5L 7s: Difference between revisions
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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. | 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 == | ||
{{MOS | {{TAMNAMS use}} | ||
=== Proposed | {{MOS data}} | ||
=== 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. | 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. | ||
{{MOS modes|Mode Names= Rat | {{MOS modes | ||
| Mode Names= | |||
Rat $ | |||
Ox $ | |||
Tiger $ | |||
Rabbit $ | |||
Dragon $ | |||
Snake $ | |||
Horse $ | |||
Goat $ | |||
Monkey $ | |||
Rooster $ | |||
Dog $ | |||
Pig $ | |||
}} | |||
== Scales == | == Scales == | ||
| Line 25: | Line 39: | ||
== Scale tree == | == Scale tree == | ||
{{ | {{MOS tuning spectrum | ||
5/4 | | 6/5 = [[Photia]], ↑ [[grackle]]; | ||
9/7 | | 5/4 = [[Helmholtz]], [[Pythagorean tuning]] (701.955{{c}); | ||
4/3 | | 9/7 = [[Garibaldi]] / [[cassandra]] | ||
11/8 | | 4/3 = Garibaldi / [[andromeda]] | ||
10/7 | | 11/8 = [[Kwai]] | ||
3/2 | | 10/7 = [[Undecental]], argent tuning (702.944{{c}); | ||
13/8 | | 3/2 = [[Edson]] | ||
5/3 | | 13/8 = [[Polypyth]], golden neogothic (704.096{{c}); | ||
12/7 | | 5/3 = [[Leapday]] | ||
7/3 | | 12/7 = [[Leapweek]] | ||
13/5 | | 7/3 = [[Supra]] | ||
8/3 | | 13/5 = Golden supra (708.054{{c}); | ||
3/1 | | 8/3 = [[Quasisuper]] / [[quasisupra]] | ||
7/2 | | 3/1 = [[Suprapyth]] | ||
6/1 | | 7/2 = [[Superpyth]] | ||
| 6/1 = ↓ [[Oceanfront]] / [[ultrapyth]] | |||
}} | }} | ||
[[Category:12-tone scales]] | [[Category:12-tone scales]] | ||
[[Category:P-chromatic| ]]<!-- main article --> | [[Category:P-chromatic| ]]<!-- main article --> | ||
[[Category:Chromatic scales]] | [[Category:Chromatic scales]] | ||
Revision as of 19:40, 28 February 2025
| ↖ 4L 6s | ↑ 5L 6s | 6L 6s ↗ |
| ← 4L 7s | 5L 7s | 6L 7s → |
| ↙ 4L 8s | ↓ 5L 8s | 6L 8s ↘ |
┌╥┬╥┬╥┬┬╥┬╥┬┬┐ │║│║│║││║│║│││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
ssLsLssLsLsL
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, 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.
|
MOS data is deprecated. Please use the following templates individually: MOS intervals, MOS genchain, and MOS mode degrees |
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 }}