What is 12-Tone Serialism?

Twelve-tone technique (or dodecaphony) is a method of composition developed by Arnold Schoenberg in the early 20th century. It uses all 12 notes of the chromatic scale in a specific order called a tone row, ensuring no note is repeated until all others have been used.

P Prime Original row

I Inversion Intervals flipped

R Retrograde Reversed order

RI Retrograde-Inversion Both combined

Prime Row (P₀)

Your tone row

12-Tone Matrix

Hover over row/column labels to highlight transformations

Select a row or column

Understanding the Matrix

Prime Forms (P)

Read left to right along each row. P₀ is the original row. Each P-form starts on a different pitch class and maintains the same interval relationships.

Inversion Forms (I)

Read top to bottom down each column. Inversion mirrors the intervals—ascending becomes descending and vice versa.

Retrograde Forms (R)

Read right to left along each row. The retrograde is simply the prime row played backwards.

Retrograde-Inversion (RI)

Read bottom to top up each column. This combines both transformations—the inversion played in reverse.

Notable Serialist Composers

Arnold Schoenberg Developed 12-tone technique

Alban Berg Violin Concerto, Wozzeck

Anton Webern Symphony Op. 21

Pierre Boulez Structures, Le Marteau

Milton Babbitt Three Compositions for Piano

Tips for Using This Tool

Generate new rows to explore different intervallic possibilities
Hover over P, I, R, or RI labels to see that transformation highlighted
Switch between integer (0-11) and letter notation based on your preference
Copy your row to use in your compositions or analysis
The matrix always starts with P₀ beginning on 0 (C) in the top-left corner