I just looked at the theme for Twelve Monkeys. It’s REALLY close to that but not exactly that.
Nope. The sound we’re looking for is ominous and creepy. Think suspense, horror, or action movie.
I’m linking the Twelve Monkeys theme because it’s REALLY close. The one I heard has an extra note in there and doesn’t have the two pauses at the beginning.
Also, the Twelve Monkeys goes high-low, and this one went low-high. But a really similar feel, especially with the discordant last note.
Bumping this to see if the afternoon crowd has any ideas.
I know it’s not this, but I thought I’d present it anyway.
Could it possibly be part of Danse Macabre?
Any chance it’s the Sherlock Holmes (Robert Downey movie) theme? (Various alterations on the theme are used in the movies and the piece, so it might not be exactly like what you heard).
Some part of “The Rumble” from West Side Story? Bernstein : Symphonic Dances from West Side Story - YouTube
Perhaps the shower scene from Psycho? At about 1:40 in.
Posting from my phone so no link included, but I’m guessing it’s the theme from Halloween. It’s also my ring tone for October.
Here it is
http://www.youtube.com/watch?v=gMLPnk9-6MM
It fits all the criteria mentioned; I’ll bet this is it.
Definitely not Halloween, although that got my hopes up because it’s a movie I’ve seen. I’m going to spend some time on YouTube looking up themes from movies I’ve seen semi-recently in hopes of stumbling upon it in blind luck.
I’d honestly think it was Twelve Monkeys, except I counted the notes and pause as the ringtone went off. Other than not fitting that pattern, it’s almost exactly the same.
Please do let the rest of us know when you find it. 
I lack the musical ability to be of any help, but I’m now quite curious as to what the final answer is.
The description under 12 monkeys says it’s “based on Libertango by Astor Piazzolla”
Even if it’s not that song, maybe you are looking for a clip of some famous Tango piece that is commonly used, like Roxanne or something else - they all sound like they could fit
I looked at the Libertango–it wasn’t as close as the 12 Monkeys version.
Not to stereotype, but the guy in the elevator was on felony probation and got off on the “piss test” floor. I’m pretty sure that the ringtone wasn’t a piece of classical music or something from a show tune. 
Because criminals and drug users never like classical musicor show tunes?
Find that asshole with the phone and ask HIM!
Not real ones.