Lumatone mapping for 60edo: Difference between revisions

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Finally found the time to crunch the math to optimise this one.
m →Magic: Forgot to mention where note 0 is in the demonstration video
 
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There are many conceivable ways to map [[60edo]] onto the [[Lumatone]] keyboard. Unfortunately, as it has multiple rings of 5ths, the [[Standard Lumatone mapping for Pythagorean]] is not one of them. Since it is [[Highly_composite_equal_division|highly composite]], many other mappings will also fail to cover the entire gamut, and even those that do will have limited range. For example, [[magic]] needs to be expanded to the [[3L 13s]] mos, at which point it only has a range of three and a half octaves.  
{{Lumatone mapping intro}} Due to the very large number of notes, even those that do will have limited range.


== Magic ==
For example, the [[magic]] mapping needs to be expanded to the [[3L 13s]] mos, at which point it only has a range of three and a half octaves. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/nlKHUDCR3pI ''60edo improv''] (2025), although with the first note 0 in the upper left corner instead of most of the way down to the lower left.
{{Lumatone EDO mapping|n=60|start=57|xstep=7|ystep=-3}}
{{Lumatone EDO mapping|n=60|start=57|xstep=7|ystep=-3}}


The [[3L 10s]] mapping is still playable and covers 5 octaves, but skips a number of chromas along the way, and this escalates with more compressed mappings.
 
The [[3L 10s]] mapping is still playable and covers 5 octaves, but skips a number of chromas along the way, and this escalates with more compressed mappings.
{{Lumatone EDO mapping|n=60|start=44|xstep=10|ystep=-3}}
{{Lumatone EDO mapping|n=60|start=44|xstep=10|ystep=-3}}


The [[amity]] mapping also suffers from chroma skips between most columns unless expanded outwards from the [[4L 3s]] mapping to the [[7L 4s]] one, which also makes octaves further apart vertically.  
== Amity ==
The [[Lumatone mapping for Amity]] also suffers from chroma skips between most columns unless expanded outwards from the [[4L 3s]] mapping to the [[7L 4s]] one, which also makes octaves further apart vertically.  
{{Lumatone EDO mapping|n=60|start=53|xstep=9|ystep=-1}}
{{Lumatone EDO mapping|n=60|start=53|xstep=9|ystep=-1}}
{{Lumatone EDO mapping|n=60|start=0|xstep=8|ystep=-1}}
{{Lumatone EDO mapping|n=60|start=0|xstep=8|ystep=-1}}


Other possible mappings include [[bleu]]
== Other mappings ==
Other possible mappings include [[bleu]] and [[tritonic]], but it is the [[fifive]] mapping that produces an octotonic scale which maximises range while providing access to all the notes and makes it easiest to play simple ratios together.
 
=== Bleu ===
{{Lumatone EDO mapping|n=60|start=4|xstep=7|ystep=-4}}
{{Lumatone EDO mapping|n=60|start=4|xstep=7|ystep=-4}}


Or [[tritonic]]
=== Tritonic ===
{{Lumatone EDO mapping|n=60|start=5|xstep=9|ystep=-7}}
{{Lumatone EDO mapping|n=60|start=5|xstep=9|ystep=-7}}


However, it is the [[fifive]] mapping that produces an octotonic scale which maximises range while providing access to all the notes and makes it easiest to play simple ratios together.
=== Fifive ===
 
{{Lumatone EDO mapping|n=60|start=27|xstep=7|ystep=2}}
{{Lumatone EDO mapping|n=60|start=27|xstep=7|ystep=2}}


{{Lumatone mapping navigation}}
{{Navbox Lumatone}}

Latest revision as of 07:26, 17 May 2025

There are many conceivable ways to map 60edo onto the onto the Lumatone keyboard. However, it has 5 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them. Since it is highly composite, many other mappings will also fail to cover the whole gamut. Due to the very large number of notes, even those that do will have limited range.

