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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: 4814
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: 3183
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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Registered: 06/16/11
Posts: 3183
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: 4814
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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Registered: 06/16/11
Posts: 3183
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
Yikes! 10000 Post Club Member

Registered: 12/11/07
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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 Offline
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Registered: 08/09/09
Posts: 324
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.]
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: 4814
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: 4814
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: 4814
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: 4814
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: 3183
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: 4814
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
Posts: 861
Loc: Scotland
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: 5963
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: 4814
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: 4814
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: 4814
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.]
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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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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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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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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.]
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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.]
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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]
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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
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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.]
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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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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
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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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#1895678 - 05/12/12 09:18 AM Re: Augmented 6th chords [Re: Kreisler]
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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

Kreisler, I had a look at this last night. The first line describes these as predominants. I have seen augmented 6th chords used in many different ways in music, especially in music that moves out of the Common Practice period. What you wrote reminds me of the basic mainstream theory I am studying, where for example you have the pivot chord and gradual movement, and also sudden movement through a chromatic change. The models are very specific and that makes them easy to understand and follow. When we get to real music - even of that period - we find a much greater variety. Is that essentially the context of the predominant idea? One way we will find the aug6 used, but not the only way?

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#1895690 - 05/12/12 09:57 AM Re: Augmented 6th chords [Re: Gary D.]
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Augmented sixths are always a predominant.

There may be additional decoration - various passing motion, suspensions, or things, but they essentially remain predominant in function.

(A wonderful example is the famous "Tristan" chord. It's an augmented sixth with an incomplete lower neighbor that leads to a V chord without the 3rd that remains unresolved. But if you look at the context of how the opening plays out, it's definitely an augmented sixth.)
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#1895701 - 05/12/12 10:26 AM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Since an augmented sixth resolves to a major triad, why can't it just stop there and treat the triad as I, instead of insisting on the augmented sixth being a predominant and treating the triad as V? In other words, why can't the augmented sixth be built on bII instead of bVI?

So, for example an Italian sixth Ab C F#, resolving outwards to G major. Why can't the piece just stay in G? Why does it have to treat G as a dominant and continue on to C?
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#1895707 - 05/12/12 10:46 AM Re: Augmented 6th chords [Re: Kreisler]
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I have seen theory viewed from different angles under different contexts. Whenever you move in a framework it is important to stay in that framework. But frameworks have edges and reality moves beyond those edges. I have seen more than one framework or system. It would be unfortunate if we only stayed in one.

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#1895713 - 05/12/12 10:59 AM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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It's like I've been given a new train set, and I want to immediately crash the locomotive into walls and fly it off the tops of dressers turning it into an airplane, instead of running it on the tracks as it was intended. wink .

I played a French sixth today and resolved it, and was very pleased that I could hear how nice the resolution felt.

I also discovered that what I call "shimmering" others might call "unstable." (I had a friend over, listening to me, and unstable was the word she used for the French sixth.)
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#1895721 - 05/12/12 11:22 AM Re: Augmented 6th chords [Re: Kreisler]
Gary D. Offline
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Originally Posted By: Kreisler
Augmented sixths are always a predominant.

No. Augmented 6ths with the names German, Italian and French are predominant because they have been defined that way.

As I have repeatedly pointed out and tried to show, perhaps unsuccessfully, is that this narrow definition is textbook thinking and will get either of us an A on a theory exam EXPECTING that exact answer.

But to say an augmented 6th chord is always a predominant assumes:

1) Any augmented 6th chord that does not resolve to a V is not an augmented 6th chord.
2) Only the German, Italian and French 6ths are augmented 6ths.

Under that narrow definition this:

Db F Ab B

Going to this:

C E G C

Is not an augmented 6th chord if it is followed by by an F, Dm, C/G, G7 C, making it a bII chord, not a bVI.

No predominant there. smile
Quote:

(A wonderful example is the famous "Tristan" chord. It's an augmented sixth with an incomplete lower neighbor that leads to a V chord without the 3rd that remains unresolved. But if you look at the context of how the opening plays out, it's definitely an augmented sixth.)

I'm ready to talk about that any time. What a WONDEFUL progression that is!

I always like to stick to music, so lets "talk Wagner"!!!
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#1895730 - 05/12/12 11:51 AM Re: Augmented 6th chords [Re: Gary D.]
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I suddenly had a picture of the original Cinderella story. The ugly stepsisters couldn't fit their big feet into the glass slipper, so they changed the shape of their foot to make it fit. Any formal theory about anything creates a good generalization about some reality. It tends to fit in most situations. But it gets fuzzy at the edges and at some point you have to squeeze reality more and more to make it fit that particular system. It forces you to see reality according to that particular system. That is why it is handy to have more than one system (eventually). I imagine that the predominant idea works well in many situations, and we can imagine implied dominants when we get to the edges, but that there can also be *other* ways of perceiving.


Edited by keystring (05/12/12 12:06 PM)

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#1895746 - 05/12/12 01:00 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Originally Posted By: Gary D.
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.

No problem. Thank you very much for your terrific detailed reply. Working from the chord symbols, it makes me really absorb what's going on by writing them out myself in notation. Now I also have to try them out at the piano and hear what they sound like. (I'm at work, but haven't brought my keyboard to work yet, so I'm just here with my music paper procrastinating on a software installation....)
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#1895773 - 05/12/12 02:18 PM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Chopin Prelude in F Minor

Page 35 in the book, Page 41 in the pdf file, last line:

Db7 moves directly to Fm.

Interesting note: in one edition, by Palmer, the first octave is B natural, then the chord immediately following changes to Db. In this one, Mikuli, and in other editions I've checked, the octave is Db, enharmonic.

1) Palmer made a mistake.
2) Palmer, who was meticulous about observing sources, kept an idiosyncratic choice in at least one choice.

