"Free as a Bird" was originally a piece of music that John Lennon composed, but never completed. The original Lennon recording was made circa 1977 in New York City. Yoko Ono gave a basic recording of the unfinished music to the remaining Beatles (Paul McCartney, George Harrison and Ringo Starr) who reunited to finalize and record the completed song.
The Beatles' overdubs and production were recorded between February and March, 1994 in Sussex, England. According to interviews, the group treated the song as though Lennon had gone on holiday and had left the song for them to complete. The original demo had to be stretched and cleaned up, as Lennon's voice was notably shaky and slightly out of time.
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The song features a classic Beatles arrangement, layered with drums, guitars (acoustic and electric), bass guitar, piano, and harmonized Beatle voices.
It ends with a slightly psychedelic coda including a strummed ukulele (an instrument for which McCartney and Harrison have expressed fondness) and the backward voice (how Beatlesque!) of John Lennon. The message, when played backward, is "Turned out nice again", which was the catch-phrase of George Formby, whom Harrison and Lennon admired. This line has been noticed by many fans as it sounds like it's saying 'made by John Lennon'. Most fans believed this was intended to be the case, until it was revealed it was in fact simply the phrase 'Turned out nice again' being played backwards. According to McCartney, the result was unintentional and was discovered only after the surviving Beatles completed the single and reviewed the result.
This page points out all the great Beatles' references peppered throughout.