A way to efficiently and effectively combine papers for musical scores
I assume you need it to lie flat when open, and don't have access to a printer that will print double size pages (e.g. A3 if you normally use A4). If you do have such a printer it's easy - fold in half and use a long arm stapler or sewing machine in the crease.
A comb binding machine would work well, giving you a book that lies nicely open. You can add, remove, and rearrange pages, and there's no tape. There is a margin needed at the seam though, so if you're joining the pages to get very long lines (which I've never seen in sheet music) this won't work.
Otherwise you can stop the residual exposed surface of tape being sticky by dusting it with talc after you've made the join. This will just brush off the paper.