Atonality, generally speaking, is the musical practice whereby the composer or performer eschews reference to a tonal center. Traditional classical music tends to start at a tonal center, depart for awhile, and then return. Through the end of the Romantic period and in to the 20th century, composers began to abandon traditional tonality in an effort to find new ways of making music. This coincided with, or perhaps led to a profound change in the way many composers wrote music. In addition to being increasingly exacting in their requirements on performers, composers began to plan layouts of pieces entirely in advance. A design is concieved, and those rules are followed to make the entire piece. This practice is known as serialism, and serial works used something called a 'tone row' or '12-tone row,' which is as far as atonality can be taken using the traditional system of pitches. A 12 tone row is a 12 note sequence of all 12 different possible pitch classes.
Tonal centers form with the repetition of notes. Play the following pattern on a keyboard: C, C, D, C, E, C, F, C, G, F, B. What does your ear want to hear next? I'll bet anything you expect to hear another C. We've made C the tonal center. What a traditional tonal piece does is mess with your head, building up tension by not returning to the tonal center, so that when you finally return, you can't wait for it. That is, generally speaking. What a 12 tone row does is it systematically avoids repeating any notes before all others have been heard, so that the listener doesn't ever form the expectation of returning to a 'tonal center.
The 12 tone row, then, helps a composer avoid creating a tonal center, because all 12 notes are given similar weight. In the example above, you hear the C first and then several times again, which establishes it as the tonal center. If you weren't allowed to play a C again until you'd played every other note in the chromatic scale, you'd find yourself much less attached to that note.
But there's more to actually composing 12 tone music than creating a row of 12 different pitches. In the simplest sort of 12 tone piece, you just repeat the original 12 tone row, called "P-0"(Prime-0) over and over again until you're finished. But there are actually many different ways composers put serial music together, and the set matrix is one of the more useful tools.
When you've finished playing a row, you can start a new one on any pitch you'd like and simply play the same intervals as before. This is known as a transposition, and every tone row has 12 transpositions. You can also play the row backwards, which is called a Retrograde, or upside-down, which is called Inversion. Finally, you can play it both backwards and upsite-down, which is called Retrograde Inversion. So we have Prime, Retrograde, Inversion, and Retrograde Inversion, and 12 transpositions of each one. These rows are shown most simply in a 12x12 matrix.Back to Set Matrix Generator