7L 1s
| ←6L 1s | 7L 1s | 8L 1s→ |
| ↙6L 2s | ↓7L 2s | 8L 2s↘ |
┌╥╥╥╥╥╥╥┬┐ │║║║║║║║││ ││││││││││ └┴┴┴┴┴┴┴┴┘
sLLLLLLL
7L 8s
7L 1s, named pine in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 150¢ to 171.4¢, or from 1028.6¢ to 1050¢. Scales of this form are always proper because there is only one small step.
Name
TAMNAMS suggests the temperament-agnostic name pine, in reference to porcupine temperament.
Theory
Low harmonic entropy scales
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
| Generator (edo) | Cents | Step ratio | Comments(Always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\8 | 150.000 | 1050.000 | 1:1 | 1.000 | Equalized 7L 1s | |||||
| 6\47 | 153.191 | 1046.809 | 6:5 | 1.200 | ||||||
| 5\39 | 153.846 | 1046.154 | 5:4 | 1.250 | ||||||
| 9\70 | 154.286 | 1045.714 | 9:7 | 1.286 | ||||||
| 4\31 | 154.839 | 1045.161 | 4:3 | 1.333 | Supersoft 7L 1s | |||||
| 11\85 | 155.294 | 1044.706 | 11:8 | 1.375 | ||||||
| 7\54 | 155.556 | 1044.444 | 7:5 | 1.400 | ||||||
| 10\77 | 155.844 | 1044.156 | 10:7 | 1.429 | ||||||
| 3\23 | 156.522 | 1043.478 | 3:2 | 1.500 | Soft 7L 1s | |||||
| 11\84 | 157.143 | 1042.857 | 11:7 | 1.571 | ||||||
| 8\61 | 157.377 | 1042.623 | 8:5 | 1.600 | ||||||
| 13\99 | 157.576 | 1042.424 | 13:8 | 1.625 | ||||||
| 5\38 | 157.895 | 1042.105 | 5:3 | 1.667 | Semisoft 7L 1s | |||||
| 12\91 | 158.242 | 1041.758 | 12:7 | 1.714 | ||||||
| 7\53 | 158.491 | 1041.509 | 7:4 | 1.750 | ||||||
| 9\68 | 158.824 | 1041.176 | 9:5 | 1.800 | ||||||
| 2\15 | 160.000 | 1040.000 | 2:1 | 2.000 | Basic 7L 1s Optimum rank range for porcupine | |||||
| 9\67 | 161.194 | 1038.806 | 9:4 | 2.250 | ||||||
| 7\52 | 161.538 | 1038.462 | 7:3 | 2.333 | ||||||
| 12\89 | 161.798 | 1038.202 | 12:5 | 2.400 | ||||||
| 5\37 | 162.162 | 1037.838 | 5:2 | 2.500 | Semihard 7L 1s General range of porcupine | |||||
| 13\96 | 162.500 | 1037.500 | 13:5 | 2.600 | ||||||
| 8\59 | 162.712 | 1037.288 | 8:3 | 2.667 | ||||||
| 11\81 | 162.963 | 1037.037 | 11:4 | 2.750 | ||||||
| 3\22 | 163.636 | 1036.364 | 3:1 | 3.000 | Hard 7L 1s | |||||
| 10\73 | 164.384 | 1035.616 | 10:3 | 3.333 | ||||||
| 7\51 | 164.706 | 1035.294 | 7:2 | 3.500 | ||||||
| 11\80 | 165.000 | 1035.000 | 11:3 | 3.667 | ||||||
| 4\29 | 165.517 | 1034.483 | 4:1 | 4.000 | Superhard 7L 1s | |||||
| 9\65 | 166.154 | 1033.846 | 9:2 | 4.500 | ||||||
| 5\36 | 166.667 | 1033.333 | 5:1 | 5.000 | ||||||
| 6\43 | 167.442 | 1032.558 | 6:1 | 6.000 | ||||||
| 1\7 | 171.429 | 1028.571 | 1:0 | → ∞ | Collapsed 7L 1s | |||||