Magic

For example, the magic mapping needs to be expanded to the 3L 13s mos, at which point it only has a range of three and a half octaves. Bryan Deister demonstrates this mapping in 60edo improv (2025), although with the first note 0 in the upper left corner instead of most of the way down to the lower left.

57
4
1
8
15
22
29
58
5
12
19
26
33
40
47
2
9
16
23
30
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51
58
5
12
59
6
13
20
27
34
41
48
55
2
9
16
23
30
3
10
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24
31
38
45
52
59
6
13
20
27
34
41
48
55
0
7
14
21
28
35
42
49
56
3
10
17
24
31
38
45
52
59
6
13
4
11
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25
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0
7
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56
3
10
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31
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1
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0
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1
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0
7
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51
58
5
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1
8
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22
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36
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50
57
4
11
18
25
55
2
9
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23
30
37
44
51
58
5
12
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26
33
40
47
54
1
8
15
22
29
13
20
27
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48
55
2
9
16
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30
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51
58
5
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26
38
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59
6
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27
34
41
48
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2
9
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23
30
56
3
10
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24
31
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45
52
59
6
13
20
27
21
28
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49
56
3
10
17
24
31
39
46
53
0
7
14
21
28
4
11
18
25
32
22
29


The 3L 10s mapping is still playable and covers 5 octaves, but skips a number of chromas along the way, and this escalates with more compressed mappings.

44
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1
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29
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29
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49
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9
56
6
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26
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56
6
33
43
53
3
13
0
10

Amity

The Lumatone mapping for Amity also suffers from chroma skips between most columns unless expanded outwards from the 4L 3s mapping to the 7L 4s one, which also makes octaves further apart vertically.

53
2
1
10
19
28
37
0
9
18
27
36
45
54
3
8
17
26
35
44
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2
11
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29
38
7
16
25
34
43
52
1
10
19
28
37
46
55
4
15
24
33
42
51
0
9
18
27
36
45
54
3
12
21
30
39
14
23
32
41
50
59
8
17
26
35
44
53
2
11
20
29
38
47
56
5
22
31
40
49
58
7
16
25
34
43
52
1
10
19
28
37
46
55
4
13
22
31
40
21
30
39
48
57
6
15
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33
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51
0
9
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27
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45
54
3
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48
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38
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56
5
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32
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14
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4
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31
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49
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1
10
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46
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48
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33
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0
9
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27
36
45
54
3
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21
30
39
48
57
5
14
23
32
41
50
59
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17
26
35
44
53
2
11
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38
47
56
40
49
58
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25
34
43
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1
10
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28
37
46
55
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6
15
24
33
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51
0
9
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27
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45
54
3
41
50
59
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26
35
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2
11
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16
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34
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1
10
42
51
0
9
18
8
17


0
8
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39
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1
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0
8
16
24
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40
48
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19
27
35
43
51
59
7
15
23
31
39
47
55
3
11
19
27
18
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34
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50
58
6
14
22
30
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54
2
10
18
26
34
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25
33
41
49
57
5
13
21
29
37
45
53
1
9
17
25
33
41
49
57
5
13
21
24
32
40
48
56
4
12
20
28
36
44
52
0
8
16
24
32
40
48
56
4
12
20
28
36
44
39
47
55
3
11
19
27
35
43
51
59
7
15
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31
39
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3
11
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27
35
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51
59
7
15
2
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18
26
34
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50
58
6
14
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30
38
46
54
2
10
18
26
34
42
50
58
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14
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5
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53
1
9
17
25
33
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49
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5
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29
56
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20
28
36
44
52
0
8
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24
32
40
48
56
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12
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35
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51
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15
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39
47
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30
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46
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2
10
18
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21
29
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1
9
17
25
33
41
44
52
0
8
16
24
32
40
15
23
31
39
47
38
46

Other mappings

Other possible mappings include bleu and tritonic, but it is the fifive mapping that produces an octotonic scale which maximises range while providing access to all the notes and makes it easiest to play simple ratios together.

