8L 4s
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Scale structure
Step pattern
LLsLLsLLsLLs
sLLsLLsLLsLL
Equave
2/1 (1200.0¢)
Period
1\4 (300.0¢)
Generator size
Bright
1\12 to 1\8 (100.0¢ to 150.0¢)
Dark
1\8 to 2\12 (150.0¢ to 200.0¢)
TAMNAMS information
Descends from
4L 4s (tetrawood)
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
4L 4s
Sister
4L 8s
Daughters
12L 8s, 8L 12s
Neutralized
4L 8s
2-Flought
20L 4s, 8L 16s
Equal tunings
Equalized (L:s = 1:1)
1\12 (100.0¢)
Supersoft (L:s = 4:3)
4\44 (109.1¢)
Soft (L:s = 3:2)
3\32 (112.5¢)
Semisoft (L:s = 5:3)
5\52 (115.4¢)
Basic (L:s = 2:1)
2\20 (120.0¢)
Semihard (L:s = 5:2)
5\48 (125.0¢)
Hard (L:s = 3:1)
3\28 (128.6¢)
Superhard (L:s = 4:1)
4\36 (133.3¢)
Collapsed (L:s = 1:0)
1\8 (150.0¢)
| ↖ 7L 3s | ↑ 8L 3s | 9L 3s ↗ |
| ← 7L 4s | 8L 4s | 9L 4s → |
| ↙ 7L 5s | ↓ 8L 5s | 9L 5s ↘ |
┌╥╥┬╥╥┬╥╥┬╥╥┬┐ │║║│║║│║║│║║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLsLLsLLsLL
8L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 4 small steps, with a period of 2 large steps and 1 small step that repeats every 300.0¢, or 4 times every octave. 8L 4s is a child scale of 4L 4s, expanding it by 4 tones. Generators that produce this scale range from 100¢ to 150¢, or from 150¢ to 200¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.
This is the chromatic scale of Golden diminished temperament.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 8|0(4) | 1 | LLsLLsLLsLLs |
| 4|4(4) | 2 | LsLLsLLsLLsL |
| 0|8(4) | 3 | sLLsLLsLLsLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
| 1-mosstep | Diminished 1-mosstep | d1ms | s | 0.0¢ to 100.0¢ |
| Perfect 1-mosstep | P1ms | L | 100.0¢ to 150.0¢ | |
| 2-mosstep | Perfect 2-mosstep | P2ms | L + s | 150.0¢ to 200.0¢ |
| Augmented 2-mosstep | A2ms | 2L | 200.0¢ to 300.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 300.0¢ |
| 4-mosstep | Diminished 4-mosstep | d4ms | 2L + 2s | 300.0¢ to 400.0¢ |
| Perfect 4-mosstep | P4ms | 3L + s | 400.0¢ to 450.0¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 3L + 2s | 450.0¢ to 500.0¢ |
| Augmented 5-mosstep | A5ms | 4L + s | 500.0¢ to 600.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | 4L + 2s | 600.0¢ |
| 7-mosstep | Diminished 7-mosstep | d7ms | 4L + 3s | 600.0¢ to 700.0¢ |
| Perfect 7-mosstep | P7ms | 5L + 2s | 700.0¢ to 750.0¢ | |
| 8-mosstep | Perfect 8-mosstep | P8ms | 5L + 3s | 750.0¢ to 800.0¢ |
| Augmented 8-mosstep | A8ms | 6L + 2s | 800.0¢ to 900.0¢ | |
| 9-mosstep | Perfect 9-mosstep | P9ms | 6L + 3s | 900.0¢ |
| 10-mosstep | Diminished 10-mosstep | d10ms | 6L + 4s | 900.0¢ to 1000.0¢ |
| Perfect 10-mosstep | P10ms | 7L + 3s | 1000.0¢ to 1050.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 7L + 4s | 1050.0¢ to 1100.0¢ |
| Augmented 11-mosstep | A11ms | 8L + 3s | 1100.0¢ to 1200.0¢ | |
| 12-mosstep | Perfect 12-mosstep | P12ms | 8L + 4s | 1200.0¢ |
Scale tree
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\12 | 100.000 | 200.000 | 1:1 | 1.000 | Equalized 8L 4s | |||||
| 6\68 | 105.882 | 194.118 | 6:5 | 1.200 | ||||||
| 5\56 | 107.143 | 192.857 | 5:4 | 1.250 | ||||||
| 9\100 | 108.000 | 192.000 | 9:7 | 1.286 | ||||||
| 4\44 | 109.091 | 190.909 | 4:3 | 1.333 | Supersoft 8L 4s | |||||
| 11\120 | 110.000 | 190.000 | 11:8 | 1.375 | ||||||
| 7\76 | 110.526 | 189.474 | 7:5 | 1.400 | ||||||
| 10\108 | 111.111 | 188.889 | 10:7 | 1.429 | ||||||
| 3\32 | 112.500 | 187.500 | 3:2 | 1.500 | Soft 8L 4s | |||||
| 11\116 | 113.793 | 186.207 | 11:7 | 1.571 | ||||||
| 8\84 | 114.286 | 185.714 | 8:5 | 1.600 | ||||||
| 13\136 | 114.706 | 185.294 | 13:8 | 1.625 | ||||||
| 5\52 | 115.385 | 184.615 | 5:3 | 1.667 | Semisoft 8L 4s | |||||
| 12\124 | 116.129 | 183.871 | 12:7 | 1.714 | ||||||
| 7\72 | 116.667 | 183.333 | 7:4 | 1.750 | ||||||
| 9\92 | 117.391 | 182.609 | 9:5 | 1.800 | ||||||
| 2\20 | 120.000 | 180.000 | 2:1 | 2.000 | Basic 8L 4s | |||||
| 9\88 | 122.727 | 177.273 | 9:4 | 2.250 | ||||||
| 7\68 | 123.529 | 176.471 | 7:3 | 2.333 | ||||||
| 12\116 | 124.138 | 175.862 | 12:5 | 2.400 | ||||||
| 5\48 | 125.000 | 175.000 | 5:2 | 2.500 | Semihard 8L 4s | |||||
| 13\124 | 125.806 | 174.194 | 13:5 | 2.600 | ||||||
| 8\76 | 126.316 | 173.684 | 8:3 | 2.667 | ||||||
| 11\104 | 126.923 | 173.077 | 11:4 | 2.750 | ||||||
| 3\28 | 128.571 | 171.429 | 3:1 | 3.000 | Hard 8L 4s | |||||
| 10\92 | 130.435 | 169.565 | 10:3 | 3.333 | ||||||
| 7\64 | 131.250 | 168.750 | 7:2 | 3.500 | ||||||
| 11\100 | 132.000 | 168.000 | 11:3 | 3.667 | ||||||
| 4\36 | 133.333 | 166.667 | 4:1 | 4.000 | Superhard 8L 4s | |||||
| 9\80 | 135.000 | 165.000 | 9:2 | 4.500 | ||||||
| 5\44 | 136.364 | 163.636 | 5:1 | 5.000 | ||||||
| 6\52 | 138.462 | 161.538 | 6:1 | 6.000 | ||||||
| 1\8 | 150.000 | 150.000 | 1:0 | → ∞ | Collapsed 8L 4s | |||||
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