Twelve Tone Composition

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For general info on twelve-tone technique not pertaining to the process of composition, see Twelve-tone technique


Arnold Schoenberg came up with his twelve-tone composition system in 1921. Nowadays, it is frequently regarded as either extinct or overly academic; as early as 1962 theorist Charles Wuorinen said that "most of the Europeans say that they have 'gone beyond' and 'exhausted' the twelve-tone system," whereas in America, "the twelve-tone system has been carefully studied and generalized into an edifice more impressive than any hitherto known." However, understanding of the twelve tone technique is essential to understanding the music of the 20th century. The technique touched every composer of the 20th century and was used to some extent by most, from Bernstein to Stravinsky to Boulez. Furthermore, the twelve-tone approach shed new light on several aspects of the compositional process that are extremely valuable to student composers. This article will first introduce the concepts behind the twelve-tone system, then walk you through the composition of a twelve-tone piece, then finally present some of the ways twelve tone techniques and concepts can help you, no matter what style of music you want to write.

The Ideas

The twelve-tone system seems very arbitrary, dry and academic at first, but it actually has its roots in the emotional, lyrical world of German Romanticism. Its main predecessor is a concept Schoenberg noticed in the works of Brahms, "Developing Variation". This refers to how Brahms derives an entire piece from a single motif (musical idea), using clever things such as retrograde (playing a melody backwards) or inversion (changing the direction of a melody: when the original goes down a 3rd, the inversion goes up a third). One nifty example of developing variation is the Piano Sonata, Op. 1 by Schoenberg's student, Alban Berg.

But why would someone want to limit oneself to a single motif? Because the main idea of the German Romantic period was to convey emotional information. It's a lot easier to get one point across strongly than a lot of little points. Music written using developing variation, along with minimalism and popular music, aims to convey small, simple pieces of information. Using repetition and consistency, it makes that information obvious.

This was all well and good for a while, but by Schoenberg's time, things in the musical world had changed. Composers such as Mahler, Hugo Wolf and Schoenberg himself had, in an effort to broaden their emotional palettes, had added so many non-chord tones and dissonances to their melodies and harmonies that some sections of their pieces (or even entire pieces) seemed to not be centered in any key. Schoenberg and company had come upon atonality.

What's the big deal about atonality? Well, traditional harmony is based on the resolution of dissonance to consonance. According to the rules, the strongest, most consonant thing that exists is the tonic chord, followed by dominant chord and so forth. In atonal music, no such hierarchy exists, and the listener has little to "hang on to".

Schoenberg's solution? To extend Brahms' idea so that one motif contains not only all the melodic material used in the piece, but also all the harmonic material. Since atonal music doesn't place higher value on some notes (tonal music emphasizes tonics, then dominants, then sub-dominants and so forth), each of Schoenberg's motifs (called tone rows) contains all twelve tones, none repeated, none more important than others. In place of the tonal heirarchy of tonic, dominant, sub-dominant and so forth, each piece had not a hierarchy, but an order of intervals that never changes. Any row can be modified in several ways that maintain the original order of pitches (transposing, playing it backwards, changing the direction of the intervals or a combination of the above). Consecutive pitches can be played simultaneously to create chords. But the order of the intervals must always be the same.

Writing a twelve tone piece

This section will guide you through the composition of your own twelve-tone piece of music.

Create a row

You can create a row in many different ways. Try to write a melody you like, and then add any of the twelve notes you didn't use to the end to create your twelve-tone row.

Study the row

What you need to do next is to find all the permutations, or versions, of the row. One way to do this is using a matrix. Remember, you can put the row in inversion (when the original goes up, the inversion goes down), or retrograde (playing the row backwards). You can also do both at once (retrograde inversion) and any of these can be transposed (as long as you transpose the whole row).

Another approach is to find harmonies that you like within the row. Play through the row, playing consecutive tones together to find chords you like.


At first, a good approach is to experiment and try to create as much material as you can from your row, both melodic and harmonic. Then try to piece them together. Try playing two different permutations at the same time, one after another, then overlapping. The twelve tone system says nothing about rhythm, so if you run into a note in your row you don't like, just turn it into a grace note. Or take a more liberal approach toward the technique and leave the note out!

Just keep this in mind: writing using the twelve tone system does NOT have to feel confining. During your first few attempts, composing with the twelve tone system will feel arbitrary and restricting. However, the more used to the system you are, the more skilled you'll be at finding things you like. Just be sure to start on a small scale (Schoenberg's first pieces using the system were short piano pieces) and stop composing when you can't write anything you like.

The system's relevance to today's student composers

Even if you chose not to use the twelve tone system in your compositions, there are still a lot of things you can learn from the system.

