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#1894892 - 05/10/12 04:52 PM Augmented 6th chords
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
There have been some questions about them, so I thought this might be a good place for disussing them.

I have some ideas but would prefer to see some discussion first before adding.

Chords that fall into this category:

German 6th
French 6th
Italian 6th

Other chords that are spelled like the German 6th but that do not resolve to the same place.

Thoughts?
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#1894909 - 05/10/12 05:09 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Registered: 06/16/11
Posts: 3181
Loc: Maine
Does this include the Neapolitan 6th, too?
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#1894911 - 05/10/12 05:15 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Loc: Maine
Oh wait, never mind. Neapolitan sixth isn't augmented.
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#1894944 - 05/10/12 06:09 PM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
You have the wrong concept.

Neopolitan 6th means major chord, built on lowered 2, is in first inversion:

It is like this: bII6 or N6.

But you can have an augmented 6th chord built on flat 2, the degree. Do you need an example, a link?
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#1894959 - 05/10/12 06:44 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Loc: Maine
Well, of course I'd love an example!

But I can manufacture the chord itself now: e.g. in C major, augmented 6th built on flat 2 would be Db, F, Ab, B. And we would expect it to resolve outwards to C E G C. Or possibly to C F A C. Or so I gather. Oh wait, resolving to C E G C would give us paralell fifths, in Db to C and Ab to G. So maybe it can only resolve to C F A C. This is for a German 6th, that has all the triad bells and whistles.

And that would mean the variants e.g. Italian 6th omitting the fifth are there precisely so you can resolve to C E C (with G omitted) without getting parallel fifths.

I've been reading about augmented sixth chords, just enough to make me very curious about them, but hopeful of finally understanding them. (I first saw these names several years ago, and they made no sense at all then.)

How come (on the other thread) you seemed to express reservations about writing say Db(#6)? You seemed to imply that only Db(7) was a legal name. But Db(#6) seems perfectly clear to me. Or did I misunderstand that you were hesitating about the #6 notation?

Now I'm not sure if I've got that fully right, but that's what I think so far, minus trying to proofread this post for a fifth time.
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#1895016 - 05/10/12 08:26 PM Re: Augmented 6th chords [Re: Gary D.]
keystring Online   content
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My first reaction to the title of "augmented sixth" is simplistic, but I also like to start with simplicity. I know the aug6 is a semitone above a major 6, and sounds like a minor 7. Meanwhile the minor 7 is an extremely important interval because it occurs in "dominant 7 chords" which have that tritone through the 7 creating a restlesness that wants resolution. In my theory books we are to constantly draw arrows showing the downward movement of that 7. Except this time we have a 6 that sounds like that 7, and I understand it doesn't move down. Meanwhile if I play an aug 6 chord, it sounds to my ear just like the dom7 but it is spelled differently.

This is a very basic sense of "what it is" before it has a function or goes anywhere.


Edited by keystring (05/11/12 12:36 AM)

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#1895070 - 05/10/12 10:51 PM Re: Augmented 6th chords [Re: Gary D.]
joflah Online   content
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Registered: 08/09/09
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Loc: St. Louis, MO, USA
My theory text says they are usually pre-dominant chords, resolving to the dominant of the key. An example in c minor is
It+6: Ab, C, F#, C (Ab to F# being the +6) to
V: G, D, G, B.
Thus the + 6 resolves outward to an octave (on the 5th degree).
So, the Ab resolves down to G while the F# resolves up to G.

The Italian +6 has the tonic doubled, the French includes the 2nd scale degree, and the German has the 3rd scale degree. The latter, to avoid parallel 5ths, has to resolve to the dominant by going through i 64.
--
Jack


Edited by Jack O'Flaherty (05/10/12 10:58 PM)
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#1895074 - 05/10/12 11:01 PM Re: Augmented 6th chords [Re: Gary D.]
Happy Birthday LadyChen Offline
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Registered: 01/25/12
Posts: 521
Loc: Canada
The only way I could make sense of these concepts was to think in terms of jazz theory and the role of tritones and tritone substitution. These are the key points that help me remember how these chords work:

- they are built on the flatted sixth degree of the scale, so in C major, they are built on Ab

- they often resolve to the V chord, which makes sense when you look at the tritones present in each aug6 chord.

- Ger6 is a 7 chord spelled funny. You take the flatted sixth scale degree, and add a major third, a perfect fifth and an augmented sixth. so in C major, it's an Ab7 chord but spelled Ab C Eb F#. And it makes sense that it resolves to G, because it has the same tritone as a D7 chord.

- Fr6 is like a II7b5 chord. You take the flatted sixth scale degree, add a major third, an augmented fourth and an augmented sixth, which gives you Ab C D F#, which I unscramble in my brain to get D F# Ab C, making D7b5. And because it is a D7, it makes sense that it resolves to G.

