More stuff about the 'Tristan chord'
The funny thing about this patch of harmony at the beginning of the prelude to the opera, is that it wasn't really very new, viewed in isolation as a combination of notes; yet it created a sensation, and over a hundred years after its premiere still retains its mystery. My task is to try to explain why and how, and on the way reveal some of the connections of 'that chord' to the rest of the opera and the history of music.
A harmonic/emotional appreciation
Let's take a closer look at the harmony: it goes like this
If you go to Amazon or some such place and search for recordings of Tristan, they usually give you a sample to listen to, usually the first minute or so of the piece. If you don't know what these funny symbols sound like when played, go and listen now. I recommend Furtwangler/EMI. Listen again. http://www.amazon.com/exec/obidos/tg/detail/-/B00005NW0D/104-0239003-5191907
This is all you hear from the beginning of the piece - three bare unsupported notes from the cellos (2), and the strange chord. Now the 3 notes actually define tonic (doh), minor sixth (la-) and dominant (sol) in A minor, so it's natural for the notes that follow to be interpreted within that key. But it resists aural interpretation. The G# (1) belongs to the dominant and the diminished chords, so it should have an E or a B as bass. Conversely the F, B and D# beneath it outline a highly dissonant chord known as the augmented sixth, which - if it had an A in it - would be a textbook example of the French sixth. This is already a very dissonant chord, but it has a familiar place within A minor: it resolves onto a less dissonant chord, the dominant 7th with E in the bass, which should finally resolve onto a consonance, the tonic chord.
Thus Wagner started two stages up on the scale of dissonance, and then threw in the oboe note G# to make the chord - what? Well, it's not more dissonant, since D# to G# is a perfect 4th whereas D# to A is a tritone. But it's tonally farther away from the consonance of the implied tonic A; in fact it's a relatively consonant interval, the half-diminished chord in Eb minor. If the oboe quickly changed note to A, then it would be easy to understand as an appoggiatura - a stressed dissonant 'wrong' note which moves on to the 'right' note with a release of tension. But the oboe refuses - and refuses - for seconds - to give us that A which would make sense of the chord in A minor. You begin to think that the strange chord is not being presented as a 'wrong' version of a chord in the key you thought the piece was in, since it makes more sense as a 'right' version in a very remote key - that Wagner is going to write a piece that changes key incomprehensibly every bar... you half resign yourself to living in the alien world of Eb minor...
At last the oboe does "resolve" onto its A, making the chord more comprehensible, more normal within A minor - but more dissonant. A musical paradox: the resolution is more dissonant than the problem chord. Now, the resulting French sixth resolves again onto the dominant seventh, and we are almost safely arrived at the home 'key'. (A key hasn't been established, only suggested - and nearly contradicted.) But there is that A# on top of the chord - although it quickly resolves, this time releasing tension in the expected way, for one moment we are still close to Eb minor, since the top three notes Bb, D, Ab (re-spelt in a flat key) could almost be a dominant 7th in that key.
Finally we have the first unambiguous tonal chord, E7 in root position. Now after that, anyone else would have resolved onto the tonic and firmly established the home key, providing a stable jumping-off point to develop further tensions and resolutions. In fact the tonic chord is an inescapable consequence - it surely must come next! But Wagner stops in mid-air and gives us the cello motive again - in a different key. That's where the analysis really begins to get complicated, and when the listener realises that instead of a conventionally structured piece with a few weird harmonies thrown in, what the instability and contradictions that mark the first phrase's attempts to establish a home key presage is an entirely new method of long-range tonal organisation, one that's going to take the whole length of the opera to arrive at a definite statement of tonality. Rather like that sentence.
