7L 1s
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.
| ← 6L 1s | 7L 1s | 8L 1s → |
| ↙ 6L 2s | ↓ 7L 2s | 8L 2s ↘ |
Scale structure
sLLLLLLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
Name
TAMNAMS suggests the temperament-agnostic name pine as the name of 7L 1s. The name is an abstraction of porcupine temperament.
Scale properties
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Details: Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
Proposed names
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.
| UDP | Cyclic order |
Step pattern |
Name Origin |
|---|---|---|---|
| 7|0 | 1 | LLLLLLLs | Bright quartal |
| 6|1 | 2 | LLLLLLsL | Dark quartal |
| 5|2 | 3 | LLLLLsLL | Bright major |
| 4|3 | 4 | LLLLsLLL | Middle major |
| 3|4 | 5 | LLLsLLLL | Dark major |
| 2|5 | 6 | LLsLLLLL | Bright minor |
| 1|6 | 7 | LsLLLLLL | Middle minor |
| 0|7 | 8 | sLLLLLLL | Dark minor |
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 out S10/S11 so that (4/3)/(11/10)3 is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 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 out 100/99 = S10 and 121/120 = S11.
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 | General range of greeley | |||||
| 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 | Golden porcupine/hemikleismic | |||||
| 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 | |||||