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augmented 6th chords ... augmented 3rd chords??

Posted by Dave Horne 
I am well acquainted with the European family of augmented 6th chords.

I play mostly swing music from the 1920's to 1950's and find myself playing the following progression ...

In C major (using standard jazz chord notation):

C/E Ab7/Eb Dm7

The voice leading of that middle chord has an Eb in the bass resolving downward to a D and the G# (Ab enharmonic) resolving upwards to an A. The interval Eb - G# is an augmented 3rd.

Now I realize most would analyze that middle chord as a passing chord (which is actually its purpose), but is this chord related to the augmented 6th chord family?

Thanks, Dave Horne
Re: augmented 6th chords ... augmented 3rd chords??
January 15, 2010 09:49AM
Just so other readers are clear on the progression, I think this is what you mean (I'm duplicating the initial G note in the alto & tenor voices just to keep my table neat).
Voice leading:

S:     C    -    C      -     C
A:     G    ^    Ab     ^     A
T:     G    v    Gb     v     F
B:     E    v    Eb     v     D

Chord: I        bVI7         ii7

Motion:
- = no change
^ = up chromatically
v = down chromatically

It's a good day when I'm forced to re-learn something I'd long since forgotten. Yes, I was reduced to reading Wikipedia to remind myself about augmented-6th chords ;)

All the augmented-6th chord variations act as a predominant, i.e. they give the composer a different way to get to V or V7 without using straight ii, IV, or V/V chords. The final chord in your sequence is itself a predominant in C so the weak connection may be that your passing chord is acting as a predominant to the predominant, if there is such a thing.

I think the connection you're trying to make is weaker than just accepting the Ab7/Eb as a passing chord. And it's a good one, in its genre.
Re: augmented 6th chords ... augmented 3rd chords??
January 15, 2010 12:59PM
Dave Horne Wrote:
-------------------------------------------------------
> I am well acquainted with the European family of
> augmented 6th chords.
>
> I play mostly swing music from the 1920's to
> 1950's and find myself playing the following
> progression ...
>
> In C major (using standard jazz chord notation):
>
> C/E Ab7/Eb Dm7
>
> The voice leading of that middle chord has an Eb
> in the bass resolving downward to a D and the G#
> (Ab enharmonic) resolving upwards to an A. The
> interval Eb - G# is an augmented 3rd.
>
> Now I realize most would analyze that middle chord
> as a passing chord (which is actually its
> purpose), but is this chord related to the
> augmented 6th chord family?
>
> Thanks, Dave Horne

Dave,

Many theorists do not consider +6 "chords" to be chords, but "sonorities" - a subtle, yet important distinction.

Remember that Ab-C-Eb-F# is but one +6 sonority.

This has confused a lot of people, especially in Jazz music where there are sonorities that sound like +6 chord, but do not necessarily function similarly (especially in terms of voice-leading).

What's important about +6 sonorities is the +6 interval - the remaining notes are just "filler" - diatonic notes. This should be evident in that there are 3 traditionally named types - Italian, French, and German yet functionally, they do the same thing - resolve to V by virtue of the +6 interval expanding to the octave root of the V chord (or I6/4 chord, etc.). In fact, there are other +6 sonorities that use notes that do not create one of the traditionally named versions, that still resolve to V in the same way. Furthermore, when +6 sonorities are created on scale degrees other than b6, the +6 STILL is the determining factor in the resolution - it's "all about" the +6 expanding to the octave, not "what type of chord this is" and more importantly "hey this looks and sounds like a dominant 7th chords in one of its many forms).

The progression you give here is a common one, really an expansion of late nineteenth century harmony - especially heard in Barbershop, Salon music, and ultimately Ragtime, Blues, and Jazz.

But, here's the "usual" guise:

C - C - C - C
Bb -A - Ab -G
G - Gb -F - E
E - Eb -D - C

Which is reversed and truncated in the "Basie Ending"

You also hear the 3rds/6ths portion of this ascending and descending in many typical "Honky Tonk" riffs.

In traditional CPP consideration, the C in the progression above is really a Pedal Tone. However, the chords could consider it leaving:

C7/E - Co7/Eb - ii%7 (m7b5) - C

Now, Co7/Eb is what CPP calls a "common tone diminished 7th chord", which is a form of neighboring or passing chord. ii%7, while a predominant harmony, takes on dominant function here as a rootless V7b9 (C being a pedal tone) or viio7 (again, C pedal). Many bassists will play a G under this penultimate chord (though I should note, it also can, and often is, considered a type of plagal cadence as well).

