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

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== Unnamed Temperament Lumatone mappings ED3/2 (EDF) ==
== Unnamed Temperament Lumatone mappings ED3/2 (EDF) ==


=== 13edf (demonstrated to work but awaiting approval) ===
=== 13edf (demonstrated to work) ===


[[Bryan Deister]] has demonstrating a mapping of [[13edf]] using a [[1L 1s (3/2-equivalent)]] scale having a 7:6 step ratio, in [https://www.youtube.com/watch?v=8oDt4CfjOyw&list=WL&index=340 ''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.
[[Bryan Deister]] has demonstrating a mapping of [[13edf]] using a [[1L 1s (3/2-equivalent)]] scale having a 7:6 step ratio, in [https://www.youtube.com/watch?v=8oDt4CfjOyw&list=WL&index=340 ''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.

Latest revision as of 21:56, 29 October 2026

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
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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
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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
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2
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2
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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
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3
7
3
7
3
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3
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3
7
3
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2
6
2
6
2
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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)

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)

89edf (demonstrated to work)

Bryan Deister has demonstrated a mapping of 89edf using an 8L 3s (3/2-equivalent) scale having a 10:3 step ratio, in 89ed(3/2) groove (2026). The rightward generator is a near just pentacircle minor second ~22/21, but also functions as as a mildly sharp greater vicesimotertial semitone ~23/22 (the pittsburghisma 484/483 is tempered out). This mapping is maximally efficient, with a range of just over three octaves (which slope upwards very gently), with no missed notes and no repeated notes.

5
15
8
18
28
38
48
1
11
21
31
41
51
61
71
4
14
24
34
44
54
64
74
84
5
15
86
7
17
27
37
47
57
67
77
87
8
18
28
38
0
10
20
30
40
50
60
70
80
1
11
21
31
41
51
61
71
82
3
13
23
33
43
53
63
73
83
4
14
24
34
44
54
64
74
84
5
85
6
16
26
36
46
56
66
76
86
7
17
27
37
47
57
67
77
87
8
18
28
38
78
88
9
19
29
39
49
59
69
79
0
10
20
30
40
50
60
70
80
1
11
21
31
41
51
61
2
12
22
32
42
52
62
72
82
3
13
23
33
43
53
63
73
83
4
14
24
34
44
54
64
74
84
5
25
35
45
55
65
75
85
6
16
26
36
46
56
66
76
86
7
17
27
37
47
57
67
77
87
8
58
68
78
88
9
19
29
39
49
59
69
79
0
10
20
30
40
50
60
70
80
1
11
81
2
12
22
32
42
52
62
72
82
3
13
23
33
43
53
63
73
83
4
25
35
45
55
65
75
85
6
16
26
36
46
56
66
76
86
7
48
58
68
78
88
9
19
29
39
49
59
69
79
0
81
2
12
22
32
42
52
62
72
82
3
15
25
35
45
55
65
75
85
48
58
68
78
88
71
81

Added: Lucius Chiaraviglio (talk) 02:23, 25 October 2026 (UTC)
Last modified: Lucius Chiaraviglio (talk) 18:05, 27 October 2026 (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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