This could be done in .Net, and could be used to create an animation for any MIDI file.
A MIDI file basically records music as a series of Note On and Note Off messages, each with an associated Pitch value. In the linked animation, each bar you see is drawn for a Note On/Note Off pair (the farther the Note Off message from its preceding Note On message, the longer the note and the longer the bar), with the vertical position of the bar representing the Pitch (the higher the note's Pitch, the closer the bar is to the top of the screen). Different instruments (just different types of organ stops in this tune) are represented in different colors.
To do this with .Net, you would start with code that reads MIDI files. Here is a good sample:
http://www.codeproject.com/KB/audio-video/MIDIToolkit.aspx
Once you've learned how to read MIDI files, the animation part could be done with GDI+, which is easy to use for drawing rectangles.
To be honest, however, this animation is very rudimentary and uninteresting. There are a lot of music visualization techniques out there that would produce a much more watchable result.