 | 2.333 | ||||||
12\101 | 225.975 | 1675.980 | 12:5 | 2.400 | ||||||
5\42 | 226.423 | 1675.532 | 5:2 | 2.500 | Semihard 8L 1s⟨3/1⟩ | |||||
13\109 | 226.839 | 1675.116 | 13:5 | 2.600 | ||||||
8\67 | 227.099 | 1674.856 | 8:3 | 2.667 | ||||||
11\92 | 227.408 | 1674.547 | 11:4 | 2.750 | ||||||
3\25 | 228.235 | 1673.720 | 3:1 | 3.000 | Hard 8L 1s⟨3/1⟩ | |||||
10\83 | 229.151 | 1672.804 | 10:3 | 3.333 | ||||||
7\58 | 229.546 | 1672.409 | 7:2 | 3.500 | ||||||
11\91 | 229.907 | 1672.048 | 11:3 | 3.667 | ||||||
4\33 | 230.540 | 1671.415 | 4:1 | 4.000 | Superhard 8L 1s⟨3/1⟩ | |||||
9\74 | 231.319 | 1670.636 | 9:2 | 4.500 | ||||||
5\41 | 231.946 | 1670.009 | 5:1 | 5.000 | ||||||
6\49 | 232.892 | 1669.063 | 6:1 | 6.000 | ||||||
1\8 | 237.744 | 1664.211 | 1:0 | → ∞ | Collapsed 8L 1s⟨3/1⟩ |
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