Automatic discovery of parallelisms and hierarchy in
music
Master's Thesis by Søren Tjagvad Madsen and Martin Elmer Jørgensen (2003)
The thesis is on musical similarities and grammatical structures of
those. It can be downloaded here: gzipped post script (11.4
MB - a lot more unpacked!), pdf (3.4 MB - some reduction
in the quality, the text looks blurred but is fine on print).
An introduction to our similarity finder system
including source code and examples can be reached here: simfinder.tar.gz.
Abstract
There are three main ideas in this thesis.
Graph representation for non-monophonic music
We have attempted to create a datastructure for the symbolic
representation of music. Based on the two most fundamental temporal
relations found in music scores, precedence and simultaneity, we have
developed a graph representation of music. A music graph may
represent both monophonic and non-monophonic music. The music graph is
a powerful and flexible abstraction that can be extended considerably
to represent almost any symbol found in notated music scores. It is
our attempt to break out of the sequential/parallel dichotomy used in
so many representations in the literature, while still basing the
representation on precedence and simultaneity. We argue that a graph
representation is a more elegant representation, because it doesn't
necessitate repeated restructuring of the data structure switching
between the two fundamental modes (sequential or parallel structures)
during the analysis and segmentation of music.
Search for musical parallelism
To search for similarities in music graphs, we have implemented the
SimFinder system. The SimFinder uses a genetic algorithm to
search for similarities in a music graph according to different
similarity measures. Whereas much of the literature considers
'only' monophonic music, the SimFinder may search a music graph for
either monophonic or non-monophonic similarities. We have experimented
with several similarity measures for both monophonic and
non-monophonic similarity. The SimFinder is a modular framework that
allows new similarity measures to be defined and easily substituted
for the ones we have defined. Similarity measures are built using a
multiple viewpoint system that allows us to analyse music from
a multitude of perspectives at once. By designing and mixing the
right viewpoints we are able to specify what we are searching for.
The SimFinder is designed so that many different kinds of viewpoints
may be combined and tested experimentally.
Segmentation using a graph grammar
We describe a selection of past uses of formal grammars for the
description of music. Just how powerful a grammar must be to be able
to adequately describe music is a subject of debate, but it seems that
something more than a context-free grammar is needed. We argue the
importance of hierarchy in music and present a segmentation algorithm
called the SimSegmenter for non-monophonic music, which is based on
the SimFinder. The SimSegmenter builds a graph grammar to
hierarchically describe a piece of music represented in a music
graph. We present some test runs on fugue and chorale subjects by
J.S.Bach.
Keywords
automated music analysis, non-monophonic music,
multiple viewpoint systems, hierarchy and formal grammars, musical
similarity and parallelism, graph representation of music, symbolic
representations of music, graph grammar.