
Wagner is taking advantage of the harmonic ambiguity in the third and fourth measures of the excerpt above. The passage can be put into simple chords as follows:

The question mark represents the lack of any harmony. What's this doing compositionally? It's creating a huge amount of tension. The listener is looking for resolution, and instead of giving it, Wagner simply takes away all harmony and leaves a two-note strand of music without any sort of context. While we're waiting for any sort of resolution, he suddenly gives us what we're not expecting—yet another unresolved dominant seven, this time an E-major minor-7 chord.
What's particularly interesting is that this isn't a new tactic. Harold C. Schonberg in his book The Great Conductors points out that "even the most important chords of the nineteenth century—the ones that open Tristan und Isolde—had previously occurred, almost note for note, in Liszt's song, Ich möchte hingehn, composed in 1845, more than ten years before Wagner 'composed' the Tristan opening." But the harmonic ambiguity Wagner uses a few measures later is actually a tactic used much, much earlier by none other than Johann Sebastian Bach in his Christmas Oratorio, BWV 248, Flösst, mein Heiland, flösst dein Namen.

Bach, too, is fragmenting his theme, taking away its unresolved harmony, and then surprising us with yet another dominant seventh chord. This can be analyzed similarly:

So, don't bother to do anything new harmonically. Chances are, Bach has already done. As Arnold Schoenberg points out in Style and Idea, Bach was really the first composer to use a tone row. Right there, in BWV 869, the final Fugue in the Well-Tempered Clavier! (Erm. Well, you get the idea.)