ï~~2.3 WTM and Natural Language Processing
(NLP)
One basic similarity of WTM to natural languages
is that people that were raised on the western culture
have an intuitive, unconscious (unstudied) knowledge of
WTM, knowledge which enables them to accept, reject
or analyze infinitely many new musical features. This
similarity makes WTM especially appropriate for a
scientific research since: (i) It provides an evaluation criterion, i.e., the judgement of the "experienced
listeners" and (ii) It justifies an "infinite space" requirement, i.e., a suggested model should be able to account
for indefinitely large number of structures.
Considering these and many other similarities
between WTM and natural languages, and in view of the
intensive research on NLP, the current state of computer
study of music seems quite surprising. One is inclined to
say that since both NLP and the computer study of
music went through a statistical-numerical period in the
W's, followed by a syntax first period, it is possible that
the computer study of music lacks some parallel to the
current semantics first" period of NLP. eMinsky 19811,
iMeehan 19801, ILaske 19801 and [Rain 1980, all
emphasize the insuificiency of syntax oriented music
theories as a basis for a music understanding research,
and suggest the Al approach as more appropriate.
2.4 An AI Approach.A1 systems are often called "open ended" systems
since their main characteristic is that they are not
intended to solve specific, well defined algorithmic tasks.
Rather, they handle incomplete, ill-defined problems, the
knowledge about which is ever growing, ever changing.
A typical AI system (if there is such a thing), must contain a lot of knowledge about its subject domain, and
must be provided with means to manipulate this
knowledge. The knowledge base constitutes a representation of that part of the world that is assumed relevant
to the problem. The language used to describe this
knowledge, and the mechanism used for reasoning determine the power of the system. For example, natural
languages are, certainly, powerful from the point of view
of expressive power and user convenience. However,
they are an unrigorous representation formalism, and
their manipulation is hard. On the other extreme, the
conventional notes notation is a rigorous and convenient
language for stating exactly which notes should be
played at every time point, but as a representation
language it is too restricted. Partially specified pieces,
and musical properties of a piece like its structure, or its
scale, cannot be represented in this language. Referring
to the role of representation in AiU. Woods says in [1983]:
"'In computer science, a good solution often
depends on a good representation. For most AIl
applications, the choice of representation is
even more difficult, since the possibilities are
substantially greater and the criteria are less
clear. The choice of representation becomes
crucial for the states of reasoning and
knowledge of intelligent agents that can understand natural language or characterize perceptual data, because the representational primitives and the system for their combination
effectively limit what such systems can perceive, know, or understand."
Knowledge representation and reasoning mechanisms
are, indeed, the key issues of AI.
One source of difficulty in designing AI systems is
that, in many cases, the subject domain is not well
defined. Compare, for example, the following two problems:
1) Sort a list of numbers, e.g., the list (2,1,5,3) should be
transformed into the list (1,2,3,5).
3) Design a system that is capable of analyzing music
according to a given theory, e.g., if the theory is: "In
Mozart music half of the chords are Seventh chords"
then the system is able to test Mozairt pieces for this
claim.
In the sorting problem, the subject domain is clear, and
no one would tend to assume that it is that specific list
that should be sorted, or that only four elements lists
should be sorted. The difficulty here is not in the stage
of problem formulation, but in designing an appropriate
algorithm. The music problem, on the other hand, is
vaguely stated. Clearly, if we design a computer program just for computing the percentage of chords in a
piece we miss the whole problem since Schenker's theory
is also an instance of this problem, as well as all the
rules appearing in textbooks of music theory. It is the
subject domain, i.e., music theory that should be
explained before we go on with the system design. The
music problem. as stated here, is exactly the ultimate
goal of the research described in this paper.
The explanation of the subject domain usually
imposes questions like:
"What part of the world is relevant to the problem?"
"What general properties can be assumed so that no
instance of the problem is ruled out?"
"What are the required properties of a representation
language?"
'On what level should the knowledge be represented?",
or, What are the representational primitives?"
"How to manipulate the knowledge about the world?"
Questions of this kind are hard, and there is hardly any
theory about how to produce good answers. The theory
of.I provides, at best, criteria for evaluation of AI systems, but the piocess of designing good AI systems is
still a matter of art.
2.5 History of this project
This research grew out of disappointment from an
experiment in which a computer program was designed
to test an hypothesis concerning harmonic progressions
([Schoenberg 1954],[Balaban 1975], [Sadai 1980]). While
the musical results were quite satisfactory, it was clear
that the representation used for this theory, i.e., a programming language, severly restricts the power of the
system, especially in terms of reliability and generalizalilitv. What was missing is a firm computational base
that can support representation, processing and even
construction of musical theories. Existing works could
not be of much help since their computational basis is
weak in many important respects, like expressive power,
simplicity, generalizability and extensibility. In particular, works on different subjects cannot be combined in a
simple way. Consequently, we decided to start a new
project, with the ultimate goal of providing a formal
basis for the study of music theories.
The questions that we faced at the beginning where
exactly of the sort presented in the previous section. At
first, we set down to characterize the basic objects, in
terms of which we expect music theories to be stated.
This was the level of representation stage. The next step
involved selection of a representation language. These
two steps are the basis for the CSM system.
3. Level of Representation
Observing that WTM does have a common terminology used in statements, descriptions, and theories of
WTM, it seems natural to take "the common
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