Lumatone mapping for 51edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
→Checkertonic/Flipped Superdiatonic with Porky Generator: Insert Bryan Deister's Tritikleismic-related 2.3.25.7 subgroup temperament mapping after this
 
(6 intermediate revisions by the same user not shown)
Line 4: Line 4:
You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
You can use the b val, which can be interpreted as either [[mavila]] or [[undecimation]], but is not a particularly great tuning for either.
{{Lumatone EDO mapping|n=51|start=33|xstep=7|ystep=1}}
{{Lumatone EDO mapping|n=51|start=33|xstep=7|ystep=1}}
[[Bryan Deister]] has used a flipped antidiatonic layout for [[51edo]] in which the generator is a mid major second at 8\51, which maps in between ~[[10/9]] and ~[[9/8]] and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~[[512/459]] (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~[[5/4]] Ptolemeic major third, and nine of these generators make a slightly sharp ~[[8/3]] perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic ([[Mavila]]/[[Undecimation]]) and [[Porky]] mappings, and is competitive with the [[Slendric]] mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is [[2L 5s]] with a step ratio of 8:7, but the octave zigzag could be used to support an [[11L 2s (4/1-equivalent)]] scale, again with a step ratio of 8:7. [https://x31eq.com/temper-pyscript/ Graham Breed's x31eq Temperament Finder] gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to [[19edo]], L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in [https://www.youtube.com/shorts/5pM8OC0fV98 ''51edo improv''] (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.
{{Lumatone EDO mapping|n=51|start=32|xstep=8|ystep=-1}}


== Slendric ==
== Slendric ==
Line 10: Line 14:


== Porcupine ==
== Porcupine ==
However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords.
However, the [[Porky]] mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. [[Bryan Deister]] demonstrates this mapping in [https://www.youtube.com/shorts/Fymg9vYO6iQ ''Northernlight - Deltarune (microtonal cover in 51edo)''] (2025).
{{Lumatone EDO mapping|n=51|start=18|xstep=7|ystep=2}}
{{Lumatone EDO mapping|n=51|start=11|xstep=7|ystep=2}}
 
== Checkertonic/Flipped Superdiatonic with Porky Generator ==
[[Bryan Deister]] has demonstrated a mapping of [[51edo]] for a [[3L 5s]] scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a [[7L 2s]] scale (flipped superdiatonic, with 7:1 step ratio) and a [[12L 3s (4/1-equivalent)]] scale (7:6 step ratio, passing right through the octave zigzag), in [https://www.youtube.com/shorts/sTPJtuHUwkg ''51edo improv''] (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~[[11/10]], as in [[Porky]], but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.
{{Lumatone EDO mapping|n=51|start=31|xstep=7|ystep=-1}}
 
== Tritikleismic-related 2.3.25.7 subgroup temperament ==
One way of treating [[51edo]] is as three versions of [[17edo]], rearranged so as to divide the fifth and the octave also into three parts each, as demonstrated by [[Bryan Deister]] in [https://www.youtube.com/watch?v=k3NOBYbiqpo ''51edo improv''] (2026-04-22). This is very much like [[landscape]] temperament in equating the octave with a stack of three near-just quasi-tempered major thirds (~[[63/50]], as 17\51), but requires use of the 2.3.25.7 subgroup; division of the fifth (~[[3/2]], as 30\51) into three parts (slightly sharp septimal major seconds ~[[8/7]], as 10\51) also puts this temperament in the [[gamelismic clan]] (thus related to [[tritikleismic]], but again using the 2.3.25.7 subgroup). The obvious scale moving up and right is [[3L 3s]] (10:7 step ratio); the obvious scale moving right and down-right is [[9L 4s (4/1-equivalent)]] (10:3 step ratio); the upward and downward movements in the latter scale nearly cancel out so that while octaves alternate between far and near, double octaves just barely slope down. The range is 5¼ octaves with no missed notes and no repeated notes.
{{Lumatone EDO mapping|n=51|start=4|xstep=10|ystep=-7}}


{{Navbox Lumatone}}
{{Navbox Lumatone}}

Latest revision as of 02:07, 30 May 2026

There are many conceivable ways to map 51edo onto the onto the Lumatone keyboard. However, it has 3 mutually-exclusive rings of fifths, so the Standard Lumatone mapping for Pythagorean is not one of them.

Antidiatonic

You can use the b val, which can be interpreted as either mavila or undecimation, but is not a particularly great tuning for either.

