Re: Analyzing this Progression

On Thu, 07 Feb 2008 21:57:45 GMT, "Steve Latham" <llatham@xxxxxxxxxxx>
wrote:

<snip>

It appears from your notation that the chord in question, from the bottom up
is, G B D G F B and it resolves to F# F# B D. That looks to me like a German
Augmented 6th resolving to i6/4. The F is enharmonic for the E#, which is G
B D E#. This is a stock Ger+6 to i6/4-V7 combo.

You are correct -- it's an aug 6 not a minor 7th. I missed the
spelling.

<snip>

Since you seem unable to distinguish between Non chord tones and chord
tones, conversation is fruitless. Analyze it as an F7 is you prefer.

I pointed to two interpretations of the sequence, one which sees the
Eb as a chromatic passing note (i.e. a NCT) and the other which sees
the sonority as a chord in it's own right. My point was that alternate
views are possible.

<snip>

You are inserting your own words here. I didn't say it couldn't be fixed to
make it more like traditional CPP harmony. It can be changed in many ways to
bring it more in line with things one might find commonly, or exceptionally
in CPP music.

Not changed, simply voiced appropriately. I take it then you agree
that it is possible to voice the OPs progression in a manner similar
to the Brahms. That being the case, the OP, who has long disappeared,
can rest assured that it was possible to interpret that portion of the
progression as valid, if infrequent, CPP behavior.

There is a fundamental difference between "always" and "mostly".
You're consistently arguing that these other behaviors of the the
seventh are exceptions to some rule, rather than equally valid
behaviors, even if you protest that you're not doing that.

Ok. IN GENERAL, 7ths of 7th chords resolve downward. There are exceptions.
By the way, IN GENERAL, 7th chords contain a Root, Third, Fifth, and
Seventh. There are exceptions. It is assumed in discussions of this nature,
that every time we say a 7th chord contains 4 notes, that there are cases
(abundant in fact) where only 3 notes may be present. We don't need to do
that. Especially for posts that don't seem to need that kind of detail. I
tell you what, you feel free next time I make the comment "7ths of 7th
chords resolve downward by step" - and even if I say ALWAYS, to interject
and say "but there are exceptional cases", and then if the poster is
interested in those exceptional cases, you can expand upon it for them.

Calm down Ringo.

<snip>

and often
"resolve" in a different register.

That's a transeferred resolution. One of the exceptions mentioned above.

So, that is an *exception*? In any case, this behavior occurs quite
frequently. Just because you agree with me doesn't make me wrong.

No, it's not an exception. The 7th still resolves down in a transferred
resolution, it simply resolves in a different part. That still applies to
the fundamental statment, 7ths in 7th chords resolve down (and if you like
to add, they may do so later than immediately, in different parts, etc, feel
free).

Steve, it was you who wrote:

That's a transeferred resolution. One of the exceptions mentioned
above.

And now you write:

>No, it's not an exception.

So, make up your mind if a transferred resolution is an exception or
not. Or perhaps an exceptional exception. In any case, I was in no
doubt that resolution took place. That's why it's called a
"resolution".

<snip>

In David Bernstein's article on "Nineteenth-century Harmonic Theory"
in the CAMBRIDGE HISTORYU OF WESTERN MUSIC THEORY, p802, he describes
a schism between (traditional) chordal approach and the voice-leading
approach with Rameau, Riemann and Schoenberg on one side and Schenker
on the other.

[Schenker] criticized theorists for overemphasizing vertical
structure rather than voice-leading.

You seem to be implying that I'm advocating a horizontal approach. I'm
simply advocating that the approach should be the one that is most
informative, or, the most informative given the situation. Bach's 1st
Prelude from WTC can be discussed both in horizontal and vertical manners,
and neither is any less informative (though both would be more informative
overall). However, discussing the verticality in many fugues might be rather
misleading. And the problem here Ian is that we have an entire group of
people (pop musicians) who are coming at theory from a chordal perspective,
and don't even understand what horizontal approaches can illuminate.

I'm simply advocating multiple approaches rather a single approach.
There's no need to choose a single approach and good reasons not to.

But my remark wasn't meant to be personal at all. I was stepping back
and looking at the general context of the underlying dispute, one
which I see in other threads in this place.

With that context in mind I sketched out a set of definitions to cover
some of the data I've seen in the past few days, taking a fresh
approach, but which you rejected in your point-wise responses, of
which I reply to just one, to whit:

<snip>

(4) It may be respelled as an augmented sixth an resolve upwards
a semitone.

