Math artist Vi Hart illustrates the relation between music and mathematical symmetry. From the YouTube page:
A visual and musical expression of mathematical symmetry groups. The transformations done to the video are equivalent to the transformations done to the notes.
These type of repeating patterns are called frieze patterns. A couple wallpaper groups are also represented.
But the video is intuitive. You don't have to completely understand it to enjoy it. (via Waxy.org)