[link to original on tumblr]
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Listening to it this time though, I remembered something that I read in The Beatles Anthology (or at least I think it was in The Beatles Anthology). I can't seem to find it again (and I don't really want to re-read large sections in an effort to find it), but it was John Lennon's explaining that Paul McCartney sings the "When I'm home" sections in "A Hard Day's Night" because he (McCartney) has a higher voice. I'm pretty sure that the McCartney-sung "Any time at all" is even higher, so that switch might be just because of the register.