4L 4s
| ↖3L 3s | ↑4L 3s | 5L 3s↗ |
| ←3L 4s | 4L 4s | 5L 4s→ |
| ↙3L 5s | ↓4L 5s | 5L 5s↘ |
4L 4s, also called tetrawood or diminished, is a moment of symmetry scale consisting of 4 large steps and 4 small steps, with a period of 1 large step and 1 small step that repeats 4 times every octave, or every 300¢. This scale is made using a generator ranging from 150¢ to 300¢, or from 0¢ to 150¢.
The minimum harmonic entropy scale with this MOS pattern is diminished[8], basically the familiar octatonic scale of 12edo.
There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)
Scale tree
| Generator | Cents | L | s | L/s | Comments | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Chroma-positive | Chroma-negative | ||||||||||
| 1\8 | 150.000 | 150.000 | 1 | 1 | 1.000 | ||||||
| 6\44 | 163.636 | 136.364 | 6 | 5 | 1.200 | Fourfives↑ | |||||
| 5\36 | 166.667 | 133.333 | 5 | 4 | 1.250 | ||||||
| 9\64 | 168.750 | 105.000 | 9 | 7 | 1.286 | ||||||
| 4\28 | 171.429 | 128.571 | 4 | 3 | 1.333 | ||||||
| 11\76 | 173.684 | 126.316 | 11 | 8 | 1.375 | ||||||
| 7\48 | 175.000 | 125.000 | 7 | 5 | 1.400 | ||||||
| 10\68 | 176.471 | 123.529 | 10 | 7 | 1.428 | ||||||
| 3\20 | 180.000 | 60.000 | 3 | 2 | 1.500 | L/s = 3/2 | |||||
| 11\72 | 183.333 | 116.667 | 11 | 7 | 1.571 | ||||||
| 8\52 | 184.615 | 115.385 | 8 | 5 | 1.600 | ||||||
| 13\84 | 185.714 | 114.286 | 13 | 8 | 1.625 | Golden diminished | |||||
| 5\32 | 187.500 | 112.500 | 5 | 3 | 1.667 | ||||||
| 12\76 | 189.474 | 110.526 | 12 | 7 | 1.714 | ||||||
| 7\44 | 190.909 | 109.091 | 7 | 4 | 1.750 | ||||||
| 9\56 | 192.857 | 107.143 | 9 | 5 | 1.800 | ||||||
| 2\12 | 200.000 | 100.000 | 2 | 1 | 2.000 | Basic tetrawood Diminished is optimal around here | |||||
| 9\52 | 207.692 | 92.308 | 9 | 4 | 2.250 | ||||||
| 7\40 | 210.000 | 90.000 | 7 | 3 | 2.333 | ||||||
| 12\68 | 211.765 | 88.235 | 12 | 5 | 2.400 | ||||||
| 5\28 | 214.286 | 85.714 | 5 | 2 | 2.500 | ||||||
| 13\72 | 216.667 | 83.333 | 13 | 5 | 2.600 | Unnamed golden tuning | |||||
| 8\44 | 218.182 | 81.818 | 8 | 3 | 2.667 | ||||||
| 11\60 | 220.000 | 80.000 | 11 | 4 | 2.750 | ||||||
| 3\16 | 225.000 | 75.000 | 3 | 1 | 3.000 | L/s = 3/1 | |||||
| 10\52 | 230.769 | 69.231 | 10 | 3 | 3.333 | ||||||
| 7\36 | 233.333 | 66.667 | 7 | 2 | 3.500 | ||||||
| 11\56 | 235.714 | 64.286 | 11 | 3 | 3.667 | ||||||
| 4\20 | 240.000 | 60.000 | 4 | 1 | 4.000 | ||||||
| 9\44 | 245.455 | 54.545 | 9 | 2 | 4.500 | ||||||
| 5\24 | 250.000 | 50.000 | 5 | 1 | 5.000 | ||||||
| 6\28 | 257.143 | 42.857 | 6 | 1 | 6.000 | Quadritikleismic↓ | |||||
| 1\4 | 300.000 | 0.000 | 1 | 0 | → inf | ||||||