7L 1s
←6L 1s | 7L 1s | 8L 1s→ |
↙6L 2s | ↓7L 2s | 8L 2s↘ |
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 |