[Smt-talk] Two thoughts on Normal Form

[Charles J. Smith]

So along these lines, what is the "normal order" of a 7th chord? 

Does it make any sense to think of functional-harmonic entities in these terms at all? 

If not, why do we expend so much thought on a conceptualization without much in the way of historical roots (so to speak)? If so, shouldn't a functionally relevant normal order have some resonance in how we think of normal order in less tonal collections?

Some quick thoughts jotted down between classes on a busy day…
Charles Smith



> 1. The first is that the standard definition of "normal form" is from a
> geometrical point of view a little awkward.  We train students to order
> pitch classes (in an ascending way, spanning less than an octave,
> transposing so that the first note is 0) so as to minimize the distance
> from the first pitch to the last.  Geometrically, the more natural thing
> to do is to order them (in an ascending way, spanning less than an
> octave, transposing so that the first note is 0), so as to minimize the
> distance from the first note to the SECOND note.
...
> Anyway, if you're bored with teaching standard "normal form" it might be
> interesting to explore these two different approaches.




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Prof. Charles J. Smith
Slee Chair of Music Theory & Director of Graduate Studies
Music Department, 220 Baird Hall, University at Buffalo
Buffalo, NY 14260
cjsmith at buffalo.edu
Office Phone: 716-645-0639
Department Fax: 716-645-3824