User:TallKite/Linnstrument layouts and MOS scales

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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

coprime row/col offsets
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
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