===       ===     =============        ====
             ===       ===           ==            ==   ==
            == ==     ===           ==           ==      =
           ==   ==== ===           ==           ==      ==
          ==     ==  ==           ==            =      ==
         ==         ==           ==             ==   == 
        ==         ==           ==               ====
       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:  David Lewin
TITLE:  Comment on John Roeder's article
KEYWORDS:  Roeder, semiotics
REFERENCE:  mto.93.0.5.roeder.art
David Lewin
Harvard University
Music Department
North Yard
Cambridge, MA 02138
     John Roeder's interesting article in MTO 0.5 prompts some thoughts on
integer/pitch and integer/pitch-class semiotics.<1>  The article of mine
to which he refers proposes a way to develop atonal or serial theory without
using integer labels (possibly mod 12) for the pitches or pitch classes.<2>  
In doing that, I used letter names for pitches or pitch-classes.  I thought
that was an improvement since the letters do not suggest algebra.  But the
letters do, still, suggest a privileged ordering -- either A B C D ... (for
obvious reasons), or C D E F ... (because of a cultural convention that
deserves more discussion than I can afford here).  And to label pitches,
as opposed to pitch classes, we require a further ordinal arrangement of
     The problem is partly linguistic: in order to MENTION the various
entities, one at a time, we are required to LIST them, if speaking.  And
in order to list them, we tend naturally to impose some ordering convention.
To the extent that Indo-European systems of writing follow that aspect of
speaking behavior (using e.g. a left-to-right linear presentation of 
symbols), we find ourselves also making a WRITTEN list, when we write down
the various entities one-at-a-time.  Perhaps other sorts of writing systems
would enable us not to be obliged to make such a list, but it is hard for
us (me) to imagine such systems.  (I do not see, e.g., how Chinese or other
sorts of ideograms could be used in this way.)  That may simply be because
we are (I am) trapped in a too-familiar complex of cultural constructs --
perhaps including the assumption of a Euclidean 2-dimensional "page."
     We have an amazingly versatile complex of constructs that enables us
to evade contradictions without taking any thought.  In the "label-free"
article, I point out that we would all label the opening harmony of the
*Eroica* as "I", but we would also be perfectly willing to read a title
page telling us that the piece was in the key of "Mi bemol," which -- if
taken "logically", should lead us to label the chord as "bIII."  Another 
example comes from the convention of labeling pitches-in-register as C'',
C', C, c, c', etc.  People who use this convention can perfectly easily decide 
in their own minds when they mean the symbols C and Eb to denote pitches-in-
a-particular-register, and when they mean the same symbols to denote pitch
classes.  Sometimes a reader, however, may experience a momentary glitch before
arriving at a decision, which is meant.  That is the main reason I prefer to
use the notation C1, C2, C3, etc. for pitches-in-register; the symbol "C"
then is always a pitch-class, never a pitch-in-register.
     The problem of mentioning-without-listing (perhaps better termed an
"impossibility"?) deserves a lot of study.  I imagine it has received some
in the semitoic literature of which I am not aware.  In conversation, I 
recently succeeded in remembering the Seven Dwarfs, in what seemed like a 
random order.  But the whole time, I was trying to visualize them marching in 
order, as in the movie.  Though I did not succeed in remembering that order, I 
am sure that there was a definite pseudo-ordinal psychological progression 
going on, that caused me to produce the names in the order I did.  People who 
professionally give lessons in remembering-many-things may have interesting
insights here, as to ordinal and non-ordinal memory aids and "maps."  Memory
may (!) be able to free itself of speaking and writing conventions, to a
certain extent.
<1> John Roeder, "Toward a Semiotic Evaluation of Music Analyses,"     
mto.93.0.5 (November, 1993).
<2> David Lewin, "A Label-Free Development for 12-Pitch-Class Systems,"
JMT 21.1 (Spring 1977), 29-48.
[1] Music Theory Online (MTO) as a whole is Copyright (c) 1994,
all rights reserved, by the Society for Music Theory, which is
the owner of the journal.  Copyrights for individual items 
published in (MTO) are held by their authors.  Items appearing in 
MTO may be saved and stored in electronic or paper form, and may be 
shared among individuals for purposes of scholarly research or 
discussion, but may *not* be republished in any form, electronic or 
print, without prior, written permission from the author(s), and 
advance notification of the editors of MTO.
[2] Any redistributed form of items published in MTO must
include the following information in a form appropriate to
the medium in which the items are to appear:
	This item appeared in Music Theory Online
	It was authored by [FULL NAME, EMAIL ADDRESS],
	with whose written permission it is reprinted 
[3] Libraries may archive issues of MTO in electronic or paper 
form for public access so long as each issue is stored in its 
entirety, and no access fee is charged.  Exceptions to these 
requirements must be approved in writing by the editors of MTO, 
who will act in accordance with the decisions of the Society for 
Music Theory.