If 2 is correct, then other editors "fixed" this odd notation, which is logical to me. But Palmer's is logical too, because it announces an augmented 6th chord (theory), but then changes the spelling to the more readable Db7 spelling, which is clear and very pianistic.

The following measure has no chord, so the feeling of Fm is implied before the final cadence that confirms the key of F minor.

If the Db is correct throughout - which would be my choice - then the spelling conflicts with the function of the chord IF we accept augmented 6th spellings as the Word of God. wink
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#1895787 - 05/12/12 02:56 PM Re: Augmented 6th chords [Re: Gary D.]
Gary D. Offline
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Chopin Nocturne in C# Minor
P. 35 in the score, P. 4 in the pdf file...

Chopin modulates to the key of Db at the con anima.

Now, go to line three, measure two.

There Chpoin uses a Db7-5, respells the top note from Cb to B, then slides to C major. So it Chopin, in the key of Db, wants to slide down to the key of C major. He isn't going to be there long, but you can hear.

So it's a bII going to I. NO WAY is it a V.

So, again, we have something that is clearly an augmented 6th chord, and in every way it sounds exactly like a French 6th chord, but we can't call it that because it is not a predominant.

Instead, it the EXACT same thing you hear jazz players talk about: tritone exchange. Since G7-5 is G B Db F, and Db7-5 is Db F G Cb, when Chopin uses the augmented 6th, Db-B, he simply inverts the G7-5, an altered dominant, thus EXCHANGING it for the Db7-5.

And that is what jazz players often refer to as the "tritone exchange". smile

Another example of how real music does not fit into boxes, and how all styles of music are much more closely related than is normally taught.

This is why we need a Big Picture approach.


Edited by Gary D. (05/12/12 03:09 PM)
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#1895875 - 05/12/12 06:23 PM Re: Augmented 6th chords [Re: keystring]
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keystring,

"Subsequent" is not a musical term, I was using its common meaning.

Very near the start of the Mozart Cm fantasia that's often coupled with the Cm sonata is an example of an aug 6th in context. There are quite a few examples in Mozart sonatas.


John
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#1895934 - 05/12/12 09:25 PM Re: Augmented 6th chords [Re: Gary D.]
LadyChen Offline
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Many sonatas use aug6 chords in the development section because they are good at building tension and creating a strong dominant feel that leads back to the tonic in the recap.

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#1895954 - 05/12/12 10:45 PM Re: Augmented 6th chords [Re: Gary D.]
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Originally Posted By: Gary D.
If the Db is correct throughout - which would be my choice - then the spelling conflicts with the function of the chord IF we accept augmented 6th spellings as the Word of God. wink


But the spellings aren't the Word of God, and that's where it's important to realize what music theory really is. It's not so much a theory of how music works as it is a description of common practice.

And being a description of common practice, it's also good to keep in mind that it doesn't describe *uncommon* practice, as in the Chopin examples you've been giving.

To find a theory that's more rigorous and comprehensive, we have to look at Neo-Riemannian approaches. The kind of imprecision you've been describing is one of the reasons Lerdahl and Jackendoff sought a new direction for music theory in their work on the subject. There is a point where the old McHose Contrapuntal-Harmonic Roman numeral approach breaks down, and that's where a Generative Theory of Tonal Music takes off. It's starting to get a bit more attention in university music departments, but it's also a difficult subject for many musicians since it takes as a starting point some linguistic principles that most musicians are unfamiliar with.
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#1896035 - 05/13/12 05:26 AM Re: Augmented 6th chords [Re: Kreisler]
Gary D. Offline
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Originally Posted By: Gary D.
If the Db is correct throughout - which would be my choice - then the spelling conflicts with the function of the chord IF we accept augmented 6th spellings as the Word of God. wink

Originally Posted By: Kreisler

But the spellings aren't the Word of God, and that's where it's important to realize what music theory really is. It's not so much a theory of how music works as it is a description of common practice.

My "Word of God" expression was highly sarcastic and aimed at all the pundits who try to round up all of us and push us into a box. smile

But I think we have to remember that Common Practice is often defined as including Romanticism. Once you start expanding concepts to fit into the music of Chopin, Liszt, Brahms, Wagner and Mahler, narrow definitions get very fuzzy. Chopin's spellings are immensely important to me for the simple reason that his music was so incredibly pianistic. For the same reason that I look at Bach and Mozart for norms of how things were done in those earlier periods, I look at Chopin for guidelines for Romanticism, specifically for piano music.
Quote:

And being a description of common practice, it's also good to keep in mind that it doesn't describe *uncommon* practice, as in the Chopin examples you've been giving.

But here is my problem with that, and I hope you will respond, because you are one of the people in this forum who always gives sound answers. Chopin is right in the MIDDLE of the Common Practice Era, as it has always been described to me. After all, he died slightly before the middle of the 1800s. His notation should make very conservative theory teachers squirm. A lot of his spelling conventions were followed by much later piano composers of Romantic music - think only of Rachmaninov, whose music was mostly WRITTEN at the end of Common Practice.
Quote:

To find a theory that's more rigorous and comprehensive, we have to look at Neo-Riemannian approaches. The kind of imprecision you've been describing is one of the reasons Lerdahl and Jackendoff sought a new direction for music theory in their work on the subject. There is a point where the old McHose Contrapuntal-Harmonic Roman numeral approach breaks down, and that's where a Generative Theory of Tonal Music takes off. It's starting to get a bit more attention in university music departments, but it's also a difficult subject for many musicians since it takes as a starting point some linguistic principles that most musicians are unfamiliar with.

