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 |