- It6 .. well, i had no good way to explain it, so I just memorized the rule. You take the flatted sixth scale degree, and add a major third and an augmented sixth (in four part harmony, the third is usually doubled .. the third is also the tonic). So you get Ab C F#. Again you have that tritone from a D7 chord, which natural resolves to G.

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#1895082 - 05/10/12 11:28 PM Re: Augmented 6th chords [Re: Gary D.]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Beethoven 5th, First Movement, Italian 6th chord
The Italian 6th chord is in Meausure 20. It is always useful to have a real example from famous music to illustrate something that otherwise would be only "theory".


Edited by Gary D. (05/11/12 12:52 AM)
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#1895102 - 05/11/12 12:45 AM Re: Augmented 6th chords [Re: LadyChen]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: LadyChen
The only way I could make sense of these concepts was to think in terms of jazz theory and the role of tritones and tritone substitution. These are the key points that help me remember how these chords work:

My instruction was 100% traditional. My only exposure to jazz was through some of my brass playing friends, but I didn't actually do any playing. I was forced, against my will, to gig in my 20s. I hated it, at first. It was not the music I loved, and I sucked at it. It was all about paying bills. But that changed, totally.

After I finally stopped gigging, my whole attitude towards music changed. I still loved the music I loved as a kid, as a teen, as an early 20-something. But I got to add a whole new set of skills to what I knew, what I could do. The biggest thing that changed was this: when I talk about theory with other musicians, it is almost always with jazz/pop players. I know stuff that most of them don't know, but they know a HUGE amount of stuff I don't know, and I'm still learning.
Quote:

- they are built on the flatted sixth degree of the scale, so in C major, they are built on Ab

This is what I teach.
Quote:

- they often resolve to the V chord, which makes sense when you look at the tritones present in each aug6 chord.

Again, this is practical. And with that point of view, the same thing happens from bII to I. Example, using Db(#6) in place of Db7, to show spelling:

Db(#6) to C. In my experience, using chord symbols, the fact that the Db(#6)chord will use B, because the melody will move smoothly from B to C, is a matter of smooth notation, elegance, and has nothing to do with that sound of the two chords, separately. It is all about how they work together. It is logical because it looks smooth, on paper.
Quote:

- Ger6 is a 7 chord spelled funny. You take the flatted sixth scale degree, and add a major third, a perfect fifth and an augmented sixth. so in C major, it's an Ab7 chord but spelled Ab C Eb F#. And it makes sense that it resolves to G, because it has the same tritone as a D7 chord.

And it will have the same kind of movement as D7/A to C/G. Here we have, in traditional theory, V of V moving to a I 6/4 chord. Reasoning backwards, lowering the A to Ab is D7-5/Ab to C/G. But that is also Ab7-5, so we have the tritone exchange. I spent thousands of dollars to get a degree, and I did not get taught that. I learned that from some very fine jazz players, for free.
Quote:

- Fr6 is like a II7b5 chord. You take the flatted sixth scale degree, add a major third, an augmented fourth and an augmented sixth, which gives you Ab C D F#, which I unscramble in my brain to get D F# Ab C, making D7b5. And because it is a D7, it makes sense that it resolves to G.

If you look at what I wrote, I think we are saying exactly the same thing.
Quote:

- It6 .. well, i had no good way to explain it, so I just memorized the rule. You take the flatted sixth scale degree, and add a major third and an augmented sixth (in four part harmony, the third is usually doubled .. the third is also the tonic). So you get Ab C F#. Again you have that tritone from a D7 chord, which natural resolves to G.

That last part is easy. It comes from the insistance that parallel 5ths are to be avoided, at any cost, and in Bach's SATB work, the reasons become pretty clear. It does not SOUND good. So by lowering the 5th (Fr6) or by throwing out the 5 altogether, parallel 5ths are gone. Which is why I uploaded the link to Beethoven's 5th. His first big cadence is Ab(#6), no third, to G7, no third.
My thinking, apparently, is so close to yours that I would have written much of what you wrote, if I had been able to sum it up so neatly.
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#1895104 - 05/11/12 12:58 AM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: PianoStudent88
Well, of course I'd love an example!

Chopin Prelude in Bb Minor
There it is.

P.7 in the score, P. 13 in the pdf file. Last line. Cb(#6)/Bb moving to Bbm, then finally Cb(#6)/Bb to Bb. Watch the neat way he brings it down in the third to last measure.

Originally Posted By: PianoStudent88
Well, of course I'd love an example!
But I can manufacture the chord itself now: e.g. in C major, augmented 6th built on flat 2 would be Db, F, Ab, B. And we would expect it to resolve outwards to C E G C. Or possibly to C F A C. Or so I gather. Oh wait, resolving to C E G C would give us paralell fifths, in Db to C and Ab to G. So maybe it can only resolve to C F A C. This is for a German 6th, that has all the triad bells and whistles.

