12 Tone Matrix Calculator

Instructions

This calculator helps identify all the pitch intervals required when using twelve-tone technique to create a twelve note music composition.

Simply enter the 12 starting tones, and the app will calculate the inversions and other forms.

If you wish you can generate a random matrix, and also view the matrix as either sharps/flats or pitch class integers.

Background

Twelve-tone technique also known as dodecaphony, twelve-tone serialism or twelve tone composition, is a method of musical composition devised by Austrian composer Arnold Schoenberg (1874–1951). It is associated with the "Second Viennese School" of composers, who were the primary users of the technique in the first few decades of its existence. The matrix itself has been referred to as a Babbitt square after the mathematician Milton Babbitt who invented it.

This style of music composition is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note through the use of tone rows, orderings of the 12 pitch classes.

All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th century composers. Many important composers who had originally not subscribed to or even actively opposed the technique, such as Aaron Copland and Igor Stravinsky have adopted it in their music.

Schoenberg himself described the system as a "Method of composing with twelve tones which are related only with one another". It is commonly considered a form of serialism. 👍