I N V E R S I O N

P

R

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M

E

 

 I0

 

 

 

 

 

 

 

 

 

 

 

 

R

E

T

R

O

G

R

A

D

E

 P0

 

 

 

 

 

 

 

 

 

 

 

 

 R0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 RI0

 

 

 

 

 

 

 

 

 

 

 

 

R E T R O G R A D E   I N V E R S I O N
  1. Traditional Matrix Construction

 

  1. 1.         Determine the original row and fill in P-0 along the top row.

  2. 2.         Write the transposition numbers above the matrix by numbering the pitches chromatically, beginning with 0 for the first note and moving up by half-step.

  3. 3.         For example, if E = 0, then F = 1, F# = 2, G = 3, etc.  Write these same numbers beneath the matrix.

  4. 4.         Fill in the transposition numbers along the outside of the left border by subtracting each of the numbers on the top border from 12, with the exception of the first number, which is always 0.

  5. 5.         Find the horizontal row with a 1 in front of it, and transpose all of P-0 up one half-step into that row.

  6. 6.         Find the horizontal row with a 2 in front of it, and transpose all of P-1 up one half-step into that row.

  7. 7.         Continue this process until P-10 is transposed up step into P-11, and the matrix is complete.