Comment on John Roeder’s article

[1] 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 registers.

[2] 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.”

[3] 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 “♭III.” 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 E♭ 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.

[4] 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.

David Lewin
Harvard University
Music Department
North Yard
Cambridge, MA 02138
lewin@husc.harvard.edu

Footnotes

1. John Roeder, “Toward a Semiotic Evaluation of Music Analyses,” mto.93.0.5 (November, 1993).
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2. David Lewin, “A Label-Free Development for 12-Pitch-Class Systems,” JMT 21.1 (Spring 1977), 29–48.
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