User:TallKite/Linnstrument layouts and MOS scales
Layouts
A Linnstrument layout is a row offset plus a column offset. The default 12edo-fourths layout is 5 1.
The three most popular hexagonal-key layouts can each be translated to the Linnstrument's square keys in two ways, shown here for 12edo:
- Bosanquet or Janko layout translates to (-1 +2) or (+1 +2)
- Wicki-Hayden layout translates to (+5 +2) or (+7 +2)
- Harmonic Table layout translates to (+4 +3) or (+7 +3)
The unison in an R C layout is R columns right and C rows down.
Pentatonic edos 5 10 15 20 25 & 30 and supersharp edos 8 13 & 18 have only 5 white keys, all else have 7 (except 6edo).
| edo | 4ths | 5ths | Bosanquet | Wicki-Hayden | Harmonic Table | Accordion | Array Mbira | Other layouts
(R <= P5, C < P4) | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| P4 1 | P5 1 | m2 M2 | A1 M2 | P4 M2 | P5 M2 | M3 m3 | P5 m3 | m3 M2 | P4 P5 | P5 P8 | ||
| 5 | 2 1 | 3 1 | 0 1 | 1 1 | 2 1 | 3 1 | 2 1 | 3 1 | --- | |||
| 6 | 2 1 ** | 3 1 ** | 1 1 * | 3 1 * | 3 2 * | 4 3 * | --- | |||||
| 7 | 3 1 | 4 1 | 1 1 | 0 1 | 3 1 | 4 1 | 1 2 * | 3 2 * | 21 | |||
| 8 | 3 1 | 5 1 | 1 2 * | 3 2 | 5 2 | 5 3 * | 5 2 * | 21 41 43 | ||||
| 9 | 4 1 | 5 1 | 2 1 | 1 1 | 4 1 | 5 1 | 2 3 | 5 3 | 31 32 52 43 | |||
| 10 | 4 1 | 6 1 | 1 2 * | 5 2 * | 4 3 * | 7 3 * | 21 31 51 32 53 | |||||
| 11 | 5 1 | 6 1 | 3 1 * | 2 1 * | 5 1 | 6 1 | 4 3 * | 7 3 * | 41 32 52 53 54 | |||
| 12 | 5 1 | 7 1 | 1 2 | 1 2 | 5 2 | 7 2 | 4 3 | 7 3 | 31 41 61 32 53 74 | |||
| 13 | 5 1 | 8 1 | 1 3 * | 2 3 * | 5 3 | 8 3 | 4 3 * | 7 3 * | 21 32 52 72 54 74 | |||
| 13b | 6 1 | 7 1 | 4 1 * | 3 1 * | 6 1 | 7 1 | 4 3 * | 7 3 * | ||||
| 14 | 6 1 | 8 1 | 1 2 * | 7 2 * | 5 4 * | 21 31 41 51 71
32 52 43 53 73 74 | ||||||
| 15 | 6 1 | 9 1 | 1 3 * | 5 4 | 9 4 | |||||||
| 16 | 7 1 | 9 1 | 3 2 | |||||||||
| 17 | 7 1 | 10 1 | ||||||||||
| 18 | 7 1 | 11 1 | 3 4 * | 7 4 * | ||||||||
| 18b | 8 1 | 10 1 | ||||||||||
| 19 | 8 1 | 11 1 | 2 3 | 1 3 | ||||||||
| 20 | ||||||||||||
| 21 | ||||||||||||
| 22 | 9 1 | 13 1 | 1 4 | 3 4 | 9 4 | 13 4 | ||||||
| 23 | 10 1 | 13 1 | 4 3 | 10 3 | 13 3 | |||||||
| 24 | ||||||||||||
| 25 | ||||||||||||
| 26 | ||||||||||||
| 27 | ||||||||||||
| 28 | ||||||||||||
| 29 | ||||||||||||
| 30 | ||||||||||||
| 31 | 13 1 | 18 1 | 3 5 | 2 5 | 13 5 | 18 5 | 10 8 | 18 8 | ||||
| 41 | 17 1 | 24 1 | 7 4 | 7 3 | 17 7 | 24 7 | 13 11 | 24 11 | 41 51 61 81 | |||
*) Not technically correct, but makes the most sense musically
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 21 | 31 | 41 | 51 | 61 | 71 | 81 | 91 | 10 1 | 11 1 | 12 1 | |
| 2 | 32 | 52 | 72 | 92 | 11 2 | |||||||
| 3 | 43 | 53 | 73 | 83 | 10 3 | 11 3 | ||||||
| 4 | 54 | 74 | 94 | 11 4 | ||||||||
| 5 | 65 | 75 | 85 | 95 | 11 5 | 12 5 | ||||||
| 6 | 76 | 11 6 | ||||||||||
| 7 | 87 | 97 | 10 7 | 11 7 | 12 7 | |||||||
| 8 | 98 | 11 8 |
MOS scales
MOS scales for edos excluding very small edos are selected to have:
- 5-12 notes
- if s=1, at most 2 small steps in a row
- L <= N/5 (upper limit is approx. M2 or m3)
- L/s ratio <= 3 (except penta-sharp-1 edos)
The first scale is the white keys, so Pyth[5] or Pyth[7]. The other MOS scales are sorted first by periods per octave, then by decreasing mingen size.
| edo | 1 | 2 | 3 | 4 | 5 | Others |
|---|---|---|---|---|---|---|
| 5 | 212 | |||||
| 6 | 222 | 33 | ||||
| 7 | 11212 | 313 | 3331 | |||
| 8 | 22121 | 323 | 211211 | 2222 | ||
| 9 | 1121112 | 2L3s | 2L1s | 4L1s | 3L3s | |
| 10 | 22222 | 4L2s | 2L6s | 3L4s | ||
| 11 | 1131113 | 3L5s | 4L3s | 5L1s | ||
| 12 | 2212221 | 2L3s | 2L1s | 3L6s | 4L4s | 6L |
| 13 | 33232 | 111311113 | 3L4s | 4L5s | 6L1s | |
| 14 | (2)7 | 3L5s | 4L1s | 6L2s | ||
| 15 | 33333 | (21)5 | 2223222 | 3131313 | 323232 | |
| 16 | 2232223 | |||||
| 17 | 3313331 | |||||
| 18 | 44343 | 2242224 | ||||
| 19 | 3323332 | |||||
| 20 | 44444 | |||||
| 21 | 5L2s | |||||
| 22 | 5L2s | 4L5s
4L1s |
1L6s
7L1s |
4L2s
6L4s |
6L2s | 2L8s |
| 23 | 3343334 | |||||
| 24 | 5L2s | |||||
| 25 | 55555 | |||||
| 26 | 5L2s | |||||
| 27 | 5L2s | |||||
| 28 | 5L2s | |||||
| 29 | 5L2s | |||||
| 30 | 5L | |||||
| 31 | 5L2s | 2L7s | 5L3s | 3L8s | ||
| 41 |