4L 2s
Brightest mode | LLsLLs | |
Period | 1\2 | |
Range for bright generator | 1\6 (200.0¢) to 1\4 (300.0¢) | |
Range for dark generator | 1\4 (300.0¢) to 2\6 (400.0¢) | |
Parent MOS | 2L 2s | |
Daughter MOSes | 6L 4s, 4L 6s | |
Sister MOS | 2L 4s | |
TAMNAMS name | citric | |
Equal tunings | ||
Supersoft (L:s = 4:3) | 4\22 (218.2¢) | |
Soft (L:s = 3:2) | 3\16 (225.0¢) | |
Semisoft (L:s = 5:3) | 5\26 (230.8¢) | |
Basic (L:s = 2:1) | 2\10 (240.0¢) | |
Semihard (L:s = 5:2) | 5\24 (250.0¢) | |
Hard (L:s = 3:1) | 3\14 (257.1¢) | |
Superhard (L:s = 4:1) | 4\18 (266.7¢) |
There are three scales with this MOS pattern that are significant minima of harmonic entropy.
The first is antikythera, or no-3's srutal/pajara, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 2.5.7.9 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.
The second is decimal, in which two generators make a 4/3, and the third is Doublewide, in which the generator is 7/6 so the period minus the generator is 6/5.
In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).
Generator | Cents | Comments | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1\6 | 200 | |||||||||||
6\34 | 211.76 | |||||||||||
5\28 | 214.29 | Antikythera is around here | ||||||||||
4\22 | 218.18 | |||||||||||
3\16 | 225 | |||||||||||
227.56 | ||||||||||||
8\42 | 228.57 | |||||||||||
600/(1+phi) | Golden lemba | |||||||||||
13\68 | 229.41 | |||||||||||
5\26 | 230.77 | |||||||||||
232.8 | ||||||||||||
7\36 | 233.33 | Lemba is around here | ||||||||||
2\10 | 240 | Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS | ||||||||||
5\24 | 250 | Decimal is around here | ||||||||||
251.89 | ||||||||||||
8\38 | 252.63 | |||||||||||
253.39 | L/s = e | |||||||||||
3\14 | 257.14 | L/s = 3 | ||||||||||
258.81 | L/s = pi | |||||||||||
4\18 | 266.67 | L/s = 4 | ||||||||||
5\22 | 272.73 | |||||||||||
6\26 | 276.92 | |||||||||||
7\30 | 280 | |||||||||||
8\34 | 282.35 | |||||||||||
9\38 | 284.21 | |||||||||||
10\42 | 285.71 | |||||||||||
11\46 | 286.96 | Doublewide is around here | ||||||||||
1\4 | 300 |