7L 1s

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←6L 1s7L 1s8L 1s→
↙6L 2s↓7L 2s 8L 2s↘
Brightest mode LLLLLLLs
Period 2/1
Range for bright generator 1\8 (150¢) to 1\7 (171.4¢)
Range for dark generator 6\7 (1028.6¢) to 7\8 (1050¢)
TAMNAMS name pine
TAMNAMS prefix pine-
Parent MOS 1L 6s
Sister MOS 1L 7s
Daughter MOSes 8L 7s, 7L 8s
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¢)
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¢)

7L 1s, also called pine, is a moment of symmetry scale consisting of 7 large steps and 1 small step, repeating every octave. This scale is made using a generator ranging from 150¢ to 171.429¢, or from 1028.571¢ to 1050¢.

There are three notable harmonic entropy minima with this MOS pattern. The lowest accuracy one 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 and more accurate 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. Thirdly and finally, tempering S10/S11 so that (4/3)/(11/10)3 is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's 11-limit) is natural, making 10/9 and 12/11 equidistant from 11/10 and offering many fruitful tempering opportunities. (Note therefore that porkypine can be seen as a trivial tuning of pine tempering 100/99 = S10 and 121/120 = S11.)

Modes

Mode names are from Porcupine temperament modal harmony. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.

Mode UDP Mode name Descriptive mode name
LLLLLLLs 7|0 octopus Bright quartal
LLLLLLsL 6|1 mantis Dark quartal
LLLLLsLL 5|2 dolphin Bright major
LLLLsLLL 4|3 crab Middle major
LLLsLLLL 3|4 tuna Dark major
LLsLLLLL 2|5 salmon Bright minor
LsLLLLLL 1|6 starfish Middle minor
sLLLLLLL 0|7 whale Dark major

Scale tree

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 pine is around here
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