4L 10s
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Step pattern
LssLsssLssLsss
sssLssLsssLssL
Equave
2/1 (1200.0 ¢)
Period
1\2 (600.0 ¢)
Bright
3\14 to 1\4 (257.1 ¢ to 300.0 ¢)
Dark
1\4 to 4\14 (300.0 ¢ to 342.9 ¢)
Related to
4L 6s (lime)
With tunings
2:1 to 1:0 (hard-of-basic)
Parent
4L 6s
Sister
10L 4s
Daughters
14L 4s, 4L 14s
Neutralized
8L 6s
2-Flought
18L 10s, 4L 24s
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 ↘ |
┌╥┬┬╥┬┬┬╥┬┬╥┬┬┬┐ │║││║│││║││║││││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sssLssLsssLssL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
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 ¢) −1 generator away from the period and 38edo almost exactly at the harmonic entropy minimum for its pattern.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.
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 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. | Scale degree | Abbrev. |
---|---|---|---|---|
8 | Augmented 3-mosdegree | A3md | Augmented 10-mosdegree | A10md |
7 | Augmented 0-mosdegree | A0md | Augmented 7-mosdegree | A7md |
6 | Augmented 4-mosdegree | A4md | Augmented 11-mosdegree | A11md |
5 | Major 1-mosdegree | M1md | Major 8-mosdegree | M8md |
4 | Major 5-mosdegree | M5md | Major 12-mosdegree | M12md |
3 | Major 2-mosdegree | M2md | Major 9-mosdegree | M9md |
2 | Major 6-mosdegree | M6md | Major 13-mosdegree | M13md |
1 | Perfect 3-mosdegree | P3md | Perfect 10-mosdegree | P10md |
0 | Perfect 0-mosdegree Perfect 7-mosdegree |
P0md P7md |
Perfect 7-mosdegree Perfect 14-mosdegree |
P7md P14md |
−1 | Perfect 4-mosdegree | P4md | Perfect 11-mosdegree | P11md |
−2 | Minor 1-mosdegree | m1md | Minor 8-mosdegree | m8md |
−3 | Minor 5-mosdegree | m5md | Minor 12-mosdegree | m12md |
−4 | Minor 2-mosdegree | m2md | Minor 9-mosdegree | m9md |
−5 | Minor 6-mosdegree | m6md | Minor 13-mosdegree | m13md |
−6 | Diminished 3-mosdegree | d3md | Diminished 10-mosdegree | d10md |
−7 | Diminished 7-mosdegree | d7md | Diminished 14-mosdegree | d14md |
−8 | Diminished 4-mosdegree | d4md | Diminished 11-mosdegree | d11md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |||
12|0(2) | 1 | LssLsssLssLsss | Perf. | Maj. | Maj. | Perf. | Aug. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. | Aug. | Maj. | Maj. | Perf. |
10|2(2) | 4 | LsssLssLsssLss | Perf. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. |
8|4(2) | 7 | sLssLsssLssLss | Perf. | Min. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. | Min. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. |
6|6(2) | 3 | sLsssLssLsssLs | Perf. | Min. | Maj. | Perf. | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Perf. | Perf. | Min. | Maj. | Perf. |
4|8(2) | 6 | ssLssLsssLssLs | Perf. | Min. | Min. | Perf. | Perf. | Min. | Maj. | Perf. | Min. | Min. | Perf. | Perf. | Min. | Maj. | Perf. |
2|10(2) | 2 | ssLsssLssLsssL | Perf. | Min. | Min. | Perf. | Perf. | Min. | Min. | Perf. | Min. | Min. | Perf. | Perf. | Min. | Min. | Perf. |
0|12(2) | 5 | sssLssLsssLssL | Perf. | Min. | Min. | Dim. | Perf. | Min. | Min. | Perf. | Min. | Min. | Dim. | Perf. | Min. | Min. | Perf. |
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 |