> When, say, G is a prominent pitch class for a while, and then I hear it come back a few minutes later, that lets me understand the structure of the piece better than if I didn't recognize it.

Give me a controlled example where the return of the prominence of pitch class G lets you understand the structure of a section of music.

Controlled example would mean:

* the orchestration used for the G is different at moment A and moment B, OR the piece is for a solo instrument. Otherwise you could be hearing a timbral connection and confusing it for a pitch class connection.

* the G at moment B is in a different octave. Otherwise you could be hearing a pitch connection and confusing it for a pitch class connection. (Esp. if you have perfect pitch.)

* the musical texture at moment A is different from moment B. Otherwise you could just be hearing a textural connection (e.g., big orchestral hit, moment where the woodwinds return, etc.) and confusing it for a pitch class connection.

* it's not a tonal piece of music. Otherwise you could be hearing the same or similar harmonic progression and confusing it with a pitch class connection.

* moment A is melodically dissimilar from moment B. Otherwise you could be hearing a melodic connection and confusing it with a pitch class connection.

I can't think of any musical moments that meet those constraints.

Oh, geez, I'm not going to go find some specific section of music that perfectly meets all these constraints. Often the pitches are at the same octave, by the way; I don't think that makes the connection any smaller. And often the texture is similar; many aspects of the music may be "recapping" and one of them happens to be pitch. I'm not "confusing anything with a pitch class connection" just because another connections happen to exist; I'm hearing more connections than I otherwise might.

I am definitely talking about non-tonal music in general, yes. Elliott Carter is a good example of a composer where I feel that absolute pitch helps me understand what is going on more than I would otherwise. But again I'm not going to dig out some particular measure of music that perfectly proves my point.

If this reply was insufficient for your needs (I fear it is) I apologize. I'm not trying to win some debate, just to elucidate a little how I feel that absolute pitch aids my music appreciation.