4L 10s
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Scale structure
Step pattern
LssLsssLssLsss
sssLssLsssLssL
Equave
2/1 (1200.0¢)
Period
1\2 (600.0¢)
Generator size
Bright
3\14 to 1\4 (257.1¢ to 300.0¢)
Dark
1\4 to 4\14 (300.0¢ to 342.9¢)
TAMNAMS information
Descends from
4L 6s
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
4L 6s
Sister
10L 4s
Daughters
14L 4s, 4L 14s
Neutralized
8L 6s
2-Flought
18L 10s, 4L 24s
Equal tunings
Equalized (L:s = 1:1)
3\14 (257.1¢)
Supersoft (L:s = 4:3)
10\46 (260.9¢)
Soft (L:s = 3:2)
7\32 (262.5¢)
Semisoft (L:s = 5:3)
11\50 (264.0¢)
Basic (L:s = 2:1)
4\18 (266.7¢)
Semihard (L:s = 5:2)
9\40 (270.0¢)
Hard (L:s = 3:1)
5\22 (272.7¢)
Superhard (L:s = 4:1)
6\26 (276.9¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 9s | ↑ 4L 9s | 5L 9s ↗ |
| ← 3L 10s | 4L 10s | 5L 10s → |
| ↙ 3L 11s | ↓ 4L 11s | 5L 11s ↘ |
┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║│││║││║││││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sssLssLsssLssL
4L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 10 small steps, with a period of 2 large steps and 5 small steps that repeats every 600.0¢, or twice every octave. 4L 10s is a child scale of 4L 6s, expanding it by 4 tones. Generators that produce this scale range from 257.1¢ to 300¢, or from 300¢ to 342.9¢.
The generator range puts a minor third (300 to 342.857 cents) -1 generator away from the period and 38edo almost exactly at the harmonic entropy minimum for its pattern.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 12|0(2) | 1 | LssLsssLssLsss |
| 10|2(2) | 4 | LsssLssLsssLss |
| 8|4(2) | 7 | sLssLsssLssLss |
| 6|6(2) | 3 | sLsssLssLsssLs |
| 4|8(2) | 6 | ssLssLsssLssLs |
| 2|10(2) | 2 | ssLsssLssLsssL |
| 0|12(2) | 5 | sssLssLsssLssL |
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 85.7¢ |
| Major 1-mosstep | M1ms | L | 85.7¢ to 300.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 171.4¢ |
| Major 2-mosstep | M2ms | L + s | 171.4¢ to 300.0¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0¢ to 257.1¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 257.1¢ to 300.0¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 300.0¢ to 342.9¢ |
| Augmented 4-mosstep | A4ms | 2L + 2s | 342.9¢ to 600.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 300.0¢ to 428.6¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 428.6¢ to 600.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 300.0¢ to 514.3¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 514.3¢ to 600.0¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 2L + 5s | 600.0¢ |
| 8-mosstep | Minor 8-mosstep | m8ms | 2L + 6s | 600.0¢ to 685.7¢ |
| Major 8-mosstep | M8ms | 3L + 5s | 685.7¢ to 900.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 2L + 7s | 600.0¢ to 771.4¢ |
| Major 9-mosstep | M9ms | 3L + 6s | 771.4¢ to 900.0¢ | |
| 10-mosstep | Diminished 10-mosstep | d10ms | 2L + 8s | 600.0¢ to 857.1¢ |
| Perfect 10-mosstep | P10ms | 3L + 7s | 857.1¢ to 900.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 3L + 8s | 900.0¢ to 942.9¢ |
| Augmented 11-mosstep | A11ms | 4L + 7s | 942.9¢ to 1200.0¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 3L + 9s | 900.0¢ to 1028.6¢ |
| Major 12-mosstep | M12ms | 4L + 8s | 1028.6¢ to 1200.0¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 3L + 10s | 900.0¢ to 1114.3¢ |
| Major 13-mosstep | M13ms | 4L + 9s | 1114.3¢ to 1200.0¢ | |
| 14-mosstep | Perfect 14-mosstep | P14ms | 4L + 10s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\14 | 257.143 | 342.857 | 1:1 | 1.000 | Equalized 4L 10s | |||||
| 16\74 | 259.459 | 340.541 | 6:5 | 1.200 | ||||||
| 13\60 | 260.000 | 340.000 | 5:4 | 1.250 | ||||||
| 23\106 | 260.377 | 339.623 | 9:7 | 1.286 | ||||||
| 10\46 | 260.870 | 339.130 | 4:3 | 1.333 | Supersoft 4L 10s | |||||
| 27\124 | 261.290 | 338.710 | 11:8 | 1.375 | ||||||
| 17\78 | 261.538 | 338.462 | 7:5 | 1.400 | ||||||
| 24\110 | 261.818 | 338.182 | 10:7 | 1.429 | ||||||
| 7\32 | 262.500 | 337.500 | 3:2 | 1.500 | Soft 4L 10s | |||||
| 25\114 | 263.158 | 336.842 | 11:7 | 1.571 | ||||||
| 18\82 | 263.415 | 336.585 | 8:5 | 1.600 | ||||||
| 29\132 | 263.636 | 336.364 | 13:8 | 1.625 | ||||||
| 11\50 | 264.000 | 336.000 | 5:3 | 1.667 | Semisoft 4L 10s | |||||
| 26\118 | 264.407 | 335.593 | 12:7 | 1.714 | ||||||
| 15\68 | 264.706 | 335.294 | 7:4 | 1.750 | ||||||
| 19\86 | 265.116 | 334.884 | 9:5 | 1.800 | ||||||
| 4\18 | 266.667 | 333.333 | 2:1 | 2.000 | Basic 4L 10s Scales with tunings softer than this are proper | |||||
| 17\76 | 268.421 | 331.579 | 9:4 | 2.250 | ||||||
| 13\58 | 268.966 | 331.034 | 7:3 | 2.333 | ||||||
| 22\98 | 269.388 | 330.612 | 12:5 | 2.400 | ||||||
| 9\40 | 270.000 | 330.000 | 5:2 | 2.500 | Semihard 4L 10s | |||||
| 23\102 | 270.588 | 329.412 | 13:5 | 2.600 | ||||||
| 14\62 | 270.968 | 329.032 | 8:3 | 2.667 | ||||||
| 19\84 | 271.429 | 328.571 | 11:4 | 2.750 | ||||||
| 5\22 | 272.727 | 327.273 | 3:1 | 3.000 | Hard 4L 10s | |||||
| 16\70 | 274.286 | 325.714 | 10:3 | 3.333 | ||||||
| 11\48 | 275.000 | 325.000 | 7:2 | 3.500 | ||||||
| 17\74 | 275.676 | 324.324 | 11:3 | 3.667 | ||||||
| 6\26 | 276.923 | 323.077 | 4:1 | 4.000 | Superhard 4L 10s | |||||
| 13\56 | 278.571 | 321.429 | 9:2 | 4.500 | ||||||
| 7\30 | 280.000 | 320.000 | 5:1 | 5.000 | ||||||
| 8\34 | 282.353 | 317.647 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 300.000 | 1:0 | → ∞ | Collapsed 4L 10s | |||||