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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
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| Volume 1, Number 4 July, 1995 ISSN: 1067-3040 |
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All queries to: mto-editor@boethius.music.ucsb.edu or to
mto-manager@boethius.music.ucsb.edu
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AUTHOR: Demske, Thomas R.
TITLE: Reply to Richard Hermann
KEYWORDS: similarity, atonal, post-tonal analysis, REL, evaluation
REFERENCE: mto.95.1.3.hermann.tlk
Thomas R. Demske
Yale University
Department of Music
143 Elm Street
New Haven, CT 06520
tdemske@minerva.cis.yale.edu
[1] Although I take issue with many points in Richard Hermann's
(1995) response to my essay on "similarity" relations, this reply
is restricted to Hermann's paragraphs 3-10, which I feel
misrepresent my position.
[2] Hermann's paragraphs 3 and 4 take me to task for being overly
harsh on intransitivity in my footnote 3 reference to "blind
subset polling." That reference in fact alludes to information
loss, and has nothing to do with transitivity. For example,
REL(5-14,6-14) = REL(5-14,6-19) = REL(5-14,6-49) = 0.546, where
Forte names stand for any particular instance of the named class.
Here are the set classes to which abstract subsets common to each
pivot and target belong:
* X * * Y * * Z *
REL(5-14,6-14) REL(5-14,6-19) REL(5-14,6-49)
2 : 1 2 3 4 5 2 : 1 2 3 4 5 6 2 : 1 2 3 4 5 6
3 : 1 3 4 7 9 3 : 3 4 5 8 9 3 : 3 5 7 8
4 : 4 4 : 16 4 : 15
[3] These common subsets determine the REL values.(1) Since
those values are equal, so are the spreads between each pair of
values; X is to Y as X is to Z, etc. But hidden behind that
sameness is an erratic divergence in the set types considered.
53% of the types used in calculating either X or Y (the union)
are also used in calculating both X and Y (the intersection).
47% of the union of X and Z are also in the intersection of X and
Z, and 64% of the union of Y and Z are also in the intersection
of Y and Z. "Intuitively," from this perspective, the value
spreads are different. (How the difference might be interpreted
is another matter; perhaps the comparison of X-Y and Y-Z spreads
should command more attention than that of X-Z and Y-Z spreads?)
But this perspective is lost when the intermediate steps of the
calculations are discarded. It is as if we move through a hidden
dimension in Rahn's (1980) "(staggeringly complex) network"
during any one REL calculation; upon obtaining the result, we
burn the bridges behind us. This sort of information loss --
hardly unique in music theory, but exacerbated by the remarkably
restricted scope of REL's object universe -- is what the "blind
subset polling" reference called into question.
============================
1. I continue my assumption of REL taken with a full-suite TEST.
Yes, as Hermann notes in his footnote 1, and as Lewin himself
noted through mto-talk, REL's original formulation allows for a
more selective TEST. The next question of course is what goes
into selecting a "suitable" TEST. This problem is roughly of the
same cut as others discussed in the essay, and so I chose not to
pursue it. Notice my footnote 4 in the essay, however, and its
mention of the "arbitrarily specified standard of subset content"
in Block and Douthett (1994).
============================
[4] The "blind subset polling" reference was only a minor
sidelight in my essay, relegated to a footnote. Its immediate
context was the much larger problem of support through intuition,
which I further addressed in a subsequent mto-talk post. I
suspect that blind subset polling grates against the intuitions
of others as well, and would be surprised if it did not play some
part in the conception of Marcus Castren's RECREL. In any case,
transitivity is not at issue here. Nor is it especially
pronounced in my paragraph 10, which Hermann also fixates upon --
despite noting, in his paragraph 3, that the "t" word appears
nowhere in the essay. I am nevertheless now deeply troubled by
the prospect that "music will be lost," a pathetic although
curious specter raised in Hermann's paragraph 4. Therefore, for
the record, and for what it is worth: intransitivity *per se*
does not strike me as overwhelmingly problematical.(2)
============================
2. See my dissertation (Demske 1993, 202-208, etc.) for one
practical approach to intransitivity in an applied setting.
============================
[5] Turning briefly now to the other purported "dissatisfactions"
of mine which Professor Hermann illuminates in his response: An
open choice of pivots is certainly not unsatisfactory in and of
itself; my concern throughout the essay was instead how to guide
the choice. (Hermann pars. 5-6) As for "strained intuition,"
again, the context there was the elusiveness of intuition, and
the inherent uncertainty of analytical models built on the
shifting sands of what may or may not be significant in the
abstract. (Hermann pars. 7-8) Finally, the matter of "context
sensitive criteria," which Hermann reads into my paragraph 13, is
properly taken up at paragraphs 16-18; there, the question is not
one of whether to acknowledge such criteria, but of how to go
about identifying and incorporating them in analysis. (Hermann
pars. 9-10)
[6] More passionately committed theorists may disagree, but I
believe that tackling this question is possible now only on an
*ad hoc* basis, and particularly so in the music Hermann cites in
his paragraph 19. Hermann reminds us that the problem of poor
results lies not *necessarily* [my added spin] with some given
theory in itself, but rather with how knowingly that theory is
applied. (Hermann's par. 13) I agree! But the knowledge
component of that formula has yet to materialize, at least with
respect to "similarity" relationships (although I do applaud
Hermann's provisional sketch, and appreciate his bibliography).
With no reliable constraints on the interaction between vague,
"context-sensitive criteria" on one hand, and an unlimited supply
of formalisms on the other, how can we rigorously evaluate any
resulting analysis?
REFERENCES CITED
Block, Steven and Jack Douthett. 1994. "Vector Products and
Intervallic Weighting." *Journal of Music Theory* 38.1:21-41.
Demske, Thomas R. 1995. "Relating Sets: On Considering a
Computational Model of Similarity Analysis." *Music Theory
Online* 1.2.
Demske, Thomas R. 1993. "Recognizing Melodic Motion in Piano
Scores: Rules and Contexts." Ph.D. diss., Yale University.
Hermann, Richard. 1995. "Towards a New Analytic Method for Post-
Tonal Music: A Response to Thomas R. Demske." *Music Theory
Online* 1.3.
Rahn, John. 1980. "Relating Sets." *Perspectives of New Music*
18.2:488-497.
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