How it fits in, or doesn't, to the rest of music
Let's review what's happened. Usually a piece is going to start with an unambiguous statement of the home key's harmony, or at least with the tonic - the keynote. Sometimes this doesn't happen immediately, and the composer creates interesting ambiguities on the way to establishing the key: Haydn was the first to use this possibility creatively. But pretty soon, you have a key and a tonic chord. Now what's happened in Tristan is that the first chord is not only a dissonance - that had been done before by Haydn, Beethoven, Schumann, Wagner himself (in Die Walkure, act 2) and others - but it's a remote and alien dissonance; one which doesn't seem to fit into the key that the first three notes seemed to be approaching, and doesn't offer a simple way to resolve into something more sensible. When it does turn itself into a less remote chord, it actually increases the pain level; finally when the resolution is on the brink of actually confirming the key we are in, relaxation is denied, and we start on another cycle of tonal ambiguity and painful revelation.
Very similar harmonies had been used many years before, notably by Haydn in the 'Chaos' introduction to his oratorio The Creation, and by Mozart in his string quartet in E flat major K428, in the slow movement (see at the end). The difference, why the harmony now made such an impact, is in the musical context: how it is placed in and relates to the long-term structure of the work. Previously such a chord had been a climax of dissonance and tension, approached from a point of relative stability and resolving onto a dominant and then to a stable tonic - safely embedded within a tonal structure. When it does resolve to the tonic, the key is all the more firmly established because of the release of tension. (Although in Haydn's Creation, he did anticipate Wagner's procedure by refusing to establish the home key for quite some time...)
Now with Wagner, the chord is the first harmony you hear, almost flat out denies the key, then ends up, tortuously, almost confirming it, after a traumatic revelation that it does make sense within the key. And the key never really is confirmed. It wasn't the chord on its own that outraged the critics, it was what he did with it, elevating tonal instability almost into a principle of composition, contradicting or leaving unfulfilled every expectation until the last bars of the piece. And the critics were right, since the same method in Schoenberg's hands ultimately led to atonality and the dissolution of the Germanic classical and romantic styles of music.
How it fits in to the opera (more speculative)
Within the context of the opera Tristan und Isolde, I see the chord as giving us, in super-concentrated form, the emotional content of one of its main (psychological) themes: the setting-up of a private thought-world by the two lovers in which normal standards of behaviour no longer apply, in which male and female, day and night, faithfulness and betrayal, are confused and inverted, and from which everyone else is excluded, not by physical barriers, but by mental ones. The lovers simply refuse to acknowledge the existence of the everyday world in which Isolde is married to King Mark. And when this private world is confronted with reality, the unreal but comforting dream is inevitably shattered, in a moment that produces both physical pain (dissonance) and emotional pain: the pain of losing your illusions, which is so great that to return to the unreal world is, for the lovers, is worth their own deaths.
The eerie, alien, but not unpleasant chord is the embodiment of the shadow world, from which they cannot emerge without a traumatic increase in pain. Just as the lovers cannot accept everyday reality but remain fatally deluded, the harmony never yields to the 'logical' conclusion that it should resolve into the bleak normality of A minor.
Now of course there are many more sides to the chord, and to the opera, but I hope this gives some insight as to why this chord is such a potent symbol and important element in the music and the drama.
Mozart's near-anticipation of Wagner
The string quartet slow movement mentioned above, which like the Tristan prelude is in 6/8 time, contains the following harmonies:
D___D#__E___D___C# G#__A___A#__B___C# (1)
F_______E________ -> D___D#__E___D___C# (2)
G#__A___A#__B___C# B___A___G#______A (3)
B___A___G#______A F_______E________ (4)
To get the first excerpt, I transposed from Ab to A; to get the second, I rearranged the parts (without changing the notes, of course) to make the voicing like Wagner's. Note the identical line G# - A - A# - B (1), the identical progression F - E (4). But also note how Mozart puts an A in the progression from B to G# (3) and resolves D# onto E, not D natural (2). However, this doesn't make the passage any less dissonant than Wagner's. But with Mozart, the G# is clearly part of the diminished 7th chord within the key A, and the chord A - D# - A - F is again clearly an augmented 6th which leads as usual to the dominant - then the dominant quickly resolves to the tonic chord of A, confirming the tonality. So while the passage is pretty dissonant, it doesn't hint at a remote and alien key like Wagner. The A# is the only 'wrong', non-harmonic note, and it quickly explains itself by resolving onto B.