Lumatone mapping for 43edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Yourmusic Productions (talk | contribs)
autopatrolled, emailconfirmed
1,865 edits
m Fix math error.
→Diatonic: Add Bryan Deister's Amavil mapping
 
Line 3: Line 3:
== Diatonic ==
== Diatonic ==
{{Lumatone EDO mapping|n=43|start=41|xstep=7|ystep=-3}}
{{Lumatone EDO mapping|n=43|start=41|xstep=7|ystep=-3}}
== Amavil (superdiatonic) ==
It is possible to use a [[7L 2s]] (5:4 step ratio) superdiatonic mapping with [[43edo]], as in [[mavila]]. Mavila itself is not a high-accuracy tuning, but it has some relatives that are high-accuracy — in this case, [[amavil]], of the [[mabila family]]. As with mavila, it uses a sub-fifth as its generator, in this case 24\43; however, unlike actual mavila, the generator is explicitly defined as something other than the fifth, which is instead left at the most accurate mapping 43edo has to offer for ~[[3/2]] (at 25\43). Instead, the sub-fifth is mapped as a mildly flat undecimal diminished fifth ~[[22/15]]. After octave-reduction, three of them make a somewhat flat classic minor sixth ~[[8/5]]; four of them make a subminor third that functions as ~[[7/6]] (sharp), ~[[13/11]] (flat), and ~[[20/17]] (diatismic minor third, close to just, only slightly sharp); six of them make a near-just pentacircle major third ~[[14/11]]; seven of them make a near-just classic major seventh ~[[15/8]]; eight of them make a moderately flat undecimal major fourth ~[[11/8]]; and ten of them make the moderately flat perfect fifth ~[[3/2]]. The range is about 3¾ octaves, which slope mildly upwards, with a generous allotment of repeated notes to mitigate vertical wraparounds.
{{Lumatone EDO mapping|n=43|start=34|xstep=5|ystep=-1}}


== Semiquartal ==
== Semiquartal ==

Latest revision as of 01:48, 30 May 2026

There are many conceivable ways to map 43edo onto the onto the Lumatone keyboard. Only one, however, agrees with the Standard Lumatone mapping for Pythagorean.

Diatonic

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

Amavil (superdiatonic)

It is possible to use a 7L 2s (5:4 step ratio) superdiatonic mapping with 43edo, as in mavila. Mavila itself is not a high-accuracy tuning, but it has some relatives that are high-accuracy — in this case, amavil, of the mabila family. As with mavila, it uses a sub-fifth as its generator, in this case 24\43; however, unlike actual mavila, the generator is explicitly defined as something other than the fifth, which is instead left at the most accurate mapping 43edo has to offer for ~3/2 (at 25\43). Instead, the sub-fifth is mapped as a mildly flat undecimal diminished fifth ~22/15. After octave-reduction, three of them make a somewhat flat classic minor sixth ~8/5; four of them make a subminor third that functions as ~7/6 (sharp), ~13/11 (flat), and ~20/17 (diatismic minor third, close to just, only slightly sharp); six of them make a near-just pentacircle major third ~14/11; seven of them make a near-just classic major seventh ~15/8; eight of them make a moderately flat undecimal major fourth ~11/8; and ten of them make the moderately flat perfect fifth ~3/2. The range is about 3¾ octaves, which slope mildly upwards, with a generous allotment of repeated notes to mitigate vertical wraparounds.

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

Semiquartal

The 4L 1s layout is also particularly notable for putting the best tuned intervals within easy reach of one-another, as also demonstrated in Skip fretting system 43 2 9, although it doesn't quite cover the whole gamut.

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

Trimean

If you want easily accessible single-step movements, the Trimean mapping is probably the best option.

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


Retrieved from "https://en.xen.wiki/index.php?title=Lumatone_mapping_for_43edo&oldid=231308"