Lumatone mapping for slendric

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This is one proposed mapping of slendric temperament to the Lumatone keyboard. 6 complete octaves are available, and modulation to distant keys is possible.

The keys marked "c" are one chroma up from 1/1, representing both 64/63 and 49/48. They keys marked "-c" are one chroma down from 1/1 (so 63/32 and 96/49).

The same mapping could be used for any extension of slendric that has the same period and generator, including Cynder, Rodan, and Guiron.


Lumatone.svg
27/16
27/14
12/7
-c
9/8
9/7
27/16
27/14
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
Y
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
X
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
28/27
32/27
14/9
16/9
c
7/6
4/3
28/27
32/27
Z

The differences between the extensions of slendric to the prime 5 can be visualized on this keyboard.

  • Cynder tempers out 81/80, so 9/8 above 9/8 is equivalent to 5/4 so 5/4 is mapped to the key marked "X".
  • Rodan, on the other hand, makes 81/80 the same as the chroma c, so 5/4 is instead mapped to the key mapped "Y", one chroma lower than "X".
  • Guiron maps 5/4 to the key marked "Z".

Cynder and guiron intersect in 36edo, so in 36edo both "X" and "Z" represent 5/4. Rodan and guiron intersect in 41edo, so in 41edo both "Y" and "Z" represent 5/4.

If the above layout is the "compressed" one then the below is an "expanded" one which has a range of only 5 octaves, but whose layout may make more intuitive sense:


Lumatone.svg
27/14
-c
9/8
9/7
27/16
27/14
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
Y
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
X
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
9/7
27/16
27/14
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
21/16
3/2
12/7
-c
9/8
28/27
32/27
14/9
16/9
c
7/6
4/3
32/21
7/4
1/1
8/7
28/27
32/27
14/9
16/9
c
28/27
Z