Australasian Computer Music Conference, August 2000

Boolean Networks for the Generation of Rhythmic Structure

Alan Dorin

http://www.cs.monash.edu.au/~aland
aland@cs.monash.edu.au

Centre for Electronic Media Art
School of Computer Science & Software Engineering
Monash University, Melbourne, Australia

Outline

Motivation (personal)

• I have only two hands, two feet and limited co-ordination...
  
  ...I love complex rhythms that I can't possibly play!
  
  
• Complex behaviour from simple rules ...life...


"Sometimes everything just comes together and suddenly you've created this wonderful organism" [Reich]

"And as the music grows in depth and complexity of texture, so the time taken for the sound organism to make itself felt is extended" [Nyman of Glass' music]


• I wanted an alternative to MIDI drum editors and step sequencers

Previous music

• Xenakis: Pleiades
  
  
• Reich: Drumming, Music for 18 Musicians, Sextet...
  
  
• Autechre: ep7
  
  
• Plastikman: Artifakts
  
  
• Jazz & Cuban, African, Chinese or Hindu percussion music
  
  ...exploit polyrhythmic structures for their 'spark'

Previous methods

• Play it
  (multiple players, hands, mallets or fingers)
  
  
• Mechanize it
  (tape recorders, metronomes, clocks, revolving arms, suspended microphones)
  
  
• Compute it (electronic sequencers, cellular automata, complex systems)
  

Two CA's, Wolfram '84

Liquiprism, Dorin '99

Turbulence (detail), McCormack '94*

Boolean networks

• Connected set of binary state-machines.
  
  
• Synchronous or asynchronous update.
  
  
• A node's future state depends on the states of nodes in the network designated as its inputs and its transition rule (AND, NOT, OR etc.)
  
  
• A node may feedback its own state as a self-input.
  
  
• Inputs may be received from outside the network.
  
  
• A Boolean network which receives no input from outside is autonomous.
  
  
• The application described below uses synchronous, autonomous Boolean networks.

Example Boolean network

The Boolean sequencer

animate notes

The Boolean sequencer user interface

Screen dump

Examples, comments etc.

• A little music please...
  
  
• Comment on software use: Not too bad but could be better with some improvements...

Future work and conclusions

• Different number of nodes in each track
  
  
• Different number of beats per minute in each track
  
  ...can then produce phasing effects like those employed by Reich
  
  
• Use sequencer as an arpeggiator
  
  
  
• Conclusion (personal): requires careful tweaking where pitched output is required but interesting polyrhythms are a cinch!

©Copyright Alan Dorin/Animaland 2000
(*Turbulence image © Copyright Jon McCormack 1994-2000)