[Smt-talk] Inception chord progression

[Dmitri Tymoczko]

A couple thoughts about the "Inception" progression:

	1) My first thought was that the first three chords are linked by the  
common Bb, while the Eb-B-G are linked by major third voice leading.   
Major third is the unique transposition that minimizes the distance  
between major triads.  So you could say we have an overlapping 4-chord  
repeating structure emphasizing, alternately, common tones and voice  
leading.
	The Tonnetz provides a nice representation of the major and minor  
triads that share a particular common note.  (These can be linked by  
LPR cycles, which are represented nicely on the Tonnetz.)  As readers  
of this list know, I've been trying to emphasize that the Tonnetz does  
not accurately reflect voice leading distances, so we shouldn't  
necessarily look to it when we want to talk about voice leading.  For  
pictures that faithfully do that, you want something like Douthett and  
Steinbach's "Cube Dance," or (even better) the continuous geometrical  
spaces representing all possible chords.

	2) The G-F# alternation in the melody suggests Gb and B as altered  
dominants of G, with Eb a deceptive resolution or tonic substitute.   
As Charles Smith said, Bmaj->Gmin dominant is reasonably common in  
twentieth-century tonal music. Gb->G is not quite as common, but can  
be made to work as a dominant.

	3) It's also worth taking a step backward and asking what kind of  
explanation we're looking for.  Perhaps this progression is supposed  
to be "weird" -- that is, to juxtapose a bunch of chromatic chords  
which don't belong to the same major scale.  From this point of view,  
the expressive force comes from negation -- the way it thwarts  
diatonic expectation -- rather than from some alternative positive  
structure.
	This is a more general issue when thinking about music (like early  
twentieth-century atonality) that thwarts established convention: to  
what extent do we want to emphasize the rule breaking, and to what  
extent to we want to emphasize the presence of alternative laws?

	4) Another interesting issue, which I've never been clear about: in  
invoking the "hyper-hexatonic system," is one committing oneself to  
the claim that these chords all have some sort of harmonic affinity?   
Or that the hexatonic scale plays some kind of motivating force in the  
music?  Is the claim that it is harmonically natural to use chords  
belonging to the same hyper-hexatonic system or that these chords have  
the same musical function?
	My inclination is to say that the hexatonic typically appears as the  
*byproduct* of efficient voice leading: what is really important is  
the efficient voice leading between, say, B and Gmin, and this  
efficient voice leading *just happens* to produce hexatonic subsets.   
(Just as, with dominant seventh chords, it just happens to produce  
octatonic subsets.)  So the scales and the "hyper hexatonic systems"  
are really byproducts, rather than syntactical or motivating elements.
	On the other hand, I do think that the shared Bb is potentially a  
motivating harmonic element in the passage.

I guess I actually think we could have a long discussion about the  
methodology of analyzing chromatic tonality -- there are some deep  
issues here that haven't been discussed that much, and that come up  
even with respect to a simple passage like this.

DT

Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)
http://music.princeton.edu/~dmitri