[Smt-talk] Mozart harmonic progression

John Cuciurean jcuciure at uwo.ca
Wed Apr 24 12:36:09 PDT 2013

Hello all,

I am enjoying reading this thread, and like others, hope that Prof. 
Proctor continues to participate -- I too have benefited from his insights.

In light of Charles Smith's latest offering, see also Beethoven's 
Variations in C minor WoO 80, with a 6th above ^6 the bass leading to 
Ger+6 over b^6 in the bass -- in this case a IV6 chord is used to 
harmonize ^6 in the bass, which is indeed preceded by a harmony that 
tonicizes IV with b^7 in the bass.

On a related note, see Purcell's "Dido's Lament" which I suspect has 
been left off this thread due to the admitted absence of an Aug 6th 
chord over b^6. That not withstanding, the voice-leading or harmonic 
approach (pick your preference) from tonic to the harmony over b^6 (iv6 
in Purcell's case) is treated in 6 (at least) different ways throughout 
the piece that resonate closely with what Charles Smith has described 
below (including voice-leading configurations that employ both a 6th 
above ^6 in the bass as well as a 7th above ^6 in the bass, as 
combinations of the two that employ a 7-6 susp over 6^ in the bass). I 
will refrain from providing further commentary at this time but simply 
offer this example as further fodder for this thread.  I will let others 
determine whether they accept iv6 as a diatonic variant of what might 
otherwise be an It+6 in Mozart's and Beethoven's settings of this 
specific bass line.

John Cuciurean
Assoc Prof of Music Theory
Western University
London, ON, Canada

On 24/04/2013 1:46 PM, Charles J. Smith wrote:
> 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 <mailto: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
>>>     _______________________________________________
>>>     Smt-talk mailing list
>>>     Smt-talk at lists.societymusictheory.org
>>>     <mailto:Smt-talk at lists.societymusictheory.org>
>>>     http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org
>>     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>>     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 <tel:716-645-0639>
>>     cjsmith at buffalo.edu <mailto:cjsmith at buffalo.edu>
>>     Mailing address;
>>     Music Department, 220 Baird Hall
>>     University at Buffalo
>>     Buffalo, NY 14260
>>     Department Fax: 716-645-3824 <tel: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 <mailto:cjsmith at buffalo.edu>
> Office Phone: 716-645-0639
> Department Fax: 716-645-3824
> _______________________________________________
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