Locating a Bridge on a new dulcimer
Instruments- discuss specific features, luthiers, instrument problems & questions
At least wo things are going on here.
In the science of acoustics on a perfectly balanced string in order to increase the tone of an instrument strung to be two octaves by one octave, you would fret the string in the precise middle. On a dulcimer, that would be the seven fret.
Nice to know, but our strings are not perfect. As you fret up the scale, strings tend to go slightly sharp. As an example stewmac.com has a fret calculator for an acoustic guitar (the closest they have to a dulcimer.) For this example, I entered an instrument with a 26" VSL. Stewmac suggests increasing the Treble E string, generally a similar string to our "d" string by 0.091" and the Bass E by 0.219". Doing some calculation, that would leave the VSL for our Treble d string at 26.091 and our Bass D string at about 26.10". Many makers will install the saddle at this slight angle.
For a dulcimer, stewmac suggests setting the break point on the saddle at 26.153" for a non compensated saddle. Stewmac has typically cheaped out on dulcimers and I do not suggest using that number.
If all you are looking for is a quick way to set your bridge, add 0.01" to the melody side and 0.10 to the Bass side when placing your saddle (it is technically not a bridge as so many dulcimer makers insist) and stop reading this post.
If you want a perfectly exact answer, you need to divide those two numbers by the number of frets you would use if your instrument were chromatic and keep adding multiples of the resulting value to the treble and bass sides of your frets. Instead of perfectly parallel frets, you would end up with frets that fanned out slightly on the bass side with the seven fret being 0.0455" further out on the treble side and 0.195 further out on the bass side. The only people I have heard that actually do that are luthiers who sell $30,000 guitars. (And I am sure someone will let me know that they do it on dulcimers.)
Day to day playing, intonation is in the ear of the musician. Dusty's solution is the same as I use, a floating saddle that the musician can adjust so that the instrument sounds best in that musician's ear.
Sorry for the long post. A good answer to your question is not easy and I look forward to reading the other responses.