[Smt-talk] I - II- IV as a progression

[Dmitri Tymoczko]

> 2a. Speaking of Brahms, one thing he does, which I love to  
> experience, is to transform a "D"-function sonority into an "S"  
> version (to "S-ify" it?) -- more to modulate than to accompany a  
> chromatic voice-leading (as in our thread). For example, C-E-G-Bb,  
> which can be heard as f:V7, would be chromatically transformed into  
> C-Eb-Gb-Bb, which can be heard as bb:ii7. While this could  
> illustrate simply Bb: II7-ii7/b5(-V-I), the situation I have in mind  
> clearly expresses the C-E-G-Bb as the result of an f-minor "S-D"  
> progression, so a true "D"-function harmony is heard first. Then it  
> is "demoted" to an "S" version, after which it can move on  
> predictably (at least briefly) to "D-T" in its new key.

This is actually a very old chromatic routine!  See, for example, the  
beginning of the development section of the first movement of Mozart's  
Symphony #40 (starting with G#7) or mm. 64ff of the second movement of  
Beethoven's Op. 54, or any number of places in Chopin (including the E  
minor prelude).  Basically, these progressions use stepwise descending  
voice leading to connect dominant sevenths, minor sevenths, French  
6ths, half-diminished sevenths, and diminished sevenths.  You end up  
with root progressions by descending semitone, descending major third,  
descending fifth, or ascending major second (which are all equal to -1  
mod 12/4, as I mentioned earlier).

These sequences have a beautiful geometrical representation in the  
center of 4-dimensional chromatic space; there's also analogous  
progressions relating three-note chords, seven note scales, diatonic  
chords, etc.

Interestingly, Al Tinney (the house pianist at one of the uptown bars  
where bebop first coalesced) referred to this progression as one of  
the distinctive harmonic innovations of bebop.  Amazing to think that  
the same progression was one of the secret chromatic "tricks" known  
and used by almost all the classical composers ...

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