ARNOLD SCHÖNBERG’S 12-TONE MATRIX
Arnold Schönberg's "Magic Square" Matrix is
studied by most music students. Starting from a 12-tone row, it calculates the
inversion, retrograde, and retrograde inversion of the tone row, and places
them at the sides of a square. It then fills in the entire square with tones
which are related to the sides. The matrix is interesting, but it is difficult
and time-consuming to calculate. Mistakes are easy to make.
The Magic Square Calculator is an Excel
spreadsheet which calculates the square for you. The tone row you specify can
be placed in any position in the matrix, and the entire matrix is instantly
recalculated. It saves a lot of time and work.
Note: You may get a message that the file is being modified. Ignore it. The file opens OK anyway.
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