The problem with all this is, we're trying to use CPP terms and functionality in a context where none of that really applies.

So for me, what's important here, and in your original progression, is the CHROMATICALLY DESCENDING 3rds. The C, if included, is really a pedal tone (filler) and the remaining line is "unimportant" as well.

The Ab - A resolution you have is "accidental". That is, we shouldn't say it's not heard. Example:

F# - G
D - Eb
C - C
Ab - G

This is a typical Fr+6 to I6/4 resolution in C minor. The Ab to D is an augmented 4th - meaning they should resolve accordingly. And they do. But, what makes this chord "go" is the dissonant +6 interval, because, it would still demand the same resolution if it were Italian (Ab C C F#) or German (Ab C Eb F#) - we could view the D as "extra impetus" I guess - it's true that we do when we have V7b9 versus V9 - it's like the b9 (Ab in C) wants "even more strongly" to go to G. But see, we have to temper this with the same thing being true in a minor iv chord - F-Ab-C is often heard as "pulling more strongly" because of the Ab - but there's no dissonance created by the Ab - it's its non-diatonic lowering of the note that makes it go.

So, a few observations:

C-E-G-A in Jazz can be C6, or an inversion of Am7 depending on the context.

In Classical music, it is ONLY an inversionof Am7.

So just because it "looks like" C6, doesn't mean we should call it C6.

Likewise, Ab7 in C, in Jazz can be a bVI7 chord.

In Classical, it could be a Ger+6 (or V7/N for example).

But calling instances of bVI7 chords in Jazz a "German +6" or even a "+6 chord" is a bit misleading, unless it's truly acting like an +6 chord. We have to remember that Jazz has had a hard time being taken seriously, especially in academic circles, and many people, in an attempt to "legitmize" Jazz, have tried to use CPP terminology to do so - some of it is applicable, but there are important distinctions.

So your chord here is "related" to +6 sonorites in that it contains an + interval that resolves, as pretty much any + sonority does. It also contains - more importantly IMHO - the parallel chromatic lines - and this is really what "leads" the progression.

And this is why, in a CPP context, theorists consider this a passing sonority, because it's "all about" the chromatic passing notes, as opposed to "resolution of chord tones".

I will add that there are what we call "diminished 3rd" chords, which are +6 chords under inversion - F#-Ab-C-Eb - but the F# and Ab resolve as they should - to G. It's still the +6 (o3) interval that's "driving" the chord.

So, Eb-F#-Ab-C "should" resolve - D-G-G-B or E-G-G-C - both unusual resolutions in the CPP era, which is why we don't find the +6 chords in that position (and remember, these chords served a specific point, that had to do with voice-leading, which is why they're not really "chords" but "sonorities").

You could make a case that your ii7 is really a rootless V9 (V11 if you include the C) and to me, that would strengthen the "+6 ness" of this chord.

I'd call it a passing chord.

Calling it a German +6 in inversion to me is using the term incorrectly or inadequately, because it's not resolving properly, and that's what the "+6" term is about. However, it's not the first time CPP terms have been misapplied to other genres, and had their previously specific definitions generalized to the point where it's "just a term" now.

HTH,
Steve





Re: augmented 6th chords ... augmented 3rd chords??
January 15, 2010 05:11PM
Guys, thanks for the responses!

What does CPP mean?

Thanks, Dave Horne
Re: augmented 6th chords ... augmented 3rd chords??
January 15, 2010 06:37PM
CPP means Common Practice Period. It's the period from around 1600 - 1900, in which the major-minor tonal system and associated harmony, etc., were developed.



Edited 1 time(s). Last edit at 01/15/2010 06:38PM by Fretsource.
Re: augmented 6th chords ... augmented 3rd chords??
January 16, 2010 10:43AM
The chord notation I used, standard jazz chord notation, does not lend itself to accurately displaying voice leading (well, except in the bass).

I studied figured bass in college and always thought that was a great way to notate exactly the voice leading you wanted. The instructions to the keyboard player dealt just with intervals and left the analysis out.

