[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.
Best,
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
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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 <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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