Schonberg's 12-Tone Matrix

Schonberg's 12-Tone Matrix is studied by most music students, and a few composers use it in their compositions. Starting from a 12-tone row, it calculates the "Prime", "Inversion", "Retrograde", and "Retrograde Inversion" orientations of the tone row, and places them at the sides of a square. It then fills in the entire square with all the half-step positions of the tone row. The matrix is interesting, but it is difficult and time-consuming to calculate. Mistakes are easy to make.

The 12-Tone Matrix Calculator is an Excel spreadsheet which calculates the square for you. It has the advantage that you do not have to input a Prime tone row. The spreadsheet allows you to place your tone row in any orientation and position you prefer. The matrix will be instantly calculated with your tone row in the position you specified. It saves a lot of time and work.

I have placed the spreadsheet in the public domain so it can be used freely.

Note: You may get a message that the file is being modified. Ignore it.

Download the 12-Tone Matrix Calculator

Your 12-Tone Row should be placed at D3 to O3. The orientation (Prime, Inv, Retro, or RI) is placed at B3, and the position (0-11) is placed at C3.

Complete instructions are at A88.

The spreadsheet is set up to print the Matrix; read the instructions (A88) before you print.


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