User:TallKite/Linnstrument layouts and MOS scales
Layouts by EDO
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 |
Layouts by pergen
| pergen | octave vector | col / row | EU | notation | up-cents | edos | notes | |
|---|---|---|---|---|---|---|---|---|
| (P8, P5) | 5/7 cols 2 rows | (M2, m2) | ---- | ---- | ---- | all single-
ring edos |
Bosanquet | |
| 1 col 1 row | (M2, P4) | ---- | ---- | ---- | Wicki-Hayden | |||
| (P8/2, P5) | 1:1 | (P4, M2/2) | vvM2 | (P4, ^1) | 100¢ + c | all even edos | Saguguti | |
| (P8, P4/2) | 5 cols -1 row | (P4/2, m2/2) | vvm2 | (^M2=vm3, ^1) | 50¢ - 2.5c | pentasharp-2n | Zozoti | |
| (P8, P5/2) | 2:7 | (P5/2, A1/2) | vvA1 | (^m3=vM3, ^1) | 50¢ + 3.5c | sharp-2n | Luluti | |
| (P8/2, P4/2) | both sharp-2n
and even |
(true double) | ||||||
| (P8/3, P5) | threeven | Triguti | ||||||
| (P8, P4/3) | 7 cols 1 row | (P4/3, A1/3) | 3vA1 | (vM2=^^m2, ^1) | 33¢ + 2.33c | sharp-3n | 7 14 21 28 35 42b
15 22 29 36 43 50 30 37 44 51 |
Triyoti |
| (P8, P5/3) | 5 cols 1 row | (P5/3, m2/3) | 3vm2 | (^M2=vvm3, ^1) | 33¢ - 1.67c | pentasharp-3n | 15 20 25 30 35b
21 26 31 36 41 46 |
Latrizoti |
| (P8, P11/3) | 1:2? | |||||||
| (P8/4, P5) | Quadguti | |||||||
| (P8, P4/4) | 9 cols 1 row | (P4/4, A2/4) | 4vA2 | (vM2, ^1) | 75¢ + 2.25c | both sharp-2n
and pentasharp-2n |
37b 47
18b 28 38 48 9 19 29 39 49 10 20 30 40b |
Laquadyoti |
| (P8, P5/4) | 7 cols -1 row | (P5/4, A1/4) | 4vA1 | (vM2, ^1) | 25¢ + 1.75c | sharp-4n | 7 14 21 28 35 42b
20 27 34 41 48 55 |
Saquadyoti |
| (P8, P) |
Third of a 4th
| 1sns | 2nds | 3rds | 4ths | 5ths | 6ths | 7ths | 8ves | 9ths | 10ths | 11ths | 12ths | 13th | 14ths | dbl 8ves |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -21
A1 100¢ |
-20
vA2 267¢ |
-19
^M3 433¢ |
-18
A4 600¢ |
-17
vA5 767¢ |
-16
^M6 933¢ |
-15
M7 1100¢ |
-14
vA8 1267¢ |
|||||||
| -14
vA1 67¢ |
-13
^M2 233¢ |
-12
M3 400¢ |
-11
vA4 567¢ |
-10
^5 733¢ |
-9
M6 900¢ |
-8
vM7 1067¢ |
-7
^8 1233¢ |
-3
P12 700¢ |
-2
vM13 867¢ |
-1
^m14 1033¢ |
0
P15 1200¢ | |||
| -7
^1 33¢ |
-6
M2 200¢ |
-5
vM3 367¢ |
-4
^4 533¢ |
-3
P5 700¢ |
-2
vM6 867¢ |
-1
^m7 1033¢ |
0
P8 1200¢ |
+1
vM9 167¢ |
