How to Write a 12-Tone Composition

Twelve-tone is a 20th-century compositional technique created by Arnold Schoenberg.  Rather than setting a piece of music in a diatonic key, the goal of 12-tone music is to use all 12 chromatic pitches equally.  To create a 12-tone composition, follow these steps:

Create Your Palette

1. Begin with a 12x12 grid.  Label your grid as in the example below:
   
2. Next, arrange the 12 chromatic pitches in any order you like.  This is your 12-tone row, which will form the basis of your composition.  Fill in the first row of the grid with your 12-tone row.  Check to make sure that you have used each note exactly once. 
   
   Example:
   
   I find it easiest to write down both spellings of the chromatic pitches.  This helps both in calculating the intervals and in proofreading your work.
3. Next, calculate the inversion of your row.  Do this by finding the inversion of each interval, and write the inverted row down the left column of your grid.
   
   Looking at the above example, the first interval is C to A.  A is a minor third down from C.  The inversion of this would be a minor third up from C, which is E-flat. 
   
   The next interval in my original row is A to G.  G is a major second down from A, so in the inversion, you would calculate a major second up from E-flat, which is F.
   
   G to E-Flat is a descending major third.  An ascending major third from F is A.
   
   The resulting inverted row is as follows:
   
   Double-check your inverted row to make sure you have used each note exactly once.
4. Fill in your grid by transposing your 12-tone row into each key listed down the left column of the grid.
   
   Example:
   
   This is your palette.  Reading from left to right, you have your original row in all 12 keys.  Reading from top to bottom, you have the inversion of your row.  Reading from right to left gives you the retrograde of your row, and reading from bottom to top gives you the inverted retrograde.
   
   Again, you can spot-check your work by making sure any given row contains exactly 12 distinct pitches.

Write Your Composition

Using the palette that you have created, write your composition.  The following rules apply:

1. Select any row in your palette:  original, inverted, retrograde, or inverted retrograde, starting on any pitch.
2. Once you begin a row, you must follow it to completion:  you must play all the pitches in order, you may not skip any pitches, and you may not repeat any pitches.
3. Notes may occur in any octave any may last any duration.  You may begin two or more notes simultaneously, as long as they occur sequentially in the row.
4. Any number of rows may be played concurrently.  They may begin and end at any time; rows do not have to start or end together.  Any types of row may be played concurrently, starting on any pitch.

Example

The following is a simple example of a composition based on the above palette.

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