Some guitars have partial frets across only certain strings, staggered with other partial frets across others, to give the desired scale in a particular tuning. This makes playing easier than if all the frets crossed all the strings, which would give many notes outside the desired scale. However, this scheme is limited to a particular tuning of the strings. This struck me as a serious drawback, since I envisioned choosing a tuning according to the needs of the composition, so I used only complete frets.
Ideally, any desired tone should be available on any string, but practically there is a limit to how close the frets can get and still be playable. (Other people have removed such limitations by using fretless guitars, but on a classical guitar the resulting sound is damped, somewhat like pizzicato violin, and I wanted clear ringing tones.) Thus, my choice of frets was a balance between wanting all tones and needing space for my fingers. To help choose, I laid out all the frets I was considering, to scale, on a piece of paper. I left extra space below the 2/1 and 3/2 frets to make them particularly easy to play.
To guide my choices out of the infinitude of possible intervals, I knew I wanted a harmonic scale of overtones 8-16:
1/1 9/8 5/4 11/8 3/2 13/8 7/4 15/8 2/1
so all these frets were essential. (I marked these frets with abalone dots on the fingerboard to give some visual points of reference.)
To get those tones on strings tuned to 3/2, 5/4, 7/4, 9/8, or 4/3 (keeping in mind various possible tunings) I included the following frets (grouped according to the string requiring them):
13/12 7/6 4/3 5/3 11/6
11/10 6/5 7/5 8/5 9/5
8/7 9/7 10/7 11/7 12/7
10/9 11/9 13/9 14/9 16/9
33/32 21/16 27/16
The frets needed to get the 13/8 and 15/8 tones on some of the strings are lacking (specifically, frets 13/10, 13/7, 15/14, 39/32, and 45/32) in order to minimize crowding on the fingerboard. The only one of those I really miss now is the 45/32 fret, but it would be unplayably close to the 7/5, so when I need it I play on the 7/5 and bend up a little. (Originally I decided to exclude the 14/9 fret as too close to the 11/7, but years of playing made me want it so much finally added it.)
In addition, I included two Pythagorean intervals:
and some other miscellaneous intervals from Partch's system to fill up some gaps:
21/20 16/15 27/20 32/21 40/21
As a result, there are 38 frets in the first 2:1, plus 14 more up to the 3:1. The number of different possible tones depends on the particular tuning. In any tuning I can get several overtone scales (not all complete) and a bewildering variety of other scales. Indeed, just about any scale I'm likely to want could be obtained with an appropriate tuning. For example, to get Partch's 43-tone scale, the tuning should include strings tuned to 1/1, 16/11, 16/5, and 8/5 (or 3/2), and so could be tuned to a utonality.
So overwhelming are the possibilities that I've used almost exclusively a single tuning chosen for simplicity, an open major chord (on D):
1/1 3/2 1/1 5/4 3/2 1/1
The tones available on each string in this tuning are shown in the Table, and the fingerboard is shown in the Photo (GIF, 96KB).
On the other hand, the closeness of frets makes sliding along a string a much smoother effect. Single melodies can be played this way using the ears rather than the eyes to determine where the slides end.
As a result of the difficulties of playing, I am unable to play solo pieces of the complexity I originally imagined. The music that I do play falls into three categories. Most often I play melodic improvisations, alone or with other musicians, exploring one or more scales, sometimes with a fixed cycle of tonal changes. Also, I play some simple solo compositions, but as this is more demanding, I do it less often. Finally, I play pieces I've composed to record on several tracks on tape, allowing me to play duets, trios, etc., where each part is played on my guitar. This yields music which satisfies my taste for complexity but which cannot be performed live.
Apart from playing music, this guitar is superb for demonstrating just intervals and scales with a familiar, acoustic sound. Having so many different tones available facilitates comparisons. As a result I've come to know the distinct sounds of various just intervals; my ear has improved tremendously. One result is that tuning up now takes a long time. The strings must be as accurately tuned as possible, otherwise the advantage of the precise harmonies is nullified.
As for determining the positions of the frets, simple theory would predict that to get an interval of, say, 5:4 would need 4/5 of the open string length, so the fret goes 1/5 of the open length from the nut. However, in real guitars, a little adjustment needs to be made to account for pressing down the string, etc. In effect, one places the frets as if the string were slightly shorter than its actual length, but this effect changes both very close to the nut and above about one-third of the string. So I made measurements on the original frets and compared with the theoretical positions to estimate how to adjust theory to practice. The results sound just right.
Mark Rankinbut I have been informed that as of 1996 he was marketing interchangeable fingerboard conversion kits at
c/o U.S. Post Office
Greenbackville, VA 23356
PO Box 1464I had a luthier do the modifications to the guitar and prepare the fingerboard "blanks", as well as one finished standard (12-tone tempered) fingerboard. I have fretted one of the blanks for blues in the key of A (with two different D's) using the following scale:
Redway, CA 95560
1/1 21/20 9/8 7/6 5/4 21/16 4/3 7/5 3/2 14/9 5/3 7/4 15/8over Pythagorean EADGBE tuning; the fingerboard looks like this. I'm still trying to decide how to fret the other two blanks...
David Canright -- DCanright@NPS.edu