5L 4s (3/1-equivalent)
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Scale structure
Step pattern
LLsLsLsLs
sLsLsLsLL
Equave
3/1 (1902.0¢)
Period
3/1 (1902.0¢)
Generator size(edt)
Bright
7\9 to 4\5 (1479.3¢ to 1521.6¢)
Dark
1\5 to 2\9 (380.4¢ to 422.7¢)
Related MOS scales
Parent
4L 1s⟨3/1⟩
Sister
4L 5s⟨3/1⟩
Daughters
9L 5s⟨3/1⟩, 5L 9s⟨3/1⟩
Neutralized
1L 8s⟨3/1⟩
2-Flought
14L 4s⟨3/1⟩, 5L 13s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)
7\9 (1479.3¢)
Supersoft (L:s = 4:3)
25\32 (1485.9¢)
Soft (L:s = 3:2)
18\23 (1488.5¢)
Semisoft (L:s = 5:3)
29\37 (1490.7¢)
Basic (L:s = 2:1)
11\14 (1494.4¢)
Semihard (L:s = 5:2)
26\33 (1498.5¢)
Hard (L:s = 3:1)
15\19 (1501.5¢)
Superhard (L:s = 4:1)
19\24 (1505.7¢)
Collapsed (L:s = 1:0)
4\5 (1521.6¢)
| ↖ 4L 3s⟨3/1⟩ | ↑ 5L 3s⟨3/1⟩ | 6L 3s⟨3/1⟩ ↗ |
| ← 4L 4s⟨3/1⟩ | 5L 4s (3/1-equivalent) | 6L 4s⟨3/1⟩ → |
| ↙ 4L 5s⟨3/1⟩ | ↓ 5L 5s⟨3/1⟩ | 6L 5s⟨3/1⟩ ↘ |
┌╥╥┬╥┬╥┬╥┬┐ │║║│║│║│║││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
sLsLsLsLL
5L 4s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 4 small steps, repeating every interval of 3/1 (1902.0¢). Generators that produce this scale range from 1479.3¢ to 1521.6¢, or from 380.4¢ to 422.7¢.
Theory
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 8|0 | 1 | LLsLsLsLs |
| 7|1 | 8 | LsLLsLsLs |
| 6|2 | 6 | LsLsLLsLs |
| 5|3 | 4 | LsLsLsLLs |
| 4|4 | 2 | LsLsLsLsL |
| 3|5 | 9 | sLLsLsLsL |
| 2|6 | 7 | sLsLLsLsL |
| 1|7 | 5 | sLsLsLLsL |
| 0|8 | 3 | sLsLsLsLL |
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 | Minor 1-mosstep | m1ms | s | 0.0¢ to 211.3¢ |
| Major 1-mosstep | M1ms | L | 211.3¢ to 380.4¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 380.4¢ to 422.7¢ |
| Augmented 2-mosstep | A2ms | 2L | 422.7¢ to 760.8¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | L + 2s | 380.4¢ to 634.0¢ |
| Major 3-mosstep | M3ms | 2L + s | 634.0¢ to 760.8¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 760.8¢ to 845.3¢ |
| Major 4-mosstep | M4ms | 3L + s | 845.3¢ to 1141.2¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 2L + 3s | 760.8¢ to 1056.6¢ |
| Major 5-mosstep | M5ms | 3L + 2s | 1056.6¢ to 1141.2¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 1141.2¢ to 1268.0¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 1268.0¢ to 1521.6¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | 3L + 4s | 1141.2¢ to 1479.3¢ |
| Perfect 7-mosstep | P7ms | 4L + 3s | 1479.3¢ to 1521.6¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 4L + 4s | 1521.6¢ to 1690.6¢ |
| Major 8-mosstep | M8ms | 5L + 3s | 1690.6¢ to 1902.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | 5L + 4s | 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 | LLsLsLsLs | Perf. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 7|1 | 8 | LsLLsLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 6|2 | 6 | LsLsLLsLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 5|3 | 4 | LsLsLsLLs | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Maj. | Perf. |
