Harmonically, my uninformed vote would be for "I Just Wasn't Made For These Times." I say uninformed because I've never learned it myself, but I have learned, by ear, some pretty complex Beach Boys songs. Having said that, I once had a gander at the chords, being played and scored, and they scared the crap out of me.
That surprises me, that you've never learned it!
And I think that's it, too. IJWMFTT.
But really, and I don't expect anybody to pay attention to this, we have to define what complex means or the conversation is meaningless.
Complexity goes beyond things like key changes. And many of you are mistaking non-diatonic chord patterns as key changes, anyway. For instance, Wonderful doesn't change keys. That's not to say it's not good, exotic stuff, it most certainly is--but key changes alone don't make something complex. Anybody can do one. Play a C chord for 3 minutes straight and then play a C-sharp chord for 2. You've changed keys, but nothing could be further from complex.
Complexity comes from the whole package. Melody, Harmony, Rhythm, Counterpoint, arrangements, etc. Complexity flows out of a command of all these things and more. It springs not from genius but from craftsmanship. A Bach or Handel fugue is complex--but it comes out of hard work. Isolate the motive of a great fugue, and it's actually pretty simple, usually. It has to be. But then you start applying techniques to the motive, you add the responses, and slowly, a complex piece of music is erected, much like a work of carpentry.
So in my opinion, we can't look at isolated elements. Who cares if there's a diminished chord or two? Who cares if there's a key change? Who cares if there's long sequence? The song has to be looked at in toto.
So here's my analysis of IJWMFTT and why I think it's "the most complex."
1. Melody: The melody is pretty chromatic, but more importantly, if you think about it as a graph, it's pretty amazing how Brian manages to draw a series of ascending arcs leading to a very natural climax and denouement. The melody is almost pure jazz, and could be fitted over all kinds of different chord changes, I think.
2. Harmony: As Adam says, the chords are very tricky and as I mentioned just above, they are not especially congenial to the melody. The inversions of the chords shift from 3rd to 2nd to 1st, which makes it hard to tell the central tonality of the piece.
3. Arrangement: In my view, Brian's best, and heaviest arrangement. The descending tympani, Basses, and Bass Harmonica pose as a strange synth bass patch. The harpsichord and piano play that distinctive figure which I would love to have witnessed Brian teaching or collaborating with Mike and Don.
4. Rhythm: Not much way out there going on here, but the temple blocks are on a somewhat unexpected beat pattern.
Now, even after describing all that, I still feel unsatisfied that I adequately described everything, and I'm not sure that I can explain the synthesis of these parts that actually adds up to the complexity. Perhaps some sort of Webisode is in order...
Superbly well informed, H.
+1.
Frankly, if nothing else blew the listener's head away, the very first chord (technically I over a II bass) is so bastard inexplicable as to be easily fielding genius. And enormously hard to pull off convincingly, which BW does with disgraceful aplomb. I could go on.
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