andrew /interview

Paul Nauert is a professor and composer here at UCSC. His work incorporates algorithmic processes to achieve his compositional goals. This synopsis gives a brief overview of some of these algorithmic techniques.

One aspect of Nauert's approach is an algorithmically defined way of looking at pitch that helps him make pitch decisions. His theory is based in the classification of both chord structures and chord progressions. Chords are broken down into their intervallic contents. Thus, two chords can be described as similar if they contain, for the most part, equal intervals between individual notes. For example, the chords <C E G> and <F A C>, both being root position major triads, contain the same intervals. Though the chords are different, and would function differently in a piece, they are intimately related.

For chord progressions, Nauert looks at the intervallic content between two chords. With the previous example of <C E G> and <F A C>, each note is merely transposed up a perfect fourth (five semitones). Thus, an interval vector that might be used to describe the chord progression would be <5 5 5>. Similarly, the progression from <C E G> to <C# G A> could be represented as <1 3 2>. By mathematically representing both the pitch content and the transition of pitches, Nauert can use the data algorithmically.

Nauert works with this data by using an algorithm to provide him with options on which chords should come next in his pieces. He then chooses the option that suits his compositional need at the given time. Because these options are mathematically structured, the piece ultimately has a mathematical structure of its own. Chords move and change in ways that is cohesive and makes sense -- this is not necessarily a typical aural sense, but Nauert describes one aspect of listening as the joy in finding patterns in pieces, i.e. pieces are puzzles to solve.

Nauert also works algorithmically with respect to rhythm, though his approach is different from pitch. He frequently generates rhythms for the entirety of a piece before writing even a single note. His generation process is based on a first-order Markov process. Since Markov processes are inherently probabilistic, Nauert is unable to predict the outcome. However, he maintains a certain amount of control in that his Markov models are typically designed by hand. That is, by constructing state transition matrices, he controls the overall character of the rhythmic feel of a piece without having complete control of every detail. From these rhythmic models, he then combines elements in different ways, juxtaposing his generated rhythms. He has also experimented in interpolation between state transition matrices, resulting in what could be described as a modulation of rhythmic character.

Nauert does not view algorithmic processes as inherently limiting, but rather a mode of expanding his creativity. By working under abstract models and developing concrete pieces from them, he must find ways to make the music not only reflect the model, but also be engaging for listeners. Beyond this, he views these "limitations" as inherently imbuing his music with some level of meaning. He views this as true for all manners of art, in that, for example, art happens within a certain time-frame, culture, or society. These in and of themselves are a form of limitation that provide context, and hence, meaning to pieces. As Harry Nilsson once said, "A point in every direction is the same as no point at all."