Here’s the sheet music, quite possibly in the wrong key.
I have no idea where this is from or who it’s by. I was just playing around with different chords on the piano, and this kind of bubbled up from within my subconcious. I swear I’ve heard it somewhere.
Anyone know of a place I can host small midi or mp3 files for free?
Played it on a mini-synth. No idea; sorry. 
Do you have absolutely no idea at all of where you heard it? Classical v. pop; movie or tv sndtrk. v. radio, etc.?
It’s really an inocuous bit. Depending on the instrumentation, something like it probably occurs in a great many soundtracks, however momentarily and incidental. Or was it the main theme from something?
I have no idea. I’m somewhat inclined to say radio. BTW, I’m 16, so this probably isn’t a song that came out long before the 80’s or 90’s, but it certainly could be.
Now with ability to read music not required!!!
http://gotdoof.com/files/mystery%20song.mid
(Hosted by my friend doofsmack)
It’s very similar to a passage from The Sorcerer, by Gilbert and Sullivan, during the betrothal scene. To almost those exact notes, the tenor sings
Soprano repeats. Then chorus.
Best I can do.
A little googling finds this: http://math.boisestate.edu/gas/sorcerer/sor10.mid
I think the part you’re referring to is at about 41 seconds in. However, I’ve definitely never heard of The Sorcerer, and I’m quite certain that I’ve heard the melody in the OP before, somewhere. Plus, it’s not quite the right rhythm. But I am very impressed that someone had so close a match.
Any other ideas?