Isn't that the elephant in the room? By the way, I have never heard the term "Generative Theory of Tonal Music", but it certainly resonates with the way I think - and I suspect the way you think. An intuitive approach is to study, carefully, the notation of every possible major figure in music, from long ago right up to the present. For the same reason that a VERY careful study of Bach is necessary to write a short chorale that might fool the average musician into thinking Bach wrote it, the same thing is true of writing in the style of any other musician. General trends or guidelines emerge from the writing of individual composers that apply TO THOSE COMPOSERS, and somehow this is linked to the same sense that allows us to immediately identify the composer of music we do not know - if we are familiar with MOST of the music by that composer but have missed a composition or two. smile


Edited by Gary D. (05/13/12 05:28 AM)
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#1896048 - 05/13/12 06:06 AM Re: Augmented 6th chords [Re: keystring]
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Originally Posted By: keystring
Kreisler, I had a look at this last night. The first line describes these as predominants. I have seen augmented 6th chords used in many different ways in music, especially in music that moves out of the Common Practice period. What you wrote reminds me of the basic mainstream theory I am studying, where for example you have the pivot chord and gradual movement, and also sudden movement through a chromatic change. The models are very specific and that makes them easy to understand and follow. When we get to real music - even of that period - we find a much greater variety. Is that essentially the context of the predominant idea? One way we will find the aug6 used, but not the only way?

My impression of Kreisler's page was that it is specifically geared towards SATB. The examples are in two staves but obvious could be put into four. The range is right for singers.

His example of the German 6th illustrates a trouble spot. Bach would be unlikely, for obvious reasons, to write a chorale in Gb. In general we find composers starting to use such a key a great deal in the Romantic period, piano music especially. In addition, often composers favor F# major over Gb major for the simple reason that a toggle from major to minor is easier. F# and Gb both have 6 flats/sharps in the key signature, but Gb minor, the key, would have 9, with two double flats.

That makes a German 6th chord in Gb rather nasty. You have to reason backwards:

The I6/4 chord will be Gb/Db. The dominant is Db7, no problem, but 1/2 step higher is D7, which you can't use. You have to use Ebb7, a real pain, and a bit of a headache-maker. You can get to it fast by writing out Eb(#6), Eb G Bb C#, then lowering the whole thing to Ebb Gb Bbb C. That allows the Ebb--C to expand to Db--Db.

If you do the same thing in F# major, suddenly you have D F# A B# moving to C# F# A# C#. You would always pick that solution, if you could, and it works perfectly for F# minor.

HOWEVER: much as in the Satie example, there are times we are "caught in flats" and need the more clumsy solution.

Kreisler's solution is backwards to mine. I always think destination (I6/4 or V of the key I am GOING to), then construct the aug 6th chord moving backwards if I have any hesitation about spelling. In simpler keys the spelling is automatic, but not in Gb major.

That is what I mean by destination (in this case Gb/Db) determining the spelling of the previous chord - Ebb(#6).

You can see why, in this case, people prefer Gr6 to I6/4 to V7 to I.
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#1896055 - 05/13/12 06:35 AM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
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Originally Posted By: keystring
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 need to go back to this a moment. Anyone who has taught for years knows that NONE of this is simple. There is a reason why most people don't get to it until college, and when this was presented to me, I saw a lot of students either lost or blindly memorizing rules to pass tests without really understanding what was going on.

The labels "French, German and Italian" show function. They "live in the RN world". They are not descriptive but prescriptive. "Neopolitan" lives in the same world. This is always a major built on the lowered second of a scale, and frquently it is in first inversion, leading the Neopolitan 6 chord. In C, that simply means a first inversion Db chord.

Augmented 6 chords are not about function, although they do tend to "expand". They can be inverted, arpeggiated, and they can even contract with the bottom moving up:

B Db F Ab to C F Ab Eb Gb Ab to G C E G

That's Db(#6)/B to Fm/C. It's up to you whether or not you consider the chord in 3rd inversion still an aug 6th chord, since that interval flipped because a dim 2nd. But it's the same chord, and the spelling is still guided by destination. B and Db converge on C, F and Ab do not move. It's just the easiest way to notate those two chords. It still is 1/2 step above the normal V7 (C7) and cadences to Fm. So it is like an inversion of a German 6th.

Db F Ab B looks like a typical German 6th, key of C.

But if it does this: Db F Ab B to C E G C, you can do this:

Db(#6) // C // F // C/G // G7 // C.

Now it is still an augmented 6th chord, it still sounds like a seven chord, it still opens up (expands), but it expands to I, not V. We have a sound, we have a spelling, but we can't be sure where it will go. We might say it has possible functionS, plural, but that's all.
Quote:

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?

Yes. This is exactly what I meant.


Edited by Gary D. (05/13/12 06:38 AM)
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#1896117 - 05/13/12 10:34 AM Re: Augmented 6th chords [Re: Gary D.]
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Initially I focused on the title of your thread, which is "augmented 6th chords" which covers every incident of aug6 chords as they are used in every period of music. Thus I was looking at their general behaviour as they would tend to occur anywhere. I tried to stay away from anything more narrow or specific. That is the reason for this:
Originally Posted By: Gary D.
Originally Posted By: keystring
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?

Yes. This is exactly what I meant.

Thank you for that answer. It seems to be a crucial point.

Going on, while your title says "Augmented 6th chords", your opening post mentioned the French, Italian, and German 6th. This is a specific use of Augmented 6th chords, and it belongs mainly to a particular period of music history. It is also functional. That is, it involves the predominant role etc. which has been discussed at length here. The difference between considering "Augmented 6ths" and considering the "German/French etc. 6th" is like the difference between discussing the nature of major chords, and discussing the Dominant chord which has a specific function in music.

You actually opened the door for both angles but in the way people tend to read posts, myself included, is that we tend to glance and think we have the gist of it and so the bottom line is easily missed.
Quote:
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.


