5L 7s
| ↖4L 6s | ↑5L 6s | 6L 6s↗ |
| ←4L 7s | 5L 7s | 6L 7s→ |
| ↙4L 8s | ↓5L 8s | 6L 8s↘ |
5L 7s is a moment of symmetry scale consisting of 5 large steps and 7 small steps, repeating every octave. This scale is made using a generator ranging from 700¢ to 720¢, or from 480¢ to 500¢.
It is the MOS pattern of the Pythagorean/schismic chromatic scale, and also the superpyth chromatic scale. In contrast to the meantone chromatic scale, in which the diatonic semitone is larger than the chromatic semitone, here the reverse is true: the diatonic semitone is smaller than the chromatic semitone, so the diatonic scale subset is actually improper.
The two distinct harmonic entropy minima with this MOS pattern 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.
The Pythagorean/schismatic version is proper, but the superpyth version is improper (it does not become proper until you add 5 more notes to form the superpyth enharmonic scale, superpyth[17]).
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
- Pepperoni12 – 271edo tuning
- Supra12 – 56edo tuning
- Archy12 – 472edo tuning
- 12-22a – 22edo tuning
Scale tree
Generator ranges:
- Chroma-positive generator: 700 cents (7\12) to 720 cents (3\5)
- Chroma-negative generator: 480 cents (2\5) to 500 cents (5\12)
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 7\12 | 700.000 | 1 | 1 | 1.000 | ||||||
| 38\65 | 701.539 | 6 | 5 | 1.200 | Photia / pontiac / grackle↑ | |||||
| 31\53 | 701.887 | 5 | 4 | 1.250 | Helmholtz, Pythagorean tuning (701.9550¢) | |||||
| 55\94 | 702.128 | 9 | 7 | 1.286 | Garibaldi / cassandra | |||||
| 24\41 | 702.409 | 4 | 3 | 1.333 | Garibaldi / andromeda | |||||
| 65\111 | 702.703 | 11 | 8 | 1.375 | Kwai | |||||
| 41\70 | 702.857 | 7 | 5 | 1.400 | ||||||
| 58\99 | 703.030 | 10 | 7 | 1.428 | Undecental | |||||
| 17\29 | 703.448 | 3 | 2 | 1.500 | Edson | |||||
| 61\104 | 703.846 | 11 | 7 | 1.571 | ||||||
| 44\75 | 704.000 | 8 | 5 | 1.600 | ||||||
| 71\121 | 704.132 | 13 | 8 | 1.625 | Golden neogothic (704.0956¢) | |||||
| 27\46 | 704.348 | 5 | 3 | 1.667 | Leapday / polypyth | |||||
| 64\109 | 704.587 | 12 | 7 | 1.714 | Leapweek | |||||
| 37\63 | 704.762 | 7 | 4 | 1.750 | ||||||
| 47\80 | 705.000 | 9 | 5 | 1.800 | ||||||
| 10\17 | 705.882 | 2 | 1 | 2.000 | Basic p-chromatic (Generators smaller than this are proper) | |||||
| 43\73 | 706.849 | 9 | 4 | 2.250 | ||||||
| 33\56 | 707.143 | 7 | 3 | 2.333 | Supra | |||||
| 56\95 | 707.368 | 12 | 5 | 2.400 | ||||||
| 23\39 | 707.692 | 5 | 2 | 2.500 | ||||||
| 59\100 | 708.000 | 13 | 5 | 2.600 | Golden supra (708.0539¢) | |||||
| 36\61 | 708.197 | 8 | 3 | 2.667 | Quasisuper / quasisupra | |||||
| 49\83 | 708.434 | 11 | 4 | 2.750 | ||||||
| 13\22 | 709.091 | 3 | 1 | 3.000 | Suprapyth | |||||
| 42\71 | 709.859 | 10 | 3 | 3.333 | ||||||
| 29\49 | 710.204 | 7 | 2 | 3.500 | Superpyth | |||||
| 45\76 | 710.526 | 11 | 3 | 3.667 | ||||||
| 16\27 | 711.111 | 4 | 1 | 4.000 | ||||||
| 35\59 | 711.864 | 9 | 2 | 4.500 | ||||||
| 19\32 | 712.500 | 5 | 1 | 5.000 | ||||||
| 22\37 | 713.514 | 6 | 1 | 6.000 | Oceanfront↓ / ultrapyth↓ | |||||
| 3\5 | 720.000 | 1 | 0 | → inf | ||||||