5L 3s (5/2-equivalent)
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Scale structure
Step pattern
LLsLLsLs
sLsLLsLL
Equave
5/2 (1586.3¢)
Period
5/2 (1586.3¢)
Generator size(ed5/2)
Bright
3\8 to 2\5 (594.9¢ to 634.5¢)
Dark
3\5 to 5\8 (951.8¢ to 991.4¢)
Related MOS scales
Parent
3L 2s⟨5/2⟩
Sister
3L 5s⟨5/2⟩
Daughters
8L 5s⟨5/2⟩, 5L 8s⟨5/2⟩
Neutralized
2L 6s⟨5/2⟩
2-Flought
13L 3s⟨5/2⟩, 5L 11s⟨5/2⟩
Equal tunings(ed5/2)
Equalized (L:s = 1:1)
3\8 (594.9¢)
Supersoft (L:s = 4:3)
11\29 (601.7¢)
Soft (L:s = 3:2)
8\21 (604.3¢)
Semisoft (L:s = 5:3)
13\34 (606.5¢)
Basic (L:s = 2:1)
5\13 (610.1¢)
Semihard (L:s = 5:2)
12\31 (614.1¢)
Hard (L:s = 3:1)
7\18 (616.9¢)
Superhard (L:s = 4:1)
9\23 (620.7¢)
Collapsed (L:s = 1:0)
2\5 (634.5¢)
| ↖ 4L 2s⟨5/2⟩ | ↑ 5L 2s⟨5/2⟩ | 6L 2s⟨5/2⟩ ↗ |
| ← 4L 3s⟨5/2⟩ | 5L 3s (5/2-equivalent) | 6L 3s⟨5/2⟩ → |
| ↙ 4L 4s⟨5/2⟩ | ↓ 5L 4s⟨5/2⟩ | 6L 4s⟨5/2⟩ ↘ |
┌╥╥┬╥╥┬╥┬┐ │║║│║║│║││ ││││││││││ └┴┴┴┴┴┴┴┴┘
sLsLLsLL
5L 3s⟨5/2⟩ is a 5/2-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 3 small steps, repeating every interval of 5/2 (1586.3¢). Generators that produce this scale range from 594.9¢ to 634.5¢, or from 951.8¢ to 991.4¢.
Theory
This scale can be thought of as a MOS generated by 5/2-equivalent jubilic temperament where 50/49 vanishes. This is one of the most simple no-threes temperaments, although in this case it is using the second-best period choice of 5/2 rather than 2/1, causing strict MOS to be generated rather than multi-MOS. The bright generator of the MOS represents 7/5~10/7 and the dark generator represents 7/4~25/14. This gives 5L 3s⟨5/2⟩ many approximations of 4:5:7 chords for no-threes harmony.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 7|0 | 1 | LLsLLsLs |
| 6|1 | 4 | LLsLsLLs |
| 5|2 | 7 | LsLLsLLs |
| 4|3 | 2 | LsLLsLsL |
| 3|4 | 5 | LsLsLLsL |
| 2|5 | 8 | sLLsLLsL |
| 1|6 | 3 | sLLsLsLL |
| 0|7 | 6 | sLsLLsLL |
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 198.3¢ |
| Major 1-mosstep | M1ms | L | 198.3¢ to 317.3¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 317.3¢ to 396.6¢ |
| Major 2-mosstep | M2ms | 2L | 396.6¢ to 634.5¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | L + 2s | 317.3¢ to 594.9¢ |
| Perfect 3-mosstep | P3ms | 2L + s | 594.9¢ to 634.5¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 2L + 2s | 634.5¢ to 793.2¢ |
| Major 4-mosstep | M4ms | 3L + s | 793.2¢ to 951.8¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 3L + 2s | 951.8¢ to 991.4¢ |
| Augmented 5-mosstep | A5ms | 4L + s | 991.4¢ to 1269.1¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 3L + 3s | 951.8¢ to 1189.7¢ |
