Ian - your second sentence is long and loaded ! I think an example would help.

I've often found that the problem with some (much?) harmonic analysis is that it is confused, wrong-headed and may well have nothing to do with what the composer is thinking. A good example of such a can of worms can be found at

http://en.wikipedia.org/wiki/Tristan_chord

Fortunately Italian, French and German sixths are mostly clearcut and I'd agree with Aaron's point. But the legit view is seldom 100% correct . . .

And the Australian 6th ?

Yes, the placement of harmonic symbols can be misleading, but it is one tool in understanding harmony that overlooks the horizontal. It takes an effort to convince students that this isn't a clunkifier.

We don't just look at the first instance of the chord, but observe that it behaves in many different ways throughout the opera, far more radically than can be explained by traditional harmonic theories. That's why Ernst Kurth's book isn't called Die Romantische Harmonik und ihre Krise in Beethoven's Es-dur Sonate. Though the first arrival in the prelude is a deceptive cadence in a minor (sort of), nobody reasonable tries to argue that the prelude really stands in A.

I'm inclined to think it is - even if it isn't necessarily the only line.

Bah. A real explanation would relate them to national characteristics.

(Interesting thread; I don't have anything constructive to add at the moment though).

I find this intensely interesting (perhaps Busoni - for whom my respoect remains immense - might have opined that I find it unhealthily so!). The "Tristan chord" - which you cite above from its much earlier appearance in that Beethoven sonata - was not "new" when Beethoven used it either, of course - but what really bothers me is this conept that Wagner somehow achieved some kind of historical importance by "undermining" tonal stability by the use of this chord in Tristan. Now this is not to undermine Wagner's achievement here but I think that, to begin with, tonal stability and the prevalence of the tonal centre was perhaps more effectively undermined by Wagner in Act III of the same work as by his use of that chord alone; next, we have to bear in mind that earlier composers have used the "Tristan chord". Lastly, however, I would return to this notion of "undermining" tonal stability. Delayed resolution and absence of tonal closure do not of themselves "undermine" tonality itself; rather the opposite, it seems tome, for they heighten the vaildity of tonal relationships. I think that, in Tristan and in parts of Siegfried and Götterdämmerung, what wagner actually did was to expand tonal horizons rather than undermine anything; the idea of "undermining" suggests something negative, whereas Wagner's widening of the possibilities of tonality and tonal relationships was very positive, so that, by the time we get to Schönberg's Kammersymphonie Nr. 1 some half-century after Tristan, the vocabulary of tonal inter-relationships had become immense by comparison to what is had been at the time of Schumann's death - all manner of levels of tension and non-tension had entered into the consciousness, without tonality per se being in any sense overthrown thereby. Of course, I do not seek to overplay Wagner's personal input into this, for other composers got into it as well, although few if any others pursued the art of delayed resolution on quite the same scale as he did.

Sorry, folks - must get off me hobby-horse (and maybe get me coat, too)! - it's all Ian's fault for raising and developing this (to me) fascinating subject area...

Best,

Alistair

This is all available in elementary harmony textbooks. What they usually leave out, though, is where the terms actually come from.

All aug6 chords contain the flatted submediant (b6) in the bass and the raised subdominant (#4) in another voice, usually the highest. These then are expected to resolve outward to the dominant (5).

The Italian adds the tonic pitch (1), and in four part writing this pitch is generally doubled. When the harmony passes on to the dominant (as is expected), one of these tonic notes must go to the leading tone (7). The other, if present, can move to the supertonic (2).

The French sixth chord adds the supertonic pitch as well, which stays put into the dominant harmony.

The German sixth chord adds the flatted mediant instead of supertonic. Since this note is a perfect fifth above the bass, however, it usually hangs around as a suspension into the dominant to avoid the sensation of parallel fifths. Alternatively, and for the same reason, this b3 can arrive early on the supertonic as a kind of anticipation. Note that in that moment of anticipation, the kraut has briefly morphed into a frog.

Old Walter Piston even distinguished between two German sixth chords, the one with the flatted mediant he called German, and the one with the raised supertonic he called "Swiss" -- as far as I know, no one took him up on this idea. But in a nutshell, the German reflects a tendency for the tone in question to resolve to the natural supertonic, while the Swiss spelling (of an identical-sounding chord, mind you) accommodates a tendency to the natural mediant, i.e., when the bass moves from b6 to 5, the #2 moves first to 3, making a six-four chord (double suspension) on the dominant. The Swiss spelling would be more common in major mode and the German more common in minor.

Both German and French can (hypothetically) omit the tonic note, but I can only think of one instance in music literature where this happens. True anoraks can think of a dozen, I'm sure.

Finally, the Neapolitan sixth chord is not an augmented sixth chord at all, but an anteater a tapir. In minor mode, this chord is like a first-inversion supertonic harmony (which is normally diminished 4-b6-2) whose "root" has been flatted to form a more consonant (major 4-b6-b2) sonority. What it makes up in pleasantness it lacks in melodic smoothness, however: the b2 has trouble resolving properly since it typically tends toward 1 (a half-step away), and yet Neapolitan harmony is, like the harmony for which it substitutes (ii), a pre-dominant harmony, so that b2 frequently makes the rather striking move straight to the leading tone (an interval of a diminished third). If b2 does go to 1 first, then once again you have a suspension.
In major mode, the Neapolitan is even more striking, since it has two notes outside the key, and we generally consider it in those instances as being "borrowed" from the minor mode. The Neapolitan only "resolves" to tonic when one thinks of it, like the jazz community on occasion, as a substitute for the dominant rather than as a fancy pre-dominant.

As for national characteristics, I don't see a particularly convenient or compelling way to show that that is very interesting or relevant. That is, until you read some of the more outrageous mnemonic devices that theory teachers come up with!

It takes most University of Illinois graduate students an entire semester, even after they have consumed a semester more as undergraduates. So an evening is quite an impressive time-frame, inc!