Hound is just "voice search" for songs: but I'd rather type than speak.
I had never heard of Midomi; just went and tested it. It seems to try to do what I'm talking about, but the "matches" seem completely random.
It may be that doing this is much harder than it seems; but what I'm talking about is really not about a specific performance, but about melodies (parts of melodies as sequences of intervals).
And it should work just as a text search engine works (matching a query to entries in an index); no special AI required for a first version.