Old Animated Jazz Musical

I don't know why, but recently this thing just flashed into my mind and it won't get out.

When I was in school, music class would show us this old looking animated musical about I believe a street performer in New York and basically his music kinda wreaking havoc? That's what I remember at least.

I also distinctly remember a long part with like a busy husband having to stop his baby from getting hurt and at one point ice skating.