I never had heard of CPP until now; I just I called the theory from that period of time, traditional theory. It would be interesting to know the first time the progression in question was first seen in the wild. As Steve wrote ... 'Barbershop, Salon music, and ultimately Ragtime ... that would also be my guesstimate as well.

While the progression I asked about does in fact have descending thirds (much like the reversed 'Basie ending'), it also contains the interval of an augmented 3rd; even though my ears are somewhat jaded, that progression still has a mildly jarring effect and thus my interest in it.

The theory text book I used in college was Allan Forte's Tonal Harmony in Concept and Practice. I looked up what he might have called this 'augmented third chord' and came across this:

Chromatic Linear Chord Defined

By chromatic linear chord is meant simply a chord entirely of linear origin which contains one or more chromatic notes. A great many of these chords are to be found in the literature. .........

The various chromatic linear chords are share one characteristic: They exploit half-step melodic progressions in one or more voices and thus intensify the motion of the diatonic chords from which they derive and which they often represent.[end quote]

Well, that's it. I sincerely appreciate all the time taken by those who responded to my initial question.

All the best, Dave Horne



Re: augmented 6th chords ... augmented 3rd chords??
January 16, 2010 11:56AM
Dave Horne Wrote:
-------------------------------------------------------
> The chord notation I used, standard jazz chord
> notation, does not lend itself to accurately
> displaying voice leading (well, except in the
> bass).

And Jazz is an improvisational art form.

>
> I studied figured bass in college and always
> thought that was a great way to notate exactly the
> voice leading you wanted.


Actually, it's not. Baroque keyboard accompanying was also an improvistary form, and figured bass evolved hand-in-hand with that process - in fact, there are a lot of commonalities between figured bass and chord charts - very interesting the way the music necessitated an "open" notational style in each case.

The instructions to the
> keyboard player dealt just with intervals and left
> the analysis out.

True, but they don't tell the voicing, or octave, and that's where the specific voice-leading comes in - though you're right in that if you see 6/4 to 5/3, it tells you the 6 should move to the 5, and the 4 to the 3, no matter where you choose to play those chord members.


>
> I never had heard of CPP until now; I just I
> called the theory from that period of time,
> traditional theory. It would be interesting to
> know the first time the progression in question
> was first seen in the wild. As Steve wrote ...
> 'Barbershop, Salon music, and ultimately Ragtime
> ... that would also be my guesstimate as well.

I would bet it appears in something like Schubert - he was sort of the progenitor of a lot of those types of progressions. Though it's certainly possible that you might find a passage like this in Bach, though it wouldn't necessarily be operating in the same way.


>
> While the progression I asked about does in fact
> have descending thirds (much like the reversed
> 'Basie ending'), it also contains the interval of
> an augmented 3rd; even though my ears are somewhat
> jaded, that progression still has a mildly jarring
> effect and thus my interest in it.

I find this interesting because I feel the same way about something like the minor iv-I cadence - it's really nothing special but there's still something "fresh" about the sound (at least I find it that way) - maybe it's because we're so inundated with "classical" harmony that ANYTHING other than V7-I sounds new and exciting, even if it's used quite frequently (to the point of cliche in some cases).


>
> The theory text book I used in college was Allan
> Forte's Tonal Harmony in Concept and Practice. I
> looked up what he might have called this
> 'augmented third chord' and came across this:
>
> Chromatic Linear Chord Defined
>
> By chromatic linear chord is meant simply a chord
> entirely of linear origin which contains one or
> more chromatic notes. A great many of these
> chords are to be found in the literature.
> .........
>
> The various chromatic linear chords are share one
> characteristic: They exploit half-step melodic
> progressions in one or more voices and thus
> intensify the motion of the diatonic chords from
> which they derive and which they often represent.

That's kind of the take that Kostka&Payne, and Gauldin take as well - I think this is a more "modern" interpretation (as opposed to say, Piston or Schoenberg's theory texts).

A great example "from the literature" are these instances in Bach Fugues where there's a simultaneous sounding of notes - these notes may or may not make up a nameable chord, but their origin is definitely from voice-leading, and theorists tend to agree that that origin should be pointed out by using a "special" name, rather than a Roman Numeral.

That's also why Kostka&Payne for example make the distinction between chord and sonority. Forte and others of that ilk also like to use "simultaneity" for sonorities that appear to be chords, but aren't really chords.

