[Smt-talk] Chord Inversion

Olli Väisälä ovaisala at siba.fi
Tue Apr 23 05:51:13 PDT 2013

Eytan Agmon wrote:
> Like Olli and others I was also puzzled by his remark. Although of  
> course I cannot speak on his behalf, it seems to me that he merely  
> overstated an obvious point for anyone who believes in the  
> existence of harmonic functions: rarely, if at all, can the  
> inversion of a chord change its function (the cadential six-four  
> chord is a conceivable exception, but perhaps only apparently so).  
> For example, in the Bach prelude that Olli cites the opening  
> "contrapuntal" progression expresses T-S-D-T much in the same way  
> that does that I-IV-V-I progression that governs the piece's large- 
> scale harmonic structure.
> This is of course not to say that chords always have a function. In  
> some contexts and usually, but not always, in inversion, chords are  
> obviously "passing," and so forth.
If we go a bit further in this example, it can be used to illustrate  
one rational approach to the question raised in recent postings: the  
relative significance of functions (in the TSD sense), on the one  
hand, and (figured) bass lines, on the other.

If we compare comparable preludes in WTC I (and elsewhere), we can  
see that the typical opening is built on the TSDT pattern Eytan  
mentions. Sometimes the TSDT chords occur in root position as in the  
D-major Prelude (I–II7–V7–I), sometimes as inversions, producing a  
smoother bass line, as in the C-major Prel., often also above a tonic  
pedal. Moreover, the S can be either II or IV and the D either V or  
VII. Hence there is a sense in which the TSDT functions do suffice  
for capturing the generic syntactic essential requirements of such  
openings, whereas the choice of inversions and bass line only  
pertains to the character of each specific case.

However, if we continue our analysis to the subsequent modulatory  
progression, the relative descriptive powers of the two approaches  
change. In terms of TSD functions, the modulatory progression (mm. 5– 
11) would be, I suppose, SDTSDT in G major. However, by no means any  
realization of SDTSDT would pass as a syntactically well-formed  
modulatory progression at this point of the piece. For such  a  
progression, the (mostly) stepwise bass line seems to be essential  
for syntax, as is exemplified by the D-major prelude's bass identical  
bass line.

While the repeated SDT cycle seems thus clearly insufficient for  
describing the modulatory progression in these preludes, one might  
ask whether such functions nonetheless have some syntactic pertinence  
alongside the bass-line requirement. I think they do; especially the  
latter SDT is significant for marking the goal dominant. However,  
consider the E-flat-major Prelude, in which the basic progression in  
mm. 5–8 is, in FB notation, Eb5–6 / D7–6 / C(7?)–6 / Bb, which  
translates to STSDT in the dominant key, demonstrating that the D  
between the first S and T ("II6" and "I6" in the dominant key) is  

These are just a few examples for illustrating a rational empirical  
approach towards examining the relative significance of different  
approaches (functions vs. figured bass) for tonal syntax in variable  

Olli Väisälä
Sibelius Academy
University of the Arts, Helsinki
ovaisala at siba.fi

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