"Good Night" - A Ringo Lullaby

The history of the song "Good Night" began back on June 28 1968 with some taped rehearsals. This was a tune written by John Lennon especially for his son Julian who was a small boy at the time. It was decided that Ringo would sing the song and that the running order on the new LP (eventually "The White Album") would end with this track.
During the rehearsals, Paul played some piano and George Martin played a shaker as Ringo sang the tune and an arrangement took place during this time. A snippet of this rehearsal can be heard commercially on the Apple 2-LP/2-CD "Anthology 3" project. This is in mono but it becomes cross-faded into the ending of the orchestral version of the song in stereo.
In the end, five takes were properly recorded with a Ringo vocal overdub completed on July 02 1968 and taken away via an acetate from the studio by George Martin for the "over the top" orchestral overdub which occurred on July 22 1968 in the large Studio 1 at EMI Studios in London.
There are three main mixes available for the tune: the first one is mono with some music edited and some extra 'whispering' vocals at the end of the tune and can be heard on the "Peter Sellers" tape which was an early mix of some of the White Album songs and given as a gift to the actor from Ringo. The main difference between the mono and stereo mixes on the official LP is that the stereo mix has the orchestra fade in at the beginning of the song whereas on the mono mix the orchestra comes in at full volume.
The "Peter Sellers" version can be found on bootleg CD such as "Unsurpassed Masters Vol. 4" and (of course) "The Peter Sellers Tape".

"Sexy Sadie" Monitor Mixes

On July 19 1968, The Beatles continued work on the new LP with a John Lennon song entitled "Sexy Sadie" which was a tune designed to describe the disappointment on John's part of the India experience with the Maharishi earlier in the year.
The rehearsals were taped at EMI Studio 2 in order to get a goo basic track. John Lennon on voice and acoustic, Paul on the organ, Ringo on drums and  George on electric. Apparently 21 takes were recorded but none of the them were used except for take 6 which appears commercially on the Apple 3-LP/2-CD "Anthology 3" project.  There is also some studio chat from the session that shows up on the commercial Anthology DVD.
The bootleg version of this evening's session consists of various playbacks of the song along with some conversation by Paul and John - it also consists of some words added to John Lennon jamming on acoustic and the subject being Mr. Brian Epstein - known on the bootleg as "Brian Epstien Blues" as well as some nasty alternate lyrics for "Sexy Sadie" alluding directly the Maharishi. This excerpt can be found on the CD "Unsurpassed Masters Vol. 4" as well as the CD "Control Room Monitor Mixes and "Complete Control Room Monitor Mixes" as well.

"A Beginning/ Don't Pass Me By" mixes.

On July 12 1968, fiddler Jack Fallon would enter the EMI Studios as he was hired to fiddle during Ringo's new song at the time: "Don't Pass Me By".  The fiddle part was added to the last track of the tape so the bass part (which was erased) had to be re-done by Paul. Some of the piano (with leslie speaker added) had to be re-done as well and this time frame is probably where that piano intro/tinkling came in for the commercial take of the song. At the same session, a mono mix of the song was completed (remix 4) and given to Ringo to take home. This is one of the songs included on a compilation of very early "White Album" mono mixes that was put on cassette and given as a gift from Ringo to actor Peter Sellers. Eventually, the early mixes were copied and released as a bootleg LP/CD entitled "The Peter Sellers Tape" as well as the CD "Unsurpassed Masters, Volume 4". The early mono mix includes some stray bass notes played during the intro to the song as well as the repeat of the first verse which was not included on the commercial version.
There are also differences between the mono and stereo mix of "Don't Pass Me By" on the commercial Apple LP/CD "The Beatles"(White Album). The mono version is sped up by a semitone compared to the stereo mix. Also, there is a different fiddle improvisation between both mixes. This is probably due to two difference takes of the fiddle overdub.
Lastly, there is an orchestral introduction to the version of "Don't Pass Me By" on the Apple 3LP/2CD "Anthology 3" version. The orchestral piece is entitled "A Beginning". This piece remains a bit of a mystery. The piece was recorded on July 22 1968; ten days after the final recording of Ringo's song. The piece also makes an appearance in the "Yellow Submarine" film near the beginning of the Liverpool scenes. Only George Martin knows for sure why this piece exists. To my ears, I don't think the original intent was to have the song lopped onto "Don't Pass Me By" as there is no musical connection; it may just have been experimental. Or as suggested by others, it may have been George Martin's attempt to have this introduction piece included on the "Yellow Submarine" soundtrack LP.