2003 CMS/ATMI National
Conference
Miami, FL
Return to: Reginald
Bain | ATMI
October 3, 2003
Numerussonorus: Using
Max/MSP to Explore the
Compositional Potential of Number Sequences and Deterministic Algorithms
Reginald
Bain, Assoc. Prof.
Composition and Theory
School
of Music
University of South Carolina
813 Assembly St.
Columbia, SC 29208 USA
rbain@mozart.sc.edu
Abstract
The concept of numerussonorus
or “sounding number,” a term borrowed from Renaissance music theorist
Zarlino, is appropriated here to refer to a pedagogical approach to the fundamental
techniques of algorithmic music composition. Following a brief historical
introduction, the terms algorithm and algorithmic composition are
carefully defined, and the concept of a compositional formalism is introduced.
Composer and theorist Otto Laske notes that algorithmic composition is often
characterized by a parametric conceptual framework, that is, a view of the
musical surface and performance in terms of the perceptual parameters of sound.
Within such a conceptual framework, the compositional process might be viewed
as the ranking of perceptual parameters such as pitch, intensity, duration
and timbre. Algorithms are used to establish an isomorphism, or mapping, between
number sequences and these perceptual parameters. In this central part of
the creative process of algorithmic composition, musical results are typically
generated and then accepted or rejected based on their usefulness to the composer.
A variety of number sequences and deterministic algorithms are explored in
this paper. Each step of the mapping process is examined using custom software
applications written in Cycling ‘74’s Max/MSP, a musical programming
environment. These applications allow users to freely investigate the mapping
process. Applications include historical examples like Guido D’Arezzo’s
text setting method (c. 1026), as well as more contemporary examples, such
as musical mappings of Messaien's communicable language, Barnsley’s
Chaos Game, the logistic difference equation, and the decimal expansion of
the number π.
Download
- Download the Presentation
Handout (pdf)
"...composers
have celebrated music's link with the logic of mathematics by introducing
parametric systems of organization (primarily in the pitch domain), which are
largely
unrelated to aural perception. In the Middle Ages these techniques were invariably
hidden, existing below a surface that conformed to stylistic norms.."
Jon Appleton, "Machine Songs III"
"...it
seems important to preserve the idea that the computer is just a tools for carrying
out a particular notion of how to compose music."
Otto Laske, "Algorithmic Composition in the New Century"
"An
algorithm may desribe a set of rules or give a sequence of operations for accomplishing
some task, or solving some problem."
Gareth Loy, "Composing with Computers"
Application Examples
Chaos Game Melody is a musical
mapping of Barnsley's Chaos Game (Barnsley 1993).
Playing
with Pi allows the user to explore mappings of the decimal expanion of
π (3.14...) to pitch.
References
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Links
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'74
Updated:
February 6, 2006
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