Shazam has that feature years ago. You could hum a tune and it'd try to find it. I don't recall it being that good.
My memory might be failing me though. There was another competitor to shazam with an orange soundcloud like logo that also has song id. It could've been that app.
It's all about getting the direction change of subsequent notes right. Up or Down is all that matters. And the nice bit is that it doesn't matter if you transpose or if you go up too far or down too far for the next note.
You'll note that you need to define a sequence of similar notes as 'down' or 'up' to make it work.
My memory might be failing me though. There was another competitor to shazam with an orange soundcloud like logo that also has song id. It could've been that app.
Edit: It was soundhound and it supports humming https://play.google.com/store/apps/details?id=com.melodis.mi...