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.
The core of this kind of composition is 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.
The app below will generate a 24 tone row matrix based on an initial tone row. Accidentals can be entered in as follows:
- Sesquiflat - db
- Flat - b
- Semiflat - d
- Semisharp - +
- Sharp - #
- Sesquisharp - +#
Note names must be entered in capital letters. Once the tone row is entered, hit submit, and the matrix will be generated.
The tone row can then be printed The app colors every other row to make navigating the matrix easier. However, by default, web browsers will not print the colors. To enable the colors to print, select Background Graphics in the print settings.
Alternatively, it can be copied and pasted into a word document.