[Smt-talk] Mozart harmonic progression

[Charles J. Smith]

Eric,

Here are those examples I promised you a few days ago.

It's been a useful exercise to go back through these, and I think I learned something from the process. There are lots of ways to categorize and manage augmented-6th chords—by the mode of the passage in which they appear, by the function and bass of the harmony from which their approach begins, and so on. At some point, however, such a taxonomy will likely yield a category containing a number of A6s in minor whose immediately preceding bass scale-step is a (major-mode-related) ^6, moving to the b^6 under the A6. Within this category, there seem to be two basic voice-leadings: those in  which the harmony over the ^6 contains a 6th, and those in which it contains a 7th. Put another way, those in which the #^4 of the A6 is approached from below (diatonic 6th) and those in which it is approached from above (diatonic 7th). Now, of course, from a larger perspective, the "chordal" status of these things can be seriously questioned; both the 6-+6 and 7-+6 voice-leadings are part of larger unfoldings of more significant harmonies. But whether you think of these local things as chords or as voice-leading configurations, there is a real difference to be observed here.

When the A6 is approached by 6-+6 voice-leading, the 6/3 sonority is often treated as a chord to be tonicized, and thus is often preceded by a 1-b7 (or even 1-7-b7) bass.

When the A6 is approached by 7-+6 voice-leading, tonicization isn't an issue; the 7th (^5) is usually sustained from a preceding Tonic—which is why a passing v6 (over a b^7 bass) is so natural a way of plugging the 1-b^6 bass gap). BTW the same passing approach through a v6 often happens with a 7-+6 figure embellishing an A6 over an unmoving bass—a situation where it's even harder (but not impossible) to hear the 7th as giving rise to a separate harmony.

The real question is how (or whether) to use a fourth sounding scale-step over the ^6; if is often omitted, but usually the implication is clearly still that of a half-diminished sonority (again, whether or not you choose to regard it as a "real chord"). Examples with this implicit hd7 onover ^6:

Beethoven, Cello Sonata in F (Op. 5/1), Mvt.III (or II, depending on how you're counting), mm. 65–66, in F minor, approached from Tonic over ^1, via the passing v6 (lots of b^3s around in surrounding stuff).

Beethoven, Coriolan Overture in C minor (Op. 62), mm. 19–20 (the 7th is very brief, hardly counting as anything more than a suspension from the preceding v6, but it does display the same 7-+6 configuration)


When there is an explicit 5th above the ^6, under the 7th, it always seems to be b^3. At least I don't have any examples where a major-mode-related ^3 is used. (If moving to a b^3-containing A6, a ^3 creates a kind of precursor to "Mozart" 5ths, which are presumably less desirable than those often-forbidden but all-too-common parallels...) Examples after Mozart with both the 7th (^5) and 5th (b^3) over ^6:

Schubert, Mass in Eb (D. 950), Credo, mm. 349–351 [the A6th doesn't contain a b^3, but instead the tenor passes from the preceding b^3 through ^2 and ^1 to the leading-tone of the Dominant)]—this passage is quoted as Ex. 478 in the 1901 ed. of Prout's 1889 Harmony book and it seems to make him nervous, as he cites some secondary functions in G minor, sparking off of the passing v6...

Bruch, Violin Concerto #1 in G minor (Op. 26), Mvt. I, leading up to rehearsal letter E [top of page 10 of the Joachim violin/piano score, published by Siegel, that is available on Petrucci]—no passing v6, however; the passing bass b7 appears under the sustained pitches of the G minor Tonic. This passage reinforces our sense that the chord over ^6 is a suspension sonority by explicitly suspending the 7th further, into the A6 chord itself.


So it turns out that none of these passages is exactly like the Mozart progression that you requested—the one that Mozart seems to have used dozens of times. But they exhibit voice-leading and harmonic sensibilities that are remarkably close to and no doubt related to Mozart's.


It is also interesting that the ^6-b^6 bass leading to an A6 is even more common in major than it is in minor, but I haven't found any examples of the 7-+6 voice-leading over those bass-scale-steps in major. My first thought was that this could have resulted from an avoidance of the precursor-Mozart-5ths parallels mentioned above, so the ^6 never has a ^3 over it, only a 6th (^4). But that's not true. There are several examples of what seems to be a minor triad on ^6 immediately preceding an A6 in major, though until the mid-19th century they all downplay the ^3. (eg Beethoven Op. 109, Variation Theme, m. 7, or even more outrageously, Haydn, Symphony #101, Mvt. IV, m. 19). By Chopin, a root-position minor submediant triad seems to have become a reasonable approach to an A6 in major (eg Ballade #3, mm. 99–101—admittedly with a substantial phrase break between).

So why isn't the 7-+6 voice-leading over ^6-to-b^6 used in major? I have no idea...

(An apparent counter-example appears in Beethoven, Sonata in Eb (Op. 7), Mvt. II, mm. 77–78, where a 7-6 suspection does appear over a ^6-b^6 bass in major, but the 6th is a diatonic 6th, ^4—an embellishment of the 6-+6 voice-leading which is very common indeed in major...)


Sorry to have gone on at such length, in such excruciating detail. Offered in the spirit of trying to be helpful.

