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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

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.

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.

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.

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.

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.

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.

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.

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.

Yes. This is exactly what I meant.

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:

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.


You have left ample room for every kind of discussion.

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.

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?

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.

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.

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.

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.

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.

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.

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.

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?

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.)

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 .

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.

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.

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.


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.