EDIT: Solved.
It’s a melody called “Playmates.”
This is a melody from a music box I remember as a child but I can’t find out what it’s called. I pieced together what I could remember using an online music box music maker program.
Here is my best guess at music notation:
A#4-G4-G4-A4-G4-F4-A#4-D4
F4-G4-F4-F4-C5-A4
F4-G4-F4-F4-D5-A#4
A#4-A#4-A#4-A#4-G4
G4-A4-G4-F4-A#4-D4
F4-G4-F4-F4-C5-A4
F4-G4-A4-A#4
Forgive the crudity of the recording. This was made after I spent an hour or so piecing together what I could remember. I am not musically inclined.
All the sound sample websites failed to help me surprisingly. ****
it sounds a little bit like Sí Bheag, Sí Mhór
Not it I’m afraid. Even tried the similar songs google recommended. It could be a waltz but I suspect its actually based on a polka.