You have left ample room for every kind of discussion. smile

At this point, having read through pages of posts, at least personally I need to sort this out and maybe I'm not alone:

- There are discussions on the specifics of Common Practice, functional things, and I'd say specific to the French etc. chords. This is where we have definitions involving the predominant role etc. Sometimes reference has been made to the "augmented 6th" and it is simply assumed that Common Practice and those functions (German etc.) are meant.

- There are discussions on the augmented 6th chord in every possible way it can occur, and the ways it can move. This goes with the part I quoted in italics. There are delightful references to jazz, and analogies of a toy to play with in free exploration which is something I'm inclined toward.

I think we need to be aware that there are these two separate angles going on. There is also an underlying problem that when we study theory formally, it is usually along Common Practice, but often we are not told that this is a limited view. So people can come away with the idea for example that augmented 6th chords only function as predominants, only function in the Common Practice way of German etc. Then in a broader exploration there can be confusion if it's not clear that there is more than one angle being viewed by various people.

I don't know if anyone else needed to have a second look at the thread, but since it helped me navigate, I decided to share it.

My thought at the moment is that when we explore the aug6 in a "generic" way, we get to see some properties that are also part of the specific German etc. chords. When we look at CP German etc. we're into a tighter functional world of predominant etc., but the predominant feel happens in all kinds of music as well - just not so specifically. I applaud this idea of a very broad exploration, because maybe it can help us climb out of some boxes.

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#1896156 - 05/13/12 12:27 PM Re: Augmented 6th chords [Re: Gary D.]
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Originally Posted By: Gary D.

I need to go back to this a moment. Anyone who has taught for years knows that NONE of this is simple. There is a reason why most people don't get to it until college, and when this was presented to me, I saw a lot of students either lost or blindly memorizing rules to pass tests without really understanding what was going on.

I admit that I already have a viewpoint that I formed a few years ago. What I see in how music is taught via theory books, is that rudiments are skipped, and even when they are not skipped, they are taught like formulas and things to be memorized. You are told rules of naming intervals without ever going into what an interval is, and sorting out the "what is" from "how it's named and how that came about". People manage to pass the tests, know how to shove notes around on the page and get the right answers but don't really know what these things are. When you get to advanced theory you are working with these things and they have never been real for you.

My suspicion is that the struggling students you saw were struggling because of what preceded in their studies, not (only) because the theory was harder or more complicated. This goes not only to not getting a true connection to basic things as they are, and as they occur in music. I suspect that it also involves learning a wrong way of relating to music and theory. If it is memorization of rules without ever being engaged, at some point you are so flooded by so many rules that it doesn't work anymore.

I would be surprised if there wasn't something to this. In the theory books that I have studied one can be tempted to memorize formulas and rules, and I saw early on that this could be a trap.

A student whom I taught told me something that for the moment I think might hold true, "I used to think that simple music was complicated. Now I see that complicated music can be reached through simple things." This was the thought that governed both my own studies and then my teaching. If these concepts of German, Italian etc. 6ths are hard, do they have to be as hard as what you observed among your classmates decades ago?

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#1896161 - 05/13/12 12:31 PM Re: Augmented 6th chords [Re: Gary D.]
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Originally Posted By: Gary D.

Augmented 6 chords are not about function, although they do tend to "expand". They can be inverted, arpeggiated, and they can even contract with the bottom moving up:

B Db F Ab to C F Ab Eb Gb Ab to G C E G

That's Db(#6)/B to Fm/C. It's up to you whether or not you consider the chord in 3rd inversion still an aug 6th chord, since that interval flipped because a dim 2nd. But it's the same chord, and the spelling is still guided by destination. B and Db converge on C, F and Ab do not move. It's just the easiest way to notate those two chords. It still is 1/2 step above the normal V7 (C7) and cadences to Fm. So it is like an inversion of a German 6th.

Db F Ab B looks like a typical German 6th, key of C.

But if it does this: Db F Ab B to C E G C, you can do this:

Db(#6) // C // F // C/G // G7 // C.

Now it is still an augmented 6th chord, it still sounds like a seven chord, it still opens up (expands), but it expands to I, not V. We have a sound, we have a spelling, but we can't be sure where it will go. We might say it has possible functionS, plural, but that's all.

This is part of kind of thing that I was looking for. Thank you. This also bridges a link or shows a relationship (what is and isn't) between the functional CP things and these broader things.


Edited by keystring (05/13/12 12:32 PM)

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#1896234 - 05/13/12 02:46 PM Re: Augmented 6th chords [Re: Gary D.]
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Due to some of the awkward voice leading (and confusion accidentals), you'll sometimes see the perfect 5th in a Ger6 chord spelled as a double augmented 4th .. and yes, it is ironic that doing so makes things simpler lol. So.. a ger6 chord built on Eb .. you get Eb, G, C# and A# (instead of Bb). We do this because, in voice leading, there is a general rule that raised notes should resolve upwards and lowered notes should resolve downwards.

In the example of the Ger7 chord spelled Eb G C# A#, it resolves to a V6/4 - V5/3 (in this example - D). When you spell the Bb enharmonically as A#, the A# resolves upwards to B. This is preferred to a Bb resolving upwards to B.

I'm not sure if these rules are also followed in piano music -- I would suspect the voice leading isn't as important as it is in choral music.

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#1896262 - 05/13/12 04:10 PM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
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Originally Posted By: keystring
Initially I focused on the title of your thread, which is "augmented 6th chords" which covers every incident of aug6 chords as they are used in every period of music. Thus I was looking at their general behaviour as they would tend to occur anywhere. I tried to stay away from anything more narrow or specific.