By the time of Chopin, parallel 5ths were no longer avoided at all cost. Cb---Gb to Bb---F is about as parallel as you can get. Rules were more strictly applied, and in many cases still are, in choral music.
Quote:

And that would mean the variants e.g. Italian 6th omitting the fifth are there precisely so you can resolve to C E C (with G omitted) without getting parallel fifths.

Correct.
Quote:

How come (on the other thread) you seemed to express reservations about writing say Db(#6)? You seemed to imply that only Db(7) was a legal name. But Db(#6) seems perfectly clear to me. Or did I misunderstand that you were hesitating about the #6 notation?

The implication has been that I have been misleading people, that armed with what I teach, my students would be laughed at in a formal theory class. Db7 is standard, and you don't use parentheses. Db(#6) is either my invention or something I came up with, to fill a gap, that may have been used by other people without my ever having seen it.

It could get messy here: Db7-5 or Db7b5 would become Db(#6)-5 or Db(#6)(b5). That notation would make me stumble. Db7b5 I can read faster. In my world, letter chords do not honor spelling. They are what they are, and we decide upon spelling (and function) by context. And I will continue to teach that.

There are standard chord symbols for any 7 chord with a flat 5, and it is only called a French 6th with the variant spelling. I have already explained my reasoning. Variations in spelling are often used to make notation more elegant, more streamlined, because of voice leading. I continue to believe that where chords go define how they function, not how they are spelled. And I continue to believe that ultimately "correct" spellings becomes obvious, not SOLELY because rules or rudiments, but because comparison with other spellings shows them to work best. I am not denying that rules are helpful, only that there comes a time when we have to get BEHIND the rules when the rules do not explain everything.

To sum up, if someone writes Db7, with a Cb, moving to C, you will still know what is happening. Same thing with Db7-5 with a Cb. But if you are writing music yourself, or if you are teaching notation, you will switch that Cb to a B, and you will be able to explain why you did it.

I want to be VERY careful.

Is anything I wrote misleading? Unclear? Over the last few days I have begun to doubt myself. frown
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#1895118 - 05/11/12 01:56 AM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
4000 Post Club Member

Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: keystring
My first reaction to the title of "augmented sixth" is simplistic, but I also like to start with simplicity. I know the aug6 is a semitone above a major 6, and sounds like a minor 7.

So far I do not see simplistic. I see a simple fact.
Quote:

Meanwhile the minor 7 is an extremely important interval because it occurs in "dominant 7 chords" which have that tritone through the 7 creating a restlesness that wants resolution. In my theory books we are to constantly draw arrows showing the downward movement of that 7.

Until I find out how to upload files, I can't do this in notation.

Let's use an Ab7 as good "example seven chord".

The first and most obvious place it wants to go is to Db. We all know that. The only reason to respell that root is if we change "mode" by deciding to move to C#m, then set up the key of C# minor. This happens in Chopin's C# Minor Waltz, the famous one. If someone needs a link, I will add one.

Other than that, change of root would be rare, and we would not want to change the triad itself except for some weird reason that I can't imagine right now.

So what we are really concerned with are two things:

Is the chord contracting - with the Gb coming down 1/2 step?

Or is it expanding, with the Gb wanting to go UP 1/2 step? If it goes up, we will end up changing its spelling to F# for reasons linked to the chromatic scale: When possible, avoid going up 1/2 step, by sound, using an augmented unison. It forces an extra accidental, which is messy. Gb going to G natural is ugly and unintuitive compared with F# going to G.

1) Contracting examples: Ab7 to Db, Ab7 to Abdim7. Ab7 to F7/A.

(Note: contrary to theoretical rules, it is likely that you will see Ab7 contract to a dim7 spelling with F on the top, same reasoning: Gb to Gbb is ugly. If you subscribe that we MUST label a dim7 by its root, you would have to rename your resulting dim7 chord, then use a slash to show the root. I have never seen that done with letter notation.)

2) Expanding examples: Ab7 to C/G, Ab7 to Cm/G, Ab7 to G. There the expansion makes a change from Gb to F# both far more common and easier to notate (fewer symbols). For obvious reasons, this movement can go towards a Gsus or a Gaug chord.
Quote:

Meanwhile if I play an aug 6 chord, it sounds to my ear just like the dom7 but it is spelled differently.

If we agree that by "dom7" we mean any chord that has that sound and that spelling, even if it is not a V7 chord, then I agree. smile


Edited by Gary D. (05/11/12 02:11 AM)
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#1895128 - 05/11/12 03:17 AM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Registered: 06/16/11
Posts: 3181
Loc: Maine
Gary, thank you for the Chopin (and the Beethoven) examples. The Chopin is spectacular! (Once I figured out that you meant Bbm, not Bm.)

Everything you said makes sense to me. Thank you for explaining about the letter symbols.

