To generate twelve tone music you follow an algorithm which takes the numbers from one to twelve as an input. These numbers can be in any order as long as each number appears only once.
Each number corresponds to a note from c (1) to h (12). These notes are written into the twelve segments the piece will consist of. Each segment should now consist of one note.
The next step is to fill in the segments, so that each segment is filled with four notes (a four chord). This is achieved by grouping the notes into four groups:
| group# | numbers | notes |
|---|---|---|
| 0 | 1, 2, 3 | c, c#, d |
| 1 | 4, 5, 6 | d#, e, f |
| 2 | 7, 8, 9 | f#, g, g# |
| 3 | 10, 11, 12 | a, a#, b |
Each note is repeated / copied into each following segment, unless another note from the same group already is present in the segment, in which case the new note will be pasted into the following segments.
From here on there are two possible ways to proceed: Monophony and Polyphony. Since there is an algorithm that creates a Monophony, we choose Monophony over Polyphony.
After twelve segments the music starts at the first segment again. This makes the timeline of twelve tone music a circle.
Note heights are not important in twelve tone music (c' is the same as c'') Therefore after going up twelve half tone steps from c (= c') you reach c (= c'') again. This makes the tone heights in twelve tone music a circle.
Combining these two geometrical shapes gives us a torus, representing the music.