Note: My theory is definitely a bit rusty and I'd be happy to be corrected if I'm way off here.
The Ab7 is a tritone substitution for the D7. They share common chord tones - the 3rd and 7th (F# and C) are enharmonic equivalents of the 7th and 3rd of the Ab7 chord.
Just to clarify, is that d# diminished > c minor > e minor > g# diminished? Post back to confirm. And what chord does it lead to?
The d#dim wants to resolve to E. Also, d#dim is a sub for D7 since it share 3 chord tones (F#, A, C) plus, the root D# is the enharmonic equivalent of the b9 of a D7 chord. The g# dim wants to resolve to A minor, the relative minor of the main key center (C Major) which may be inferring a deceptive cadence of sorts.
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Where is this exactly on the chart - right at the end? It is a bit different progression that I found elsewhere for this tune, for example, see
here and
here. Those changes look like this:
Fdim/C/G#7/G7/C (don't quote me on the rhythm)
Fdim (F-Ab-Cb-Ebb) resolves to C since it's the same chord (different inversion) as Bdim (B-D-F-Ab). G#7 (aka: Ab7) is a tritone sub for D7, which moves to G7 and resolves to C.
As far was what to play, your best bet is to outline the chord tones, they will voicelead nicely versus trying to blow changing diminished or mixolydian scales every measure or half measure.
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