5L 7s
| ↖4L 6s | ↑5L 6s | 6L 6s↗ |
| ←4L 7s | 5L 7s | 6L 7s→ |
| ↙4L 8s | ↓5L 8s | 6L 8s↘ |
┌╥┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║│││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLssLsLsL
5L 12s
5L 7s, also called p-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 7 small steps, repeating every octave. 5L 7s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 700¢ to 720¢, or from 480¢ to 500¢.
5L 7s represents the chromatic scales of Pythagorean/schismic and superpyth, the former being proper but the latter improper until expanded by 5 more notes, producing superpyth[17]. Such scales are characterized by having a small step (diatonic semitone) that is smaller than the chroma (chromatic semitone), the reverse of 7L 5s.
The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean such that 64/63 is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.
Modes
The modes are named by Eliora after Chinese zodiac animals. 5L 7s is the opposite mos to 7L 5s, named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature.
- 11|0 LsLsLssLsLss - Rat
- 10|1 LsLssLsLsLss - Ox
- 9|2 LsLssLsLssLs - Tiger
- 8|3 LssLsLsLssLs - Rabbit
- 7|4 LssLsLssLsLs - Dragon
- 6|5 sLsLsLssLsLs - Snake
- 5|6 sLsLssLsLsLs - Horse
- 4|7 sLsLssLsLssL - Goat
- 3|8 sLssLsLsLssL - Monkey
- 2|9 sLssLsLssLsL - Rooster
- 1|10 ssLsLsLssLsL - Dog
- 0|11 ssLsLssLsLsL - Pig
Scales
- Pythagorean12 – Pythagorean tuning
- Garibaldi12 – 94edo tuning
- Cotoneum12 – 217edo tuning
- Edson12 – 29edo tuning
- Pepperoni12 – 271edo tuning
- Supra12 – 56edo tuning
- Archy12 – 472edo tuning
- 12-22a – 22edo tuning
Scale tree
| Generator(edo) | Cents | Step Ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 7\12 | 700.000 | 500.000 | 1:1 | 1.000 | Equalized 5L 7s | |||||
| 38\65 | 701.538 | 498.462 | 6:5 | 1.200 | Photia / pontiac / grackle | |||||
| 31\53 | 701.887 | 498.113 | 5:4 | 1.250 | Helmholtz, Pythagorean tuning (701.9550¢) | |||||
| 55\94 | 702.128 | 497.872 | 9:7 | 1.286 | Garibaldi / cassandra | |||||
| 24\41 | 702.439 | 497.561 | 4:3 | 1.333 | Supersoft 5L 7s Garibaldi / andromeda | |||||
| 65\111 | 702.703 | 497.297 | 11:8 | 1.375 | Kwai | |||||
| 41\70 | 702.857 | 497.143 | 7:5 | 1.400 | ||||||
| 58\99 | 703.030 | 496.970 | 10:7 | 1.429 | Undecental | |||||
| 17\29 | 703.448 | 496.552 | 3:2 | 1.500 | Soft 5L 7s Edson | |||||
| 61\104 | 703.846 | 496.154 | 11:7 | 1.571 | ||||||
| 44\75 | 704.000 | 496.000 | 8:5 | 1.600 | ||||||
| 71\121 | 704.132 | 495.868 | 13:8 | 1.625 | Golden neogothic (704.0956¢) | |||||
| 27\46 | 704.348 | 495.652 | 5:3 | 1.667 | Semisoft 5L 7s Leapday / polypyth | |||||
| 64\109 | 704.587 | 495.413 | 12:7 | 1.714 | Leapweek | |||||
| 37\63 | 704.762 | 495.238 | 7:4 | 1.750 | ||||||
| 47\80 | 705.000 | 495.000 | 9:5 | 1.800 | ||||||
| 10\17 | 705.882 | 494.118 | 2:1 | 2.000 | Basic 5L 7s Scales with tunings softer than this are proper | |||||
| 43\73 | 706.849 | 493.151 | 9:4 | 2.250 | ||||||
| 33\56 | 707.143 | 492.857 | 7:3 | 2.333 | Supra | |||||
| 56\95 | 707.368 | 492.632 | 12:5 | 2.400 | ||||||
| 23\39 | 707.692 | 492.308 | 5:2 | 2.500 | Semihard 5L 7s | |||||
| 59\100 | 708.000 | 492.000 | 13:5 | 2.600 | Golden supra (708.0539¢) | |||||
| 36\61 | 708.197 | 491.803 | 8:3 | 2.667 | Quasisuper / quasisupra | |||||
| 49\83 | 708.434 | 491.566 | 11:4 | 2.750 | ||||||
| 13\22 | 709.091 | 490.909 | 3:1 | 3.000 | Hard 5L 7s Suprapyth | |||||
| 42\71 | 709.859 | 490.141 | 10:3 | 3.333 | ||||||
| 29\49 | 710.204 | 489.796 | 7:2 | 3.500 | Superpyth | |||||
| 45\76 | 710.526 | 489.474 | 11:3 | 3.667 | ||||||
| 16\27 | 711.111 | 488.889 | 4:1 | 4.000 | Superhard 5L 7s | |||||
| 35\59 | 711.864 | 488.136 | 9:2 | 4.500 | ||||||
| 19\32 | 712.500 | 487.500 | 5:1 | 5.000 | ||||||
| 22\37 | 713.514 | 486.486 | 6:1 | 6.000 | ↓ Ultrapyth / Oceanfront | |||||
| 3\5 | 720.000 | 480.000 | 1:0 | → ∞ | Collapsed 5L 7s | |||||