User:Lucius Chiaraviglio/Keyboard Layout Lab/Non-Octave Lumatone mappings

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This page is for Lumatone mappings for non-octave tuning systems. Identifying a temperament for non-octave tunings will be difficult due to lack of exploration compared to octave temperaments, so that is currently not a factor for separation of pages.

Unnamed Temperament Lumatone mappings ED17/16

1ed17/16 (demonstrated to work

Bryan Deister has demonstrated a mapping of 1ed17/16, in equal step 17/16 (2025). This is implemented as a 2L 2s scale in a repeat space of 10 instances of 17/16.

0
3
2
5
8
1
4
1
4
7
0
3
6
9
2
3
6
9
2
5
8
1
4
7
0
3
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
6
9
2
5
8
1
4
7
0
3
6
9
2
5
8
1
4
7
0
3
7
0
3
6
9
2
5
8
1
4
7
0
3
6
9
2
5
5
8
1
4
7
0
3
6
9
2
5
8
1
4
6
9
2
5
8
1
4
7
0
3
6
4
7
0
3
6
9
2
5
5
8
1
4
7
3
6

Added: Lucius Chiaraviglio (talk) 03:35, 3 November 2025 (UTC)
Last Modified: Lucius Chiaraviglio (talk) 23:35, 3 November 2025 (UTC)

Unnamed Temperament Lumatone mappings ED7/6

9ed7/6 (demonstrated to work)

Bryan Deister has demonstrated a mapping of 9ed7/6 using a zig-zag 1L 1s (7/6-equivalent) scale having a 5:4 step ratio, in 9ed(7/6) improv (2025). Notes appear to be the same in rows, but actually progress higher by a whole equave (septimal minor third 7/6) at a time.

4
4
8
8
8
8
8
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
6
6
6
6
6
6
6
6
6
6
6
6
6
1
1
1
1
1
1
1
1
1
1
1
5
5
5
5
5
5
5
5
0
0
0
0
0
4
4

Added: Lucius Chiaraviglio (talk) 18:14, 20 October 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 08:20, 24 October 2025 (UTC)

Unnamed Temperament Lumatone mappings ED4/3

8ed4/3 (demonstrated to work)

Bryan Deister has demonstrated a mapping of 8ed4/3 using a 1L 4s (4/3-equivalent) scale (oriented nearly vertically) having a 4:1 step ration, in 8ed(4/3) improv (2025).

0
4
3
7
3
7
3
2
6
2
6
2
6
2
6
5
1
5
1
5
1
5
1
5
1
5
4
0
4
0
4
0
4
0
4
0
4
0
4
0
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
2
6
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
5
1
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
4
0
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
7
3
6
2
6
2
6
2
6
2
6
2
6
2
6
2
5
1
5
1
5
1
5
1
5
1
5
0
4
0
4
0
4
0
4
7
3
7
3
7
2
6

Added: Lucius Chiaraviglio (talk) 06:59, 18 October 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 03:33, 20 October 2025 (UTC)

Unnamed Temperament Lumatone mappings ED3/2 (EDF)

13edf (demonstrated to work but awaiting approval)

Bryan Deister has demonstrating a mapping of 13edf using a 1L 1s (3/2-equivalent) scale having a 7:6 step ratio, in 13ed(3/2) improv (2026). This makes the fifths slope downwards (with a wraparound for all but the root note), but the range is 16 fifths contiguous, or 18 fifths if counting the bass and treble fifths that have some missed notes.

7
0
1
7
0
6
12
2
8
1
7
0
6
12
5
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
0
6
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
0
6
6
12
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
0
5
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
1
7
11
4
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
8
10
3
9
2
8
1
7
0
6
12
5
11
4
10
3
9
2
3
9
2
8
1
7
0
6
12
5
11
4
10
3
2
8
1
7
0
6
12
5
11
4
10
8
1
7
0
6
12
5
11
7
0
6
12
5
0
6

Added: Lucius Chiaraviglio (talk) 05:59, 6 May 2026 (UTC)
Last modified: Lucius Chiaraviglio (talk) 03:30, 8 May 2026 (UTC)

60edf (demonstrated to work)

Bryan Deister has demonstrated a mapping of 60edf using a 5L 1s (3/2-equivalent) scale having a 11:5 step ratio, in 60ed(3/2) improv (2025). It takes advantage of nearly equal errors in the 2nd and 13th harmonics and a near-just 7th harmonic to make the (rightward) generator a near-just tridecimal 2/3-tone (~14/13), as 11\60ed3/2, and three of these yield the sound of a classic major third (as 33\60ed3/2), although ~5/4 itself is mapped inconsistently to 32\60ed3/2. The range is a bit over five fifths with a moderate upwards slope, but at the cost of missing a few notes in each fifth.

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

Added: Lucius Chiaraviglio (talk) 06:59, 18 October 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 03:33, 20 October 2025 (UTC)

Unnamed Temperament Lumatone mappings ED8/5

7ed8/5 (demonstrated to work)

Bryan Deister has demonstrated a mapping of 7ed8/5 using a 1L 1s (8/5-equivalent) scale having a 5:2 step ratio and rotated to proceed right and up, in 7ed(8/5) improv (2025). Right by one key is 5\7ed8/5, which yields a near-just ~7/5 but also gets mapped as a very flat (but still consistent) ~10/7; two of these yield a very flat octave (~2/1). Down-right by one key is 3\7ed8/5, which functions as a fairly sharp ~17/14 and a very flat ~21/17. Up one key is 2\7ed8/5, which sounds like a near-just septimal whole tone (~8/7), but actual ~8/7 is instead inconsistently mapped to 1\7ed8/5, thus requiring 2\7ed8/5 to be mapped as a very sharp ~9/8 or a fairly flat ~15/13. Superficially, the range appears to be slightly over five instances of 8/5, and the overall 8/5 slope is very gently upward; however, due to the rotated and very wide-stepping scale pattern, the actual range is over nineteen octaves (as demonstrated in the video by the production of some extremely high notes); proceeding in the normal rightward and slightly downward direction instead yields a scale of 5L 1s (4096/625-equivalent) having a 5:3 step ratio.

0
5
3
1
6
4
2
1
6
4
2
0
5
3
1
4
2
0
5
3
1
6
4
2
0
5
2
0
5
3
1
6
4
2
0
5
3
1
6
4
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
4
2
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
3
1
6
4
2
0
5
3
1
6
4
2
0
5
0
5
3
1
6
4
2
0
5
3
1
6
4
2
0
5
3
1
6
3
1
6
4
2
2
0

Added: Lucius Chiaraviglio (talk) 07:42, 19 October 2025 (UTC)
Last modified: Lucius Chiaraviglio (talk) 07:41, 23 October 2025 (UTC)

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