Question about the 6 1/2 fret
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@overdrive, please note that your description of frets and scale positions only holds true if the open string is the tonic. In traditional dulcimer playing, different tunings are used for different modes, and the tonic changes depending on the tuning. So yes, in DAd (mixolydian) the tonic is the open string. But in DAA (ionian) the tonic is found at the 3rd fret. In DAC (aeolian) the tonic is found at the 1st fret. Basically, the pattern of whole and half steps in the scale or mode determines where on the fretboard you find the tonic.
I suspect that the 6+ fret was added so that you could get the two "major" sounding modes (ionian & mixolydian) out of a single tuning (1-5-8 or DAd). I doubt people started tuning more in DAd than DAA simply because they wanted to play a small number of mixolydian tunes all the time.
And as people started playing chords and fretting across all the strings, DAd offers a greater melodic range (three notes worth!) out of a single chord position than does DAA. Chording in DAA sounds more concise and coherent to my ear, but it requires a lot more hand movement to play in a basic chord/melody style.