Did some searching and based on several sites, it looks like mixing it with vinegar is a pretty common cleaner.
Simply mix a couple tablespoons of cream of tartar with a small amount of white vinegar. There are no exact amounts; you want to end up with a thin paste. Start with about half a capful of vinegar and adjust accordingly. After doing it once you’ll discover the right consistency.
Apply it to the glass with a paper towel, a sponge or your fingers and wait two to three hours. Remove it — and the gunk — with a damp sponge and dry with a towel. If some stubborn spots remain, just do it again. This costs mere pennies per application and cream of tartar is one of the few things in the baking aisle with an indefinite shelf life. It will still be good five years from now.