A flat or G sharp: Same tone, but different note. Why?

[jiatu]

https://i1149.photobucket.com/albums/o598/Jiatu/01%20Ask%20Me%20Now_zpsoqnsqzav.jpg

Above is a link to an image taken from Thelonious Monk: Easy Piano Solos, "Ask Me Now". The last note of the first measure (in the image) is an A Flat. But when used in a chord (next measure) it changes to a G Sharp. Why is that? What creates the decision to use one or the other? Why not just use two G sharps?

[visitor]

because the chord has an added 6th, so in B major the submediant tone or a major 6th from tonic B natural is G sharp.  writing it for A flat would mean it's a double flated or a diminished leading tone or 7th which would be strange and hard to account for.

[louispodesta]

because the chord has an added 6th, so in B major the submediant tone or a major 6th from tonic B natural is G sharp.  writing it for A flat would mean it's a double flated or a diminished leading tone or 7th which would be strange and hard to account for.

Thank you for detailed and concise accuracy.

Also, per a composer named Brahms, and another composer name Rachmaninoff, they did this all the time.  I guess their music could be considered to be on the same level as T. Monk.

[keypeg]

because the chord has an added 6th, so in B major the submediant tone or a major 6th from tonic B natural is G sharp.  writing it for A flat would mean it's a double flated or a diminished leading tone or 7th which would be strange and hard to account for.

This was discussed in another forum.  It might make more sense for that chord to be written as a Cb, and then the added sixth would be Ab rather than G#.  The next chord over is designated as "C" (major) which is impossible with C E G# which would make it a Caug.  With those sharps in the RH we get these spellings:

B 6/9 as B D# G# C# (rather than it having been spelled as Cb Eb Ab Db)
"C" (as designated in the notation) as C E D# G# (which is not a C major chord)
"Db" (as designated) as Db F G# C# .... why not write it as Db F Ab Db?
D dim as D F G# C#

The previous measure is all flats.  Why not make that first chord notated as a Cb chord?

In the other forum, a jazz musician wrote something like that in jazz, conventions are looser, and another suggested (as I had wondered) that Cb would have made more sense.

Visitor, you talk about B major, but we are not in B major.  (Not sure what key we are in, but B seems unlikely, I'd think).  We also don't have other measures for context.  For example, does the music move to E in the next measure?

[chopinlover01]

@ Above: The B is the next chord. The A flat from the Ab7 is repeated in a B6-9 chord, which progress to C, which then goes up in tenths, presumably to E flat (that would be my guess, anyways). I haven't played the piece, whatever it is, by Monk, but I'd be interested to hear it.
Cheers!

[keypeg]

@ Above: The B is the next chord. The A flat from the Ab7 is repeated in a B6-9 chord, which progress to C, which then goes up in tenths, presumably to E flat (that would be my guess, anyways). I haven't played the piece, whatever it is, by Monk, but I'd be interested to hear it.
Cheers!

But it could also be expressed as Cb, given everything else before and after.  This was suggested in the other forum by more than one person.  You have 3 more beats, and 3 "chords" indicated, including the "C major chord" that has a G# in it rather than G.  Would there be an argument for expressing this as a Cb6-9 instead of B6-9, given the rest of the measure and what precedes it?  Conversely, is there an argument against doing so?