[Smt-talk] Passing and Neighboring 6/4s

[Dmitri Tymoczko]

On Feb 1, 2010, at 12:20 PM, SKostka at aol.com wrote:

> Sorry to be so late to respond to this, but I was traveling with no  
> access to our book. It is not true that Dorothy Payne and I say (or  
> even imply) that vi->V and vi->viio are "unacceptable." In fact, on  
> p. 117 (6th edition) you'll find that "...the diagrams represent  
> norms of harmonic practice observed by theorists over the years in  
> the works of a large number of tonal composers. They do not  
> represent rules; they are just guidelines for your use..."

Sorry, I should've used the word "abnormal" rather than  
"unacceptable."  The issue here is whether the norms described in the  
K&P text correspond to the norms found in actual music.  For instance,  
in the Mozart sonatas, V is the second-most common destination for vi,  
after ii.  In other words, vi goes to V *more often* than it goes to  
IV.  Here we find a discrepancy between the musical norm and the K & P  
norm.  It's precisely the sort of conflict that one often finds in  
grammar books based on intuition rather than actual counting.

The Kostka/Payne "harmonic map" derives (like a few other things in  
that book) from McHose's unjustly forgotten text, "The Contrapuntal  
Harmonic Technique of the 18th Century," which attempts to list the  
statistically most common destinations for each chord.  I've also been  
very influenced by McHose, to the point where I sometimes describe  
myself as doing "neo-McHosian theory."  However, I suspect that Kostka/ 
Payne go a bit wrong by generalizing McHose's statistical findings  
from Bach to tonal harmony more generally.

I also think that the K&P "map of harmonies" somewhat mischaracterizes  
the importance of descending-fifths progressions.  In my recent  
(virtual) SMT presentation, and in my forthcoming book ("A Geometry of  
Music," OUP, appearing in September or so), I suggest that one can get  
a better model of tonal progressions by utilizing the descending  
circle of thirds, rather than the circle of fifths.

I -> vi -> IV -> ii -> viio -> V

The norm is that any chord can move rightward by any amount; however,  
chords can move leftward only by following a small number of specific  
paths (V->I, V->vi, viio->I, IV->I, and vi->I6).

[Technical note: sometimes I teach that viio shouldn't go to V, but  
sometimes I allow it; in the music I've looked at, viio is much more  
likely to go to V than is V to go to vii.]

There's a diagram here:

http://music.princeton.edu/~dmitri/SMT2009.pdf

I've found that this diagram is very easy to teach to students, and  
gives a much better fit to the progressions actually found in tonal  
harmony.  It also elucidates some nice features of the style, such as  
the connection between "harmonic tonality" and "sequential tonality,"  
as well as the fact that different chords have a different tendency to  
move by "strong" progressions (descending fifth, third, or ascending  
step).  (That is, the closer a chord is to the right side of the map,  
the more likely it is to move "strongly," as discussed in "Root  
Motion, Function, Scale Degree.")  This structure also intersects  
nicely with recent work on voice leading, as it arranges diatonic  
triads according to voice leading distance.

For these reasons, I would argue that the descending-thirds map is  
more principled, more accurate, and somewhat simpler than the K&P  
alternative.

BTW, I generally like K&P -- when I use a text, I typically use it  
rather than Aldwell/Schachter.

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