Lumatone mapping for Bohlen–Pierce: Difference between revisions

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The following mapping of [[Bohlen-Pierce]] temperament to the [[Lumatone]] keyboard has these desirable properties:
The following mapping of [[Bohlen–Pierce]] temperament to the [[Lumatone]] keyboard has these desirable properties:
* It is a mapping of the full rank-2 temperament, not just the equal temperament 13ed3. In other words, C{{sharp}} = D{{flat}} enharmony is not assumed.
* It is a mapping of the full rank-2 temperament, not just the equal temperament 13ed3. In other words, {{nowrap|C♯ {{=}} D♭}} enharmony is not assumed.
* Its range is over 6 full tritaves.
* Its range is over 6 full tritaves.
* Modulation into quite distant keys is possible.
* Modulation into quite distant keys is possible.
Line 289: Line 289:




The corresponding mapping of the equal temperament is this. Unlike the above mapping C{{sharp}} and D{{flat}} are equivalent here.
The corresponding mapping of the equal temperament is this. Unlike the above mapping C♯ and D♭ are equivalent here.


{{Lumatone EDO mapping|n=13|xstep=3|ystep=-2|start=0}}
{{Lumatone EDO mapping|n=13|xstep=3|ystep=-2|start=0}}


[[Category:Lumatone mappings]]
[[Category:Lumatone mappings]]

Revision as of 16:11, 20 November 2024

The following mapping of Bohlen–Pierce temperament to the Lumatone keyboard has these desirable properties:

  • It is a mapping of the full rank-2 temperament, not just the equal temperament 13ed3. In other words, C♯ = D♭ enharmony is not assumed.
  • Its range is over 6 full tritaves.
  • Modulation into quite distant keys is possible.
  • The BP diatonic modes ("Lambda" and so on) have a pleasing zigzag shape on the keyboard.
B
D
A
C
E
G
J
B
D
B
D
F
H
A
C
E
G
J
B
D
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
H
A
C
E
A
C
E
G
J
B
D
F
H
A
C
E
G
J
B
D
F
F
H
A
C
E
G
J
B
D
F
H
A
C
E
F
H
A
C
E
G
J
B
D
F
F
H
A
C
E
F


The corresponding mapping of the equal temperament is this. Unlike the above mapping C♯ and D♭ are equivalent here.

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