A Computational Model for Rule-Based Microtonal Music Theories and Composition

Abstract

A Computational Model for Rule-Based Microtonal Music Theories and Composition Torsten Anders and Eduardo r. Miranda Motivation Microtonal music is an influential facet of twentieth and 21st cen tury music composition. Composers that contributed significantly to microtonal music include characters as diverse as Julián Carrillo, Ben Johnston, Harry Partch, Horatiu Rädulescu, Karlheinz Stock hausen, James Tenney, Ivan Wyschnegradsky and La Monte Young (in alphabetical order). As microtonal music opens wide areas of uncharted musical territory, computational support can be very helpful for navigating this 48 Perspectives of New Music unfamiliar landscape. For example, various software plays back microtonal music, which allows for listening to the music during the composition process. Most sound synthesis programming systems allow for microtonal sound generation (e.g., Csound (Boulanger 2000); SuperCollider (McCartney 2002); Max/MSP (Miller Puckette 2002) and PureData (M. Puckette 1996)). Other systems assist in the development and analysis of microtonal scales, such as Scala by Manuel Op de Coul; CSE by Aaron Hunt; and L'il Miss' Scale Oven by Jeff Scott. These programs can also help to retune various MIDI synthesizers and samplers. In this paper, however, we are interested in computational support for the composition process itself, a field commonly called computer aided composition (or algorithmic composition). For example, consider a composer who wants to create a progression of microtonal chords that follows some rules on harmony. Some of her rules are inspired by conventional harmony. For example, a relatively simple rule states that consecutive chords should often share common tones. She conceives other rules for a specific piece or section she is working on (e.g., certain chords should contain specific microtonal intervals). The composer plans to use different textures in her piece. For instance, some sections consist of a melody with accompaniment; other sections are contrapuntal. These textures should always express an underlying microtonal harmony progression. The rules on harmony are complemented by rules on the individual parts. For example, non harmonic tones may be allowed for more smooth melodic lines, but these are restricted by specific rules in order to make the harmony still recognizable (e.g., passing tones may be allowed). Other rules restrict simultaneous notes (e.g., she may want to avoid unisons and octaves). The composer may also want that each part consists of certain motifs. Many existing computer-aided composition systems support microtonal pitches, including often-used systems such as Max/MSP & PureData; OpenMusic & PWGL (Assayag et al. 1999; Laurson, Kuuskankare, and Norilo 2009); SuperCollider; JMSL (Larry Polansky, Phil Burk, and Rosenboom 1990; Didkovsky and Philip L. Burk 2001); Common Music (Taube 1997); and Fractal Tune Smithy by Robert Walker. However, complex music theories like the microtonal theories of harmony or counterpoint sketched above are difficult to model with these systems. Music theories such as harmony or counterpoint are traditionally stated in a modular way by a set of rules, where musical parameters (e.g., a single pitch) are often affected by multiple rules at the same time. This approach allows for a formal description of a complex A Computational Model for Rule-Based Microtonal Music 49 network of interval relations in music, which is necessary for theories of harmony or counterpoint. Important interval examples are the sequence of intervals in a melody, the intervals between melodic peaks, the set of intervals between simultaneously sounding notes, the set of intervals that form an implied harmony (which may last longer than individual notes), the intervals between chord roots, the intervals that form an underlying scale (mode), how scales/modes are transposed in modulations and so forth. The systems mentioned above only partly embrace this complexity. These systems make it very hard to describe a network of interval relations, because they make it hard to affect parameters (e.g., pitches) by more than a single rule at a time. For example, typically either only the horizontal (melodic) or only the vertical (harmonic) dimension is controlled. This restriction is caused by the underlying programming model of these systems, which efficiently map sets of known values to sets of values to compute (as in a function). Complex music theories that describe a network of interval relations are far more easily formalized using a programming model...