> 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.