I always say this to the jazzers who feel like they have to identify everything as a chord (especially if they're trying to analyze CPP music): Just because it looks like a chord, doesn't mean it necessarily is.

How old is that Forte book David - I'd be interested in checking it out.

Steve

Re: augmented 6th chords ... augmented 3rd chords??
January 16, 2010 12:44PM
Steve, what you wrote regarding Schubert and the possibility that the progression might have been used by him certainly crossed my mind. When I studied Schubert lieder in college I came very close to dedicating my musical life to the analysis of his works. Whew ... that was a close one. :)

The book by Forte is out of print though I have two in my possession. As a jazz player I love the keyboard patterns at the end of most chapters.

The patterns are to be played using the same exact voicing and more importantly, in very key. They have come in very handy when backing singers and having to play whatever the singer wants in whatever key they think is best at the moment. As things get more involved in the text book, the patterns also become more involved. The book alone is worth the price just for those keyboard patterns. I have the first edition and a later edition; the first is from 1962. I like that edition since the quality of the paper was thicker and rougher than the later editions.

I'm 59 and take a few days every year just to work through those patterns.

If you enter Tonal Harmony in Concept and Practice into Amazon, you'll see some second hand books to be had. The text can be rather dry but I really liked his explanation of things.

If you buy a copy contact me personally after you've worked through a handful of his Basic Keyboard Pattern # 1 and 2 at the end of most chapters. If you have students I know you'll pass them on to them.

All the best, Dave Horne (I'm easy to find, just enter my name and the Netherlands into Google and my site should be the first hit.)








Edited 3 time(s). Last edit at 01/17/2010 11:16AM by Dave Horne.
filamentbuster
Re: augmented 6th chords ... augmented 3rd chords??
January 19, 2010 10:16AM
Hey Steve, I was wondering if you could clarify on something you said:

The b9 in the G7b9 chord feels the need to resolve because of the dissonance it creates with the other members of the chord (m2 between the root and the b9)

However the minor iv chord does not feel the need to resolve because the chromatic note is dissonant, but because of the fact that stepwise motion is preferred to skips? Did I read this right?

Thank you.
Re: augmented 6th chords ... augmented 3rd chords??
January 19, 2010 05:50PM
Dave Horne Wrote:
-------------------------------------------------------
> Steve, what you wrote regarding Schubert and the
> possibility that the progression might have been
> used by him certainly crossed my mind. When I
> studied Schubert lieder in college I came very
> close to dedicating my musical life to the
> analysis of his works. Whew ... that was a close
> one.
>

Yeah, glad you escaped that one :-)

Steve
Re: augmented 6th chords ... augmented 3rd chords??
January 19, 2010 06:08PM
filamentbuster Wrote:
-------------------------------------------------------
> Hey Steve, I was wondering if you could clarify on
> something you said:
>
> The b9 in the G7b9 chord feels the need to resolve
> because of the dissonance it creates with the
> other members of the chord (m2 between the root
> and the b9)

7ths and 9ths are chordal dissonances and thus need to resolve down by step in the CPP.

So a G9 resolves to C for the reason above. But read below...

>
> However the minor iv chord does not feel the need
> to resolve because the chromatic note is
> dissonant, but because of the fact that stepwise
> motion is preferred to skips? Did I read this
> right?
>
> Thank you.

When you've established a key (remember, we're talking CPP here), altered notes have a tendency to resolve to diatonic tones in the direction they're going. Thus raised notes want to continue to go up, and lowered notes want to continue down.

Once you've established C Major, and introduction of G# wants to go to A, and Ab wants to go to G.

Aurally, we can't tell the difference, but in a harmonic context, usually enough aural information is present to help lead our ears.

So, obviously a G# in an E7 chord is going to lead to an A (in an F chord deceptively, or Am chord).

We *expect* an F Major as the IV chord, so adding the lowered 6 (making it F minor) wants to go to 5 - so adding b6 to the IV chord in Major keys makes the iv want to move to I "much more strongly" (there's already a tendency for 6 to move to 5 in both Major and minor keys, but lowering 6 in major gives it "more oomph").

If you've established a minor key, the opposite is true, because iv is the expected harmony. Raising 6 (as in IV) makes it want to go UP (to raised 7, a common progression).