The Beethoven Italian 6th is so very dramatically placed.. I wonder if I can hear it, and hear the following chord. That is, hear them as something with a unique character, more than just notes.

I am amazed and impressed by all the examples you have. It's like you have a mental filing cabinet of all the notation you've ever seen, and can pull it up at will to illustrate any point as needed.
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#1895131 - 05/11/12 03:29 AM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: PianoStudent88
Gary, thank you for the Chopin (and the Beethoven) examples. The Chopin is spectacular! (Once I figured out that you meant Bbm, not Bm.)

My typing sucks. If I type something long, it will be incomprehensible unless I make myself read it out loud before posting it. The weird thing is that I am an excellent proof-reader for other people.

I actually wanted to have a go at the Satie, the first one in the set. My first impression is that it could be renotated to read easily without detracting one whit from the music itself.

In Bach and Mozart the writing is usually so incredibly clear. At that time it is as if composers assumed:

1) Good players would play their music well without too many directions.
2) Poor ones would mess it up, no matter what.

By the time we hit the 19th century, the custom seemed to have moved towards "micro-managing". It is almost as if composers thought that IF they could put enough detailed instructions into their music, it would guarantee that their music would not be butchered.

Often in their attempt to make their thoughts crystal clear I think they actually drive us away from what they had in mind - overkill.

Satie didn't so that with directions, but he certainly did with flats! wink
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#1895157 - 05/11/12 04:48 AM Re: Augmented 6th chords [Re: Gary D.]
drumour Offline
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Registered: 10/08/05
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The remarkable thing about aug 6ths is that at the point of sounding they want to resolve in a way very different from their corresponding 7th chords. Aug 6ths rarely present an ambiguity where we have to wait for a resolution to clarify. The expectations set up by aug 6ths are rarely subverted by composers in their resolutions unlike in the case of 7ths. What follows a harmony may be determined (by no means always) by that harmony but a subsequent never defines what precedes it; if anything it can only define a specific context. Aug 6ths in tonal music are functional chords which can, depending on context, be dramatic and striking or so smooth as to be almost over-looked. A further strange thing about aug 6ths is that what they demand in resolution doesn't seem to be a result of cultural conditioning, which might be argued for the far more common 7th chords.


John
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#1895186 - 05/11/12 07:06 AM Re: Augmented 6th chords [Re: Gary D.]
currawong Offline
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Registered: 05/15/07
Posts: 5936
Loc: Down Under
Originally Posted By: Gary D.
Until I find out how to upload files, I can't do this in notation.
See if this works, Gary smile (presumably it will work for a scan of music, too.)

Monica's How to post a photo instructions

1.) First step, and this is critical, resize your photos to about 450-600 pixels. You accomplish this through photoshop or some other photo editing software. My father in law did this part of the process for me so I can't help you any more than that, but I do gather that it's very important to do the resizing BEFORE you upload the photos.

2.) Then go to the PianoWorld uploading site:

http://www.pianoworld.com/Uploads/fileuploader2.html

This is going to give you a screen where you enter your login name, e-mail address, and then you browse for the location of your photo on your computer which you then attach. There will also be a box that says "file information". I have no idea what they really want there, but I just made up a title like 'first picture of new piano." Then you click submit. That is going to bring you to a new screen that will ask you to search for your name among submitters. This is the most confusing part of the process, because that part of the web site is not working and you will not find your name there. Just ignore it, and instead go back to the main file uploader site and repeat the process for each of your remaining photos.

3.) Within a few minutes, you should receive an e-mail from PianoWorld giving you the URL for your newly uploaded photos. You'll get one e-mail per photo. You will need to copy and paste these URLs into your message.

4.) To do that, go back to the thread where you want to post your photo. Click on the "full reply" box. This will bring up all the options you need. Write whatever text you want, and when you're ready to include the photo, click on the little blue-shaded box below called "image" (under the column 'instant UBB code'). That will pull up a little box in your message where you can paste the URL for your first photo. And then just repeat as necessary. But it is CRUCIAL to click that little "image" box; otherwise, all that goes in is the URL itself, not the photo in all its glory.
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#1895383 - 05/11/12 02:21 PM Re: Augmented 6th chords [Re: currawong]
Gary D. Offline
4000 Post Club Member

Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: currawong
Originally Posted By: Gary D.
Until I find out how to upload files, I can't do this in notation.
See if this works, Gary smile (presumably it will work for a scan of music, too.)

Monica's How to post a photo instructions

1.) First step, and this is critical, resize your photos to about 450-600 pixels. You accomplish this through photoshop or some other photo editing software. My father in law did this part of the process for me so I can't help you any more than that, but I do gather that it's very important to do the resizing BEFORE you upload the photos.

