7L 1s

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7L 1s
Pattern LLLLLLLs
Period 2/1
Generator range 1\8 (150.0¢) to 1\7 (171.4¢)
Parent MOS 1L 6s
Daughter MOSes 8L 7s, 7L 8s
Sister MOS 1L 7s
TAMNAMS name pine
Equal tunings
Supersoft (L:s = 4:3) 4\31 (154.8¢)
Soft (L:s = 3:2) 3\23 (156.5¢)
Semisoft (L:s = 5:3) 5\38 (157.9¢)
Basic (L:s = 2:1) 2\15 (160.0¢)
Semihard (L:s = 5:2) 5\37 (162.2¢)
Hard (L:s = 3:1) 3\22 (163.6¢)
Superhard (L:s = 4:1) 4\29 (165.5¢)

There are two notable harmonic entropy minima with this MOS pattern. The first is porcupine, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is greeley, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

Scales of this form are always proper, because there is only one small step.

Generator Cents Scale in EDO steps Comments
1\7 171.43 1 1 1 1 1 1 1 0
6\43 167.44 6 6 6 6 6 6 6 1
5\36 166.67 5 5 5 5 5 5 5 1
4\29 165.52 4 4 4 4 4 4 4 1 L/s = 4
163.97 π π π π π π π 1 L/s = π
3\22 163.64 3 3 3 3 3 3 3 1 L/s = 3
162.87 e e e e e e e e 1 L/s = e
8\59 162,71 8 8 8 8 8 8 8 3
13\96 162.5 13 13 13 13 13 13 13 5
5\37 162.16 5 5 5 5 5 5 5 2 Porcupine is in this general region
7\52 161.54 7 7 7 7 7 7 7 3
2\15 160 2 2 2 2 2 2 2 1 Optimum rank range (L/s=2/1) porcupine
158.37 √3 √3 √3 √3 √3 √3 √3 1
5\38 157.89 5 5 5 5 5 5 5 3
13\99 157.58 13 13 13 13 13 13 13 8 Golden porcupine / golden hemikleismic
8\61 157.38 8 8 8 8 8 8 8 5
(11\84) 157.14) 11 11 11 11 11 11 11 7 π π π π π π π 2
3\23 156.52 3 3 3 3 3 3 3 2
10\77 155.84 10 10 10 10 10 10 10 7 Greeley is around here
7\54 155.56 7 7 7 7 7 7 7 5
4\31 154.84 4 4 4 4 4 4 4 3
5\39 153.85 5 5 5 5 5 5 5 4
6\47 153.19 6 6 6 6 6 6 6 5
1\8 150 1 1 1 1 1 1 1 1