4L 4s
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Brightest mode | sLsLsLsL | |
Period | 1\4 | |
Range for bright generator | 0\4 (0.0¢) to 1\8 (150.0¢) | |
Range for dark generator | 1\8 (150.0¢) to 1\4 (300.0¢) | |
Parent MOS | 4edo | |
Daughter MOSes | 8L 4s, 4L 8s | |
Sister MOS | 4L 4s | |
TAMNAMS name | tetrawood; diminished | |
Equal tunings | ||
Supersoft (L:s = 4:3) | 3\28 (128.6¢) | |
Soft (L:s = 3:2) | 2\20 (120.0¢) | |
Semisoft (L:s = 5:3) | 3\32 (112.5¢) | |
Basic (L:s = 2:1) | 1\12 (100.0¢) | |
Semihard (L:s = 5:2) | 2\28 (85.7¢) | |
Hard (L:s = 3:1) | 1\16 (75.0¢) | |
Superhard (L:s = 4:1) | 1\20 (60.0¢) |
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 |