I would not get real music. Go to the craft store and their scrapbooking section. On a sale, you can get scrapbook pages that are printed with music motifs (looking like sheet music) for as little as 20 to 50 cents a page (full price they can be from $1.00 to several bucks, but the craft stores like Michaels and A.C. Moore often have these papers on sale). I've seen these music papers that had a sepia-toned look that made them look antique.
Going to a craft store might be faster and easier than digging around in thrift stores. Thrift stores can be very hit or miss on items as specific as sheet music.
Unless you are doing really large centerpieces you might be able to cut these large scrapbooking pages in half to get what you want.
I've also seen wrapping paper in rolls, made to look like sheet music.
An alternative would be to ask a local music store if it has any old sheet music it is going to "remainder" because it's not selling. You might be able to cut a deal with them to take some off their hands cheaply if you don't care what the actual music is. But I still think any music-patterned paper could work as well and be cheaper.