24-Tone Row Matrix Generator

12-tone music is a 20th-century style of music which was pioneered by Arnold Schoenberg. This style of music uses all chromatic pitches equally. The concept of 12-tone music can be extended to 24-TET. Each pitch cannot be used again until all pitches have been used once. As a consequence, 24 tone row matrices are much larger than their 12-Tone counterparts.

The core is in the initial tone row. The tone row is the initial ordering of pitches. All pitches must be used, and none can be repeated. Once the initial tone row is created, the composer can use the pitches in this order, as well as in the following orders:

  • Inverted - all intervals are flipped. A major third up becomes a major third down, for example.
  • Retrograde - the order of intervals is switched. The last interval happens first, 2nd to last happens 2nd, etc.
  • Inverted Retrograde - the intervals are flipped, and the order is switched.

A tone row matrix can be used to generate this information. The top of the matrix represents the prime tone row. Each subsequent row represents the prime row offset by a certain interval, where the start note is different, but all intervals are the same. The inversions, retrogrades, and retrograde inversions can be found in the following manner:

  • Inverted - start on the top row and read downwards. The leftmost column represents the inversion starting from the original root pitch.
  • Retrograde - start from the rightmost column and read leftwords. The bottom row represents the retrograde starting from the original root pitch.
  • Inverted Retrograde - start from the bottom row and read upwards. The rightmost column represents the inverted retrograde starting from the original root pitch.
Matrix Generator






Learn More...

Dig deeper into the world of 24-TET with the resources below!

Introduction to Quarter Tones - Quarter Tone Composition In Western music, 12-Tone Equal Temperament, or 12-TET, is the standard for defining where all of the notes lie. The octave is divided in... Composition Software - Quarter Tone Composition Not all music notation software support quarter tone notation and playback. However, there are a few options for composers who wish to co... Introduction to Quarter Tone Composition $24.99 22.99

The purpose of this book is to introduce composers to the world of 24-TET.  Quarter tonality presents new melodic and harmonic possibilities that can bring about previously unexplored textures, colors, and atmospheres to music.

Quarter Tone Technique for Saxophone $29.99

The goal of this technique book is to encourage saxophonists to learn this technique and to encourage composers to write for it. Quarter tonality presents new melodic and harmonic possibilities that can bring previously unexplored textures, colors, and atmospheres to music.



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