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How to retrieve parts from the 12-tone matrix


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Dear friends,

There is a function to make the 12-tone matrix

(twelve-tone-matrix '(3 11 10 2 1 0 6 4 7 5 9 8))

                       I 
 
           0  8  7 11 10  9  3  1  4  2  6  5 
 
      0    3 11 10  2  1  0  6  4  7  5  9  8 
      4    7  3  2  6  5  4 10  8 11  9  1  0 
      5    8  4  3  7  6  5 11  9  0 10  2  1 
      1    4  0 11  3  2  1  7  5  8  6 10  9 
      2    5  1  0  4  3  2  8  6  9  7 11 10 
 P    3    6  2  1  5  4  3  9  7 10  8  0 11   R  
      9    0  8  7 11 10  9  3  1  4  2  6  5 
     11    2 10  9  1  0 11  5  3  6  4  8  7 
      8   11  7  6 10  9  8  2  0  3  1  5  4 
     10    1  9  8  0 11 10  4  2  5  3  7  6 
      6    9  5  4  8  7  6  0 10  1 11  3  2 
      7   10  6  5  9  8  7  1 11  2  0  4  3 
                         RI 

 

The function returns the 48 form matrix of the original 12-tone row.

Questions:

1) How can I get some excerpts from the Matrix ?

2) For example, if I want to make a combinatoriality between two hexachords of the matrix, like, for example, 

the first hexachord of P-0 (3 11 10  2  1  0)

+ the second hexachord of RI-8 (3 2 6 4 7 5)

how can I retrieve the values from the matrix ?

Is there some keyword ?

Whth this retrieving possibility, the matrix can be very useful for composition.

 

Best !

Julio

 


 

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image.thumb.png.12aa3f48b9778b11c3fd458b1cf2bbc4.png

 

For example:

How to combine from the matrix

 

P0 - second hexachord (F# E G F A G#)  

with

 

RI5 - first hexachord (D# D F# E G F)

 

Or any hexachordal combination from the matrix (even if it does not form an agregate...)

 

Best,

Julio

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More control:

(twelve-tone-matrix '(3 11 10 2 1 0 6 4 7 5 9 8))

Original Prime Order: (3 11 10 2 1 0 6 4 7 5 9 8) 
Pitch: (eb4 b4 bb4 d4 cs4 c4 fs4 e4 g4 f4 a4 gs4) 
 
                          I 
 
           0  8  7 11 10  9  3  1  4  2  6  5 
 
      0    3 11 10  2  1  0  6  4  7  5  9  8 
      4    7  3  2  6  5  4 10  8 11  9  1  0 
      5    8  4  3  7  6  5 11  9  0 10  2  1 
      1    4  0 11  3  2  1  7  5  8  6 10  9 
      2    5  1  0  4  3  2  8  6  9  7 11 10 
 P    3    6  2  1  5  4  3  9  7 10  8  0 11   R  
      9    0  8  7 11 10  9  3  1  4  2  6  5 
     11    2 10  9  1  0 11  5  3  6  4  8  7 
      8   11  7  6 10  9  8  2  0  3  1  5  4 
     10    1  9  8  0 11 10  4  2  5  3  7  6 
      6    9  5  4  8  7  6  0 10  1 11  3  2 
      7   10  6  5  9  8  7  1 11  2  0  4  3 
 
                         RI 

(setf array 
      (build-array
       (row-matrix '(3 11 10 2 1 0 6 4 7 5 9 8))))
       
(get-array 11 7 6 array :direction 'right)
=> (11 2 0 4 3 10)

(get-array 11 7 6 array :direction 'up)
=> (11 10 2 0 3 1)

 

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