This search engine will name that tune for you:

Maybe the following problem (here described by Bernard Levin) looks familiar to you.

"... what if we cannot read, or write, a single note of music? What if we think that A flat major is an army officer who has had the misfortune to be run over by a tank? Are we to long in vain for the ability to discover what we are trilling, or the trombone-playing busker in the street is tootling, or the maiden at the piano glimpsed behind the lace curtains is tinkling?"

The answer is: No, not if we search for a melody with "Melodyhound", the "name that tune" search engine.

There are two ways of using this search engine. You can whistle a tune to the computer, and it will tell you the "Parsons Code" of what you have whistled, which you can then use to find the title and composer in the database.

Parson's Code?

In his "Directory of Tunes and Musical Themes" (Spencer Brown, 1975), D. Parsons showed that a simple encoding of tunes that ignores most of the information in the musical signal can still provide enough information for distinguishing between a large number of tunes.
Each pair of consecutive notes is coded as "U" ("up") if the second note is higher than the first note, "R" ("repeat") if the pitches are equal, and "D" ("down") otherwise. Rhythm is completely ignored. Thus, the first theme from Beethoven's 8th symphony that is shown above would be coded DUUDDDURDRUUUU. Note that the first note of any tune is used only as a reference point and does not show up explicitly in the Parsons code. You can enter an asterisk (*) in the Parsons code field for the first note.

Pretty amazing but the system is geared toward classical and folk music right now, with 10,000 classical and 15,000 folk melodies entered. There are only about 100 "popular" melodies available.