One of my favorite piano pieces that I learned when I was still taking lessons at Stanford was one of Grieg's Lyric Pieces, Op. 54 No. 4, Notturno. It's a beautiful little piece, full of nice, juicy chords, and with lots of opportunities to practice the 2-against-3 that I was just learning at the time. I also liked it a lot for its uniqueness: it wasn't something typical that everyone always did, like Für Elise. I didn't know anyone else who played it, and to this day I feel a little more like it's "mine" than I do about most other pieces I play.
There was one thing about it that always slightly perplexed me, though. One particular chord: the Ab in measure 10 (for those of you following along in your scores at home). It always just seemed to come out of the blue, sandwiched in there between two identical measures of D7 stuff. (Just for context, the piece as a whole is in C.) I couldn't understand why it was there at all, and when I asked my teacher about it he just shrugged the question off, saying something about how "it was the Romantic Era -- they could just do things like that." He was generally a good teacher, and I liked him, but with four or five students to get through in an hour, we didn't get to have much in the way of in-depth discussions.
So I pretty much just wrote that off as one of the mysteries of music and concentrated on just learning to play the darn thing. That was about three years ago now. Then yesterday I was playing it again, for the first time in a few months, and it suddenly struck me that it makes complete sense for that chord to be there. The Ab is a tritone away from its neighboring D's, and an Ab7 is what you would get if you did a tritone substitution on the D7. This particular Ab chord was missing the 7th, but that really just makes it stand out more in a piece where pretty much everything has added 7ths, if not 9ths or beyond.
So why is this tritone thing interesting? Because of how it ties in with the descending chromatic bass lines that are so prevalent throughout the whole piece. But how is that related? Well, if you take a circle of fifths progression and do a tritone substitution on every other chord, then you get a beautifully chromatic descending bass line (a fun trick I learned when I took a Jazz Theory class). And why would you want to do that? Because that's precisely what happens on the last page of this Nocturne for about six measures. Grieg even draws extra attention to it by dropping the threes out of the 2-against-3, and rolling several of the chords. It's wonderful. All of a sudden I was just looking at this piece and seeing connections all over it.
I kept poking around in the score for a little while longer, just because it was neat to take a fresh look at a piece I stopped actively thinking about a couple years ago. I noticed that the Bb9 chord leading into the più mosso is actually really closely related to the E9 that follows it (two shared notes and semitone neighbors on everything else). The Ab-D bit also appears again, on top of an E-Eb-D bass line. All sorts of interesting things. Music theory is fun.