7L 1s

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7L 1s
Brightest mode LLLLLLLs
Period 2/1
Range for bright generator 1\8 (150.0¢) to 1\7 (171.4¢)
Range for dark generator 6\7 (1,028.6¢) to 7\8 (1,050.0¢)
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 Remainder Scale in EDO steps Comments
1\7 171.43 0.00 1 1 1 1 1 1 1 0
6\43 167.44 27.91 6 6 6 6 6 6 6 1
5\36 166.67 33.32 5 5 5 5 5 5 5 1
4\29 165.52 41.38 4 4 4 4 4 4 4 1 L/s = 4
163.97 52.19 π π π π π π π 1 L/s = π
3\22 163.64 54.55 3 3 3 3 3 3 3 1 L/s = 3
162.87 59.92 e e e e e e e e 1 L/s = e
8\59 162.71 61.02 8 8 8 8 8 8 8 3
13\96 162.5 62.5 [13 13 13 13 13 13|13 13 13 13 13 13 13] 5
5\37 162.16 64.86 5 5 5 5 5 5 5 2 Porcupine is in this general region
7\52 161.54 69.23 7 7 7 7 7 7 7 3
2\15 160 80 2 2 2 2 2 2 2 1 Optimum rank range (L/s=2/1) porcupine
158.37 91.43 √3 √3 √3 √3 √3 √3 √3 1
5\38 157.89 94.73 5 5 5 5 5 5 5 3
13\99 157.58 96.97 [13 13 13 13 13 13|13 13 13 13 13 13 13] 8 Golden porcupine / golden hemikleismic
8\61 157.38 98.36 8 8 8 8 8 8 8 5
(11\84) (157.14) (100) [11 11 11 11 11 11|11 11 11 11 11 11 11] 7 π π π π π π π 2
3\23 156.52 104.348 3 3 3 3 3 3 3 2
10\77 155.84 109.09 [10 10 10 10 10 10|10 10 10 10 10 10 10] 7 Greeley is around here
7\54 155.56 111.11 7 7 7 7 7 7 7 5
4\31 154.84 116.13 4 4 4 4 4 4 4 3
5\39 153.85 123.08 5 5 5 5 5 5 5 4
6\47 153.19 127.66 6 6 6 6 6 6 6 5
1\8 150 150 1 1 1 1 1 1 1 1