2.) Then go to the PianoWorld uploading site:

http://www.pianoworld.com/Uploads/fileuploader2.html

This is going to give you a screen where you enter your login name, e-mail address, and then you browse for the location of your photo on your computer which you then attach. There will also be a box that says "file information". I have no idea what they really want there, but I just made up a title like 'first picture of new piano." Then you click submit. That is going to bring you to a new screen that will ask you to search for your name among submitters. This is the most confusing part of the process, because that part of the web site is not working and you will not find your name there. Just ignore it, and instead go back to the main file uploader site and repeat the process for each of your remaining photos.

3.) Within a few minutes, you should receive an e-mail from PianoWorld giving you the URL for your newly uploaded photos. You'll get one e-mail per photo. You will need to copy and paste these URLs into your message.

4.) To do that, go back to the thread where you want to post your photo. Click on the "full reply" box. This will bring up all the options you need. Write whatever text you want, and when you're ready to include the photo, click on the little blue-shaded box below called "image" (under the column 'instant UBB code'). That will pull up a little box in your message where you can paste the URL for your first photo. And then just repeat as necessary. But it is CRUCIAL to click that little "image" box; otherwise, all that goes in is the URL itself, not the photo in all its glory.



Currawong,

Many thanks. THIS time I save the directions both on my hard drive and on a back-up. Note to self - do what we tall students - Put things in the right place!

Gary
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#1895394 - 05/11/12 02:53 PM Re: Augmented 6th chords [Re: drumour]
Gary D. Offline
4000 Post Club Member

Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: drumour
The remarkable thing about aug 6ths is that at the point of sounding they want to resolve in a way very different from their corresponding 7th chords. Aug 6ths rarely present an ambiguity where we have to wait for a resolution to clarify.

That is probably true, but there is no reason why we can't have this, in a composition clearly written in the key of C:

G7 [G(#6)] or G Ge6 can be used to slide down 1/2 step, either to reorient in the key of F# major/minor OR to move through that chord through F# to B major or B minor, either temporily, or for a long time. The sneakier the composer, the more stealthy he can be about sliding chromatically. smile

The German 6th spelling signals an expasion of the root and the augmented 6th. The result is a downward movement, 1/2 step.

If we are in the key of C and the use Ab Ge6, it is like another kind if "deception". We are going to Db, oops, no we aren't - we are sliding right back to C major.

If, on the other hand, we are clearly in the key of Db major, that same Ab Ge6 will not alert us that it is going to "slither down" until the next chord. The spelling, if we are reading the music, will alert us in advance to what the composer is up to.
Quote:

What follows a harmony may be determined (by no means always) by that harmony but a subsequent never defines what precedes it; if anything it can only define a specific context.

You lost me there. "A subsequent never defines what precedes it"??? Could you give a musical example?
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#1895443 - 05/11/12 05:33 PM Re: Augmented 6th chords [Re: Gary D.]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
G7 chord - or is it?

Measure 6:

G7 chord.

1) It's not really a German 6th, because it's spelled wrong.
2) It really IS a German 6th, but Chopin was too stupid to write it correctly - (silly ignorant man wrote cool sounding music but did not know his rudiments).
3) Chopin really DID know what he was doing, and chose the spelling that seemed clearest to him.
4) Chopin dumbed down the notation because he was making it easier for students to read.
5) It's really an early composition, so he had not yet learned his rudiments.
6) I have no respect for the composer because I even brought up this point.

All sarcasm above is fully intentional. laugh
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#1895449 - 05/11/12 05:49 PM Re: Augmented 6th chords [Re: Gary D.]
drumour Offline
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"You lost me there. "A subsequent never defines what precedes it"??? Could you give a musical example?"


That's not a reasonable request - disingenuous? - the opposite view is illogical and not thought through. A subsequent may clarify a context it may subvert an expectation it may fulfil an expectation. It doesn't define what precedes it. If you want to argue otherwise you w ill be either indulging some weird semantics or sophistry.

John
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#1895451 - 05/11/12 05:52 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Registered: 06/16/11
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Loc: Maine
Gary, what do you mean by Ge6 in the post just above your latest post?

I'm ducking the Chopin question for now! (I'm vacillating between 1 and 3, but I figure I better have a good reason for 1 if I choose it.)
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#1895464 - 05/11/12 06:27 PM Re: Augmented 6th chords [Re: drumour]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: Gary
"You lost me there. "A subsequent never defines what precedes it"??? Could you give a musical example?"

Originally Posted By: Drumour

That's not a reasonable request - disingenuous?

I honestly do not know what that means. Subsequent, what comes next? And if so, next chord? Next section? The reason I ask is that if we move from G7 to C, a very simple idea, then those two chords alone will strongly suggest V7 I. If, on the other hand, we have some kind of sequence, defining either of those chords is much harder, as in:

G7 C, F#7 to B, F7 to Bb. That gets rather nasty with RNs.

That kind of series might be even more common like this:

G7-5 C, F#7-5 to B, F7-5 to Bb.

