3L 8s
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Scale structure
Step pattern
LssLsssLsss
sssLsssLssL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
7\11 to 2\3 (763.6¢ to 800.0¢)
Dark
1\3 to 4\11 (400.0¢ to 436.4¢)
TAMNAMS information
Descends from
3L 5s (checkertonic)
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
3L 5s
Sister
8L 3s
Daughters
11L 3s, 3L 11s
Neutralized
6L 5s
2-Flought
14L 8s, 3L 19s
Equal tunings
Equalized (L:s = 1:1)
7\11 (763.6¢)
Supersoft (L:s = 4:3)
23\36 (766.7¢)
Soft (L:s = 3:2)
16\25 (768.0¢)
Semisoft (L:s = 5:3)
25\39 (769.2¢)
Basic (L:s = 2:1)
9\14 (771.4¢)
Semihard (L:s = 5:2)
20\31 (774.2¢)
Hard (L:s = 3:1)
11\17 (776.5¢)
Superhard (L:s = 4:1)
13\20 (780.0¢)
Collapsed (L:s = 1:0)
2\3 (800.0¢)
| ↖ 2L 7s | ↑ 3L 7s | 4L 7s ↗ |
| ← 2L 8s | 3L 8s | 4L 8s → |
| ↙ 2L 9s | ↓ 3L 9s | 4L 9s ↘ |
┌╥┬┬╥┬┬┬╥┬┬┬┐ │║││║│││║││││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sssLsssLssL
3L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 8 small steps, repeating every octave. 3L 8s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 763.6¢ to 800¢, or from 400¢ to 436.4¢.
This scale has versions relating to ditonic/coditone, roman, bossier, sqrtphi and squares.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 10|0 | 1 | LssLsssLsss |
| 9|1 | 8 | LsssLssLsss |
| 8|2 | 4 | LsssLsssLss |
| 7|3 | 11 | sLssLsssLss |
| 6|4 | 7 | sLsssLssLss |
| 5|5 | 3 | sLsssLsssLs |
| 4|6 | 10 | ssLssLsssLs |
| 3|7 | 6 | ssLsssLssLs |
| 2|8 | 2 | ssLsssLsssL |
| 1|9 | 9 | sssLssLsssL |
| 0|10 | 5 | sssLsssLssL |
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 109.1¢ |
| Major 1-mosstep | M1ms | L | 109.1¢ to 400.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 218.2¢ |
| Major 2-mosstep | M2ms | L + s | 218.2¢ to 400.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 327.3¢ |
| Major 3-mosstep | M3ms | L + 2s | 327.3¢ to 400.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 400.0¢ to 436.4¢ |
| Augmented 4-mosstep | A4ms | 2L + 2s | 436.4¢ to 800.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 400.0¢ to 545.5¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 545.5¢ to 800.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 400.0¢ to 654.5¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 654.5¢ to 800.0¢ | |
| 7-mosstep | Diminished 7-mosstep | d7ms | L + 6s | 400.0¢ to 763.6¢ |
| Perfect 7-mosstep | P7ms | 2L + 5s | 763.6¢ to 800.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 800.0¢ to 872.7¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 872.7¢ to 1200.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 800.0¢ to 981.8¢ |
| Major 9-mosstep | M9ms | 3L + 6s | 981.8¢ to 1200.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 2L + 8s | 800.0¢ to 1090.9¢ |
| Major 10-mosstep | M10ms | 3L + 7s | 1090.9¢ to 1200.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 3L + 8s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\11 | 763.636 | 436.364 | 1:1 | 1.000 | Equalized 3L 8s | |||||
| 37\58 | 765.517 | 434.483 | 6:5 | 1.200 | ||||||
| 30\47 | 765.957 | 434.043 | 5:4 | 1.250 | ||||||
| 53\83 | 766.265 | 433.735 | 9:7 | 1.286 | ||||||
| 23\36 | 766.667 | 433.333 | 4:3 | 1.333 | Supersoft 3L 8s | |||||
| 62\97 | 767.010 | 432.990 | 11:8 | 1.375 | ||||||
| 39\61 | 767.213 | 432.787 | 7:5 | 1.400 | ||||||
| 55\86 | 767.442 | 432.558 | 10:7 | 1.429 | ||||||
| 16\25 | 768.000 | 432.000 | 3:2 | 1.500 | Soft 3L 8s | |||||
| 57\89 | 768.539 | 431.461 | 11:7 | 1.571 | ||||||
| 41\64 | 768.750 | 431.250 | 8:5 | 1.600 | ||||||
| 66\103 | 768.932 | 431.068 | 13:8 | 1.625 | ||||||
| 25\39 | 769.231 | 430.769 | 5:3 | 1.667 | Semisoft 3L 8s | |||||
| 59\92 | 769.565 | 430.435 | 12:7 | 1.714 | ||||||
| 34\53 | 769.811 | 430.189 | 7:4 | 1.750 | ||||||
| 43\67 | 770.149 | 429.851 | 9:5 | 1.800 | ||||||
| 9\14 | 771.429 | 428.571 | 2:1 | 2.000 | Basic 3L 8s Scales with tunings softer than this are proper | |||||
| 38\59 | 772.881 | 427.119 | 9:4 | 2.250 | ||||||
| 29\45 | 773.333 | 426.667 | 7:3 | 2.333 | ||||||
| 49\76 | 773.684 | 426.316 | 12:5 | 2.400 | ||||||
| 20\31 | 774.194 | 425.806 | 5:2 | 2.500 | Semihard 3L 8s Squares | |||||
| 51\79 | 774.684 | 425.316 | 13:5 | 2.600 | ||||||
| 31\48 | 775.000 | 425.000 | 8:3 | 2.667 | ||||||
| 42\65 | 775.385 | 424.615 | 11:4 | 2.750 | ||||||
| 11\17 | 776.471 | 423.529 | 3:1 | 3.000 | Hard 3L 8s | |||||
| 35\54 | 777.778 | 422.222 | 10:3 | 3.333 | ||||||
| 24\37 | 778.378 | 421.622 | 7:2 | 3.500 | Bossier | |||||
| 37\57 | 778.947 | 421.053 | 11:3 | 3.667 | ||||||
| 13\20 | 780.000 | 420.000 | 4:1 | 4.000 | Superhard 3L 8s | |||||
| 28\43 | 781.395 | 418.605 | 9:2 | 4.500 | ||||||
| 15\23 | 782.609 | 417.391 | 5:1 | 5.000 | ||||||
| 17\26 | 784.615 | 415.385 | 6:1 | 6.000 | ↓ Ditonic, Roman | |||||
| 2\3 | 800.000 | 400.000 | 1:0 | → ∞ | Collapsed 3L 8s | |||||