12-Tone Row & Matrix Generator
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.
Why are there two ways to label R and RI?
Straus (same-subscript) labels — the convention in Straus's Introduction to Post-Tonal Theory and most current textbooks — give each retrograde the same subscript as the row it reverses: R₄ is P₄ played backward, and RI₉ is I₉ played backward. The subscript tells you the row's lineage.
First-pitch labels — an older convention you'll still meet in some scores and older texts — name R and RI rows by the first pitch class you actually hear (the right or bottom edge of the matrix). The subscript tells you the starting note instead.
Same rows, same music — only the names differ. Use whichever matches your textbook; the toggle relabels the matrix instantly.
Prime Row (P₀)
Your tone row12-Tone Matrix
Hover over row/column labels to highlight transformations
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
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