Grammar-based music composition

L-Systems have traditionally been used as a popular method for the modelling of spacefilling curves, biological systems and morphogenesis. In this paper, we adapt string rewriting grammars based on L-Systems into a system for music composition. Representation of pitch, duration and timbre are encoded as grammar symbols, upon which a series of re-writing rules are applied. Parametric extensions to the grammar allow the specification of continuous data for the purposes of modulation and control. Such continuous data is also under control of the grammar. Using non-deterministic grammars with context sensitivity allows the simulation of Nth-order Markov models with a more economical representation than transition matrices and greater flexibility than previous composition models based on finite state automata or Petri nets. Using symbols in the grammar to represent relationships between notes, (rather than absolute notes) in combination with a hierarchical grammar representation, permits the emergence of complex music compositions from a relatively simple grammars.

[1]  DeWitt H. Parker,et al.  Philosophy in a New Key , 1941 .

[2]  Joseph Schillinger.  The mathematical basis of the arts , 1948 .

[3]  B. Ghiselin,et al.  The Creative Process , 2010 .

[4]  M. Gell-Mann,et al.  Physics Today. , 1966, Applied optics.

[5]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[6]  F. Barron.  Creative person and creative process , 1969 .

[7]  Max V. Mathews,et al.  GROOVE—a program to compose, store, and edit functions of time , 1970, CACM.

[8]  R. Voss,et al.  ‘1/fnoise’ in music and speech , 1975, Nature.

[9]  William Buxton,et al.  The Use of Hierarchy and Instance in a Data Structure for Computer Music , 1978, ICMC.

[10]  C. Roads,et al.  Grammars as Representations for Music , 1979 .

[11]  S. R. Holtzman,et al.  A generative grammar definition language for music , 1980 .

[12]  S. R. Holtzman,et al.  Using Generative Grammars for Music Composition , 1981 .

[13]  Kevin I. Jones,et al.  Compositional Applications of Stochastic Processes , 1981 .

[14]  N. J. Zabusky,et al.  Computational Synergetics and Innovation in Wave and Vortex Dynamics , 1984 .

[15]  Curtis Abbott,et al.  Programming languages for computer music synthesis, performance, and composition , 1985, CSUR.

[16]  N. Galanti.  [On the creative process]. , 1987, Revista medica de Chile.

[17]  Hans P. Moravec.  Mind Children: The Future of Robot and Human Intelligence , 1988 .

[18]  Roger Penrose,et al.  Précis of The Emperor's New Mind: Concerning computers, minds, and the laws of physics , 1990, Behavioral and Brain Sciences.

[19]  Gareth Loy,et al.  Composing with computers: a survey of some compositional formalisms and music programming languages , 1989 .

[20]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[21]  A. Lindenmayer,et al.  Developmental models of herbaceous plants , 1990 .

[22]  W H Zurek.  The Emperor's New Mind. Concerning Computers, Minds, and the Laws of Physics. Roger Penrose. Oxford University Press, New York, 1989. xiv, 466 pp., illus. $24.95. , 1990, Science.

[23]  F. Richard Moore,et al.  Elements of computer music , 1990 .

[24]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants-The Virtual Laboratory , 1990 .

[25]  P. Johnson-Laird.  Human and Machine Thinking , 1992 .

[26]  Przemyslaw Prusinkiewicz,et al.  Parametric l-systems and their application to the modelling and visualization of plants , 1992 .

[27]  Przemyslaw Prusinkiewicz,et al.  Animation of plant development , 1993, SIGGRAPH.

[28]  Jon McCormack,et al.  Interactive evolution of L-System grammars for computer graphics modelling , 1993 .

[29]  David G. Green,et al.  Complex Systems: From Biology to Computation , 1993 .

[30]  N Oreskes,et al.  Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences , 1994, Science.

[31]  John Fitch,et al.  Nature Music and Algorithmic Composition , 1995 .

[32]  Douglas A. Lyon.  Using stochastic petri nets for real-time nth-order stochastic composition , 1995 .