Again, RNs would be tricky.
Quote:

- the opposite view is illogical and not thought through. A subsequent may clarify a context it may subvert an expectation it may fulfil an expectation. It doesn't define what precedes it. If you want to argue otherwise you w ill be either indulging some weird semantics or sophistry.

No weird semantics, no sophistry. But it is very hard to address blanket statements when there is no music to talk about, or no musical examples. I might agree with you.

Here is what I am thinking, using letters not for chord names but for the idea of sequence:

X to Y, we can judge the relationship X has to Y. That is a relative thing. But if Z comes next, and we do not yet know what Z is, we do not yet know what Y's relationship to Z is.

G7 to C. We can say that G7 is the V7 of the key of C major, and that relationship is there. But if the next chord sounds like C7, we might guess, through experience and associations, that the C7 will be spelled C E G A# and is about to slip to B/E. Or it might just be spelled normally, moving to F, the chord. Or it might go somewhere else.

I said, in another thread, that if G7 moves to C, it is highly likely, almost a given that the C chord will determine the spelling of the G7. And if the next chord is C Ge6 chord followed by E/B, the E/B chord is going to determine the spelling of the C Ge6 chord.

That is what I meant when I said that the destination chord, which may be a TEMPORARY destination chord, will determine the previous chord's spelling. I think that is simple, and it may be too simplistic. That's why I asked for examples to the contrary. If I'm wrong, I'll be glad to admit it.


Edited by Gary D. (05/11/12 06:28 PM)
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#1895468 - 05/11/12 06:35 PM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: PianoStudent88
Gary, what do you mean by Ge6 in the post just above your latest post?

I'm ducking the Chopin question for now! (I'm vacillating between 1 and 3, but I figure I better have a good reason for 1 if I choose it.)

G B D E#, German 6th chord, augmented 6th chord, misspelled G7 chord, G(#6), G Ge6, G ge6, G ge6th.

I always hear a German 6th chord as a "seven chord" because my hearing is based on sound, not notation. I just hear it as a "7 chord that goes somewhere different". I know how to teach it, I know how to answer test questions, I know what the "right answer is", but that is how I hear it. wink
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#1895476 - 05/11/12 07:04 PM Re: Augmented 6th chords [Re: Gary D.]
keystring Online   content
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Registered: 12/11/07
Posts: 11706
Loc: Canada
Originally Posted By: Gary D.
[quote=keystring]My first reaction to the title of "augmented sixth" is simplistic, but I also like to start with simplicity. I know the aug6 is a semitone above a major 6, and sounds like a minor 7.
Quote:

So far I do not see simplistic. I see a simple fact.

Thank you for this, because I took a risk in being "simple" in my response. Your wording under the title is actually about the French, German and Italian sixths and that is what everybody generally talked about. Coming out with something less sophisticated, namely that the aug6 is a chord that has a sixth a half step higher than a major 6 sounds "simple" and stating the obvious.

I was thinking that maybe this is the first thing that we should know, and not assume that we may know it - just what is the character of the chord as a chord? So that's why I went after that. And then of course there is the "seven chord" sound which you explored. I was hesitating about the "dominant 7". The problem is that while when we say C7 we mean a specific type of chord (major triad, minor 7), the term "seven chord" is ambiguous. But "dominant" means a specific function and that again is a problem.

Quote:

Let's use an Ab7 as good "example seven chord"....
Is the chord contracting - with the Gb coming down 1/2 step?

Or is it expanding, with the Gb wanting to go UP 1/2 step? ...


What I am understanding from the angle you are looking at, is that you are considering both where the chord wants to go, and what direction its notes are moving to go there (expanding or contracting). This in turn influences the spelling conventions, which among other things will influence whether that top note is a minor 7 (Gb) or its enharmonic equivalent augmented 6 (A#). Do I have it?

And then of course there are the usual rules about German, Italian, and French.

Demystification and/or other ways of seeing it?

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#1895488 - 05/11/12 08:01 PM Re: Augmented 6th chords [Re: Gary D.]
Kreisler Offline


Registered: 11/27/02
Posts: 13792
Loc: Iowa City, IA
Back when I was teaching university theory, I made this little tutorial. A lot of people seemed to find it helpful:

https://www.box.com/s/fdad7c765d0841413947
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#1895506 - 05/11/12 08:45 PM Re: Augmented 6th chords [Re: drumour]
keystring Online   content
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Registered: 12/11/07
Posts: 11706
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Originally Posted By: drumour
"A subsequent never defines what precedes it"

John, at the risk of appearing ignorant, I'd like to ask about this. I looked up "subsequent" as a musical term in my Harvard dictionary of musical terms and googled it with no results. Actually I think your sentence is part of a sequence of things and I'd like to understand what you are actually saying. It is quite condensed. In an attempt to understand I'll try to take it apart and paraphrase which I hope is ok.