Bleu

4
11
7
14
21
28
35
3
10
17
24
31
38
45
52
6
13
20
27
34
41
48
55
2
9
16
2
9
16
23
30
37
44
51
58
5
12
19
26
33
5
12
19
26
33
40
47
54
1
8
15
22
29
36
43
50
57
1
8
15
22
29
36
43
50
57
4
11
18
25
32
39
46
53
0
7
14
4
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18
25
32
39
46
53
0
7
14
21
28
35
42
49
56
3
10
17
24
31
38
0
7
14
21
28
35
42
49
56
3
10
17
24
31
38
45
52
59
6
13
20
27
34
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48
55
10
17
24
31
38
45
52
59
6
13
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27
34
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48
55
2
9
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30
37
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51
58
5
12
19
27
34
41
48
55
2
9
16
23
30
37
44
51
58
5
12
19
26
33
40
47
54
1
8
15
22
51
58
5
12
19
26
33
40
47
54
1
8
15
22
29
36
43
50
57
4
11
18
25
8
15
22
29
36
43
50
57
4
11
18
25
32
39
46
53
0
7
14
21
32
39
46
53
0
7
14
21
28
35
42
49
56
3
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17
24
49
56
3
10
17
24
31
38
45
52
59
6
13
20
13
20
27
34
41
48
55
2
9
16
23
30
37
44
51
58
5
12
19
54
1
8
15
22
11
18

Tritonic

5
14
7
16
25
34
43
0
9
18
27
36
45
54
3
2
11
20
29
38
47
56
5
14
23
32
55
4
13
22
31
40
49
58
7
16
25
34
43
52
57
6
15
24
33
42
51
0
9
18
27
36
45
54
3
12
21
50
59
8
17
26
35
44
53
2
11
20
29
38
47
56
5
14
23
32
41
52
1
10
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28
37
46
55
4
13
22
31
40
49
58
7
16
25
34
43
52
1
10
45
54
3
12
21
30
39
48
57
6
15
24
33
42
51
0
9
18
27
36
45
54
3
12
21
30
56
5
14
23
32
41
50
59
8
17
26
35
44
53
2
11
20
29
38
47
56
5
14
23
32
41
50
59
16
25
34
43
52
1
10
19
28
37
46
55
4
13
22
31
40
49
58
7
16
25
34
43
52
1
45
54
3
12
21
30
39
48
57
6
15
24
33
42
51
0
9
18
27
36
45
54
3
5
14
23
32
41
50
59
8
17
26
35
44
53
2
11
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29
38
47
56
34
43
52
1
10
19
28
37
46
55
4
13
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31
40
49
58
54
3
12
21
30
39
48
57
6
15
24
33
42
51
23
32
41
50
59
8
17
26
35
44
53
43
52
1
10
19
28
37
46
12
21
30
39
48
32
41

Fifive

27
34
36
43
50
57
4
38
45
52
59
6
13
20
27
47
54
1
8
15
22
29
36
43
50
57
49
56
3
10
17
24
31
38
45
52
59
6
13
20
58
5
12
19
26
33
40
47
54
1
8
15
22
29
36
43
50
0
7
14
21
28
35
42
49
56
3
10
17
24
31
38
45
52
59
6
13
9
16
23
30
37
44
51
58
5
12
19
26
33
40
47
54
1
8
15
22
29
36
43
11
18
25
32
39
46
53
0
7
14
21
28
35
42
49
56
3
10
17
24
31
38
45
52
59
6
27
34
41
48
55
2
9
16
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30
37
44
51
58
5
12
19
26
33
40
47
54
1
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15
22
29
36
50
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4
11
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32
39
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7
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35
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49
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3
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7
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35
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49
56
13
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2
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37
44
51
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36
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0
7
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55
2
9
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29
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57
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59
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