5L 7s
5L 7s 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.
| ↖ 4L 6s | ↑ 5L 6s | 6L 6s ↗ |
| ← 4L 7s | 5L 7s | 6L 7s → |
| ↙ 4L 8s | ↓ 5L 8s | 6L 8s ↘ |
ssLsLssLsLsL
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, th simpler and less accurate temperament known as archy in which 64/63 is tempered out.
Scale properties
- This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.
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Proposed names
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. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.
| UDP | Cyclic order |
Step pattern |
Mode names |
|---|---|---|---|
| 11|0 | 1 | LsLsLssLsLss | Rat |
| 10|1 | 8 | LsLssLsLsLss | Ox |
| 9|2 | 3 | LsLssLsLssLs | Tiger |
| 8|3 | 10 | LssLsLsLssLs | Rabbit |
| 7|4 | 5 | LssLsLssLsLs | Dragon |
| 6|5 | 12 | sLsLsLssLsLs | Snake |
| 5|6 | 7 | sLsLssLsLsLs | Horse |
| 4|7 | 2 | sLsLssLsLssL | Goat |
| 3|8 | 9 | sLssLsLsLssL | Monkey |
| 2|9 | 4 | sLssLsLssLsL | Rooster |
| 1|10 | 11 | ssLsLsLssLsL | Dog |
| 0|11 | 6 | 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
{{MOS tuning spectrum | 6/5 = Photia, ↑ grackle; | 5/4 = Helmholtz, Pythagorean tuning (701.955{{c}); | 9/7 = Garibaldi / cassandra | 4/3 = Garibaldi / andromeda | 11/8 = Kwai | 10/7 = Undecental, argent tuning (702.944{{c}); | 3/2 = Edson | 13/8 = Polypyth, golden neogothic (704.096{{c}); | 5/3 = Leapday | 12/7 = Leapweek | 7/3 = Supra | 13/5 = Golden supra (708.054{{c}); | 8/3 = Quasisuper / quasisupra | 3/1 = Suprapyth | 7/2 = Superpyth | 6/1 = ↓ Oceanfront / ultrapyth }}