So, a G7b9 in C has "extra" pull - the 7th and 9th, as dissonances to the chordal root demand a stepwise descending resolution, and the 9th (in an established Major key mind you) being lowered, even more strongly wants to pull down.

So it's a "double-whammy" which is probably why this became such a popular "dramatic" chord in the Romantic period harmonic vocabulary.

Steve



filamentbuster
Re: augmented 6th chords ... augmented 3rd chords??
January 20, 2010 06:44AM
Thanks Steve!

Sorry to stray off the topic, but I'll try and make this my last question =)

I've never really thought of there being different types of dissonance (Silly, I know) but after your post about the G7b9 and the Fm chord (in the key of C) I came up with this conclusion:

Harmonic dissonance - Dissonance due to the members of the "clashing" with eachother, like a b9 or a natural 11. Like in a G7 chord, the B and F create that nasty diminished fifth, which wants to resolve to a nice major third of C and E.

Melodic dissonance - Dissonance created by the insistence of altered tones to resolve to diatonic tones. There doesn't necessarily have to be a dissonance within the chord. For example, the Ab in an Fm chord wants to resolve down to a G (in the key of C) but that isn't because it causes a strong dissonance in the chord (m3 is a fairly consonant interval) but because the Ab doesn't "belong" in the key of C.

Does this make sense? Thanks, I really appreciate the help =)
If steve doesn't mind me interjecting...

I also feel there are two types of dissonance, but I'd characterise them differently.

1. Functional dissonance.
It's the kind of harmonic tension that contains an expectation of resolution; usually in a particular direction, but sometimes in any of a few directions. But the central aspect is the "tendency".
Eg, when we hear a G7 chord (at least in CPP music, or most jazz or popular music), we expect a C or Cm chord to follow (which of those we expect will depend on what's happened before the G7).

2. Non-functional dissonance.
This is dissonance without a tendency to move anywhere. IOW, a "colour" on a chord. Again, however, it depends on our expectation, which can be created by the preceding music.
Eg, if we hear a G7 chord in blues or in modal jazz, we probably wont expect it to move to C. A G7 chord can be held or sustained as a "mixolydian tonic" - and often is in blues or rock music. If we are familiar with that kind of usage, the tendency the chord has in CPP music doesn't apply.
(Ie, the tendency is not inherent in the chord itself, it's something we've learned to perceive, and can equally well unlearn. While there is a physical basis to the dissonance, to do with complex interaction of overtones, that complexity needn't be unpleasant or feel restless. Those interpretations of the sound are cultural.)
IOW, we hear the internal tritone in the chord (B-F) as just a nice kind of complex sound in its own right, not a tension that itches to move somewhere else.


The "melodic dissonance" you describe is an interesting third kind, because it ]depends wholly on what we've heard previously. I think I'd prefer not to call this "dissonance" at all, but a "tendency" of some kind. (I suspect steve will provide a more erudite interpretation.;))
The Ab note in the key of C is "chromatic", and as such would be expected to be "corrected" by a move to a diatonic note - which could be G or (if call it G#) A - again depending on surrounding harmonies or melodic movements.
Re: augmented 6th chords ... augmented 3rd chords??
January 20, 2010 07:43PM
jonr Wrote:
-------------------------------------------------------
I think I'd prefer
> not to call this "dissonance" at all, but a
> "tendency" of some kind. (I suspect steve will
> provide a more erudite interpretation.)
> The Ab note in the key of C is "chromatic", and as
> such would be expected to be "corrected" by a move
> to a diatonic note - which could be G or (if call
> it G#) A - again depending on surrounding
> harmonies or melodic movements.


Actually, I don't have anything to add (yet I will :-) - "tendency" is the typical word.

Though I don't know of any classifications, we might call those diatonic tones in the key that move toward members of the tonic triad "tendency tones" (as many do):

In C:


B - C
A - G
F - E or G, though to E exhibits a "more satisfactory" move.
D - C or E, and again, to C is "more satisfactory".

We might call those chromatically altered tendency tones "heightened tendency tones" or something.

Ab - G in Major

B - C in Minor
A - B in Minor


These notes are available through mode mixture, but the rest are "secondary tendency tones", which as Jon aptly put, is "functional" chromaticism. So for example, Bb in C Major, can be borrowed from C minor, but it most commonly appears a the 7th of a V7/IV chord, and thus becomes functional - read on...