What you thought of was exactly what I had in mind. To get to what you wrote about later, EVERYTHING I present tends to be "in a generic way". My learning style is to grab a big picture first, then move to specifics.

1) Any chord that sounds like these - C7, C7-5, can have at LEAST two spellings, sometimes more:

C E G Bb or C E G A#------------- C E Gb Bb or C E Gb A# or C E F# A#

2) This idea is true regardless of root, or spelling of root.

3) The spelling will become intuitive according to the spelling of the next chord:

C E G Bb---> C F A--->
C E G A#---> B E G B--->
C E Gb A#--->PROBLEM!!!!--->I can't think of a reason for this spelling...
C E F# A#--->B D# F# B--->

We now come to the Great Divide.

1) Starting where Kreisler starts in his tutorial, which by the way is solid as a rock, this C7-5 chord is going to be spelled C E F# A#; it's pretty much dead certain that it will go to B, then to E or Em. The function makes it a French 6th.

But to people who specialize in music of that area, the chord symbols I am using are going to look like Martian. In Bach's time there will be a C in the bass and if there are symbols, #4 and #6 will go over the bass note - figured bass. I can't copy and quote Kreisler, but it's right there on his page. He mentions #6/3 (It.), #6/#4 (Fr.) and #6/5(Gr.)

2) Starting where I was when I arrived at college, C7 goes just about anywhere, by sound. You can have:

a) C7 Eb7 Gb7 A7 (Debussy)

b) C7 // Cm7 // Cm7b5 // Cdim7 // B7, anyone from Bach on...

c) C7 // A7/C# // D7 // B7/D# (Brahms, but earlier and later)

d) C7 // F // Db7 Gb (etc.) warming up choruses and singers, also standard "up a 1/2 step pop music cliche".

e) C7 // E/B

That just scratches the surface.

In other words, if you have a very good ear and you have played tons of music, of all styles, you are already used to all these sounds. If the ear is already there, spelling becomes a detail, a fine point. You learn to talk to people according to the world they live in. Some people only understand figured bass, some only RNs, some only letters.

The Divide:

Those who are familiar with and comfortable with letter notation AND PREFER IT are used to dealing in sound as the main focus. Most likely they will be "mapping" music as it goes along, hearing and sensing progressions or patterns that are often taught with RNs. Letters don't say a thing about function.

That "world" is not linked to spelling, and it takes some getting used to if you are in the world of Bach and Mozart. I don't have to write C(6#/#4) if I want to go to B. C7-5 to B will get the job done. If I want C# E G A# to go to C# E F# A#, C#dim7 to F#7/C# works just fine. 7 doesnt mean m7 in notation. it means m7 by sound, which of course can be aug 6. And dim7 or °7 doesn't mean a diminished 7. It means either that or a major 6th. Context tells which is right for spelling.

In contrast, figured bass is specific. It is specific to a key, and there is no ambiguity about spelling.

Bridging these two systems is not easy, but RNs often come close.
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#1896268 - 05/13/12 04:24 PM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
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Originally Posted By: keystring
What I see in how music is taught via theory books, is that rudiments are skipped, and even when they are not skipped, they are taught like formulas and things to be memorized. You are told rules of naming intervals without ever going into what an interval is, and sorting out the "what is" from "how it's named and how that came about". People manage to pass the tests, know how to shove notes around on the page and get the right answers but don't really know what these things are. When you get to advanced theory you are working with these things and they have never been real for you.

Playing from music, playing by ear, and notating what you create are fragmented. If you are learning to write music and you have the drive to create your own music, all the rules in the world are going to create themselves as you solve problems.
Quote:

My suspicion is that the struggling students you saw were struggling because of what preceded in their studies, not (only) because the theory was harder or more complicated. This goes not only to not getting a true connection to basic things as they are, and as they occur in music. I suspect that it also involves learning a wrong way of relating to music and theory. If it is memorization of rules without ever being engaged, at some point you are so flooded by so many rules that it doesn't work anymore.

I don't know what went wrong. This was between 1966 and 1972. I only know that it was all easy for me, and it wasn't for most of the others.
Quote:

If these concepts of German, Italian etc. 6ths are hard, do they have to be as hard as what you observed among your classmates decades ago?

I don't know. I remember a story of a piano student who drew stain-glass windows as an answer to a theory exam. Then the professor asked him why, he said: "Dr. Boda, I just don't understand any of this, so I just drew pretty pictures."

That same student flew through some of the hardest Chopin Etudes as if they were child's play. Now, could he write music? I doubt it.

But in general the people who were most lost were singers - singers who did not play an instrument. The whole "world of notation" was new to them, and they had to start from scratch.
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#1896273 - 05/13/12 04:34 PM Re: Augmented 6th chords [Re: Gary D.]
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Gary, my point was that I believe that people may be given the most elementary theory in a shallow way, when these are actually the essence of music. If they get into the habit of relating to theory as a set of rules, this will trip them up in advanced theory. If they cannot connect to basic things like intervals in a real way, then that will trip them up too. So I am suggesting that the difficulty at the university level might be caused by what happened before.

Of course another cause would be if the advanced material was taught in a bad way. Or all of the above.

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#1896276 - 05/13/12 04:42 PM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
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Originally Posted By: keystring
Gary, my point was that I believe that people may be given the most elementary theory in a shallow way, when these are actually the essence of music. If they get into the habit of relating to theory as a set of rules, this will trip them up in advanced theory. If they cannot connect to basic things like intervals in a real way, then that will trip them up too. So I am suggesting that the difficulty at the university level might be caused by what happened before.

Of course another cause would be if the advanced material was taught in a bad way. Or all of the above.

My thought:

I have a friend who always got As in geometry and algebra. She needed those As. Working like that earned her a scholarship.

