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Hello all,<br>
<br>
I am enjoying reading this thread, and like others, hope that Prof.
Proctor continues to participate -- I too have benefited from his
insights. <br>
<br>
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. <br>
<br>
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.<br>
<br>
Best,<br>
John Cuciurean<br>
Assoc Prof of Music Theory<br>
Western University<br>
London, ON, Canada<br>
<br>
<br>
<br>
<br>
<div class="moz-cite-prefix">On 24/04/2013 1:46 PM, Charles J. Smith
wrote:<br>
</div>
<blockquote
cite="mid:AC7ABD07-52E3-4EE9-8940-993644D58CBC@buffalo.edu"
type="cite">Eric,
<div><br>
</div>
<div>Here are those examples I promised you a few days ago.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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:</div>
<div><br>
</div>
<div>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).</div>
<div><br>
</div>
<div>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)</div>
<div><br>
</div>
<div><br>
</div>
<div>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:</div>
<div><br>
</div>
<div>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...</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div><br>
</div>
<div>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).</div>
<div><br>
</div>
<div>So why isn't the 7-+6 voice-leading over ^6-to-b^6 used in
major? I have no idea...</div>
<div><br>
</div>
<div>(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...)</div>
<div><br>
</div>
<div><br>
</div>
<div>Sorry to have gone on at such length, in such excruciating
detail. Offered in the spirit of trying to be helpful.</div>
<div><br>
</div>
<div>CS</div>
<div><br>
<div>
<div><br>
</div>
<div><br>
</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<div dir="ltr">
<div>I did sort of include K. 550 in the same phenomenon
in my mind -- you're right!<br>
</div>
<div><br>
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. <br>
<br>
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. :-)<br>
<br>
</div>
<div>Thanks for the reply!<br>
<br>
Eric<br>
</div>
</div>
<div class="gmail_extra"><br>
<br>
<div class="gmail_quote">On Mon, Apr 22, 2013 at 5:03 PM,
Charles J. Smith <span dir="ltr"><<a
moz-do-not-send="true"
href="mailto:cjsmith@buffalo.edu" target="_blank">cjsmith@buffalo.edu</a>></span>
wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0
.8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="word-wrap:break-word">Eric et al,
<div><br>
</div>
<div>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).</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.)</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>Cheers,</div>
<div>Charles</div>
<div><br>
</div>
<div>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...</div>
<div><br>
<div>
<div><br>
</div>
<div><br>
</div>
<br>
<blockquote type="cite">
<div>
<div class="h5">
<div dir="ltr">
<div>
<div>
<div>
<div>
<div>
<div>Colleagues,<br>
<br>
</div>
Point of curiosity -- those of
you with corpus studies of
Mozart at hand may have a
ready answer to this.<br>
<br>
</div>
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:<br>
<br>
</div>
i - v6 - #viø7 - +6 - V (or
cadential 6/4)<br>
<br>
</div>
So, in d minor, for instance:<br>
<br>
</div>
Dm - Am/C - Bø7 - It+6 - A<br>
<br>
</div>
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?<br>
<br>
<br>
<div>
<div>
<div>
<div>-- <br>
<div>
<div>
<div>
<div>Eric Knechtges, DM<br>
Assistant Professor,
Coordinator of
Composition/Theory<br>
Northern Kentucky
University </div>
</div>
</div>
</div>
</div>
</div>
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<div style="font-size:12px">Prof.
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