Lynn, probably not good form to jump in on an old thread, but from your description of the deep body and the photos of the peg head and strings, it is pretty apparent you have a five-string, four-course, baritone dulcimer. If the VSL is 28", give or take an inch, a common Mixolydian tuning would be A-E-a-aa (bass to melody-doublet) with corresponding string gauges of 34bw-22bw-14-14,14 (where "bw" = bronze wound and gauge means x/1,000"). With this tuning you can change to a "New Ionian" (aka Reverse Ionian) tuning by lowering that wound middle string from E to D (A-D-a-aa). In doing so you've gone from Mixolydian in A to New Ionian in D.
If the unwound middle string next to the melody-doublet look a tad thicker than the melody strings my guess would be a "1-3-5" tuning, i.e. A-C-E-aa with maybe 16 to 18 gauge for the E. Lots of luck with that unless you've dabbled with 1-3-5 before. I'd stick with the baritone mixolydian described previously and experiment with the quick change to New Ionian.
If you play with someone who is in DAd tuning you can do simple back and forth rounds in keys of A and D while you are in A Mixolydian mode or duets while in D New Ionian mode.
updated by @jim-hedman: 03/29/18 02:09:55AM