7L 5s: Difference between revisions
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m Wording for smallstep and chroma |
Added back most of the old wording for intro |
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro|Other Names=m-chromatic}} | {{MOS intro|Other Names=m-chromatic}} | ||
7L 5s represents the chromatic scale of [[meantone]], or meantone chromatic scale. Such scales are characterized by having a small step ([[diatonic semitone]]) that is larger than the [[chroma]] ([[chromatic semitone]]), the reverse of [[5L 7s]]. | |||
Meantone is the only notable harmonic entropy minimum. | |||
== Modes == | == Modes == | ||
Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness. | Both [[User:Eliora|Eliora]] and [[User:Ganaram inukshuk|Ganaram]] have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness. | ||
Revision as of 09:11, 14 February 2024
| ↖ 6L 4s | ↑ 7L 4s | 8L 4s ↗ |
| ← 6L 5s | 7L 5s | 8L 5s → |
| ↙ 6L 6s | ↓ 7L 6s | 8L 6s ↘ |
┌╥╥┬╥┬╥╥┬╥┬╥┬┐ │║║│║│║║│║│║││ ││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLsLsLLsLsLL
Generator size
TAMNAMS information
Related MOS scales
Equal tunings
7L 5s, also called m-chromatic, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 5 small steps, repeating every octave. 7L 5s is a child scale of 5L 2s, expanding it by 5 tones. Generators that produce this scale range from 500 ¢ to 514.3 ¢, or from 685.7 ¢ to 700 ¢. 7L 5s represents the chromatic scale of meantone, or meantone chromatic scale. Such scales are characterized by having a small step (diatonic semitone) that is larger than the chroma (chromatic semitone), the reverse of 5L 7s.
Meantone is the only notable harmonic entropy minimum.
Modes
Both Eliora and Ganaram have independently proposed mode names based on names of the months. The latter scheme uses mode names from the Gregorian calendar, starting with January assigned to the step pattern LsLsLsLLsLsL, with successive rotations assigned to successive months. The latter scheme is based on month names from the Roman calendar, starting with Mensis Martius as the brightest mode, with successive month names for each mode by descending brightness.
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 11|0 | 1 | LLsLsLLsLsLs |
| 10|1 | 6 | LLsLsLsLLsLs |
| 9|2 | 11 | LsLLsLsLLsLs |
| 8|3 | 4 | LsLLsLsLsLLs |
| 7|4 | 9 | LsLsLLsLsLLs |
| 6|5 | 2 | LsLsLLsLsLsL |
| 5|6 | 7 | LsLsLsLLsLsL |
| 4|7 | 12 | sLLsLsLLsLsL |
| 3|8 | 5 | sLLsLsLsLLsL |
| 2|9 | 10 | sLsLLsLsLLsL |
| 1|10 | 3 | sLsLLsLsLsLL |
| 0|11 | 8 | sLsLsLLsLsLL |
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 11|0 | 1 | LLsLsLLsLsLs |
| 10|1 | 6 | LLsLsLsLLsLs |
| 9|2 | 11 | LsLLsLsLLsLs |
| 8|3 | 4 | LsLLsLsLsLLs |
| 7|4 | 9 | LsLsLLsLsLLs |
| 6|5 | 2 | LsLsLLsLsLsL |
| 5|6 | 7 | LsLsLsLLsLsL |
| 4|7 | 12 | sLLsLsLLsLsL |
| 3|8 | 5 | sLLsLsLsLLsL |
| 2|9 | 10 | sLsLLsLsLLsL |
| 1|10 | 3 | sLsLLsLsLsLL |
| 0|11 | 8 | sLsLsLLsLsLL |
Scales
- Meaneb471a – an equal beating tuning of meantone
- Meantone12 – 31edo tuning
- Ratwolf – 20/13 wolf fifth tuning of meantone
- Meaneb471 – the other equal beating tuning of meantone
- Flattone12 – 13-limit POTE tuning of flattone
Scale tree
Generator ranges:
- Chroma-positive generator: 500 cents (5\12) to 514.2857 cents (3\7)
- Chroma-negative generator: 685.7143 cents (4\7) to 700 cents (7\12)
| Generator | Cents | L | s | L/s | Comments | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| 5\12 | 500.000 | 1 | 1 | 1.000 | ||||||
| 28\67 | 501.493 | 6 | 5 | 1.200 | ||||||
| 23\55 | 501.818 | 5 | 4 | 1.250 | ||||||
| 41\98 | 502.041 | 9 | 7 | 1.286 | ||||||
| 18\43 | 502.326 | 4 | 3 | 1.333 | Meantone / meridetone | |||||
| 49\117 | 502.564 | 11 | 8 | 1.375 | ||||||
| 31\74 | 502.703 | 7 | 5 | 1.400 | Meantone / huygens / grosstone | |||||
| 44\105 | 502.857 | 10 | 7 | 1.428 | ||||||
| 13\31 | 503.226 | 3 | 2 | 1.500 | ||||||
| 47\112 | 503.571 | 11 | 7 | 1.571 | ||||||
| 34\81 | 503.704 | 8 | 5 | 1.600 | Meantone | |||||
| 55\131 | 503.817 | 13 | 8 | 1.625 | Golden meantone (503.7855¢) | |||||
| 21\50 | 504.000 | 5 | 3 | 1.667 | Meantone / meanpop | |||||
| 50\119 | 504.202 | 12 | 7 | 1.714 | ||||||
| 29\69 | 504.348 | 7 | 4 | 1.750 | ||||||
| 37\88 | 504.545 | 9 | 5 | 1.800 | ||||||
| 8\19 | 505.263 | 2 | 1 | 2.000 | Basic m-chromatic (Generators smaller than this are proper) | |||||
| 35\83 | 506.024 | 9 | 4 | 2.250 | ||||||
| 27\64 | 506.250 | 7 | 3 | 2.333 | ||||||
| 46\109 | 506.422 | 12 | 5 | 2.400 | ||||||
| 19\45 | 506.667 | 5 | 2 | 2.500 | Flattone | |||||
| 49\116 | 506.897 | 13 | 5 | 2.600 | Golden flattone (506.9365¢) | |||||
| 30\71 | 507.042 | 8 | 3 | 2.667 | ||||||
| 41\97 | 507.216 | 11 | 4 | 2.750 | ||||||
| 11\26 | 507.692 | 3 | 1 | 3.000 | ||||||
| 36\85 | 508.235 | 10 | 3 | 3.333 | ||||||
| 25\59 | 508.475 | 7 | 2 | 3.500 | ||||||
| 39\92 | 508.696 | 11 | 3 | 3.667 | ||||||
| 14\33 | 509.091 | 4 | 1 | 4.000 | ||||||
| 31\73 | 509.589 | 9 | 2 | 4.500 | ||||||
| 17\40 | 510.000 | 5 | 1 | 5.000 | ||||||
| 20\47 | 510.638 | 6 | 1 | 6.000 | ||||||
| 3\7 | 514.286 | 1 | 0 | → inf | ||||||