She never understood those things. She just memorized the rules, and specific answers to specific problems. Now she remembers none of it. If she had ever need the information taught in those courses, she would have had no choice but to start again, from scratch.
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#1896466 - 05/13/12 11:45 PM Re: Augmented 6th chords [Re: Gary D.]
LadyChen Offline
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Originally Posted By: Gary D.


I have a friend who always got As in geometry and algebra. She needed those As. Working like that earned her a scholarship.

She never understood those things. She just memorized the rules, and specific answers to specific problems. Now she remembers none of it. If she had ever need the information taught in those courses, she would have had no choice but to start again, from scratch.


That was me in math and calculus 15 years ago. Now I remember nothing. And I admit, I was in the same with music theory as a kid. I got great marks -- I knew all my rules, and I was great at memorizing things. I didn't start to really understand theory until I started playing jazz and forced myself to listen and try to understand how chord progressions 'worked'. And I'm totally NOT trying to say that you have to play jazz to get this stuff -- just that you need to connect all the theoretical stuff to how notes SOUND, why certain combinations of notes pull in certain directions, etc.

I think too many teachers teach theory away from the piano. I'm starting to think that theory and ear training should happen at the same time. Thoughts?

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#1896472 - 05/13/12 11:58 PM Re: Augmented 6th chords [Re: Gary D.]
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Gary mentioned C E Gb A# as a spelling with no purpose. What about C E Gb A# -- move to D F B (or B D F B), and then continue somewhere else from this glorious diminished chord. (I'm spelling out the whole chord here, not using chord letter names.)
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#1896521 - 05/14/12 02:22 AM Re: Augmented 6th chords [Re: Gary D.]
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I've been thinking about where chords can move to and addressing it combinatorially: start with a chord and look at all possibilities of moving one or more notes by half-steps or whole steps, up or down. Thinking about a IV V progression -- e.g. F A C F to G G B D -- I should perhaps permit moves of a third as well, but I'm trying to limit the combinatorial possibilities.

Is there any validity to this approach?

Of course having thought of this small step approach, I'm immediately tempted to convert my new train into an airplane and move from any chord to any chord. But I'm trying to restrict myself to conservative steps to start with. Actually, given that any set of three or four notes can't be that far from any other set of three or four notes, given that there are only 12 notes in an octave, maybe all chords are actually close to each other by small steps. Hmmmm.

This is what happens when you let a mathematician (by training) loose on chord progression smile .


Edited by PianoStudent88 (05/14/12 02:23 AM)
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#1896535 - 05/14/12 04:16 AM Re: Augmented 6th chords [Re: LadyChen]
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Originally Posted By: LadyChen

I think too many teachers teach theory away from the piano. I'm starting to think that theory and ear training should happen at the same time. Thoughts?

I think at first that we have to make students aware of what they are playing on another level. It is so easy to have it all go on auto-pilot. Good readers will get the music right, and if they are natural memorizers, everything will sound fine. But really important things will be missing. There will be no deep understanding of what composers are doing, and of course there will be no growing compositional skills.

My biggest problem as a teacher - NEVER enough time to cover everything.
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#1896541 - 05/14/12 04:43 AM Re: Augmented 6th chords [Re: PianoStudent88]
Gary D. Offline
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Originally Posted By: PianoStudent88
Gary mentioned C E Gb A# as a spelling with no purpose. What about C E Gb A# -- move to D F B (or B D F B), and then continue somewhere else from this glorious diminished chord. (I'm spelling out the whole chord here, not using chord letter names.)

Sooner or later it is possible that any bizarre spelling will turn out to be a valid choice in some strange place, but generally we can rule out certain spellings as not NORMALLY useful.

C E Gb A# will have the sound of a C7-5 chord, but as with all "letter chords", no spelling is indicated. So we have to ask ourselves where the sound is going, then think the spelling through.

You are thinking about this:

C E Gb A# --> D F B (or B D F B)

That just sounds odd to me, and I mean the sound itself. Do you like that sound? Are you sure you are not pushing notes around, intellectually, without fully listening to what you are coming up with. Do you like the sound of B D F B, alone? If you have a diminished triad and then double the root, adding the octave, I think you are creating a very weak sound. Hmm...

The spelling bothers me even more because Gb to A# is a second, but since G--A is a major second, you have a doubly augmented 2nd.

Why would you want that?

There is a very good reason why we avoid things like this: Cb---G#. Again you have a doubly augmented interval, this time a 5th. If you run into something that odd, I would at least think you would be dealing with music that is WAY out of the realm of tonal music.
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#1896547 - 05/14/12 05:20 AM Re: Augmented 6th chords [Re: Gary D.]
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Originally Posted By: Gary D.
Do you like that sound? Are you sure you are not pushing notes around, intellectually, without fully listening to what you are coming up with. ....

There seems to be something crucial here which goes to the heart of what doesn't work well in the theory books or instruction: intellectual pushing around of notes, and what is the role of listening?

I don't know if it's too much a sidetrack to mention books, since our study material might be part of it. I was reminded of the Oxford Book of Harmony which I found 2nd hand. They were trying to get away from how theory was taught back in the 1960's. The first thing they taught was to listen to how a chord played different ways made you feel, and they did that with other things like rhythms or a progression. Then you went to writing, keeping that experience in mind. They had all the usual theory, but starting with playing with sound and listening to its effect.

Quote:
So we have to ask ourselves where the sound is going, then think the spelling through.

You have mentioned "where the sound is going" often. It seems an obvious thing but maybe we tend to miss it? I think that when I started theory, a chord was a static thing which was followed by another chord. But in fact a chord is in the process of becoming another chord, and the spelling alerts us to the fact. There is a certain magic to the idea. smile

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#1896566 - 05/14/12 07:06 AM Re: Augmented 6th chords [Re: PianoStudent88]
Exalted Wombat Offline
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Originally Posted By: PianoStudent88
Actually, given that any set of three or four notes can't be that far from any other set of three or four notes, given that there are only 12 notes in an octave, maybe all chords are actually close to each other by small steps.


