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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) 1994 Society for Music Theory
| Volume 0, Number 6      January, 1994    ISSN:  1067-3040   |
  All queries to: mto-editor@husc.harvard.edu
AUTHOR:  Roeder, John
TITLE:   response to comments
KEYWORDS:  Roeder, semiotics, memory, computer models
REFERENCE:  mto.93.0.5.roeder.art
Roeder, John
University of British Columbia
School of Music
6361 Memorial Rd.
Vancouver, BC, V6T 1Z2 CANADA
Ordering and Logic in Music Signification
[1] David Lewin's comments about my article point out how the 
codes we use to represent pitch -- either numbers of letters 
-- impose order on the pitches.  The impulse to order does 
indeed seem to be at least a very deep cultural convention.  
It presents some difficulties to children learning about 
pitch classes, of course, when they must remember that A 
comes "after" G.  Even 0 coming after 11 is not immediately 
intuitive to younger musicians (born into a culture which, as 
Douglas Adams says, thinks digital watches are a pretty good 
[2] However, to a certain extent we learn about pitches as 
ordered irrespective of the conventions we use to name it.  
For example, a fledging pianist learns about pitch structure 
by playing with the *right hand* an *ascending* *white key* 
*major scale*.  Certainly there are pragmatic reasons for 
some of these conventions.  Playing white keys requires no 
forward displacement, whereas black keys are forward and up 
in physical space.  (Anyone want to study how physical 
motions required by the layout of keyboards correlate with 
musical structure?)  And most people have better motor 
control over their right hand.  But why play the "ascending" 
scale going up?  It's harder than "descending", and it is not 
typical of closural musical behavior.  (Many music majors I 
teach prefer closing their soprano lines with a high 7-to-1 
scale-degree succession, rather than low 2-1 or 7-1; I'm sure 
this comes from practicing ascending scales; as non music-
majors that have less or no performing experience seem to 
prefer low closure.)
[3] It also occurs to me, after reading Lewin's ruminations 
about whether we can name things without listing them, that 
musical relations, although not intrinsically ordered, can 
help induce order on collections of nonmusical sememes.  A 
famous mnemonic for the kings and queens of England uses 
musical (and poetic) properties of meter and timbral 
association (end rhyme), among other devices, to induce 
various partial orderings among the names.
Willy, Willy, Harry, Ste,
Harry, Dick, John, Harry Three,
One, Two, Three Neds, Richard Two
Henry Four, Five, Six -- then who?
Edward Four, Five, Dick the Bad,
Harries twain and Ned the Lad,
Mary, Bessie, James the Vain,
Charlie, Charlie, James again,
William and Mary, Anna Gloria,
Four Georges, William and Victoria,
Ned Seventh ruled till 1910,
When George the Fifth came in, and then
Ned went when Mrs. Simpson beckoned,
Leaving George and Liz the second.(1)
[excluding Lady Jane Grey, the kings and queens of England, 
in chronological order, are William the Conquerer, William 
II, Henry I, Stephen, Henry II, Richard I, John, Henry III, 
Edward I, II, and III, Richard II, Henry IV, V, and VI, 
Edward IV and V, Richard III, Henry VII and VIII, Edward VI, 
Mary I, Elizabeth I, James I, Charles I and II, James II, 
William II and Mary, Anne, George I, II, III and IV, William 
IV, Victoria, Edward VII, George V, Edward VIII, George VI 
and Elizabeth II.]
So while some of our sign systems impose orderings on music, 
music systems are also capable of inducing ordering on other 
semantic systems.
1. Susan Ferraro, *Remembrance of Things Fast*, New York: 
Dell Publishing, 1990, p. 17.
[4] Stephen Smoliar expresses some justifiable skepticism 
about semiotic views of music.   I understand much of his 
trepidation.  Semiotic theory, by claiming that anything can 
serve as a sign-vehicle for anything else,  poses an apparent 
challenge to the hegemony of positivist thinking upon which 
much science and some music theory is founded.  I take 
comfort in the view that the *possibility* of a multiplicity 
of denotative systems does not imply that they are all 
equally valid or useful to a particular musical culture.  In 
my article I restricted my application of semiotic theory to 
exposing meaning or misrepresentation.   I do not claim that 
Schumann's analysis is more meaningful to us than our own 
approaches, only that it has more meaning that we might be 
led to suppose by confronting the text that apparently 
signifies refers to little musical content.  
