Formal structure of  "Birthday":
Intro/Tag (v) 0:00-0:22 A major
Verse 1 0:22-0:43 A major
Break (drums) 0:43-0:56 A major
Transition 0:56-1:10 (E major)
Middle 8 1:10-1:28 C major
Tag (verse) 1:28-1:48 A major
Break (guitar) 1:48-1:55 (transitional)
Middle 8 1:55-2:12 C Major
Verse 2 (ext) 2:12-2:35 A major
Coda (ind.) 2:35-2:42 A major
Comments: "Birthday" has an unusual and fascinating structure.
The verses, which are often one of the primary formal sections of a pop song, in this case carry significantly less structural weight because the two verses (and really it's the same verse heard twice - the lyrics are identical each time) are heard first at the beginning and once again at the end, and nowhere in between. The only other Beatles song to date that do anything similar is  "Sergeant Pepper's Lonely Hearts Club Band", but "Pepper" employed a very deliberate formal design (it's palindromic) while "Birthday" is anything but deliberate - the novel and unpredictable structure yields no obvious patterns, which helps provide the song with an improvisatory feel, much like  "All Together Now". Additionally, the second verse features a one-measure extension at the very end, that helps segue to the coda.
Tonally, it uses two keys a minor third apart (A and C) - something the Beatles had done previously on  "Another Girl",  "You're Going to Lose That Girl",  "Here There and Everywhere",  "A Day in the Life",  "Lucy in the Sky With Diamonds",  "Lady Madonna", and to a much lesser extent  "Good Day Sunshine". In this case, the middle 8s are both in C major, while the rest of the song is in the "primary tonic" of A major.
Bridging these sections, of course, are a series of transitions. After the first verse, a drum break leads to a transitional passage ("Yes, we're going to a party, party...") that culminates in the middle 8, with it's new tonality. That transition is implemented again but in a very different way at 1:48. This time instead of a drum break followed by a transition, the bass and lead guitar play the break. But despite the switch in instrumentation, the structural function is the same: they both lead to the middle 8. (Consideration of how these two transitions function tonally will be saved for a later harmonic analysis blog.)
This blog is a workshop for developing my analyses of The Beatles' music.