ï~~FOUNDATIONS FOR ARTIFICIAL INTELLIGENCE RESEARCH OF WESTERN TONAL MUSIC
Mira Balaban
Department of Computer Science
State University of New York at Albany
Abstract
The computer study of music began in the late 50's.
Yet. there is no general computer research on music, and
existing works do not provide any stable base for further
research. What is missing is a formal basis for the comprter modelling o()f nmusic theory. Two main subjects in
thie develol)pment of such a basis are the selection of
primitives and of a representation language(s). A computer system. called CNSM (Comnputer Study of Music),
that is based on a formal study of these two subjects for
Western Tonal Music (WTNI) was built. The ultimate
goal of this system is to lay a "corner stone" for a general formal study of WTM. This paper summarizes the
theory behind CSM. its implementation, and our plans
for future research.
1. Introduction
The study of music (especially WTM) provides an
extraordinary domain for an Artificial Intelligence (Al)
researchl. A field of intensive human activity, with no
coherent theory. but with a large (unformal) theoretical
basis and with criteria for performance evaluation. Yet,
thirty years of work on computer analysis of music did
-not initiate any general research on computer modeling
of VWTM theory. Moreover, existing works do not provide any stable base for further research. Specific works
with weak computational basis and unclear theoretical
content cannot be combined to handle larger areas.
Artificial Intelligence, backed by its computational
methodology for handling unformal knowledge, provides
a most promising approach for building a formal basis
for music research. Altogether. both fields are likely to
benefit from a niarriage of music and Al research.
Looking for a firm unified computational basis to
support representation, processing and possibly construction of many musical theories, we started this work with
a study of appropriate formal mechanisms for the computer processing of WTM. Two low level "primitives"
standing for the musical concepts of Notes, Intervals and
the syntactic aspect of Twelve-Tone-pieces were suggested as building blocks for the common terminology of
WTM. The study of appropriate representation forms
first implied the inadequacy of known grammatical
models. The suggested formalism was developed in two
successive abstractions, beginning from a conceptual
framework consisting of concepts, attributes and relationships, through its abstraction as a set of units called
Generalized-Concepts (G-C-s), into a further abstraction
as a set of constraints systems.
This theoretical basis was implemented in a PROLOG system, called CSM, that supports a general study
of WTM. The kernel of CSM's knowledge base consists
of the core concepts of WTM theories, formalized within
the G-C model with a first order predicate language, and
it can )e easily extended to handle real theories of
WT.\I.
In what follows we discuss the selected primitives,
the C-C, model and CSM's control. (For a detailed
description see [lilaba:n 1982, 198-1a., 1984b].)
2. Background
2.1 Computer study of music
The beginning of computer music and computer
aided music research is marked by the pioneering work
of Hiller and Issacson in the 50's. The early works
focused on the application of either numerical or probabilistic or statistical, or information based methods to
musical data bases. ([Hiller & Issacson 19591, [Brooks et
al. 1957], [Pinkerton 1956], [Lincoln 19701.) The main
weak:ess of these systenis was their expressive power,
which was limited to that of finite automata. This
period in the study of music, reminds the failure of the
"mechanical translation" of natural languages, which
was based on similar methods, and happened in about
the same time.
A linguistics oriented period, based on elements of
music theory, began about ten years later. Ideas from
generative grammnars were used to synthesize melodies,
perform harmonic analvsis. study Schenker's theory and
other applications (jRothgeb 19681, [Slawson 1968,
Winograd 19681, Lidov & Gabura 19731, [Smoliar 1976,
Sundberg & Line blom 19761, [Frankel. Rosenschein
Snoliar 1976.1978). Smoliar 19801, [Kassler 1977], [Laske
1972.1975]).
Most works on the computer study of music focus
on WTM. They share three important properties: their
musical scope is quite restricted, they do not claim the
ability to generalize their scope, and, excepting
Winograd's work, there is no study of computational fornalisms per se. In particular, there is no general, formal, computer study of WTM.
2.2 WTM Theory
Though, there are specific, domain restricted
theories that admit formal computational models (e.g.
Schenker's and more recently Narmour's "Implication -
Realization" model [1977], and Lerdahl and Jackendolls
"Generative Theory of Tonal Music" [1983]), there is no
generally accepted, wel defined theory of WTAM. Therefore, a theoretical study of music is a study of "human
activity" which lacks a completely organized theory, i.e.,
a typical area for an.AI research.
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ICMC '85 Proceedings
