Functional Representations of Music
James McDermott∗
, University College Dublin.
April 30, 2012
Music is an interesting domain for the study of computational creativity. Some generative formalisms for
musical composition (e.g. Markov chains) achieve plausible music over short time-scales (a few notes) but
appear to be “meandering” over longer time-scales. Imposing a sense of teleology or purpose is an important
goal in creating valuable music.
In the field of evolutionary computation (EC), researchers draw inspiration from Darwinian evolution to
address computational problems. EC can be applied to aesthetic and creative domains. Although EC is
commonly used to generate music, key open issues remain. Formal measurement of the quality of a piece of
music in a computational fitness function is an obvious obstacle. A naive representation for music, such as
a list of integer values each corresponding directly to a note, will tend to produce disorganised music.
In previous work, Hoover et al. [1, and later] showed that a functional representation could impose
organisation and a sense of purpose. In this system, music is represented as a function of time. A fixed
piece of pre-existing music is used as a “scaffold”: the system then evolves functions, i.e. mappings from the
scaffold to new accompanying material. Time-series of numerical “control” variables are also proposed as a
means of imposing structure on the music. Fitness is judged interactively.
The XG project is partly inspired by this work. It discards the “scaffold”, but relies on the time-series
of control variables (see Figure 1).
Time (beats)
Bar Beat x,y,z
bar
mod +
sin2
sin2
beat
+
+ sin2 +
x
unaryy
sin
sin2
sin2
z
unary- +
output sin2 output sin2
unary- sin2
unaryoutput
Figure 1: Time-series of control variables
(left) impose a bar/beat structure and an
overall AABA structure. The evolved function
(right) maps these variables to numerical
outputs, once per time-step. The outputs are
interpreted as music.
It also differs in its internal representation for the mappings (a simple language of arithmetic functions,
with special accumulator functions at the outputs to control volume), and its use of a computational (noninteractive)
fitness function. Surprisingly good results arise using this representation in combination with a
simple fitness function which rewards variety in the output music. Neither the functional representation nor
the fitness function is alone capable of producting good results. More details are available in a full paper [2]
and online1.
A longer-term goal of the XG project is to create large-scale musical works as mappings from pre-existing
time series arising in nature and human affairs, and from non-musical artforms such as film or still images
with a sequential aspect.
<references_biblio/>
[1] Amy K. Hoover, M. P. Rosario, and Kenneth O. Stanley. Scaffolding for interactively evolving novel drum tracks for existing
songs. In Proceedings of EvoWorkshops, volume 4974 of LNCS, page 412. Springer, 2008.
[2] James McDermott and Una-May O’Reilly. An executable graph representation for evolutionary generative music. In GECCO
’11, Dublin, 2011.
∗Funded by IRCSET/Marie Curie; jamesmichaelmcdermott@gmail.com 1http://www.skynet.ie/~jmmcd/xg
1
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