So F# in C, as part of a V/V chord, obviously takes on the tendency of 7-8 in the key of G - that's (an example of) Functional Chromaticism.

Other Chromaticism can simply be "decorative" or "embellishing" and non-functional.

So I think this "heightened tendency" idea (brought about really through borrowing, not chromaticism per se) is between those two.

Steve


Re: augmented 6th chords ... augmented 3rd chords??
January 20, 2010 07:55PM
filamentbuster Wrote:
-------------------------------------------------------
> Thanks Steve!
>
> Sorry to stray off the topic, but I'll try and
> make this my last question =)
>
> I've never really thought of there being different
> types of dissonance (Silly, I know) but after your
> post about the G7b9 and the Fm chord (in the key
> of C) I came up with this conclusion:
>
> Harmonic dissonance - Dissonance due to the
> members of the "clashing" with eachother, like a
> b9 or a natural 11. Like in a G7 chord, the B and
> F create that nasty diminished fifth, which wants
> to resolve to a nice major third of C and E.

Yes, but remember, it's not really the B-F that's the issue in the resolution of a G7 - it's the Root and the 7th (G-F) interval that's the problem. The B-F is, in a sense, "merely a by-product" of the addition of the 7th,

That said, there is of course the fact that F has a tendency to go to E in the key, and B to C, and D to C or E - so the resolution of V7-I seems "so right".

So an "extra" dissonance included in a chord gives it a little more direction - or maybe we should say, it makes one resolution seem "stronger" than others, whereas chords without the "extra" dissonance (such as a Dm7 with only the 7th being dissonant) are a little "more versatile" in their resolutions.

>
> Melodic dissonance - Dissonance created by the
> insistence of altered tones to resolve to diatonic
> tones. There doesn't necessarily have to be a
> dissonance within the chord. For example, the Ab
> in an Fm chord wants to resolve down to a G (in
> the key of C) but that isn't because it causes a
> strong dissonance in the chord (m3 is a fairly
> consonant interval) but because the Ab doesn't
> "belong" in the key of C.
>

Yeah - I agree, but let's say that in this case, we have to hear enough material to give us a context against which a tone can be compared - whereas in a chord obviously we get to hear more notes against which to judge any dissonance.

But again, as Jon and my other response points out, there's really three categories, or better, a continuum of bot melodic and harmonic dissonance.

Then there's another thing to consider - when you hear something like a passing tone, it can create BOTH a melodic and harmonic dissonance simultaneously - the resolution then depends on whether it's heard or intended to be heard as melodic, harmonic, or both.

Steve

filamentbuster
Re: augmented 6th chords ... augmented 3rd chords??
January 20, 2010 10:42PM
Sorry if this is dragging on, just tell me if you think it'd be wise to start a new thread:
"when you hear something like a passing tone, it can create BOTH a melodic and harmonic dissonance simultaneously - the resolution then depends on whether it's heard or intended to be heard as melodic, harmonic, or both."

Could you go into a little more detail on this please? Like, how you would imply the different resolutions you suggested (melodic vs harmonic) and how they would resolve (melodically vs harmonically)? Thanks a bunch =) (I hope I understand this right)
stevel Wrote:
-------------------------------------------------------
> Yes, but remember, it's not really the B-F that's
> the issue in the resolution of a G7 - it's the
> Root and the 7th (G-F) interval that's the
> problem. The B-F is, in a sense, "merely a
> by-product" of the addition of the 7th,

That's surprising. I'd have thought the B-F tritone was a more dissonant interval than the G-F minor 3rd?

In the plain triad, G-B goes well enough to C-C (octaves), to make a perfect cadence (in C).
Seems to me the F makes a pair with the B, not the G, as the tritone resolves by two opposite half-step moves.
Obviously the G "roots" the tritone (literally) - prevents it sounding like the opposite tritone (Cb-F, of Db7 going to Gb).
And all the tones (including the 5th) work together (as you say).

>
> That said, there is of course the fact that F has
> a tendency to go to E in the key, and B to C, and
> D to C or E - so the resolution of V7-I seems "so
> right".

Yes.