CS




> I did sort of include K. 550 in the same phenomenon in my mind -- you're right!
> 
> Fascinating observation, by the way!  I hadn't thought of that equivalence with Tristan, but it makes sense as a pre-cursor, especially if we eventually accept Ger+6/^1 as a dominant substitute (pre-cursor to the "tritone sub").  Interestingly, I know of an instructor just up I-75 from me at Miami University of Ohio who teaches the Tristan chord as a pre-dominant chord because it's a "tritone sub for a iiø7".  I can't say I agree with that analysis, but I see how he gets there, and that seems tangentially related to your observation... although his version puts the cart before the horse.  
> 
> If only Mozart had used that augmented sixth chord as a dominant to the Neapolitan at some point -- we would have had the Tristan chord in toto, long before Wagner!  Ah, well.  :-)
> 
> Thanks for the reply!
> 
> Eric
> 
> 
> On Mon, Apr 22, 2013 at 5:03 PM, Charles J. Smith <cjsmith at buffalo.edu> wrote:
> Eric et al,
> 
> As a minor point of interest, this is the type of progression that I cited, oh, thousands of years ago now, in "Functional Extravagance" (MTS 1986), as one possible conceptual origin of the Tristan chord progression—in that the third and fourth chords in your formulation have some kind of equivalence with the first two "chords" in the Tristan Vorspiel (assuming the G# as chord-tone, of course).
> 
> Whether or not you find that claimed equivalence persuasive, there are lots of examples that I collected over the years, and you're right—a remarkable number of them are by Mozart. But not all.
> 
> My notebooks of examples are at school, and I'm home, so I can't give you the details at the moment, but will be able to tomorrow. (This situation is one reason that we've started the process of digitizing all these collected examples and storing them in the cloud, where at some point they might even be searchable...a process that will probably take at least another thousand years or so...I certainly don't expect to live to see the end of it.)
> 
> One preliminary question: how wedded are you to the v6 as being exactly the second chord in the succession? If memory serves me well, Mozart has a variety of ways of getting to the half-diminished-7th chord, some over a passing bass, some not. ("Functional Extravagance" quotes a well-known passage from the first movement of Mozart K. 550, which leaps thither directly from a Tonic over b3.) But he did seem inordinately fond of the double Dominant Preparation, first a modally-mixed chord (bass 6 from major, upper voice b3 from minor), followed by an augmented 6th as the bass passes down through b6 to 5. This chord-succession is strange and distinctive enough, no matter how it is approached, that you could justify thinking of it as the essential component, with a variety of approaches being the window-dressing. Whether Mozart invented the progression, I can't say—but whether or not he was the first, others (not least of whom might even be Wagner) then got a lot of further mileage from it.
> 
> Cheers,
> Charles
> 
> PS One further point to complement the FE observation is the number of times that this Tristan-chord progression appears later in the opera, even in the Vorspiel itself, shoehorned back into a context where both chords are DPs, first over 6, then b6—i.e. followed by a clear Dominant over 5. (See Vorspiel mm. 89–90 in D, and then most tellingly mm. 99–100, in C!) All of these might well serve as "incomplete" examples of the progression you seek, without the Tonic or the passing chord...
> 
> 
> 
> 
>> Colleagues,
>> 
>> Point of curiosity -- those of you with corpus studies of Mozart at hand may have a ready answer to this.
>> 
>> There is a certain harmonic progression that seems to pop up in Mozart's music in minor keys, and I have yet to find an example of this exact progression in any other composer.  Arguments of counterpoint vs. harmony aside, here is the basic idea:
>> 
>> i - v6 - #viø7 - +6 - V (or cadential 6/4)
>> 
>> So, in d minor, for instance:
>> 
>> Dm - Am/C - Bø7 - It+6 - A
>> 
>> While I know that chromatic and diatonic descents to the dominant are commonplace and have a rich history, it is this precise sequence of harmonies that I haven't found in any other composer with nearly the frequency that I've seen it in Mozart.  Does anyone have examples of this from another composer?  Is it more common in Mozart than his contemporaries?
>> 
>> 
>> -- 
>> Eric Knechtges, DM
>> Assistant Professor, Coordinator of Composition/Theory
>> Northern Kentucky University
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> 
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> Prof. Charles J. Smith
> Slee Chair of Music Theory & Director of Graduate Studies
> Director, Slee Institute of Tonal Harmony (420 Baird Hall)
> Academic office: 410 Baird Hall
> Office Phone: 716-645-0639
> cjsmith at buffalo.edu
> 
> Mailing address;
> Music Department, 220 Baird Hall
> University at Buffalo
> Buffalo, NY 14260
> Department Fax: 716-645-3824
> 
> 
> 
> 
> 
> 
> 
> 
> -- 
> Eric Knechtges, DM
> Assistant Professor, Coordinator of Composition/Theory
> Northern Kentucky University



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Prof. Charles J. Smith
Slee Chair of Music Theory & Director of Graduate Studies
Office: 410 Baird Hall
Director, Slee Institute for Tonal Harmony (420 Baird)

Mail address:
Music Department, 220 Baird Hall, University at Buffalo
Buffalo, NY 14260

cjsmith at buffalo.edu
Office Phone: 716-645-0639
Department Fax: 716-645-3824





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