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

Bryan Deister has used a flipped antidiatonic layout for 51edo in which the generator is a mid major second at 8\51, which maps in between ~10/9 and ~9/8 and is distinct from both, A possible constitution of this interval in 51edo is the septendecimal major second ~512/459 (~|9 -3 0 0 0 0 -1⟩), which maps correctly to 8\51 and is very close by direct approximation. Two of these generators make a fairly flat ~5/4 Ptolemeic major third, and nine of these generators make a slightly sharp ~8/3 perfect eleventh. Octaves alternate between near and far, but the range is just one missing note 47 short of being 5 full octaves, which compares favorably with the standard Antidiatonic (Mavila/Undecimation) and Porky mappings, and is competitive with the Slendric mapping. (Another possibility would be to move the first note 0 up and left, which would instead put the missing note in the first octave.) The most straightforward scale within an octave is 2L 5s with a step ratio of 8:7, but the octave zigzag could be used to support an 11L 2s (4/1-equivalent) scale, again with a step ratio of 8:7. Graham Breed's x31eq Temperament Finder gives no name for this temperament; it is 19 & 51 in the 2.3.5.17 subgroup, but if this layout was actually adapted to 19edo, L and s steps would exchange size classes to make this a flipped Diatonic layout. This layout is demonstrated in 51edo improv (2025-05-02), with some additional notes outside the 5 (almost) full octaves cut off in and near the upper left and lower right corners due to the use of only 2 MIDI channels.

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

Slendric

Instead, it is probably better to use one of the mappings that reaches the perfect 5th in three generator steps. Of these, the Slendric mapping has the greater range.

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

Porcupine

However, the Porky mapping is probably more intuitive to people used to using a heptatonic scale and simple 5-limit ratios in chords. Bryan Deister demonstrates this mapping in Northernlight - Deltarune (microtonal cover in 51edo) (2025).

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

Checkertonic/Flipped Superdiatonic with Porky Generator

Bryan Deister has demonstrated a mapping of 51edo for a 3L 5s scale rotated (checkertonic, with 7:6 step ratio), that also lends itself to a 7L 2s scale (flipped superdiatonic, with 7:1 step ratio) and a 12L 3s (4/1-equivalent) scale (7:6 step ratio, passing right through the octave zigzag), in 51edo improv (2025-02-03). The rightward generator is 7\51, which is a near-just large undecimal neutral second ~11/10, as in Porky, but this mapping is sufficiently different from the Porky layout as to warrant a different name. The range is a bit over 4¼ octaves, and the octaves alternate between near/far and mid.

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

Tritikleismic-related 2.3.25.7 subgroup temperament

One way of treating 51edo is as three versions of 17edo, rearranged so as to divide the fifth and the octave also into three parts each, as demonstrated by Bryan Deister in 51edo improv (2026-04-22). This is very much like landscape temperament in equating the octave with a stack of three near-just quasi-tempered major thirds (~63/50, as 17\51), but requires use of the 2.3.25.7 subgroup; division of the fifth (~3/2, as 30\51) into three parts (slightly sharp septimal major seconds ~8/7, as 10\51) also puts this temperament in the gamelismic clan (thus related to tritikleismic, but again using the 2.3.25.7 subgroup). The obvious scale moving up and right is 3L 3s (10:7 step ratio); the obvious scale moving right and down-right is 9L 4s (4/1-equivalent) (10:3 step ratio); the upward and downward movements in the latter scale nearly cancel out so that while octaves alternate between far and near, double octaves just barely slope down. The range is 5¼ octaves with no missed notes and no repeated notes.

4
14
7
17
27
37
47
0
10
20
30
40
50
9
19
3
13
23
33
43
2
12
22
32
42
1
47
6
16
26
36
46
5
15
25
35
45
4
14
24
50
9
19
29
39
49
8
18
28
38
48
7
17
27
37
47
6
43
2
12
22
32
42
1
11
21
31
41
0
10
20
30
40
50
9
19
29
46
5
15
25
35
45
4
14
24
34
44
3
13
23
33
43
2
12
22
32
42
1
11
39
49
8
18
28
38
48
7
17
27
37
47
6
16
26
36
46
5
15
25
35
45
4
14
24
34
1
11
21
31
41
0
10
20
30
40
50
9
19
29
39
49
8
18
28
38
48
7
17
27
37
47
6
16
24
34
44
3
13
23
33
43
2
12
22
32
42
1
11
21
31
41
0
10
20
30
40
50
9
19
6
16
26
36
46
5
15
25
35
45
4
14
24
34
44
3
13
23
33
43
2
12
22
29
39
49
8
18
28
38
48
7
17
27
37
47
6
16
26
36
46
5
15
11
21
31
41
0
10
20
30
40
50
9
19
29
39
49
8
18
34
44
3
13
23
33
43
2
12
22
32
42
1
11
16
26
36
46
5
15
25
35
45
4
14
39
49
8
18
28
38
48
7
21
31
41
0
10
44
3
View • Talk • Edit Lumatone mappings 
← 48edo • 49edo • 50edo • Lumatone mapping for 51edo • 52edo • 53edo • 54edo →


Retrieved from "https://en.xen.wiki/index.php?title=Lumatone_mapping_for_51edo&oldid=231310"