1L 8s
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Scale structure
Step pattern
Lssssssss
ssssssssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
8\9 to 1\1 (1066.7¢ to 1200.0¢)
Dark
0\1 to 1\9 (0.0¢ to 133.3¢)
Related MOS scales
Parent
1L 7s
Sister
8L 1s
Daughters
9L 1s, 1L 9s
Neutralized
2L 7s
2-Flought
10L 8s, 1L 17s
Equal tunings
Equalized (L:s = 1:1)
8\9 (1066.7¢)
Supersoft (L:s = 4:3)
25\28 (1071.4¢)
Soft (L:s = 3:2)
17\19 (1073.7¢)
Semisoft (L:s = 5:3)
26\29 (1075.9¢)
Basic (L:s = 2:1)
9\10 (1080.0¢)
Semihard (L:s = 5:2)
19\21 (1085.7¢)
Hard (L:s = 3:1)
10\11 (1090.9¢)
Superhard (L:s = 4:1)
11\12 (1100.0¢)
Collapsed (L:s = 1:0)
1\1 (1200.0¢)
| ↑ 1L 7s | 2L 7s ↗ | |
| 1L 8s | 2L 8s → | |
| ↓ 1L 9s | 2L 9s ↘ |
┌╥┬┬┬┬┬┬┬┬┐ │║│││││││││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
ssssssssL
1L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 8 small steps, repeating every octave. Generators that produce this scale range from 1066.7¢ to 1200¢, or from 0¢ to 133.3¢.
This MOS represents temperaments like Miracle and Negri. Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3\28 (around 14/13).
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 8|0 | 1 | Lssssssss |
| 7|1 | 9 | sLsssssss |
| 6|2 | 8 | ssLssssss |
| 5|3 | 7 | sssLsssss |
| 4|4 | 6 | ssssLssss |
| 3|5 | 5 | sssssLsss |
| 2|6 | 4 | ssssssLss |
| 1|7 | 3 | sssssssLs |
| 0|8 | 2 | ssssssssL |
Degrees
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||
| 8|0 | 1 | Lssssssss | Perf. | Aug. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 7|1 | 9 | sLsssssss | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 6|2 | 8 | ssLssssss | Perf. | Perf. | Min. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 5|3 | 7 | sssLsssss | Perf. | Perf. | Min. | Min. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 4|4 | 6 | ssssLssss | Perf. | Perf. | Min. | Min. | Min. | Maj. | Maj. | Maj. | Perf. | Perf. |
| 3|5 | 5 | sssssLsss | Perf. | Perf. | Min. | Min. | Min. | Min. | Maj. | Maj. | Perf. | Perf. |
| 2|6 | 4 | ssssssLss | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Maj. | Perf. | Perf. |
| 1|7 | 3 | sssssssLs | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. |
| 0|8 | 2 | ssssssssL | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Dim. | Perf. |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Perfect 1-mosstep | P1ms | s | 0.0¢ to 133.3¢ |
| Augmented 1-mosstep | A1ms | L | 133.3¢ to 1200.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 266.7¢ |
| Major 2-mosstep | M2ms | L + s | 266.7¢ to 1200.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 400.0¢ |
| Major 3-mosstep | M3ms | L + 2s | 400.0¢ to 1200.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 533.3¢ |
| Major 4-mosstep | M4ms | L + 3s | 533.3¢ to 1200.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 5s | 0.0¢ to 666.7¢ |
| Major 5-mosstep | M5ms | L + 4s | 666.7¢ to 1200.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 6s | 0.0¢ to 800.0¢ |
| Major 6-mosstep | M6ms | L + 5s | 800.0¢ to 1200.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 7s | 0.0¢ to 933.3¢ |
| Major 7-mosstep | M7ms | L + 6s | 933.3¢ to 1200.0¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 8s | 0.0¢ to 1066.7¢ |
| Perfect 8-mosstep | P8ms | L + 7s | 1066.7¢ to 1200.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | L + 8s | 1200.0¢ |
Scale tree
Generator ranges:
- Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
- Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
| Small step (chroma-negative generator) |
Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1\9 | 133.333 | 1 | 1 | 1.000 | ||||||
| 5\46 | 130.435 | 6 | 5 | 1.200 | ||||||
| 4\37 | 129.730 | 5 | 4 | 1.250 | ||||||
| 7\65 | 129.231 | 9 | 7 | 1.286 | ||||||
| 3\28 | 128.571 | 4 | 3 | 1.333 | ||||||
| 8\75 | 128.000 | 11 | 8 | 1.375 | ||||||
| 5\47 | 127.660 | 7 | 5 | 1.400 | ||||||
| 7\66 | 127.273 | 10 | 7 | 1.429 | ||||||
| 2\19 | 126.316 | 3 | 2 | 1.500 | Negri | |||||
| 7\67 | 125.373 | 11 | 7 | 1.571 | ||||||
| 5\48 | 125.000 | 8 | 5 | 1.600 | ||||||
| 8\77 | 124.675 | 13 | 8 | 1.625 | Golden negri (124.7656¢) | |||||
| 3\29 | 124.138 | 5 | 3 | 1.667 | ||||||
| 7\68 | 123.529 | 12 | 7 | 1.714 | ||||||
| 4\39 | 123.077 | 7 | 4 | 1.750 | ||||||
| 5\49 | 122.449 | 9 | 5 | 1.800 | ||||||
| 1\10 | 120.000 | 2 | 1 | 2.000 | Basic 1L 8s (small steps larger than this are proper) | |||||
| 4\41 | 117.073 | 9 | 4 | 2.250 | Miracle | |||||
| 3\31 | 116.129 | 7 | 3 | 2.333 | Miracle/revelation | |||||
| 5\52 | 115.385 | 12 | 5 | 2.400 | ||||||
| 2\21 | 114.286 | 5 | 2 | 2.500 | ||||||
| 5\53 | 113.208 | 13 | 5 | 2.600 | Golden misneb (113.0153¢) | |||||
| 3\32 | 112.500 | 8 | 3 | 2.667 | ||||||
| 4\43 | 111.628 | 11 | 4 | 2.750 | ||||||
| 1\11 | 109.091 | 3 | 1 | 3.000 | ||||||
| 3\34 | 105.882 | 10 | 3 | 3.333 | ||||||
| 2\23 | 104.348 | 7 | 2 | 3.500 | ||||||
| 3\35 | 102.857 | 11 | 3 | 3.667 | ||||||
| 1\12 | 100.000 | 4 | 1 | 4.000 | Ripple | |||||
| 2\25 | 96.000 | 9 | 2 | 4.500 | Passion | |||||
| 1\13 | 92.308 | 5 | 1 | 5.000 | ||||||
| 1\14 | 85.714 | 6 | 1 | 6.000 | ||||||
| 0\1 | 0.000 | 1 | 0 | → inf | ||||||