Twelve-tone music

In the previous page, we saw how simple statistical factors can make a large difference in the overall sound of a musical passage, with properties such as conjunct melodic motion, harmonic consistency, and acoustic consonance contributing to the sense of "tonality." It is interesting that a number of twentieth-century composers attempted to replace these traditional methods of musical organization with alternative strategies.

One of the most common of these systems is the twelve-tone system, in which a piece is organized around a particular ordering of the twelve notes on the piano keyboard. For instance, the first twelve-tone piece (Schoenberg's Op. 25 suite for piano) is organized around the ordering E-F-G-C#-F#-D#-G#-D-B-C-A-Bb. This ordering can be played backwards or forwards, or transposed so that it starts on a different note, or "turned upside down" (inverted) so that ascending motions become descending motions and vice versa. (This produces an ordering that starts E-D#-C#...). Combinations of these transformations are also possible.

Since the twelve-tone method is supposed to replace traditional tonality, it is interesting to compare the effects of the two systems. To do this, we can repeat the experiment on the previous pages, constraining random notes according to the twelve-tone system.

  1. We begin with random notes, three at a time at a constant rhythm.
  2. Now constrain the notes in each melodic line so that they each articulate allowable transformations of the Op. 25 series.
  3. Alternatively, we can require that the chords themselves articulate the series: for instance, the first chord can contain the first three notes of an allowable ordering, the second chord the next three notes, and so on.
  4. Some composers have tried to combine these two strategies, but this can be quite difficult: in general, it may not be possible to have both the melodic lines and the harmonies articulating allowable transformations of the underlying ordering. Twelve-tone theorists have explored this problem under the name "combinatoriality."

These examples suggest that the twelve-tone system is significantly less powerful than the traditional tonal system: the preceding sequences all sound fairly similar, even though one is random and the other two obey the norms of twelve-tone composition. (In fact, Schoenberg noted that it is much harder to compose twelve-tone than tonal music, perhaps because the system does less work for you.) In the 1950s, composers grew increasingly aware of this fact, leading them to explore other organizational strategies. Some, such as John Cage, embraced randomness as a compositional strategy, composing music by rolling dice or consulting astrological charts.

Contemporary audiences might scoff at the idea of composing music randomly, using "chance operations." But the idea has a certain logic to it: after all, if (at least some) people responded favorably to twelve-tone music, and if twelve-tone organization does not produce effects that are significantly different from random organization, it stands to reason that audiences might also respond favorably to randomly composed music!