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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