If I recall correctly.. a zither looks like a hammered dulcimer? (somewhat like a harp with a box underneath it)
If all the strings are fixed, I'd tune it some sort of modal scale, and pluck it or hammer it. That would probably be the most musical solution. Given that the original setup used same gauge strings for everything (which I doubt) You can try to recalculate its original tuning from the lengths of each of the catches. (whatever you call it.. where you wrap the string around)
But, of course, you can probably cross string it, so it goes in zig zags for a sort of "prepared Zither" idea..
How about using different gauge strings, so you can tune the 15 into the harmonic series? (doubt any string can handle that sort of stress) Then, you can have a sort of hammond drawbar effect, where the partials sound at different volumes. Strum the whole thing, sample it to use as an STS instrument.
Randomly tune it, and throw marbles at the string.. hehe, how John Cage-ish
Or if you run out of ideas, you can always butter saute it with 2 cups diced onion, add 4 cups chicken stock, 1 cup diced carrots, 2 cup diced celery. Let simmer uncovered for 30 minutes, season to taste. Serves 3-4 hungry musicians.
If left over, let simmer some more 'till half the water has evaporated (so it's become buyon), put in a bottle and refrigerate for further use. You've got your very own bottle of Zither stock.