| 4|4 | 2 | LsLsLsLsL | Perf. | Maj. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 3|5 | 9 | sLLsLsLsL | Perf. | Min. | Perf. | Maj. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 2|6 | 7 | sLsLLsLsL | Perf. | Min. | Perf. | Min. | Min. | Maj. | Min. | Perf. | Min. | Perf. |
| 1|7 | 5 | sLsLsLLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 0|8 | 3 | sLsLsLsLL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Dim. | Min. | Perf. |
Scale tree
| Generator(edt) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\9 | 1479.298 | 422.657 | 1:1 | 1.000 | Equalized 5L 4s⟨3/1⟩ | |||||
| 39\50 | 1483.525 | 418.430 | 6:5 | 1.200 | ||||||
| 32\41 | 1484.453 | 417.502 | 5:4 | 1.250 | ||||||
| 57\73 | 1485.088 | 416.867 | 9:7 | 1.286 | ||||||
| 25\32 | 1485.902 | 416.053 | 4:3 | 1.333 | Supersoft 5L 4s⟨3/1⟩ | |||||
| 68\87 | 1486.586 | 415.369 | 11:8 | 1.375 | ||||||
| 43\55 | 1486.983 | 414.972 | 7:5 | 1.400 | ||||||
| 61\78 | 1487.426 | 414.529 | 10:7 | 1.429 | ||||||
| 18\23 | 1488.487 | 413.468 | 3:2 | 1.500 | Soft 5L 4s⟨3/1⟩ | |||||
| 65\83 | 1489.483 | 412.472 | 11:7 | 1.571 | ||||||
| 47\60 | 1489.865 | 412.090 | 8:5 | 1.600 | ||||||
| 76\97 | 1490.192 | 411.763 | 13:8 | 1.625 | ||||||
| 29\37 | 1490.721 | 411.234 | 5:3 | 1.667 | Semisoft 5L 4s⟨3/1⟩ | |||||
| 69\88 | 1491.306 | 410.649 | 12:7 | 1.714 | ||||||
| 40\51 | 1491.729 | 410.226 | 7:4 | 1.750 | ||||||
| 51\65 | 1492.303 | 409.652 | 9:5 | 1.800 | ||||||
| 11\14 | 1494.393 | 407.562 | 2:1 | 2.000 | Basic 5L 4s⟨3/1⟩ Scales with tunings softer than this are proper | |||||
| 48\61 | 1496.620 | 405.335 | 9:4 | 2.250 | ||||||
| 37\47 | 1497.284 | 404.671 | 7:3 | 2.333 | ||||||
| 63\80 | 1497.790 | 404.165 | 12:5 | 2.400 | ||||||
| 26\33 | 1498.510 | 403.445 | 5:2 | 2.500 | Semihard 5L 4s⟨3/1⟩ | |||||
| 67\85 | 1499.188 | 402.767 | 13:5 | 2.600 | ||||||
| 41\52 | 1499.618 | 402.337 | 8:3 | 2.667 | ||||||
| 56\71 | 1500.134 | 401.821 | 11:4 | 2.750 | ||||||
| 15\19 | 1501.543 | 400.412 | 3:1 | 3.000 | Hard 5L 4s⟨3/1⟩ | |||||
| 49\62 | 1503.158 | 398.797 | 10:3 | 3.333 | ||||||
| 34\43 | 1503.871 | 398.084 | 7:2 | 3.500 | ||||||
| 53\67 | 1504.532 | 397.423 | 11:3 | 3.667 | ||||||
| 19\24 | 1505.714 | 396.241 | 4:1 | 4.000 | Superhard 5L 4s⟨3/1⟩ | |||||
| 42\53 | 1507.210 | 394.745 | 9:2 | 4.500 | ||||||
| 23\29 | 1508.447 | 393.508 | 5:1 | 5.000 | ||||||
| 27\34 | 1510.376 | 391.579 | 6:1 | 6.000 | ||||||
| 4\5 | 1521.564 | 380.391 | 1:0 | → ∞ | Collapsed 5L 4s⟨3/1⟩ | |||||
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