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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) 1995 Society for Music Theory
| Volume 1, Number 3        May, 1995      ISSN:  1067-3040   |
  All queries to: mto-editor@boethius.music.ucsb.edu or to
AUTHOR: Demske, Thomas
TITLE: Response to Parncutt
KEYWORDS: similarity, perception
REFERENCE: mto.95.1.2.demske.art
Thomas Demske
Music Department
Connecticut College
270 Mohegan Avenue
New London, CT  06320
[1] Richard Parncutt proposes a perceptual approach to similarity
analysis based on, "average subjective judgment of global
similarity by a representative group of listeners."  Even if it
were possible to achieve a general consensus on such a standard,
I would be uncertain about how to apply it in musical contexts.
[2] The "modified harmonic fluctuation" model of Messiaen's chord
succession described in my essay was a rhetorical expedient.
Most readers tentatively accepted the possibility of a connection
between perceived breaks in surface continuity and low (whatever
that means) REL, ASIM, and ATMEMB values.  Competing clusters,
based on different pivots or on different cutoff points relative
to a single pivot, could thus presumably be evaluated according
to how well they conformed to perception.  (Recall that
evaluation in general, and not perception in particular, was the
focus of the essay.)  But there are many basic difficulties here.
One lies in identifying precisely what percepts might be
appropriate testing grounds for the evaluation.  (Cf. paragraph
16 in the essay.)  Another is that of isolating the "similarity"
relationship component from other factors contributing to a goal
percept.  (Cf. paragraph 17 in the essay.)
[3] My working assumption throughout was that REL and comparable
functions have something to do with perception.  However valid
that assumption may or may not be, the two problems mentioned
above remain even for functions more securely grounded in that
area.  If I understand Professor Parncutt's paragraph 6
correctly, he is suggesting a table lookup function (?), where
the table entries have been determined empirically through
experimentation.  I suppose that this means asking subjects to
rate "global similarity" for 29 x 29 = 841 pairs of chords (or
841 x 2 = 1682, to check for immediate order effects).  Perhaps
the chords would be sounds, extracted from a single performance
-- maybe normalized somehow, maybe not.  It might even be
possible (maybe!) to explain what "global similarity" means, so
that subjects would have some idea of what to shoot for.
[4] By construction, the proposed function should have something
to do with perception.  But how far would that "something"
extend?  Given competing clusters of the 29 chords under the
proposed function, our hope would be to select only good clusters
by listening to the piano ostinato.  What to test against is the
first decision: smooth progressions, surface grouping boundaries,
shifts in large-scale harmonic region?  Whatever we decide will
likely require considerable extrapolation in order to relate it
to the exhaustive process of discrete chord pairings used in
deriving the function; each step in the extrapolation increases
the distance between the function's application and its
perceptual grounding.  Next, given a goal percept, would we
necessarily reject a clustering because it conflicts with the
percept?  Other factors not addressed through the experimental
binary comparisons could take control in such situations --
contour changes; local tessitura; rhythm; clarinet, violin, and
cello parts; voice leading.  (Recent mto-list exchanges on
enharmonicism seem especially relevant to me here.)  The problem
is in determining how far mitigating factors are operative, and
how far they should be taken into account, when judging
similarity-based boundaries according to perception.
[5] David Lewin suggested in a recent mto-talk post that we drop
the "similarity" label when referring to functions like REL,
RECREL, etc.  I suspect a wee bit of tongue-in-cheek here; I also
doubt whether the SMT language police budget allows opening a new
front in the continuing war on objectionable signifiers.  So,
what I suggest instead is that we recognize "context-free
similarity" for the oxymoron that it is.  (On a volunteer basis,
of course.)  Similarity presupposes a context.  The context of REL
is a particular intellectual apparatus.  The context of (what I
understand to be) Professor Parncutt's proposed similarity
measure is a particular experimental setting.  I would not at all
suggest abandoning "similarity" functions.  Like all reasonably
well-developed constructs, they hold nice potential for
theorists.(1)  What I do suggest is applying more energy toward
understanding their limits.(2)
1. See, for example, Chapter 6 of Marcus Castren's oft-mentioned
dissertation, "RECREL: A Similarity Measure for Set-Classes"
(Ph.D. diss., Sibelius Academy, 1994).  Also, Allen Forte
obtained remarkably interesting results some twenty-plus years
ago with his R0, R1, R2, and Rp relationships (*The Structure of
Atonal Music*, Yale University Press, 1973).  Those relationships
have been much maligned in the subsequent similarity literature.
I think a more sympathetic re-evaluation, especially of Forte's 
analytical applications, could prove very illuminating.
2. Richard Hermann's response reached me only as I finished
writing this.  I will reply (if appropriate) after studying it.
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