[Smt-talk] Addendum on Bach

Dmitri Tymoczko dmitri at Princeton.EDU
Sat Jan 23 12:56:55 PST 2010

Very interesting points from Hali Fieldman, which prompt me to give my  
"What is Traditional Harmonic Theory?" speech again.  Apologies to  
anyone who has heard or read it already.

> I've not been following this thread in minute detail, and perhaps  
> that accounts for my being a bit surprised at the way it has  
> developed.  The surprise is that it appears that all/every  
> succession of a chord to the next is being considered to be a  
> progression of chords as such.  There are very few patterns of  
> chords that feel like "progressions" to me, that possess in my ear  
> that kind of clearly-directed energy.

The key point is that if you consider basically all and every chord to  
be a real chord, you find very clear structure: the chords progress in  
extremely regular ways.  For instance, root position V rarely goes to  
root position IV, and there are almost no ascending-thirds root  
progressions (in any inversion).  This is the central observation of  
traditional harmonic theory, dating back to Rameau if not before, and  
it has held up very well -- indeed, it is as well-confirmed a theory  
as we have in our discipline.

This theory, as I interpret it, is a theory about the structure of  
music.  It is not a theory about our psychological responses.  It  
says: in the key of C major, the notes G-B-D progress in such and such  
ways, but not in others.  (Insofar as there is psychology involved it  
is mainly the psychology of the composer: there is something in the  
composer's brain that accounts for the structure we see in the  
music.)  Whether you hear the G-B-D as a "real" chord, or even as a  
dominant, is an interesting question, but it does not fall within the  
purview of traditional harmonic theory, understood in the way I  
understand it -- that is, as a kind of "grammar" that describes the  
structure of tonal music.

Now obviously, in some repertoires, not every apparent chord is a  
chord -- for instance, I mentioned the case of weak-eighth chords in  
the Bach chorales.  Some of these weak-eighth chords are definitely  
harmonic, but others aren't.  This is a rather subtle matter.   
Nevertheless, to a good first approximation, chords lasting longer  
than a certain minimum value can mostly be considered "real  
harmonies."  If one does this, one finds a wealth of structure that  
would be very hard to explain, were we to say that these apparent  
chords were "unreal" by virtue of (for instance) being simple  
agglomerations of passing tones.

>  Instead, it seems like much of the wealth of the tonal language is  
> invested in managing the pace of directed motion, so that it can  
> slacken or tighten in countless nuanced ways without being heard to  
> resolve a particular tension, and without losing track of its path  
> even when directedness is at low ebb.  Some wise heads see melodic  
> motion in the bass, as differentiated from harmonic motion, as  
> responsible for a significant part of that role (I'm not naming  
> Schenker because it isn't clear to me that his project was aimed at  
> sorting out tonal music's many kinds of energy/tension).

I agree.  The richness of tonal music cannot be explained by harmonic  
grammar alone.  But neither does linguistics does not explain the  
beauty of a particular Shakespeare sonnet.

Again, it is very important to separate out the myriad projects that  
go under the rubric of "music theory."  Traditional harmonic theory,  
as I understand it, is something like the grammar of chords.  It bears  
only indirectly on analysis (analogous to literary criticism) or music  

>  When the bass is melodic, it is highly likely to be part of  
> vertical consonance(s); those verticalities might look like chords,  
> and we may be able to give them Roman-numeral names, but whether or  
> not they *function* as chords -- as carrying the **harmonic**  
> responsibilities of the scale-degrees upon which they are built --  
> is, I think, something different altogether.

In 95-98% of the cases, the apparent chords progress as predicted by  
traditional harmonic theory.  In this sense, they do indeed function  
as chords.

There are other meanings for the term "function" -- including  
psychological ones.  But it is not clear that the musical grammarian  
needs to take these into account.  In language, the theory of syntax  
is largely independent of the theory of stress, or of pragmatics, etc.

If you're at all interested in these issues, there is a discussion of  
the difference between "psychological function" and "syntactic  
function" in my article "Root Motion, Function, Scale Degree."


Dmitri Tymoczko
Associate Professor of Music
310 Woolworth Center
Princeton, NJ 08544-1007
(609) 258-4255 (ph), (609) 258-6793 (fax)

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