>
> So an "extra" dissonance included in a chord gives
> it a little more direction - or maybe we should
> say, it makes one resolution seem "stronger" than
> others, whereas chords without the "extra"
> dissonance (such as a Dm7 with only the 7th being
> dissonant) are a little "more versatile" in their
> resolutions.

Right. Could you spell out some classic resolutions for a Dm7? (I mean, I'm familiar with the move to G7, but I was wondering about others, and what the classic voicings might be.)

Re: augmented 6th chords ... augmented 3rd chords??
January 22, 2010 12:36PM

>
> That's surprising. I'd have thought the B-F
> tritone was a more dissonant interval than the G-F
> minor 3rd?

You mean minor 7th.

You have to remember that historically, internal dissonances were not a concern for composers - dissonance was considered FROM THE BASS.

Thus C-E-G is stable, and E-G-C is stable, even though it contains the dissonant interval of a 4th - but see, the 4th is not made with the bass. But, G-C-E is not stable - it is, in the CPP, a chord needing resolution (or it is treated as a linear/embellishing sonority).

To further this point, B-D-F. Dissonant, not used. F-B-D. Dissonant, not used. BUT, D-F-B - it matters not that it contains a tritone, because the upper notes are both consonant with the bass. Thus diminished triads appear in first version to "lessen" the overall dissonance that is created initially by the o5.

Now again, that doesn't mean the tritone is not a factor in this chord's progression. It moves to C-E-C for example. But the majority of that push is created by the tendency tones the chord contains, not specifically the dissonant tritone (though our modern ears certainly hear that as a component).

Another example is in earlier modal music - where all this originates - in the Phrygian mode. The cadence in Phrygian was F-A-D to E-G(#)-E. People in that time would have heard that as just a satisfactory an ending as any of the modes that use (or included) a raised 7th that creates a "diminished leading tone".

So in that case, it's more about the tendency of the degrees than the actual quality created - though over time it seems composers began to favor a penultimate sonority that DID include a tritone - probably because they were beginning to hear the tritone as an "added bonus" in the resolution of the chord. But I'd also have to say that, another issue the tritone creates is a "tonal identifier" - it's a chord that's unique to the key - you know, all major keys have six major, and six minor triads, and only one diminished triad. And that's what gave way to the birth of tonality.

So, for a G Major chord - G-B-D is a stable, consonant sonority. The addition of the F creates an unstable 7th that needs to resolve, and that, in addition to the tendency tones included, is what drives the chord - notice in fact that the G is already a stable tone, and one possible resolution is to have it move to A for a Deceptive Cadence. So it's "really" about the B, D and F moving to C, C and E.

Now again, this one particular 7th chord is unique in a key, so the tritone can be considered an "extra factor" or "added bonus" that, in tonal music, solidifies its resolution.

But, let's take a chord that sounds identical:

G-B-D-E#.

It resolves to F#-A(#)-C#-F# as a German +6 chord.

Where are the dissonances?

With the bass, the +6
Internally, the B-E# is an +4, and D-E# is an +2 (though aurally a m3)

What are the tendency tones? Well this chord usually appears in the key of B, so let's take B Minor:

G is b6 - should go to 5 (F#)
E# is #4 - should to to 5

B and D are stable tones.

And in fact, in B minor, this chord will very often resolve to:
F#-B-D-F#. That is, the tendency tones go where they should, and the stable tones stay. Of course, this produces another unstable sonority which itself needs to resolve, but that's another matter.

So, does the tritone resolve in the +6 example? Well, it certainly moves - and the chromatically altered note does move in the direction in which it's been altered - but the resolution does not HAVE to be to A(#)-F#, the B could remain. And that's why +6 chords are "about" the +6 interval (among other reasons discussed previously).

Additionally, we should consider non-dominant dominant 7th structure chords. VII7 in minor (Bb-D-F-Ab in C minor) and IV7 in minor (F-A-C-Eb) They don't necessarily "resolve their tritone" as a means of resolution - it's more a happenstance that the tritones do resolve to other diatonic tones. But the real impetus is, for example in IV7, the raised 6.

So I think we get to a point (with 7th chords) where the original dissonance that caused the need for resolution, when added, creates a secondary internal dissonance in some cases, and when considered with the tendencies of the chord tones, creates a sonority where those elements seem inseparable.


