To begin with, “Not A Second Time” is a Fab Four song from their album, “With The Beatles”. This was The Beatles’ second British album from 1963, of course. Meanwhile, in America it was on the album, “Meet the Beatles!”
In Detail
Album
Recorded: 11th September, 1963
Genre: Rock
Track Duration: 2:08
Record Label: Parlophone
Songwriter: Lennon-McCartney
Producer: George Martin
Engineer: Norman Smith
Performers
John Lennon: double-tracked vocal, also the acoustic guitar
Paul McCartney: bass
George Harrison: acoustic guitar
Ringo Starr: drums
George Martin: piano

With The Beatles Album (1963)
Track Source
Not A Second Time
This song, written and sung by John Lennon, featured on Fab Four’s second studio album, “With The Beatles”. Obviously, the songs on the album were subject to scrutiny from the critics.
“Harmonic interest is typical of their quicker songs, too, and one gets the impression that they think simultaneously of harmony and melody, so firmly are the major tonic sevenths and ninths built into their tunes, and the flat submediant key switches, so natural is the Aeolian cadence at the end of Not A Second Time (the chord progression which ends Mahler’s Song of the Earth)”.
William Mann
The Times (December, 1963)
This obviously drew confusion from the singer/songwriter.
“I still don’t know what it means at the end, but it made us acceptable to the intellectuals. It worked and we were flattered. I wrote Not A Second Time and, really, it was just chords like any other chords. To me, I was writing a Smokey Robinson or something at the time”.
John Lennon
Anthology
A further interview confirms Lennon’s confusion over the term, “Aeolian cadence”.
“To this day I don’t have any idea what they are. They sound like exotic birds.”
John Lennon
All We Are Saying, David Sheff
Be that as it may, the song certainly graces the album. However, the song is noticeable in that George Harrison is missing from the line-up having no need for a prominent lead guitar. However, George Martin makes good use of the piano within the song’s structure.
Recording Studio
The Beatles Began recording “Not A Second Time” on the 11th September, 1963, in Studio Two of the EMI Studios in London during the 7.00pm–10.15pm sessions. The band recorded five takes but with overdubs that number went up to nine.
The creation of the final mono mix was on the 30th September while the stereo version became available on the 29th October.