User:TallKite/Linnstrument layouts and MOS scales
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).
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 21 | 31 | 41 | 51 | 61 | 71 | 81 | 91 | T1 | E1 | |
| 2 | 32 | 52 | 72 | 92 | E2 | ||||||
| 3 | 43 | 53 | 73 | 83 | T3 | E3 | |||||
| 4 | 54 | 74 | 94 | E4 | |||||||
| 5 | 65 | 75 | 85 | 95 | E5 | ||||||
| 6 | 76 | E6 | |||||||||
| 7 | 87 | 97 | T7 | E7 |
| Suggested layouts | Preset MOS scales | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| edo | 4ths | 5ths | Bosanquet | Wicki-Hayden | Harmonic Table | Other layouts
(R <= P5, C < P4) |
1st scale = white keys | ||||||||
| P4 1 | P5 1 | m2 M2 | A1 M2 | P4 M2 | P5 M2 | M3 m3 | P5 m3 | 1 | 2 | 3 | 4 | 5 | etc. | ||
| 5 | 2 1 | 3 1 | 0 1 | 1 1 | 2 1 | 3 1 | 2 1 | 3 1 | --- | 212 | |||||
| 6 | 2 1 ** | 3 1 ** | 1 1 * | 3 1 * | 3 2 * | 4 3 * | --- | 222 | 33 | ||||||
| 7 | 3 1 | 4 1 | 1 1 | 0 1 | 3 1 | 4 1 | 1 2 * | 3 2 * | 21 | 11212 | 313 | 3331 | |||
| 8 | 3 1 | 5 1 | 1 2 * | 3 2 | 5 2 | 5 3 * | 5 2 * | 21 41 43 | 22121 | 2L1s | 2L4s | 4L | |||
| 9 | 4 1 | 5 1 | 2 1 | 1 1 | 4 1 | 5 1 | 2 3 | 5 3 | 31 32 52 43 | 1121112 | 2L3s | 2L1s | 4L1s | 3L3s | |
| 10 | 4 1 | 6 1 | 1 2 * | 5 2 * | 4 3 * | 7 3 * | 21 31 51 32 53 | 22222 | 4L2s | 2L6s | 3L4s | ||||
| 11 | 5 1 | 6 1 | 3 1 * | 2 1 * | 5 1 | 6 1 | 4 3 * | 7 3 * | 41 32 52 53 54 | 1131113 | 3L5s | 4L3s | 5L1s | ||
| 12 | 5 1 | 7 1 | 1 2 | 1 2 | 5 2 | 7 2 | 4 3 | 7 3 | 31 41 61 32 53 74 | 2212221 | 2L3s | 2L1s | 3L6s | 4L4s | 6L |
| 13 | 5 1 | 8 1 | 1 3 * | 2 3 * | 5 3 | 8 3 | 4 3 * | 7 3 * | 21 32 52 72 54 74 | 33232 | 111311113 | 3L4s | 4L5s | 6L1s | |
| 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 |
(2)x7 | 3L5s | 4L1s | 6L2s | |||||
| 15 | 6 1 | 9 1 | 1 3 * | 5 4 | 9 4 | 33333 | (21)x5 | 2223222 | 4L3s
3131313 |
6L3s
323232 |
|||||
| 16 | 7 1 | 9 1 | 3 2 | 2232223 | |||||||||||
| 17 | 7 1 | 10 1 | 3313331 | ||||||||||||
| 18 | 7 1 | 11 1 | 3 4 * | 7 4 * | 44343 | 2242224 | |||||||||
| 18b | 8 1 | 10 1 | |||||||||||||
| 19 | 8 1 | 11 1 | 2 3 | 1 3 | 3323332 | ||||||||||
| 20 | 44444 | ||||||||||||||
| 21 | 5L2s | ||||||||||||||
| 22 | 5L2s | 4L5s
4L1s |
1L6s
7L1s |
4L2s
6L4s |
6L2s | 2L8s | |||||||||
| 23 | 10 1 | 13 1 | 4 3 | 10 3 | 13 3 | 3343334 | |||||||||
| 24 | 5L2s | ||||||||||||||
| 25 | 55555 | ||||||||||||||
| 26 | 5L2s | ||||||||||||||
| 27 | 5L2s | ||||||||||||||
| 28 | 5L2s | ||||||||||||||
| 29 | 5L2s | ||||||||||||||
| 30 | 5L | ||||||||||||||
| 31 | 13 1 | 18 1 | 3 5 | 2 5 | 13 5 | 18 5 | 10 8 | 18 8 | 5L2s | 2L7s | 5L3s | 3L8s | |||
*) Not technically correct, but makes the most sense musically
MOS scales are selected to have
- 5-12 notes
- if s=1, at most 2 small steps in a row (except for very small edos)
- L <= N/5 (approx. M2/m3)
- L/s ratio <= 3 (except penta-sharp-1 edos)
MOS scales are sorted first by periods per octave, then by decreasing mingen size.