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<br><div><div>Eytan Agmon wrote:</div><blockquote type="cite"><p dir="LTR"><span lang="en-us"><font face="Calibri">Like Olli and others</font></span><span lang="en-us"> <font face="Calibri">I was also puzzled by his remark. Although of course I cannot speak on his behalf, it seems to me that he merely overstated a</font></span><span lang="en-us"><font face="Calibri">n</font></span><span lang="en-us"><font face="Calibri"> obvious point for anyone</font></span><span lang="en-us"> <font face="Calibri">who</font></span><span lang="en-us"><font face="Calibri"> believes in the existence of harmonic functions</font></span><span lang="en-us"><font face="Calibri">:</font></span><span lang="en-us"><font face="Calibri"> rarely, if at all,</font></span><span lang="en-us"><font face="Calibri"> can the</font></span><span lang="en-us"> <font face="Calibri">inversion</font></span><span lang="en-us"> <font face="Calibri">of a chord</font></span><span lang="en-us"> <font face="Calibri">change</font></span><span lang="en-us"><font face="Calibri"></font></span><span lang="en-us"><i> <font face="Calibri">its function</font></i></span><span lang="en-us"><font face="Calibri"> (the cadential six-four chord</font></span><span lang="en-us"><font face="Calibri"> 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.</font></span></p><p dir="LTR"><span lang="en-us"><font face="Calibri">This is</font></span><span lang="en-us"><font face="Calibri"> of course not to say that chords</font></span><span lang="en-us"> <font face="Calibri">always</font></span><span lang="en-us"><i> <font face="Calibri">have</font></i></span><span lang="en-us"><font face="Calibri"> a</font></span><span lang="en-us"><font face="Calibri"> function.</font></span><span lang="en-us"> <font face="Calibri">In s</font></span><span lang="en-us"><font face="Calibri">ome</font></span><span lang="en-us"> <font face="Calibri">contexts and</font></span><span lang="en-us"> <font face="Calibri">usually, but not always, in inversion</font></span><span lang="en-us"><font face="Calibri">,</font></span><span lang="en-us"><font face="Calibri"> chords</font></span><span lang="en-us"><font face="Calibri"></font></span><span lang="en-us"> <font face="Calibri">are obviously "passing," and so forth.</font></span></p><div><span lang="en-us"></span></div></blockquote></div>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.<div><br></div><div>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.</div><div><br></div><div>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.</div><div><br></div><div>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.</div><div><br></div><div>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.</div><div><br></div><div>Olli Väisälä</div><div>Sibelius Academy</div><div>University of the Arts, Helsinki</div><div><a href="mailto:ovaisala@siba.fi">ovaisala@siba.fi</a></div><div><br></div><div><br></div><div><br></div></body></html>