3 History

3.5 Precedents

Swarm Synth grew from John Cage's idea of music as organised sound and from Craig Reynolds' flock (3.2). It also stands in a longer line of music made from mathematics and from systems. The works below are not its sources; they are neighbours that show what it shares with others and where it goes its own way.

3.5.1 Iannis Xenakis

Xenakis, an engineer and architect as well as a composer, built music from mathematics more radically than anyone before him. Several of his ideas are close to Swarm Synth's.

• Metastaseis (1953–54): string glissandi drawn as straight lines that together make curved surfaces. The same ruled surfaces became the Philips Pavilion at the Brussels World's Fair of 1958.
• Pithoprakta (1955–56): clouds of pizzicati for 46 strings, shaped like the motion of gas molecules. No single note matters; the statistics of the whole cloud is the music. This is the precedent closest to a flock heard as one body.
• Achorripsis (1956–57): the density of events chosen by probability (the Poisson distribution).
• Analogique A et B (1958–59): Markov chains, and the first music built from grains of sound — the ancestor of every granular synthesis, and of the grains in Swarm Synth's crackle and shaker.
• Herma (1961): sets and their logic as musical structure.
• Nomos Alpha (1965–66): for solo cello. Its sections follow the 24 rotations of a cube (a group in the mathematical sense), and its pitches come from "sieves", patterns of numbers built from congruences. Xenakis dedicated it to Aristoxenus, Évariste Galois and Felix Klein.
• Polytope de Montréal (1967): light and sound composed as one spatial structure.
• Mycenae-Alpha (1978): drawn on UPIC, a system that turns drawings directly into sound — what is drawn is what is heard.
• GENDY3 (1991): dynamic stochastic synthesis, where the waveform itself is a random walk; sound made from a formula alone, without samples.

His book Formalized Music (1963, English 1971) gathers these methods.

3.5.2 Swarms that make music

• Tim Blackwell, Swarm Music (2002): an improvising system in which the positions of a particle swarm become musical events, and a human player's sound attracts the swarm and steers it. With Michael Young, Blackwell developed it further ("Self-organised music", Organised Sound, 2004), including a swarm-driven granulator, around stigmergy — communication through changes in a shared environment, as in social insects.
• Martin Neukom, Daniel Bisig and John Flury, Interactive Swarm Orchestra (Zurich University of the Arts, 2006–08): flocking algorithms controlling sound synthesis and the placement of sounds in space, with visitors tracked by cameras who could disturb the acoustic flock. Bisig later carried swarm simulations into dance.

These works mostly turn where the particles are and how they move into notes. Swarm Synth takes another road: its sound comes from relations — two birds meeting, a flock forming, a flock crossing the grid (2.4). A swarm whose rules are switched off is silent, however much it moves.

3.5.3 Other mathematical music

• Lejaren Hiller and Leonard Isaacson, Illiac Suite (1957): the first music composed by a computer, from rules and Markov chains.
• Conlon Nancarrow, Studies for Player Piano: canons whose voices run at tempo ratios such as √2 : 2 (Study 33) and e : π (Study 40), impossible for human players.
• Steve Reich, Piano Phase (1967): one pattern played against itself, drifting slowly out of phase.
• Per Nørgård, the infinity series: one self-similar number series generating whole melodies.
• György Ligeti, Études for piano (from 1985): overlapping patterns close to the fractal and chaotic images he admired.
• Brian Eno, Music for Airports (1978): tape loops of unrelated lengths that never meet the same way twice — an early generative music.
• Curtis Roads, Microsound (2001): the theory of sound built from grains, in Xenakis' line.
• Ryoji Ikeda, datamatics (from 2006): data and mathematics shown and heard at once.

3.5.4 Where Swarm Synth stands

From Xenakis it shares the idea that a mass of small events, heard together, makes a form of its own, and that sound can be made from formulas without recordings. Unlike his clouds, which he calculated and wrote out, the swarm is computed live and can be played. From the swarm instruments before it, it differs in what it listens to: not positions but relations. And with UPIC and the Polytopes it shares the wish that picture and sound be one thing — what you see is what you hear.

References: Iannis Xenakis, Formalized Music (1971; revised 1992); Thomas DeLio, "Iannis Xenakis' Nomos Alpha: The Dialectics of Structure and Materials", Journal of Music Theory (1980); Tim Blackwell (with Peter Bentley), "Improvised music with swarms", IEEE Congress on Evolutionary Computation (2002), and, with Michael Young, "Self-organised music", Organised Sound 9/2 (2004); Daniel Bisig, Martin Neukom and John Flury, "Interactive Swarm Orchestra" (Generative Art, 2007); Curtis Roads, Microsound (2001).