How to use intervals

One of the most important contributions of atonal, and especially serial, music is the focus put on intervals. American composer Lou Harrison pointed out in his Music Primer that there was a well-worn hierarchy of intervals in tonal Classical music. "Melodies", he wrote, "were generally felt to progress by 'seconds', chords were constituted of 'thirds', & their roots often proceeded by 'fourths' and 'fifths'" Although you can still use this hierarchy in the twelve tone system (see Berg's violin concerto, below), it is certainly not easy to do; whatever intervals you choose for your row can be used both as melodic and harmonic material. Unless you are taking an unusually contrapuntal approach, it is very hard to separate out different interval types for different uses.

Thanks to the shift away from tonality, melodies no longer needed to have anything to do with seconds, chords could be made of 2nds (See Henry Cowell's work with piano clusters) or 4ths and 5ths (Listen to the harmonies of Paul Hindemith) and roots could be approached from anywhere you darn well please. People no longer had to worry about how each note related to the tonic of the piece. Instead, people were free to think about how each note related to its neighbors, and to devote a lot of thought to the different flavors and significances each interval has. (Read the first chapter of Vincent Persichetti's 20th Century Harmony for more thoughts on intervals)

Berg's Violin Concerto

The row to Berg's beautiful violin concerto is composed only of 3rds and 2nds. Even with inversions, that leaves Berg a limited intervallic palette. However, it really is all that Berg needs. He uses the thirds to produce some beautiful, even tonal, harmonies. In fact, Berg manages to quote an entire Bach chorale in the last movement. As to melodic elements, the 2nds take care of that rather nicely. Of course, Berg does take a rather liberal view of composing with the twelve tone system (at one point he creates a new melody by using every other note of the row), but this is no crime, and the beautiful music that results justifies whatever he did to get there.

Lou Harrison's Concerto for Violin with Percussion

A piece inspired by Berg's concerto, and using similar techniques (but not twelve-tone) is Lou Harrison's Concerto for Violin with Percussion. In this piece, the violin (the only instrument in the piece with definite pitch) plays a part composed only with three intervals WITHOUT inversion: the minor 2nd, major 3rd and major 6th. If you can get your hands on a recording, it's a fascinating listen: Harrison is able to mix an emotional romantic-style violin part with Gamelan-like percussion, without anywhere allowing the limited intervallic content to make the piece sound academic.


Although composers had certainly thought a lot about development before Schoenberg's technique, Schoenberg's ideas brought musical development into the spotlight. Schoenberg's pupil Adolph Weiss catalogued 9 ways of varying a musical motive:

  1. changing the intervals and/or notes but holding the rhythms
  2. changing the rhythm and holding notes and/or intervals
  3. simultaneous combination of these two
  4. inversion
  5. augmentation
  6. diminution
  7. elision
  8. interpolation
  9. retrograde.

A composer can use any one of these or several in combination.

Changing the intervals and/or notes but holding the rhythms

This is what Beethoven does in the beginning of his 5th Symphony.

Changing the rhythm and holding notes and/or intervals

In Scheherezade, Rimskii-Korsakov changes the rhythm to change Scheherezade's theme into the theme of the Kalendar Prince. Another example of this is Steve Reich's Violin Phase. In this piece, the violinist prerecords a tape and plays on top of it at a slightly faster tempo, getting out of sync and creating fascinating resulting interplay with the tape.


Inversion is a way to keep the same intervals while getting different pitches. It can either be exact, or modified to fit into a scale or mode.

Rhythmic Augmentation and Diminution

Playing an entire melody slower (augmentation) or faster (diminution) than the original.

Elision and Interpolation

Either leaving out notes (elision) or adding notes (interpolation). An extreme example is Les Moutons de Panurge by Frederic Rzewski, which starts off playing only the first note of the theme, then the first and second notes, and so on. When the musicians finally get to the point where they are playing the entire 65 note theme, they start subtracting notes from the beginning, until finally they are only playing the last note of the theme. Score on


Retrograde, and other reordering of pitches, can frequently be hard to hear melodically. However, one perk that makes retrogrades cool is that they maintain the same pitch and interval content of the given motif. If you want to extend a section harmonically, but not repeat a motif exactly, using a retrograde may be a good idea.


Harrison, Lou "Lou Harrison's Music Primer", Edition Peters

Twelve-tone technique - Wikipedia, the free encyclopedia, [[1]]

Green, Douglass "Form in Tonal Music", pub. 1965

Schoenberg, Arnold "Preliminary Exercises in Counterpoint"

External Resources - Twelve Tone Matrix Calculator