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       M U S I C          T H E O R Y         O N L I N E
                     A Publication of the
                   Society for Music Theory
          Copyright (c) 1993 Society for Music Theory
| Volume 0, Number 3      June, 1993      ISSN:  1067-3040    |
  All queries to: mto-editor@husc.harvard.edu
AUTHOR: Smoliar, Stephen
TITLE: Commentary on Justin London's MTO 0.2 article
REFERENCE: mto.93.0.2.london.art
File: mto.93.0.3.smoliar.tlk
There is one minor nit I would like to dispense with quickly concerning the
matter of style.  I felt as if this document had rather a parade of straw men
in it.  Each paragraph let me to raise my eyebrows and say, "Yes, but what
about . . . ?," only to find that the but-what-about was covered in the
following paragraph!  It would have been nice had Justin not led us down
quite so many garden paths in order to make his point, but perhaps I just
happen to feel that way because I am in the thick of this stuff right now.
What I REALLY want to write about is a but-what-about stone which was left
unturned by Justin's discussion.  It's a pretty heavy stone, though:  But
what about the fact that there is already a researcher who has worked out
a potentially interesting quantitative model which not only accounts for
the dynamic nature of meter but may even provide a viable quantification
of just how loud some of those rests are?  The research in question is named
Peter Desain, and I want to address his work because I have been hard a work
colleague Henkjan Honing.
(As an aside, my original intention was to write this review for ARTIFICIAL
INTELLIGENCE.  However, it began to grow into something more like a paper than
a review;  so I ended up sending it to COMPUTER MUSIC JOURNAL.  Until I read
Justin's paper, it had not occurred to me that it might be suitable for MUSIC
THEORY SPECTRUM.  For now, however, I just want to summarize one particular
aspect of the work reported in this book.)
Desain's model is called an EXPECTANCY SPACE.  It was actually introduced to
comparatively evaluate systems concerned with the detection of metric beat in
performances of music.  For example, given a timetable of MIDI events from a
keyboard performance, the system being evaluated should be capable to
translating the real-time durations of events into the discrete symbols
of music notation.  An algorithm to solve this problem was first proposed
by Christopher Longuet-Higgins in the Seventies, and Desain wanted to compare
the performance of this algorithm with a system of his own design based on a
neural network.
The principle behind the expectancy space is similar to that of Meyer's
expectations.  Given a past history of duration events, the question is
whether or not that history predisposed the model in favor of certain durations
rather than others.  For example, if the last six events have all been
interpreted as the duration of an eighth note, the expectancy space gives
what amounts to a high probability that the next note will also be an eighth
note, somewhat lower probabilities that it will be a sixteenth or quarter note,
and so on down to a very low probability that it will be a whole note.  Note
that the purpose of the algorithm is to reflect how the interpretation system
actually performs, but that means that each interpretation system in turn may
be viewed as reflecting a particular kind of listening behavior.
Neither of the systems being compared present particularly convincing
expectancy spaces.  This is because they are both based on the rather
trivial goal of trying to establish simple integer ratios between successive
durations.  Thus, everything is evaluated on a note-by-note basis without any
attempt to hypothesize how notes are grouped into measures or any other
higher-level construct.  However, the expectancy space could be used to
evaluate any other system which tries to take this sort of rhythmic dictation.
What is important is that it treats such a system as a dynamic function
processing data in real time and displays the relationship between specific
data and the behavior of that function.
The most important element of this technique is that it is quantitative.  One
is not dealing with highly subjective measurements which try to capture how
strong an expectation it.  At any moment in the course of a performance, the
system gives a numerical weight of predisposition for the duration of the next
event.  If that next event does not happen, as would be the case with a rest,
it would not be too far fetched to interpret that weight as the "loudness" of
the rest.
The only real problem with Desain's results to date is that you have to have a
model implemented before you can evaluate it with an expectancy space.  Thus,
the main thing we learn from his report is that note-to-note relations do not
give us a particularly effective model, particularly when they only take
duration into account.  If one were to try to develop more realistic
expectancy spaces, one would first have to assemble a more comprehensive
model, taking account not only the recognition that duration is organized
at a higher level than individual notes but also the roles of other parameters
of performance, such as the pitches of the notes being performed, their
dynamics, and perhaps their articulation.  Such a model may still be a
ways in the future, but the expectancy space now obliges US to think much
more seriously and quantitatively about how it could be implemented.
Let me close with one final nit.  In paragraph [14] Justin writes:  "Meter is
neither a parameter like pitch or timbre, nor is it a part of a nested
measuring of durational patterns and/or periodicities.  It is something
that is heard and felt."  Are not ALL aspects of musical sound elements
that are "heard and felt?"  Justin's acknowledgement of phenomenology is
all very well and good, but I do not think he gives it sufficient attention.
