fingering for this mystery piece

[shoshin]

okay i'm trying to work out the best fingering for this and I have a couple options. Nothing strikes me is the best yet so I thought I'd ask you guys.

C4 at the middle C  in key of A flat
pairs of notes played together:

Acends:
C4 + A4 flat
E4 flat + B4 flat
A4 flat + C5

Descends by reversing ...bonus if u can guess the name of the tune from that small section