This is a Japanese dorama based off of the manga, Nodame Cantabile by Tomoko Ninomiya, and it will be an anime in early 2007.
A short synopsis:
Megumi Noda, or "Nodame," is a piano student at Momogaoka College of Music. Although she is an extremely talented pianist who can play by ear, she can't read music. She also hates to take a bath or clean her room. For her daily meals, she usually grabs something out of her friend's lunchbox. Nodame soon falls in love with Momogaoka's top student, Shinichi Chiaki. Born into a musical family, he plays the piano and violin brilliantly. Although his major is piano, he has secret ambitions to become a conductor.
Based on the big hit comic book by Tomoko Ninomiya, this is the romantic comedy of two completely different personalities.
- Fuji-TV
You can find the RAWs at D-addicts and the soft-subs at S-projects.org There are 9 episodes out so far and the series is geared towards 11 episodes.
Teaser (I did not make this GIF, I'm not quite sure who, but full credits to that person):

@ Hyo - If you have something you would like to add, just PM or reply in this thread. ^^
EDIT: I forgot to mention that the dorama will cover the first nine volumes out of sixteen. The manga is still on-going.