@slugsack said:

How does the rhythm punctuate the key changes if it does anything at all? For example, have there been corresponding rhythmic shifts?

Excellent question.

Often, yes. Fishman is as attuned to the subtleties of improvisational dynamism and motion as the rest of the band, but because he doesn't play a pitched instrument, he likely feels these harmonic/melodic shifts much in the same way we, as listeners, do. I obviously don't know for certain, but I would be surprised if his ear is as melodically and harmonically trained as the other guys simply because he does not have to make corresponding shifts in his own playing (i.e. he won't sound dissonant if he doesn't follow a particular melodic or harmonic change the way the other three would).

However, Fishman often does make shifts when he senses a new jam segment starting. As the rest of the band shifts into a new tonal space with its own distinct affect, Fishman is often quick to follow by a corresponding shift in rhythm or beat. For example, listen to the 7/31/15 Kill Devil Falls: from around 9:00 to 9:45, the band solidifies a mode mixing shift from C major to C minor, and Fishman responds by matching his accents to Trey's rhythmic accents (one of Fish's most unique traits is that, for most of the early years of Phish, he followed Trey and not Mike. It's very rare in rock music for a drummer to follow the melodic instruments rather than the other bass instrument - indeed this is why the bass and drums are referred to as the "rhythm section." . The "KDF" beat is breaking down as Fishman senses the mode mixture happening.

The modulation in this jam starts right at 9:52, when Trey plays a rising riff that then falls to G, and Mike immediately hammers a low G as if to say "yes, let's go to G minor now." The band then gets quieter, bringing everything down in energy and dynamic, and again, Fishman follows. But part of the reason Trey/Mike/Pags changed their timbre was because they knew they were now in a different key. Fishman doesn't change anything drastically, but he does follow the rest of the band in affect and mood, playing more erratically on toms, matching rhythmic accents from Trey and Page with his own cymbal and snare accents, and generally disrupting the previous "KDF" beat further.

So the short answer is yes, Fishman has rhythmic shifts for modulations, sometimes. But it's not for necessarily the same reasons that the rest of the band changes keys. Page switches keys because he knows that he will sound dissonant against Mike and Trey if he doesn't and he doesn't (always) want that to happen. He also modulates because he is in a musical conversation with Mike and Trey, and as they move the conversation, he does too. Fish is having a slightly different relationship to this harmonic conversation. He changes his rhythms, slightly as to not disrupt the groove, because he senses the conversation has moved, although because he is not a participant in the harmonic conversation, he doesn't have to change anything.

Fishman does not use different toms for different keys, though, or to put it more technically, he does not have specific timbres for specific keys. His choice of sound (whether it's cymbals, toms, snares, or blocks/bell) is independent from tonality.