ANYTHING which is either a musical object or a parameter of a musical object
is ultimately a construction of the interpreting mind.  That is as true of the
sonority of a minor triad in first inversion as it is of a ternary metric
pattern.  The real question concerns the nature of the operations of
construction which are brought into play in the course of listening.
Justin is quite right that they are dynamic for meter;  but, most likely,
they are dynamic for all other aspects as well.  The dynamic nature is not
the issue.  More important will be how well we shall be able to describe that
nature in quantitative terms.
From smoliar@iss.nus.sg Thu Apr 22 12:18:46 1993
Date: Thu, 22 Apr 93 20:52:16+080
From: Stephen Smoliar <smoliar@iss.nus.sg>
To: smt-list@husc
Subject: Comment on London's MTO Article
Joel Lester raises some interesting points in his response to the London
article.  I think it is particular important to recognize the score as
a set of instructions for performance whose information content should
not be confused with that of sounding music.  My guess is that one could
augment his list of cues through which the sounding music can guide how
one tap's one's foot;  but enumerating those cues is not as important as
acknowledging that such cues are there to be "picked up" from the audible
However, no matter how rich our supply of cues may be, it is rarely foolproof.
Ultimately, there really is no good answer to the question:  How do we know
when to begin counting?  The only absolute answer is:  We don't;  we
HYPOTHESIZE a count.  If we then discover that our count really does
not "fit," we update our hypothesis.  It is this updating of a running
hypothesis which makes the model "dynamic," in London's sense of the word.
Unfortunately, his paper only began to scratch the surface of those dynamics
(as did Desain's work, coming from a different direction).  The biggest rub,
however, has to do with the question of "goodness of fit:"  How do we determine
whether or not our current hypothesis should be abandoned.  That, I think, is
where the sorts of cues Joel enumerated enter the picture.  If too many of
those cues offer too much evidence against where the hypothesis says the
downbeat is, then it is time to change hypotheses.
As a final point I think it is probably important that most of the cues which
tend to be invoked to assess the running hypothesis are SURFACE features.  When
one analyzes a score, one can find no end of "deep" structural features which
offer evidence as to where the downbeat REALLY is.  However, I content that
those features are another part of the landscape of instructions for
performance.  Listeners tend not to read scores, just as listeners to
natural language tend not to diagram the sentences they hear.  Rather,
they pick up on surface features and respond to them.  Perhaps, then,
the real ART of performance concerns how the deep features which are
the result of careful analysis may be made available as surface features
to the listening ear.
Stephen W. Smoliar; Institute of Systems Science
National University of Singapore; Heng Mui Keng Terrace
Kent Ridge, SINGAPORE 0511
Internet:  smoliar@iss.nus.sg	FAX:  +65-473-9897

I am getting a bit worried about the way in which we are all jumping on Example
3 in Justin's paper.  What worries me the most is a methodological danger which
I shall call "selective denial of context."  It seems as if each interpretation
chooses to bar certain experiential elements from the context in order to make
its point, and I am not sure this is a terribly healthy way to go.
For example, I have now read several accounts which basically have tried to
abstract away from the way in which Example 3 is actually notated, as if any
intelligent ear should be able to infer the notation from the listening
experience.  This strikes me as being akin to looking down the wrong end
of a telescope.  I prefer Lester's view of the score as a set of instructions
for performance.  Thus, in this case the "game" is not one of inferring where,
and how hard, to tap your foot.  The score tells you that already;  and it is
the responsibility of the performer to make sure you "get the message."
Rather, the "game" is determining when you bring your foot down which
particular emphasis on a rest;  where, to some extent, the energy of
your stomp may then me taken as a rough measure of the loudness of the
rest.  This is not a question of the listener resolving any ambiguities
which are latent in the score.  That's the performer's job.  Rather, the
question is how the performer endows the listener with a mental state based
on expectancies which set his foot tapping in the first place.  The reason
I trotted out my Desain hobby horse at the beginning of this discussion was
because his expectancy space provides a means by which such a mental state
may be inferred from strings of perceived durations.
Having said all that, let me now stir up the pot which a bit more context which
has received little attention.  Having now sung Example 3 to myself so many
times that it is beginning to invade my dreams, I have discovered that it is
beginning to co-mingle with some more concrete musical memories.  For example,
while the resemblance is not note perfect, it begins with a gesture which we
all know and love from the last movement of Beethoven's first symphony.  I feel
that such a "family resemblance" is particularly important when considering the
"responsibility" of the performer.  What I mean is that, because this
particular passage is so similar in both pitch and rhythm to a passage
which is in so many listeners' memories, the performer really does not
have to do very much to communicate this particular set of score instructions.
Indeed, the memory may well be triggered before even that first rest has been
reached, thus making it all the easier for a mind with a rich memory to control
the tapping foot.
Stephen W. Smoliar; Institute of Systems Science
National University of Singapore; Heng Mui Keng Terrace
Kent Ridge, SINGAPORE 0511
Internet:  smoliar@iss.nus.sg	FAX:  +65-473-9897
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