source file: mills2.txt
Date: Sat, 22 Feb 1997 06:58:01 -0800

Subject: Diatonic Analysis Insufficient

From: Matt Nathan <mattn@ix.netcom.com>

> > [Matt Nathan]
> > " The fact that
> > the third of this chord lies close to the tonic of the key
> > should not be taken to mean that they are both tonics of
> > the key, one being "wandered", any more than the leading
> > tone should be considered a "wandered" tonic, or the major
> > third of the V of ii (near C# in C) should be considered a
> > "wandered" tonic. "
>
> [Gary Morrison]
> Frankly I wouldn't buy that. If the harmony makes clear
> that you're playing a vi chord, then its third is the tonic.
> That's built into the definition of diatonic triads.

Sure, but definitions are not music. I say let the
music make the definitions, not the reverse. Harmony
can "make clear" at least two different chords which
a simple diatonic analysis would be incapable of
distinguishing. This leaves the analyser with a false
dilemna of deciding which one is the correct chord.
Either is correct, depending on the harmonic context.
Here are the quickest progressions which get you to these
two distinct chords while keeping one or more common
tones between successive chords:

1/1 5/4 3/2  (major triad built on 1/1 root)
5/3 1/1 5/4  (minor triad on 5/3 root)

and

1/1 5/4 3/2  (major on 1/1)
3/2 15/8 9/8  (major on 3/2)
9/8 27/20 27/16  (minor on 9/8)
27/16 81/80 81/64  (minor on 27/16)

The first example sends us directly to the relative minor.
The second example leaves us in a place that is distant
from the original key and which sets up some tension to
be unwound on the way home. It's a shame that these two
chords are confounded by a diatonic assumption.

If you decide "there are only 7 notes, so I will only
use 7 notes", then you're going to have to use tuning
systems which purposely incorporate distributed errors
to consolidate (confound by single representation) the
many pitch classes which would normally result from
various (JI) root motions.

> If the harmony is ambiguous enough to confuse a leading
> tone with a tonic, then that would not fall within the
> realm of diatonic harmony.

If a diatonic analysis is crippled enough to confuse 81/80
with 1/1, then it doesn't fall within the realm of usefulness.

The wonderful ability of harmony to carry us into new areas
is hobbled by having to reuse pitches from a previous context.
As any jazz player knows, you "blow over the changes", you
don't just keep playing the same scale.

Matt Nathan

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