Mean tone dulcimer?
General mountain dulcimer or music discussions
As Dusty Turtle say, this is NOT a dumb question!! It is a question which opens up many doors, and once you start opening the doors, you will have more and more questions. This is basically the large field of "Tunings and Temperaments" or sometimes referred to as "Microtunings" or "microtonality" -- basically all pointing to the whole idea of notes in between the keys of a piano (or smaller than a half-step).
There is some great discussion here, and many of you seem to have a good handle on the overall, general ideas of where frets might go. I particularly resonate with the single string stretched across a board of some sort, where you map out the divisions of the string - which will give you the harmonic series. If you get the harmonic series: dividing a string into 2 (2nd harmonic), 3 (3rd harmonic), 4 (4th harmonic), 5 (5th harmonic), 6 (6th harmonic), 7 (7th harmonic), and so on----then you can see how easy it is to build a just-intonation scale based on VERY simple small-integer ratios:
1/1 - 9/8 - 5/4 - 4/3 - 3/2 - 5/3 - 15/8 - 2/1
These would correspond to the frequency ratios of C - D - E - F - G - A - B - C ---- if you want fret spacing for your dulcimer's bass string (this is for 6+ fret only here - computing the normal 6th fret is another ballgame), you would use the inverse of these (frequency is inversely proportional to string length), remembering that the string length is the distance from each fret to the Bridge. To get your distance from the nut to a fret, just subtract that from the open nut-to-bridge V.S.L.
Another very important thing to remember on the dulcimer is that -- in C - G - G (1 - 5 - 5 Ionian) Tuning, the middle and melody strings will NOT go up EXACTLY as the bass string, because they are tuned to the 5th of the scale (so you start from 3/2 at the nut on these strings, and this time you will have the natural 6th fret and NOT the 6+). So, I'm basically saying here that it is not possible ALWAYS to have one fret go all across the fingerboard like they do on guitars, banjos, and modern dulcimers.
The wikipedia entry on just intonation is superb on deriving all this:
I really need to get around to making some sort of an adjustable-fret dulcimer -- individually adjustable frets for each string. Of course one way around this is to use bagpipe tuning 1 - 8 - 8 (I know this works well for just tuning because my 1966 Jethro Amburgey is pretty close to just tuning and bagpipe tuning ROCKS on this!). Sorry about all the detail and ratios, but it really comes down to this kind of stuff, and there are many, many worthwhile web sites to help you get it.
I may be able to answer your questions, or at least I may be able to point the way to some good web resources. Thanks for the great thread!! BTW, I'm a major fan of Equal Temperament, mostly because I play a lot of chords and want to be in tune with keyboard synthesizers.