In contrast to "traditional" mountain dulcimers, which have diatonic fretboards, it's also possible to build chromatic dulcimers. I often jokingly call mine Martian Dulcimers, as the chromatic fretboard is sometimes seen as an space invader in the mountain dulcimer world — and also because I first used them on the Twang Darkly album Martian Archaeology. I've built both acoustic and electric chromatic dulcimers; they are used extensively on my various recordings.
Sometimes, folks in the dulcimer community assume that the chromatic dulcimer is best suited for what is termed "chordal playing" — as contrasted with the presumed appropriate "traditional" use of the mountain dulcimer focused on the modes of the major scale (for example, Appalachian/English folk music idioms tend towards Mixolydian, Ionian, Aeolian, and Dorian modes). I see this as a false dichotomy and use the chromatic dulcimer across a full spectrum of modal approaches. This spectrum includes Appalachian-compatible music based upon the modes of the major scale, but it also encompasses the so-called "altered" or "synthetic" modes into the delightfully adventurous realm of polymodal chromaticism.
So, a chromatic dulcimer, like the mountain dulcimer, is well-suited to modal mountain music, but the full fretboard provides access to a wider variety of modal concepts than the the seven "Western modes." I use this extended palette with my trio Twang Darkly, where we don't just do mountain music, we do Martian mountain music.