Then again Ian, it is not a 7th. It's an +6.

The sonority can be either, depending on the environment. In some
cases it's necessary to respell a 7th as an augmented 6th. That's
precisely what happened when you corrected the Haydn example I cited.
Here's a similar Hadyn example where I think the note starts out as a
minor 7th and then converts to an aug 6th, as follows.

The D minor second movement of my favorite Haydn piano trio, Hob.XV:24
lands on a 6/4 C, no third at bar 13. The piano plays a repeated 6/3 C
major chord in the right hand. The violin adds an alternating <A Bb>
figure. In bar 14 the piano and cello adds a Bb bass to the still
repeating chords and the fiddle runs down the scale <Bb A G F E D C >
and then back up, <D E F# G F#>. All of them land on an 6/4 E minor in
the next bar which proceeds to B7 and root position E minor.

This is basically the same as the other Hadyn example, except that I
think, particularly looking at the violin part, that the chord starts
out in bar 13 as C7, and that the 7th, Bb, only becomes an augmented
sixth, A#, towards the end of bar 14.

<snip>

But submit it to MTO or JSTOR or something, and see what they say. You might
be on to something.

Who needs 'em when we're already happy campers right here in downtown
rec.music.theory!

This morning I was thinking about the various cases I'd come across in
the past few days and arrived at a simple model which handles all the
data easily.

To avoid some baggage I'm calling the vertical sonorities "entities".
Entities look like chords, but they are not necessarily chords and are
not subject to traditional constraints placed on chords. We observe
what entities do without much interpretation.

Entities sit in a kind of limbo, existing just before a decision takes
place as to whether they're bona fide *chords* or just passing
constellations or whatever. Nevertheless, entities have well-defined
behaviors, and that's the subject at hand.

The observations below apply only to the examples I've presented, each
of which has been restricted to reasonably independent and reasonably
populated entities.

In the table below:

Categories are *representative* of the behaviors I've encountered.

Upper and lower members are two notes belonging to an *entity*.
All motion is step-wise. In this table all 7ths are minor 7ths.

The interval is the interval between the members. The penultimate
line labels the columns as consonant or dissonant. The last line
attaches a case number to each case.

Frequent Less frequent Rare Aug. Sixth Category
<C B > <C B > <C C > <C C > <C D> <C C#> <B#C#> Upper member
<D D > <D E > <D C > <D E > <D D> <D C#> <D C#> Lower member
7 6 7 5 7 8 7 6 7 8 7 8 aka 6+ 8 Interval
D C D C D C D C D C D C D C Cons./Diss.
#1 #2 #3 #4 #5 #6 #7 Case #

In each case motion is from a dissonance to a consonance.

In the *frequent category* the upper member falls. The lower member
remains static or may rise.

In the *less frequent* category the upper member remains static and
the lower member rises or falls. The upper member is usually
*prepared*, a constraint that once applied more generally to to the
*frequent category*. The static upper member may appear, or even act,
as a pedal (as sometimes applies to the lower member in the *frequent*
category).

The *rare* category consists of a single case. Pattern-wise it belongs
with the (case) #1, the first *frequent* case where the lower member
remains static. As a pair, #1 and #5 match #3 and #4.

In the *aug. sixth* category the minor seventh interval is spelled as
an augmented sixth (although often notated as a minor seventh).

There are further constraints regarding the remaining notes which are
added to complete the actual entities, but these are well-known and
need not be repeated here.

What's the point of this table? It maps the standard examples and my
counter-examples to a single model whose permutations are pretty much
exhausted by the examples. It shows the relationships that connect all
the examples and orthogonalises their behaviors.

With this model in place I can now look at more difficult examples
where entities are less densely populated. For example, here's a
Mozart case, just a few bars before my previous Mozart example
(K314c(333) 1st Mvt b19) which shows the characteristic behavior of
case #3 (within an pedal context).

<Bb Bb G Bb A G F |E >
< C C C C | >
<G E F D |C >
Dm7->C

Finally, here are representative cases that I *haven't seen* (although
there's the Schumann [C7 B7 C7 B7] to consider). The table is arranged
as above except that some 7ths are major 7ths.

Not Seen Category
<C B > <C D > <C D > <C Bb> Upper member
<D C > <D E > <D C > <D E > Lower member
7 7 7 7 7 9 7 5- Interval
D D D D D D D D Consonant/Dissonant
#8 #9 #10 #11 Case #

In each case the motion is from dissonance to dissonance. I haven't
really been on the lookout for case #11.

.

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