+2
^m10 333¢ |
+3
P11 500¢ |
||||
| 0
P1 0¢ |
+1
vM2 167¢ |
+2
^m3 333¢ |
+3
P4 500¢ |
+4
v5 667¢ |
+5
^m6 833¢ |
+6
m7 1000¢ |
+7
v8 1167¢ |
|||||||
| +7
v1 -33¢ |
+8
^m2 133¢ |
+9
m3 300¢ |
+10
v4 467¢ |
+11
^d5 633¢ |
+12
m6 800¢ |
+13
vm7 967¢ |
+14
^d8 1133¢ |
|||||||
| +14
^d1 -67¢ |
+15
m2 100¢ |
+16
vm3 267¢ |
+17
^d4 433¢ |
+18
d5 600¢ |
+19
vm6 767¢ |
+20
^d7 933¢ |
+21
d8 1100¢ |
| -20
vA2 267¢ |
-19
^M3 433¢ |
-18
A4 600¢ |
||||||||||
| -18
A4 600¢ |
-17
vA5 767¢ |
-16
^M6 933¢ |
-15
M7 1100¢ |
-14
vA8 1267¢ |
-13
^M2 233¢ |
-12
M3 400¢ |
||||||
| -12
M3 400¢ |
-11
vA4 567¢ |
-10
^5 733¢ |
-9
M6 900¢ |
-8
vM7 1067¢ |
-7
^8 1233¢ |
-6
M2 200¢ |
-3
P12 700¢ |
-2
vM13 867¢ |
-1
^m14 1033¢ |
0
P15 1200¢ | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| -6
M2 200¢ |
-5
vM3 367¢ |
-4
^4 533¢ |
-3
P5 700¢ |
-2
vM6 867¢ |
-1
^m7 1033¢ |
0
P8 1200¢ |
+1
vM9 167¢ |
+2
^m10 333¢ |
+3
P11 500¢ |
|||
| 0
P1 0¢ |
+1
vM2 167¢ |
+2
^m3 333¢ |
+3
P4 500¢ |
+4
v5 667¢ |
+5
^m6 833¢ |
+6
m7 1000¢ |
+7
v8 1167¢ |
|||||
| +6
low m7 -200¢ |
+7
v1 -33¢ |
+8
^m2 133¢ |
+9
m3 300¢ |
+10
v4 467¢ |
+11
^d5 633¢ |
+12
m6 800¢ |
+13
vm7 967¢ |
+14
^d8 1133¢ |
||||
| +12
low m6 -400¢ |
+13
low vm7 -233¢ |
+14
^d1 -67¢ |
+15
m2 100¢ |
+16
vm3 267¢ |
+17
^d4 433¢ |
+18
d5 600¢ |
+19
vm6 767¢ |
+20
^d7 933¢ |
+21
d8 1100¢ |
Quarter-fifth
| 1sns | 2nds | 3rds | 4ths | 5ths | 6ths | 7ths | 8ves | 9ths | 10ths | 11ths | 12ths | 13th | 14ths | dbl 8ves |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| +7
^1 25¢ |
+8
M2 200¢ |
+9
vM3 375¢ |
+10
~4 550¢ |
+11
^5 725¢ |
+12
M6 900¢ |
+13
vM7 1075¢ |
+14
^^8 1250¢ |
|||||||
| 0
P1 0¢ |
+1
vM2 175¢ |
+2
~3 350¢ |
+3
^4 525¢ |
+4
P5 700¢ |
+5
vM6 875¢ |
+6
~7 1050¢ |
+7
^8 1225¢ |
|||||||
| -7
v1 -25¢ |
-6
~2 150¢ |
-5
^m3 325¢ |
-4
P4 500¢ |
-3
v5 675¢ |
-2
~6 850¢ |
-1
^m7 1025¢ |
0
P8 1200¢ |
+1
vM2 175¢ |
+2
~3 350¢ |
+3
^4 525¢ |
||||
| -14
vv1 -50¢ |
-13
^m2 125¢ |
-12
m3 300¢ |
-11
v4 475¢ |
-10
~5 650¢ |
-9
^m5 825¢ |
-8
m7 1000¢ |
-7
v8 1175¢ |
-3
v5 675¢ |
-2
~6 850¢ |
-1
^m7 1025¢ |
0
P8 1200¢ |
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 |