"Aug 6ths rarely present an ambiguity where we have to wait for a resolution to clarify. The expectations set up by aug 6ths are rarely subverted by composers in their resolutions unlike in the case of 7ths. What follows a harmony may be determined (by no means always) by that harmony but a subsequent never defines what precedes it; if anything it can only define a specific context. "

I understand that you are setting up how the aug 6th is different than the 7th chord. In the first sentence you are saying that the 7th has ambiguity (can do a number of things) but the aug6 does not have that character. " The expectations set up by aug 6ths are rarely subverted by composers in their resolutions unlike in the case of 7ths. " This says the same thing.

What follows a harmony may be determined (by no means always) by that harmony.... I am guessing that "what follows a harmony" actually gives us the definition of "subsequent" because that is what this word means literally.

"... but a subsequent never defines what precedes it; " so what follows the harmony cannot define what is before it.

When you say "a harmony" - would the aug6 chord be "a harmony"? So in other words, if I understand this:
the aug6 is set up in such a way that what follows it must go a certain way, and that makes it unambiguous, unlike the seven chord, in view of your whole paragraph?

I am with Gary that it might be easier to follow with an actual example. Requesting an example is not a case of challenging, but of getting a picture of what you are saying.

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#1895513 - 05/11/12 09:18 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
3000 Post Club Member

Registered: 06/16/11
Posts: 3181
Loc: Maine
Do composers sometimes use these chords deceptively? Kreisler's explanation sheet says the augmented sixth chords are built on the flat sixth scale degree and resolve outward to the dominant. For example, Ab C Eb F# resolving to G B D G in the key of C.

But equally you could take any seventh chord, and resolve it outwards. For example, in the key of C, start with G B D F. Rewrite F as E# if you're feeling fussy. Resolve, not to C, but to F#.

Hmmm, I think I've just managed to recapitulate what Gary's been saying. Now I need to look at his Beethoven and Chopin examples and see if they're the textbook variety of bVI(aug6) resolving to V, or if they're this other deceptive kind.

I can see how the textbook variety might announce itself aurally, because if you had clever ears, you could hear those two chromatic tones as being chromatic, and perhaps with enough aural experience come to expect it to resolve to V (or to I 64 and then V). That sets up a new way for composers to be deceptive: resolve as if the German 6th were a dominant 7th. E.g. in the key of C, go to Ab Ge6. Adjust the spelling to Ab7 if you wish. The listener can't tell what spelling you're using, though. Then resolve, not to G or C 64, but to Db.

OK, now I'm sure I'm just recapitulating what's already been said. But it's starting to make sense to me.
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#1895518 - 05/11/12 09:33 PM Re: Augmented 6th chords [Re: Gary D.]
Kreisler Offline


Registered: 11/27/02
Posts: 13792
Loc: Iowa City, IA
Originally Posted By: Gary D.
G7 chord - or is it?

Measure 6:

G7 chord.


It's Chopin doing a little bit of everything. The G Major on beat 1 is something of a pivot chord. It serves as III, the relative Major of e minor, but it also serves as vi in b minor.

Of course, the notes G and B are also common to two other predominant harmonies in b minor - iv and ii (half dim 7). Chopin adds the E (also found in iv and ii) in beat 2 of the LH, along with the F.

And the F is an interesting note - it could be seen as a lower neighbor to the F# or as a respelled E# of an (incorrectly) resolved Gr+6.

In the moment, however, it's not necessarily heard as such, since it could also be a simple G7 - an applied dominant leading to C Major, or V7/VI in e minor.

The "incorrect" resolution is also interesting, since the parallel fifths (G-F# and D-C#) exist regardless of how we interpret the chord.

Except that Chopin's not an idiot. The reason parallel fifths are to be avoided is that they don't make for very good counterpoint, but Chopin isn't writing counterpoint in the LH, he's writing a simpler harmonic texture, so the parallel fifths (in addition to being somewhat obscured by an octave displacement that takes the middle line D to the higher D) aren't a problem.

Regardless of how we analyze it (and this is probably a case where any good analysis would take the form of prose rather than simple labeling), the fact remains that Chopin has given us a very clever bit of harmonic sleight-of-hand that makes perfect sense. That is, until you try to make sense of it. laugh
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#1895548 - 05/11/12 11:41 PM Re: Augmented 6th chords [Re: Kreisler]
Gary D. Offline
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Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: Kreisler
Back when I was teaching university theory, I made this little tutorial. A lot of people seemed to find it helpful:

https://www.box.com/s/fdad7c765d0841413947

thumb
This is VERY nice.

I think you would be a bit mean to make your students work out augmented 6th chords in the key of Gb. In F# it is a snap, and then F# minor is covered too. wink

Your key of Gb is going to ask for an Ebb7, Eb G Bb Db coverted to Ebb Gb Gbb Dbb, then respelled to Ebb Gb Bb *D*. This immediately solves your third example. Convert to SATB and it flows effortlessly to Gb/Db, then cadence.

