fingerboard for harmonic scales
The goal of this fingerboard is to get one or more 8-tone harmonic scales:
1/1 9/8 5/4 11/8 3/2 13/8 7/4 15/8
Adding 5 more tones includes the same scale on the 4/3, with the 13-tone result
1/1 13/12 9/8 7/6 5/4 4/3 11/8 3/2 13/8 5/3 7/4 11/6 15/8
I considered adding another 5 tones to get another harmonic scale on the 3/2, but the 21/16 would make the 4/3 hard to play, and the 39/32 would make the 5/4 hard, too. But the other three added tones are a bit sharp of others, but still with a decent gap above each, so I decided to include them. The 16-tone scale is then
1/1 33/32 13/12 9/8 7/6 5/4 4/3 11/8 45/32 3/2 13/8 5/3 27/16 7/4 11/6 15/8
See also the harmonic melodic diagram below.
I am not firmly decided on a tuning for the strings yet. If I keep the same Pythagorean tuning I used for the blues fingerboard, then I would call E the 1/1, with the result as shown at left. But I might prefer some sort of D tuning, maybe DADGAD...
The graphics on this page are bitmapped versions of the EPS files
harm_f.eps (frets) and
harm_h.eps (diagram).
last updated 1999 Oct 10
David Canright
-- DCanright@NPS.edu