>
> In the plain triad, G-B goes well enough to C-C
> (octaves), to make a perfect cadence (in C).
> Seems to me the F makes a pair with the B, not the
> G, as the tritone resolves by two opposite
> half-step moves.

True, but consider that, a cadence of G-B-D to C-E-G is certainly acceptable. It doesn't HAVE to have the tritone. So the resolution of G as V to C as I in C Major is already set (by the tendency tones and root movement). Adding the F adds a dissonance with the bass, and as an added bonus, gives us a unique structure which is a tonal identifier, and creates an internal dissonant interval. And let's not forget that in minor, one of the notes moves by whole step, so the half step is not a factor.


> Obviously the G "roots" the tritone (literally) -
> prevents it sounding like the opposite tritone
> (Cb-F, of Db7 going to Gb).

Ah yes - but, the +6 example above negates that. The G "roots" the sonority, but the chord's resolution is dictated by the dissonant interval created with the bass (+6 vs. 7th).

And therein lies the reasoning for the oft mentioned classification of the tritone as a "depends on the context" reosolution. People have tried to "classify" dissonances (and intervals) on a more to less scale - m2 is "more dissonant" than M7 for example. But in these, the tritone is usually listed as "variable" or "depends".

I think that our modern ears have been "corrupted" by - especially in jazz - the use of a tritone as a "stand in" for a dominant 7th chord. It's because of the unique interval that that works. And the resolution we hear is "satisfactory" because we can "fill-in" the rest having hear far too many V7-I cadences over the years :-)



>
> Right. Could you spell out some classic
> resolutions for a Dm7? (I mean, I'm familiar with
> the move to G7, but I was wondering about others,
> and what the classic voicings might be.)
>
>

Let's go back to two part writing:

F
G

could resolve to:

F - E
G - G (mediant resolution)

F - E
G - A (deceptive resolution)

F - E
G - C (authentic resolution)

In the Renaissance, we have all of these types of resolutions. But, in the Baroque and Classical (and from then on) we see - with a "key" of C in mind, a preference for the deceptive and authentic resolutions, because a mediant resolution as given here creates "backwards" motion away from the tonic, which is counter to the point of tonal music to begin with. But in the Renaissance, which was still modal, the desire to get to the final was less of a consideration that voice-leading and melody line.

So, once we get into a tonal context, all three resolutions are available, but due to the tendency tones, and the inclusion of the tritone, some of the resolutions don't sound like they "progress", and are thus not used often, if at all (you'll find them more frequently in contrapuntal textures).

C-E-G-B can resolve to C-E-A, F-A-(C), or D-F-A. It does all three.

D-F-A-C - D-F-B, G-B-(D) or, less commonly, E-G-B (the minor key counterpart will resolve to III, which sounds like a vii%7-I in the relative major, and is often better considered that).

E-G-B-D - E-G-C, A-C-(E), or F-A-C. All three are common (though certainly, for all of these, root movement of a 5th is the most common, where possible)

F-A-C-E - F-A-D and G-B-D - B-D-F would only happen in a sequence and even then would appear as a 7th chord to keep the sequence going to iii.

G-B-D-F - C-E-G and A-C-E - G-B-E doesn't happen except in contrapuntal textures where the chord is in a non-dominant context, which is of course rare.

A-C-E-G - A-C-F, D-F-(A), but not B-D-F in root position. In minor, you will encounter A-C-Eb-G (#vi%7) and it does move to B-D-F in root position - a rare progression in general, but certainly possible, and a hold over from previous generations.

B-D-F-A - C-E-G and certainly B-D-G (though usually B-D-F-G). E-G-(B) would only happen in sequences (and then, rarely by comparison.

Then there are other types of resolutions based on voice-leading. In a sense, these above represent 7-6 resolutions with a change of bass in two of the types.

So functional 7ths as dissonances with the bass have three potential resolutions which, in the tonal era, become dictated by additional factors such as tendency tones, secondary resolutions, etc. such that some resolutions become more typical, and some atypical.

Boy, you opened a can of worms :-)

Steve




stevel Wrote:
-------------------------------------------------------
> > >
> > That's surprising. I'd have thought the B-F
> > tritone was a more dissonant interval than
> the G-F
> > minor 3rd?
>
> You mean minor 7th.

Duh - of course!

Thanks for all the rest - interesting stuff!
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