| Major 6-mosstep | M6ms | 4L + 2s | 1189.7¢ to 1269.1¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 4L + 3s | 1269.1¢ to 1388.0¢ |
| Major 7-mosstep | M7ms | 5L + 2s | 1388.0¢ to 1586.3¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 5L + 3s | 1586.3¢ |
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 7|0 | 1 | LLsLLsLs |
| 6|1 | 4 | LLsLsLLs |
| 5|2 | 7 | LsLLsLLs |
| 4|3 | 2 | LsLLsLsL |
| 3|4 | 5 | LsLsLLsL |
| 2|5 | 8 | sLLsLLsL |
| 1|6 | 3 | sLLsLsLL |
| 0|7 | 6 | sLsLLsLL |
Scale tree
| Generator(ed5/2) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\8 | 594.868 | 991.446 | 1:1 | 1.000 | Equalized 5L 3s⟨5/2⟩ | |||||
| 17\45 | 599.274 | 987.040 | 6:5 | 1.200 | ||||||
| 14\37 | 600.227 | 986.087 | 5:4 | 1.250 | ||||||
| 25\66 | 600.876 | 985.437 | 9:7 | 1.286 | ||||||
| 11\29 | 601.705 | 984.609 | 4:3 | 1.333 | Supersoft 5L 3s⟨5/2⟩ Jubilic is in this region | |||||
| 30\79 | 602.398 | 983.916 | 11:8 | 1.375 | ||||||
| 19\50 | 602.799 | 983.515 | 7:5 | 1.400 | ||||||
| 27\71 | 603.246 | 983.068 | 10:7 | 1.429 | ||||||
| 8\21 | 604.310 | 982.004 | 3:2 | 1.500 | Soft 5L 3s⟨5/2⟩ | |||||
| 29\76 | 605.304 | 981.010 | 11:7 | 1.571 | ||||||
| 21\55 | 605.683 | 980.630 | 8:5 | 1.600 | ||||||
| 34\89 | 606.007 | 980.306 | 13:8 | 1.625 | ||||||
| 13\34 | 606.532 | 979.782 | 5:3 | 1.667 | Semisoft 5L 3s⟨5/2⟩ | |||||
| 31\81 | 607.108 | 979.206 | 12:7 | 1.714 | ||||||
| 18\47 | 607.524 | 978.789 | 7:4 | 1.750 | ||||||
| 23\60 | 608.087 | 978.227 | 9:5 | 1.800 | ||||||
| 5\13 | 610.121 | 976.193 | 2:1 | 2.000 | Basic 5L 3s⟨5/2⟩ Scales with tunings softer than this are proper | |||||
| 22\57 | 612.261 | 974.052 | 9:4 | 2.250 | ||||||
| 17\44 | 612.894 | 973.420 | 7:3 | 2.333 | ||||||
| 29\75 | 613.375 | 972.939 | 12:5 | 2.400 | ||||||
| 12\31 | 614.057 | 972.257 | 5:2 | 2.500 | Semihard 5L 3s⟨5/2⟩ | |||||
| 31\80 | 614.697 | 971.617 | 13:5 | 2.600 | ||||||
| 19\49 | 615.101 | 971.212 | 8:3 | 2.667 | ||||||
| 26\67 | 615.584 | 970.729 | 11:4 | 2.750 | ||||||
| 7\18 | 616.900 | 969.414 | 3:1 | 3.000 | Hard 5L 3s⟨5/2⟩ | |||||
| 23\59 | 618.393 | 967.920 | 10:3 | 3.333 | ||||||
| 16\41 | 619.049 | 967.264 | 7:2 | 3.500 | ||||||
| 25\64 | 619.654 | 966.660 | 11:3 | 3.667 | ||||||
| 9\23 | 620.731 | 965.582 | 4:1 | 4.000 | Superhard 5L 3s⟨5/2⟩ | |||||
| 20\51 | 622.084 | 964.230 | 9:2 | 4.500 | ||||||
| 11\28 | 623.195 | 963.119 | 5:1 | 5.000 | ||||||
| 13\33 | 624.911 | 961.402 | 6:1 | 6.000 | ||||||
| 2\5 | 634.525 | 951.788 | 1:0 | → ∞ | Collapsed 5L 3s⟨5/2⟩ | |||||