Someone like Chopin would do it, and probably does somewhere. Thinking about this a bit more, it may be the reason he chose F# major and not Gb major for his Barcarolle. smile
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#1895609 - 05/12/12 03:54 AM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
4000 Post Club Member

Registered: 08/30/08
Posts: 4810
Loc: South Florida
Originally Posted By: PianoStudent88
Do composers sometimes use these chords deceptively? Kreisler's explanation sheet says the augmented sixth chords are built on the flat sixth scale degree and resolve outward to the dominant. For example, Ab C Eb F# resolving to G B D G in the key of C.

Specific augmented sixth chords are used on bVI. Those include the three "countries", Italian, French and German. But beware: they are the bVI chords of the key you are GOING to, not NECESSARILY of the one you are IN. And no key signature is necessary to tell you your new destination. They either take you up to bVI, in the key you are already in and then back down again (net result is no movment) - OR they allow you to jump to ANY other key.

Example: I am in C major. I would like to jump to B:

C F C *G7* B/F# F#7 B. I am in a new key. I moved down 1/2 step. G7, which I always explain as the "misspelled" seven chord, must then be spelled G B D E#, or USUALLY is. There are exceptions, but mostly in Romantic music and later, and not in counterpoint.

Another example: I am in C major. I do this:

C F C *G7-5* F# B C# C#7 F#. I have now moved to F# major. My misspelled G7-5, G B C# E, which is spelled like a French 6th, is not one because it is treating my G7-5 as a bII.

I wish I had the energy to notate this. The chord symbols are confusing. Be sure to insert spaces between each chord.

I hope I am not being horrendously complicated. In person I could show you this in a heartbeat.

There is an ending in a Chopin prelude in which he moves from a sweeping Db7 chord with a downward arpeggio straight to Fm. So here it is in the bVI position, the right degree, but the jump is absolutely non-standard, and therefore VERY cool.

There is another composition in which he uses a Gr6, using Kreisler's abbreviation, but he appears to "misspell" it. He uses the conventional V7 spelling until the LAST repetiton of the chord, then there he switches the spelling to show function. If you are looking for rules, Chopin will totally screw you up, and so will the compositions of MANY fine composers, but if you study them long enough, the reason for not following rules - which I think of more as conventions that are guidelines - become clear. In the end, although you may not agree with the choice, it can always be defended. Geniuses seldom make such choices out of sheer ignorance or from carelessness.

The important thing is always to use SOUND as your guide, not NOTATION. If it feels like a duck and sounds like a duck, in music it does does not have to LOOK like a duck.
Quote:

But equally you could take any seventh chord, and resolve it outwards. For example, in the key of C, start with G B D F. Rewrite F as E# if you're feeling fussy. Resolve, not to C, but to F#.

What comes after the F# chord will tell you if you are really going there (I chord) or if F# is the dominant and is going next to B or Bm

That is exactly correct. But rewriting is not fussy, because that E# is going to move up to F#. In general, whenever a voice moves chromatically, you try to avoid repeating a letter, which F to F# does.
Quote:

Hmmm, I think I've just managed to recapitulate what Gary's been saying. Now I need to look at his Beethoven and Chopin examples and see if they're the textbook variety of bVI(aug6) resolving to V, or if they're this other deceptive kind.

Beethoven's chord is an Italian 6th, conventional spelling. But the top note jumping from C to G is not typical of earlier periods. It is a jolt. A stabbing chord. Bam, Bam. Always expect Beethoven to do the unexpected, equally true of all geniuses.
Quote:

I can see how the textbook variety might announce itself aurally, because if you had clever ears, you could hear those two chromatic tones as being chromatic, and perhaps with enough aural experience come to expect it to resolve to V (or to I 64 and then V). That sets up a new way for composers to be deceptive: resolve as if the German 6th were a dominant 7th. E.g. in the key of C, go to Ab Ge6. Adjust the spelling to Ab7 if you wish. The listener can't tell what spelling you're using, though. Then resolve, not to G or C 64, but to Db.

Here is what you are leading to: Cm G7 Cm, Ab7 Db, Ab7 Db, G7 Cm. That is a jolt, ragged, harsh, in your face, so very Beethoven like, just shaking different dominants in your face. There A7 will be spelled in the ordinary manner.

Similar, but also different:

C G7 C, Ab7 Db7 Ab7 Db7, *Ab7* C/E G7 C. Now the LAST Ab7 chord will be respelled as the Gr6 chord because it slides back to C. Spelling shows where it is going. Where it is going determines spelling. If the spelling convention is not followed, you will not have trouble reading it or hearing it, because the function is independent of the notation. And that is why I call a Gr6 a 7 chord, for students but warn them to put, in parentheses, Gr6. This links the sound, which does not change, to the spelling, which usually does.
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