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
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 |
Temperament interpretations
 |
Todo: expand |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0¢ to 211.3¢ |
| Perfect 1-mosstep | P1ms | L | 211.3¢ to 237.7¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 237.7¢ to 422.7¢ |
| Major 2-mosstep | M2ms | 2L | 422.7¢ to 475.5¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 475.5¢ to 634.0¢ |
| Major 3-mosstep | M3ms | 3L | 634.0¢ to 713.2¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 713.2¢ to 845.3¢ |
| Major 4-mosstep | M4ms | 4L | 845.3¢ to 951.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 951.0¢ to 1056.6¢ |
| Major 5-mosstep | M5ms | 5L | 1056.6¢ to 1188.7¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 1188.7¢ to 1268.0¢ |
| Major 6-mosstep | M6ms | 6L | 1268.0¢ to 1426.5¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 6L + s | 1426.5¢ to 1479.3¢ |
| Major 7-mosstep | M7ms | 7L | 1479.3¢ to 1664.2¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 7L + s | 1664.2¢ to 1690.6¢ |
| Augmented 8-mosstep | A8ms | 8L | 1690.6¢ to 1902.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | 8L + s | 1902.0¢ |
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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