[Smt-talk] Chord Inversion

Ildar Khannanov solfeggio7 at yahoo.com
Tue Apr 23 19:15:04 PDT 2013

Dear Olli,
this discussion is fascinating! Thank you for bringing this up. It makes previous deliberations clearer and more useful.
I agree with you that TSDT is most effective in the expositional segments, where it delineates the key. I have been thinking for a long time about how this syntactic cycle (the circle, the grip, in fact) can work in the context of modulation (large scale modulation, what German theorists called grosse Modulation). The TSDT has cognitive foundation: it is based on our instinct of grabbing and not letting go of the tonal center. This is happening against our will: once I have captured the key, I cannot let it go. When in this circle, I do not want to get out of it. So, Bach does some interesting maneuvers with this cycle, I think. Well, I better write a small article on this topic.
As for the unfortunate exchange with Dr. Proctor, I think I understand what he means. It was Leo Bussler who said that chromatically altered chords act the same way as unaltered, but the further we go into late-Romantic harmony, more we notice that some transformations (alterations along with inversions) freeze. My teacher Yuri Kholopov called this effect disalteration. So, the Gr+6, for example, receives the root on scst lowered 6 in major. We know, that it is not its actual root, but in real music making of the late 19th century it becomes insignificant.
Ildar Khannanov
Peabody Conservatory
Solfeggio7 at yahoo.com

--- On Tue, 4/23/13, Olli Väisälä <ovaisala at siba.fi> wrote:

From: Olli Väisälä <ovaisala at siba.fi>
Subject: Re: [Smt-talk] Chord Inversion
To: "Eytan Agmon" <agmonz at 012.net.il>, "smt-talk smt" <smt-talk at societymusictheory.org>
Date: Tuesday, April 23, 2013, 7:51 AM

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 optional.

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 contexts.

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

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