[Smt-talk] (One of Two:) Thoughts on Normal Form

art samplaski agsvtp at hotmail.com
Mon Sep 17 14:25:26 PDT 2012

So, concerning Dmitri's actual post:) back on 5 Sept....

I'd like to comment on his 2nd point. (My reading of _AGoM_
was interrupted a year ago and I just don't know enough to
say anything useful on his 1st point.)

Dmitri gives an example of V7->I upper voice movement in Bach
chorales written in his "set of ordered pairs" version of
normal form, with exegesis:

> [H]ere are all the five most common upper-voice voice-leading normal
> forms for all the V7 -> I progression in Bach's chorales.
> [0, -4], [3, -2], [6, -1]   362 occurrences
> [0, -1], [2, 0], [6, 1]     120 occurrences
> [0, 1], [3, -2], [6, -1]     53 occurrences
> [0, -2], [3, -1], [5, 0]     19 occurrences
> [0, -4], [3, 2], [6, -1]     10 occurrences
> Remember these are upper voices, to be supplemented with a 5-1 in the bass.  
> In this case, "voice leading normal form" helps us reduce a wide range
> of contrapuntal practice to a few basic schemas. The first, which is
> overwhelmingly the most popular, has the leading tone falling to the fifth.
> The second has a doubled root in the V7, with notes moving in the expected
> way. The third produces an incomplete I chord with tripled root. The fourth
> has no leading tone (and occurs most often in eighth notes, following another
> inversion of V7. The fifth produces a doubled third.

Before anything else, I want to stress that I absolutely
love the results and want to see much more! This is exactly
the type of investigation where data-driven corpus studies
can provide very valuable material for areas such as style
analysis. (A statement that, e.g., "This formulation is very
(a)typical for Haydn" is an assertion about statistical
likelihood; to be more than ultimately mere opinion, it
needs to be backed up with error bars and the like.)

Next: having done lots of computer programming in my life
and a fair bit of statistics, I understand his formulation
as a very useful and indeed necessary type of back-end data
structure for writing a program to find out, "So just what
are JSB's most common voice-leading paradigms?" The key
phrase is _back-end_.

Dmitri prefaces the example by saying:
> This can be pretty useful in tonal theory and pedagogy.

Sorry, but if he's suggesting that we talk this way to
Written Theory I students then I have to disagree. I'm not
math-phobic by any means, but the ordered-pair format gave
*me* a headache trying to decipher it. I'm willing to bet
$$ I don't have that if this were presented to a freshman
class not consisting of only computer science majors, the
results would likely be, uhh, not pretty...

The mantra for all techie-types should be, "User-Friendly
Interface Is the Only Criterion--Always.":) After the numbers
are crunched, write the V-L paradigms in conventional notation
(you can do each example in a different key if you prefer:)
and state underneath them the counts and frequency percentages.
It's clean, simple, and won't frighten the neighbors' horses.

If I have misunderstood Dmitri's prefatory statement about
using this idea of normal form for pedagogical purposes, I
offer my most sincere apologies in advance and respectfully
request a clarification.

Art Samplaski
Ithaca, NY

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