Yes, smooth voice-leading is certainly a factor in making one chord followed by another sound good.

Maybe you should forget harmony for a bit and go back to 2-part counterpoint. Write a melody that accompanies another melody. 2nds, 7ths and (particularly) tritones will have a feeling of tension, 3rds, 5ths and unisons one of resolution. Take a "tension" interval, add another tension interval to intensify it further, or add a neutral interval to pad it out. The interval has grown into a chord.

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#1896605 - 05/14/12 08:56 AM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Originally Posted By: Gary D.
You are thinking about this:

C E Gb A# --> D F B (or B D F B)

That just sounds odd to me, and I mean the sound itself. Do you like that sound? Are you sure you are not pushing notes around, intellectually, without fully listening to what you are coming up with. Do you like the sound of B D F B, alone? If you have a diminished triad and then double the root, adding the octave, I think you are creating a very weak sound. Hmm...

OK, I confess to creating BDFB by pushing around letters. But now that I've listened to it, no, it doesn't sound particularly odd. What do you mean by a weak sound?

I like it this way: C7-5 Bdim C. But then I confess to really liking diminished chords.

Originally Posted By: Gary D.
The spelling bothers me even more because Gb to A# is a second, but since G--A is a major second, you have a doubly augmented 2nd.

Why would you want that?

Why not? If Bdim is to follow, then isnt Gb---A# the correct spelling to precede F---B? LadyChen mentioned the spelling with the doubly augmented fourth upthread for the German sixth; rare but happens. Couldn't this fall in the same camp?

Originally Posted By: Gary D.
There is a very good reason why we avoid things like this: Cb---G#. Again you have a doubly augmented interval, this time a 5th.

Wait, I don't see Cb---G# in what I wrote. Or do you just mean it as an example of a wierd interval? But if the voice leading suggests that spelling, why not? A doubly augmented fifth is the same as a major sixth, so it wouldn't sound odd, even if it might look odd, like Satie's double flats.

Originally Posted By: Gary D.
If you run into something that odd, I would at least think you would be dealing with music that is WAY out of the realm of tonal music.

Uh-oh. Guilty as charged. I'm thinking about my combinatorial proposal as above, and the idea of going to anywhere from anywhere (albeit by smooth voice-leading), vs. the principles of common practice period harmony which I'm learning which cut out a lot of possibilities.

But really, C7-5 to Bdim does not sound angular to me in the way atonal music does. This may well go back to the fact that I don't think I hear harmony or intervals in music as clearly (or at least, as consciously) as other people do.

Exalted Wombat, thank you for the suggestion about 2 part counterpoint. I'll try it out.
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#1896674 - 05/14/12 11:10 AM Re: Augmented 6th chords [Re: Gary D.]
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I played Piano88's C E Gb A# => D F B
It sounds "edgy" to me. Everything is moving up: C to D, A# to B. I am picturing music that wants to keep moving up in an edgy way and then start losing the edginess (fully diminished with its two tritones) by turning into another kind of chord. I am also asking myself where it moves to. I also wonder whether, when E and Gb both resolve to F, if this gives the F any kind of significance which in turn is asking for a different chord?

I am also not a harmony-hearing person naturally. I may hear one thing and think "I like this" but miss something else that doesn't belong.

What about the question of where you want to end up as being the starting point of your thought? Does it belong here?

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#1896676 - 05/14/12 11:11 AM Re: Augmented 6th chords [Re: Exalted Wombat]
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Originally Posted By: Exalted Wombat

Maybe you should forget harmony for a bit and go back to 2-part counterpoint. Write a melody that accompanies another melody. 2nds, 7ths and (particularly) tritones will have a feeling of tension, 3rds, 5ths and unisons one of resolution. Take a "tension" interval, add another tension interval to intensify it further, or add a neutral interval to pad it out. The interval has grown into a chord.

I really like this way of seeing things as one angle.

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#1896710 - 05/14/12 12:25 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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keystring, thanks for trying out my chord! smile smile smile . What if you play it with the added B on the bottom: C E Gb A# --> B D F B? Does that change the sound?

I admit that I'm not fitting into either of what I think are Gary's desiderata, a) of going by ear and b) of going by what's been found in notation of actual pieces.

I'm wondering (I'm not sure this is apropos of augmented sixths, but it comes up for me here because this thread has me thinking a lot about harmony), if what would be really beneficial for me would be an ear and score course, in this sense: listen to music, state what it feels like, where there are noticeable things going on -- a sense of rest, a sense of sadness, a sense of joy, a sense of something unexpected happening. Then look at the score and see if those senses correlate to something particular that the composer is doing.

I have access to a music library with lots of scores and lots of CDs, so this would be a doable project for me.
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#1896766 - 05/14/12 03:19 PM Re: Augmented 6th chords [Re: Gary D.]
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Just FYI - Pianostudent88's chord is the basis of the 9th Scriabin sonata. It's the sonority heard on the downbeats of the opening measures, the end of the sonata, and at various places throughout.

It's spelled C# F G B. Of note is that Scriabin notates the same music using different intervals at the beginning of the piece. The RH and LH play the exact same material, but with different spellings.

The sonority is structural. In the development, we find the same sound, transposed to E Ab Bb D. The original sonority returns in the recapitulation - a fascinating way of following traditional sonata form outside the conventions of tonal harmony. Rather than tonic-dominant-tonic, we get original-transposed-original. (And the usual thematic progressions as well - a clear first and second theme.)
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#1896772 - 05/14/12 03:31 PM Re: Augmented 6th chords [Re: Gary D.]
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Kreisler, are you saying that the chord in the Scriabin has the same movement? I.e:
Piano88's is: C E Gb A# to D F B
Therefore if Scriabin's chord is doing the same thing, we would have:
C# F G B going to D# F#(Gb?) C
if it is the same movement.

