A wide array of songs could fit in answering this question. Yet, for me, the immediate connection I made was to The Beatles' "A Day in the Life." It features a strong shift in musical dynamics that contribute to a profound effect on the listener.
The song is one of Lennon and McCartney's most significant contributions to musical history. It actually consists of half a song from each of them. Combined, the song features two very distinct uses of musical dynamics. The first part of the song consists of Lennon singing about events in the news. This vision of "a day in the life" is one in which his echoing voice and deliberate cadence contribute to an "other- wordly" feel. The use of the strum guitar and piano background is subtle and effective in evoking such a feel. This portion of the song concludes with Lennon's vocals, "I'd love to turn you on..."
The second part of the song takes place after an orchestral swell that causes the listener to experience a level of altered being. Undercut immediately with McCartney's cadence of a normal day in the life of a commuter, one experiences a shift in tempo and articulation. This vision of "a day in the life" is much more deliberate, almost bringing the listener back to a daily grind of routine in which there is something identifiable. "Woke up, fell out of bed, dragged a comb across my head" helps to bring a routine that the reader can understand and to which connection is immediate. However, this feeling is quickly undercut once again with Lennon's vocalizing after a day dream.
After another brief orchestral swipe, the final portion of the song features the repetition of the same musical elements of the first part. With Lennon's reprise of "I'd love to turn you on," the listener once again has to confront the orchestral swell, only this time concluded by the hitting of a piano chord and extended for 45 seconds as the song ends. The constant shift of musical dynamics contributes to a profound effect on the listener to recognize that there is little ordinary to "a day in the life," both in song and consciousness.