Many music analysts and music psychologists agree that one of the most
important steps in achieving a satisfying interpretation of a musical
surface is the identification of important instances of repetition.

Our goal is to build a computational model of expert music cognition and
it seems clear that one of the most important components in such a model
would be an algorithm that can identify the most important instances of
repetition in a musical surface.

Existing algorithms for discovering repeated patterns in musical data are
limited in various ways. For example, some can process only monophonic
music, others are incapable of finding patterns "with gaps" and so on.

A new algorithm called SIA will be presented that discovers complete sets
of translation-invariant patterns ("translational equivalence classes") in
multi-dimensional datasets.

SIA takes a multidimensional dataset as input and generates as output a
set of "translational equivalence classes" (TECs). Two patterns in a
dataset are said to be "translationally equivalent" if and only if one can
be obtained from the other by translation alone. Each pattern in a dataset
is a member of exactly one TEC and the TEC to which a pattern belongs
contains all and only those patterns to which the pattern is
translationally equivalent.

SIA generates for each of the largest repeated patterns in a dataset the
TEC that contains that pattern. The set of TECs generated by SIA for a
musical surface represented as a multidimensional dataset typically
contains those instances of repetition that are considered to be musically
most interesting.

Dave Meredith is a Research Fellow in the Computing Science Department at
City University, London. Since October 1999 he has been working with
Geraint Wiggins on an EPSRC funded project whose goal is to develop
improved computational models for the processes involved in expert music
cognition. In particular, he is interested in modelling the perception of
similarity in music.

Dave did his undergraduate degree at Cambridge University where he studied
Natural Sciences for one year and then Music for two years. He then
defected to "the other place" (Oxford, Music Department) to study for his
doctorate. He is still trying to persuade them to give him a PhD in
mathematical music theory.