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#1896775 - 05/14/12 03:36 PM Re: Augmented 6th chords [Re: Kreisler]
Gary D. Offline
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Originally Posted By: Kreisler
Just FYI - Pianostudent88's chord is the basis of the 9th Scriabin sonata. It's the sonority heard on the downbeats of the opening measures, the end of the sonata, and at various places throughout.

It's spelled C# F G B. Of note is that Scriabin notates the same music using different intervals at the beginning of the piece. The RH and LH play the exact same material, but with different spellings.

The sonority is structural. In the development, we find the same sound, transposed to E Ab Bb D. The original sonority returns in the recapitulation - a fascinating way of following traditional sonata form outside the conventions of tonal harmony. Rather than tonic-dominant-tonic, we get original-transposed-original. (And the usual thematic progressions as well - a clear first and second theme.)

Holy smokes Batman - the Scriabin 9th!!!

Maybe we should talk about the fact that Scriabin started out writing music much like Chopin's, so his foundation was 100% tonal.

E Ab Bb D immediately feels and sounds like an E7-5 chord to me. In other words, feeling and sound are visceral for me. The notation stimulates pushing down the right keys, mentally, and that stimulates the sound. Without going to the score, and later I'd like to do that, the first thing that hits me about the spelling is that this:

E Ab Bb D--->>>>Eb Ab Bb Db

is just one of the logical chromatic movements. Your spelling now makes perfect sense to me in such a situation because the chromatic movement is very clean. But I need to look at what Scriabin wrote. He may be doing something very different.

Let me see if I can find the score and link it. We would be going down a very interesting rabbit hole. Maybe a thread for this?
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#1896804 - 05/14/12 04:31 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Gary has started the new thread, but I'll mention here: keystring, no, it looks like it has the 7b5 chord, but not the movement to the diminished chord. Alas.
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#1896840 - 05/14/12 05:30 PM Re: Augmented 6th chords [Re: Gary D.]
Gary D. Offline
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quote=Kreisler]Just FYI - Pianostudent88's chord is the basis of the 9th Scriabin sonata.
[/quote]
Kreisler,

Since we have no score here, and talking about such things out of context is just a tease, I started a new thread. wink
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#1896849 - 05/14/12 05:47 PM Re: Augmented 6th chords [Re: keystring]
Gary D. Offline
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Originally Posted By: keystring
Kreisler, are you saying that the chord in the Scriabin has the same movement? I.e:
Piano88's is: C E Gb A# to D F B
Therefore if Scriabin's chord is doing the same thing, we would have:
C# F G B going to D# F#(Gb?) C
if it is the same movement.

My conclusion: he is doing what I do, taking the chord's SOUND and linking it to interesting uses of it, regardless of spelling.

This is what makes it such a different approach to take the sound FIRST, listen to where it GOES to, and then you can figure out why a chord (or anything) is spelled as it is. Rules still are invaluable, and knowing this is always good. But in the end, there things that are outside of all rules that you find in any book, or even that any other musician can give you.

Which you know, of course. wink

Edit: Scriabin is not doing at all what PP88 had in mind, neither in spelling nor in where the chord is going to. smile


Edited by Gary D. (05/14/12 06:27 PM)
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#1896866 - 05/14/12 06:17 PM Re: Augmented 6th chords [Re: Gary D.]
PianoStudent88 Offline
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Well, really I started out by trying to solve a spelling puzzle. But once written, yes, one would like to know what it sounds like. I think it sounds fine; Gary thinks it sounds weak, although presumably the 7b5 and diminished explorations in Scriabin's 9th Sonata are more interesting.
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#1896870 - 05/14/12 06:33 PM Re: Augmented 6th chords [Re: Gary D.]
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Originally Posted By: Gary D.

Edit: Scriabin is not doing at all what PP88 had in mind, neither in spelling nor in where the chord is going to. smile


Thank you. For me this was the crucial question since the point - and what is being emphasized - is movement, and not just whether a chord exists. I can see the other point you made about the composer pursuing sound. That is interesting and I am glad that Kreisler pointed out the piece and the chord.

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#1896895 - 05/14/12 07:47 PM Re: Augmented 6th chords [Re: Gary D.]
Gary D. Offline
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Just to sum up my points. Then, if someone disagrees with me, at least I will know WHAT they disagree with.

Any chord has its own sound. It does not a function until it is context. That means:

1) If a chord starts a piece, we can't have any idea where it going without hearing or seeing the next chord. We know nothing for sure.

2) If a chord ENDs a piece, the spelling will be 100% standard in tonal music.

3) In any other normal circumstance, a chord will be following something and will preceed something. If there is an obvious relationship between a chord and the chord following it, the following chord will determine the spelling of the chord leading TO it.

4) Most spelling problems can be solved with rules, but the rules were not invented to DICTATE spelling but rather to EXPLAIN it to people who are learning. In unusual circumstances there are no rules to go by. At that point pure logic is the only guide.

5) There are at least three ways of notating or describing chords.

a) Figured bass. It does not say anything about function, but it does specify spelling.

b) RNs (Roman numerals). RNs are an attempt to describe the logic behind what chords do. Sometimes the work brillianty, other times the fail miserably. Chromaticism stretches the system to the limit. In Impressionism (and beyond) they don't work well because they were not made for such music.

c) Letter chords: they don't say anything about function, and they also do not specify spelling. They are as specific as possible about what we hear, at the moment, or the "sounds we should be creating", but everything else is left up to us.
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