5L 7s: Difference between revisions
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'''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[ | '''5L 7s''' is the MOS pattern of the [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] chromatic scale, and also the [[superpyth]] chromatic scale. In contrast to the [[7L 5s|meantone chromatic scale]], in which diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, so the [[5L 2s|diatonic scale]] subset is actually [[Rothenberg propriety|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 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. | ||
| Line 78: | Line 78: | ||
| || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 || | | || || || || || 47\80 || 705.000 || 9 || 5 || 1.800 || | ||
|- | |- | ||
| || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>( | | || 10\17 || || || || || 705.882 || 2 || 1 || 2.000 || Basic p-chromatic <br>(Fifths smaller than this are proper) | ||
|- | |- | ||
| || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 || | | || || || || || 43\73 || 706.849 || 9 || 4 || 2.250 || | ||
Revision as of 13:48, 12 February 2022
| ↖ 4L 6s | ↑ 5L 6s | 6L 6s ↗ |
| ← 4L 7s | 5L 7s | 6L 7s → |
| ↙ 4L 8s | ↓ 5L 8s | 6L 8s ↘ |
Scale structure
ssLsLssLsLsL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
5L 7s 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 diatonic semitones are larger than chromatic semitones, here the reverse is true: diatonic semitones are smaller than chromatic semitones, 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 doesn't become proper until you add 5 more notes to form the superpyth "enharmonic" scale, superpyth[17]).
Modes
- 11|0 LsLsLssLsLss
- 10|1 LsLssLsLsLss
- 9|2 LsLssLsLssLs
- 8|3 LssLsLsLssLs
- 7|4 LssLsLssLsLs
- 6|5 sLsLsLssLsLs
- 5|6 sLsLssLsLsLs
- 4|7 sLsLssLsLssL
- 3|8 sLssLsLsLssL
- 2|9 sLssLsLssLsL
- 1|10 ssLsLsLssLsL
- 0|11 ssLsLssLsLsL
Scales
- Pythagorean12 – Pythagorean tuning
- Cotoneum12 – 217edo tuning
- Garibaldi12 – 94edo tuning
- Supra12 – 56edo tuning
- Archy12 – 472edo tuning
- 12-22a – 22edo tuning
Scale tree
| Generator | Fifth (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 | |||||
| 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 (Fifth = 704.0956 cents) | |||||
| 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 (Fifths 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 (Fifth = 708.0539 cents) | |||||
| 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 | ||||||