[5] Smoliar also says:  "I find it a bit  difficult to wade 
through much of the arcane language of the semiotic theorists 
when it seems to me as if it could all be articulated so much 
easier in LISP.  (This is not to say that LISP solves all 
problems.  Rather, it often helps us to formulate clearer 
questions, even when answering those questions turns out to 
be very difficult.)"  Although I too have used LISP and 
Prolog representations extensively to help formulate my own 
and others' theories, I find myself disagreeing with Smoliar 
that AI representations should be privileged.  Symbolic and 
logic-based representations have limitations that I have 
discussed elsewhere.  Briefly:  "While [a symbolic logic 
representation] of musical structure is based mainly on the 
knowledge of event properties, the information in a mere 
property list is insufficient.  Just to represent all the 
types of segments ... (let alone incorporate them into more 
abstract structures!) we must also know which event relations 
are transitive, which are commutative, and which induce order 
(for example, pitch does, timbre doesn't); we must know the 
boundary-defining values for various properties; we must know 
how segment-defining collective properties of segments relate 
to the properties of their events; and we must know of 
segment-defining processes, relations, or properties external 
to the sonological data at hand.  [There are other] specific 
weaknesses of a propertied-event representation of atonal 
music, in which an event always has a given property and all 
properties are equally available for determining a relation . 
[The representation runs] counter to our musical intuitions 
that registral lines have a different quality of coherence 
from that of chords, intuitions partially expressed by the 
distinctions we have made between various musical properties 
in defining the other types of segment.  Similarly, the 
strength of segmental associations depends crucially upon the 
nature of the event properties from which the collective 
property of the segment is derived."(2)
2. John Roeder, "Issues of Representation in the Analysis of 
Atonal Music," in  *Proceedings of the First Workshop on 
Artificial Intelligence and Music, St. Paul, Minnesota*, 
Menlo Park: AAAI, 1988, p. 147.  See also John Roeder, 
"Logic-Programming Models of Music: A Semiotic Evaluation," 
in *Music and Science*,  Seattle: Center for the Creation and 
Interdisciplinary Study of Music, University of Washington, 
1991, pp. 16-36.  
[6] Smoliar's main point is that since "description is not so 
much a matter of the describing agent passing a code to the 
receiving agent as it is a matter of the two agents mutually 
negotiating towards a point where they have some confidence 
that they are both talking about the same thing," that 
theories of music analysis should focus on the negotiation.  
I agree that the negotiation process is important to 
description, but what are the agents negotiating about except 
the codes that they will use?  We must still be able to 
evaluate the agreed-upon codes critically,  and Eco's theory 
helps us do it.
[7] Some readers may wonder, in light of the current 
discussion thread about the nature of the musical work, what 
"music" is being modeled in the systems I cite. My article 
was vague about the nature of the musical work; referring to 
it only as the semantic plane, and to its contents only as 
"psychophysical quantities".  This perhaps simplistic term 
reflects my belief that some of "the essence" of a musical 
work is rooted in common way humans -- composers and 
listeners -- perceive sound and sound relations.  Some 
intersubjectivity is genetically programmed.  Certainly there 
is also a strong cultural component to "the essence of a 
work", because what we hear as essential can be altered by 
experience and practice (we call it "ear training").   But 
this problematizes the notion of an invariant essence that is 
more than raw psychoacoustic quantities that "anyone" can 
hear.  However we understand the essence of the work, I hope 
the point of my article is clear that we should be careful in 
constructing sign-vehicles to represent it.
[8] Reader's interested in a more modern, and very complex
"literary" analysis should look at Anthony Burgess's 
"Stendhalian transcription" of Mozart's K. 550 in 
*On Mozart: A Paean for Wolfgang*, Boston: Houghton-Mifflin,
1991, pp. 93-103.  (Feminist scholars may also be interested
in the gender stereotypes in this narrative.)
John Roeder
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