4L 8s
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Scale structure
Step pattern
LssLssLssLss
ssLssLssLssL
Equave
2/1 (1200.0¢)
Period
1\4 (300.0¢)
Generator size
Bright
2\12 to 1\4 (200.0¢ to 300.0¢)
Dark
0\4 to 1\12 (0.0¢ to 100.0¢)
TAMNAMS information
Descends from
4L 4s (tetrawood)
Ancestor's step ratio range
2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent
4L 4s
Sister
8L 4s
Daughters
12L 4s, 4L 12s
Neutralized
8L 4s
2-Flought
16L 8s, 4L 20s
Equal tunings
Equalized (L:s = 1:1)
2\12 (200.0¢)
Supersoft (L:s = 4:3)
7\40 (210.0¢)
Soft (L:s = 3:2)
5\28 (214.3¢)
Semisoft (L:s = 5:3)
8\44 (218.2¢)
Basic (L:s = 2:1)
3\16 (225.0¢)
Semihard (L:s = 5:2)
7\36 (233.3¢)
Hard (L:s = 3:1)
4\20 (240.0¢)
Superhard (L:s = 4:1)
5\24 (250.0¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
| ↖ 3L 7s | ↑ 4L 7s | 5L 7s ↗ |
| ← 3L 8s | 4L 8s | 5L 8s → |
| ↙ 3L 9s | ↓ 4L 9s | 5L 9s ↘ |
┌╥┬┬╥┬┬╥┬┬╥┬┬┐ │║││║││║││║│││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLssLssLssL
4L 8s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 8 small steps, with a period of 1 large step and 2 small steps that repeats every 300.0¢, or 4 times every octave. 4L 8s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 200¢ to 300¢, or from 0¢ to 100¢.
This is the minor chromatic scale of Diminished temperament. Its period of 300¢ (~6:5) is divided into L s s, making a universally proper scale, but the harmonic entropy minimum for it is not particularly low. The name for this MOS scale is p-chro tetrawood.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 8|0(4) | 1 | LssLssLssLss |
| 4|4(4) | 3 | sLssLssLssLs |
| 0|8(4) | 2 | ssLssLssLssL |
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 100.0¢ |
| Augmented 1-mosstep | A1ms | L | 100.0¢ to 300.0¢ | |
| 2-mosstep | Diminished 2-mosstep | d2ms | 2s | 0.0¢ to 200.0¢ |
| Perfect 2-mosstep | P2ms | L + s | 200.0¢ to 300.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | L + 2s | 300.0¢ |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 300.0¢ to 400.0¢ |
| Augmented 4-mosstep | A4ms | 2L + 2s | 400.0¢ to 600.0¢ | |
| 5-mosstep | Diminished 5-mosstep | d5ms | L + 4s | 300.0¢ to 500.0¢ |
| Perfect 5-mosstep | P5ms | 2L + 3s | 500.0¢ to 600.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | 2L + 4s | 600.0¢ |
| 7-mosstep | Perfect 7-mosstep | P7ms | 2L + 5s | 600.0¢ to 700.0¢ |
| Augmented 7-mosstep | A7ms | 3L + 4s | 700.0¢ to 900.0¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 2L + 6s | 600.0¢ to 800.0¢ |
| Perfect 8-mosstep | P8ms | 3L + 5s | 800.0¢ to 900.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | 3L + 6s | 900.0¢ |
| 10-mosstep | Perfect 10-mosstep | P10ms | 3L + 7s | 900.0¢ to 1000.0¢ |
| Augmented 10-mosstep | A10ms | 4L + 6s | 1000.0¢ to 1200.0¢ | |
| 11-mosstep | Diminished 11-mosstep | d11ms | 3L + 8s | 900.0¢ to 1100.0¢ |
| Perfect 11-mosstep | P11ms | 4L + 7s | 1100.0¢ to 1200.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 4L + 8s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\12 | 200.000 | 100.000 | 1:1 | 1.000 | Equalized 4L 8s | |||||
| 11\64 | 206.250 | 93.750 | 6:5 | 1.200 | ||||||
| 9\52 | 207.692 | 92.308 | 5:4 | 1.250 | ||||||
| 16\92 | 208.696 | 91.304 | 9:7 | 1.286 | ||||||
| 7\40 | 210.000 | 90.000 | 4:3 | 1.333 | Supersoft 4L 8s | |||||
| 19\108 | 211.111 | 88.889 | 11:8 | 1.375 | ||||||
| 12\68 | 211.765 | 88.235 | 7:5 | 1.400 | ||||||
| 17\96 | 212.500 | 87.500 | 10:7 | 1.429 | ||||||
| 5\28 | 214.286 | 85.714 | 3:2 | 1.500 | Soft 4L 8s | |||||
| 18\100 | 216.000 | 84.000 | 11:7 | 1.571 | ||||||
| 13\72 | 216.667 | 83.333 | 8:5 | 1.600 | ||||||
| 21\116 | 217.241 | 82.759 | 13:8 | 1.625 | ||||||
| 8\44 | 218.182 | 81.818 | 5:3 | 1.667 | Semisoft 4L 8s | |||||
| 19\104 | 219.231 | 80.769 | 12:7 | 1.714 | ||||||
| 11\60 | 220.000 | 80.000 | 7:4 | 1.750 | ||||||
| 14\76 | 221.053 | 78.947 | 9:5 | 1.800 | ||||||
| 3\16 | 225.000 | 75.000 | 2:1 | 2.000 | Basic 4L 8s Scales with tunings softer than this are proper | |||||
| 13\68 | 229.412 | 70.588 | 9:4 | 2.250 | ||||||
| 10\52 | 230.769 | 69.231 | 7:3 | 2.333 | ||||||
| 17\88 | 231.818 | 68.182 | 12:5 | 2.400 | ||||||
| 7\36 | 233.333 | 66.667 | 5:2 | 2.500 | Semihard 4L 8s | |||||
| 18\92 | 234.783 | 65.217 | 13:5 | 2.600 | ||||||
| 11\56 | 235.714 | 64.286 | 8:3 | 2.667 | ||||||
| 15\76 | 236.842 | 63.158 | 11:4 | 2.750 | ||||||
| 4\20 | 240.000 | 60.000 | 3:1 | 3.000 | Hard 4L 8s | |||||
| 13\64 | 243.750 | 56.250 | 10:3 | 3.333 | ||||||
| 9\44 | 245.455 | 54.545 | 7:2 | 3.500 | ||||||
| 14\68 | 247.059 | 52.941 | 11:3 | 3.667 | ||||||
| 5\24 | 250.000 | 50.000 | 4:1 | 4.000 | Superhard 4L 8s | |||||
| 11\52 | 253.846 | 46.154 | 9:2 | 4.500 | ||||||
| 6\28 | 257.143 | 42.857 | 5:1 | 5.000 | ||||||
| 7\32 | 262.500 | 37.500 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 0.000 | 1:0 | → ∞ | Collapsed 4L 8s | |||||