Fret choices for Just Intonation Guitars
This is an informal article about my choices of frets for guitars in Just Intonation.
I started with a classical guitar (Giannini) many years ago, and wrote an article about that guitar. More recently (fewer years ago), I bought a Martin 00016 steel-string guitar and an interchangeable fingerboard kit from Mark Rankin, and hired a luthier to make the modifications and the fingerboard blanks including a standard (12-tone equal tempered) fingerboard. After some thought, I fretted one fingerboard based on the idea of blues in A, using a 7-limit scale. Lately, I'm considering fretting another fingerboard to get harmonic scales (8-16) on E and A.
Here are some issues that arose:
How close can frets be?
On my Giannini, I chose frets straight across, and lots of 'em (37 in the first octave). All the frets are playable. The closest frets are 4mm apart, center to center, and the frets themselves are 2mm wide, so the gap is a fret-width. With frets this close, one needs to be very careful to get the fret heights uniform to insure playability and no buzz. In my experience, fret separations of 6mm or more are relatively easy to play. (The closest frets on my Martin fingerboard are 5mm, but the upper note is not in the scale; see below.)
Of course, to play such frets requires precise finger placement, but no extra pressure is required. Naturally, wider fret spacing makes for easier playing, particularly when trying to play chords. Barred chords with staggered frets can be tricky.
Extra frets just above others are not a problem
In some cases on the Martin fingerboard, it was easiest to use a full fret where the scale would call for a partial fret with a gap. Provided this extra fret was just above (sharp) of the scale fret, the extra fret did not get in the way. For example, the 3/2 fret gives a 27/16 on the B (9/8) string, just (a comma) above the fret for 5/3. The extra (27/16) fret does not make the usual fret (5/3) any harder to play, and because it is so close, it hardly reduces the space to the fret above (7/4), so that one is really no harder to play either.
This led me to the realization that an "alternate" note will not get in the way provided it is a comma sharp of a "standard" note in the scale. The alternate itself will be harder to play, but the rest of the scale won't. (Unfortunately for my blues fingerboard, the alternate D is 21/16, which is below the standard D 4/3, so playing the standard D 4/3 requires particular attention.) I plan to take advantage of this in future fingerboards, to throw in a few extra (sharp) notes that I can get when I really want them.
The open strings don't have to be tuned to the scale
I am pretty slow about tuning the strings, in part because I am very particular about getting it as right as I can, to my ear. (I tune by harmonics, and it works very well for me. Even when I tune tempered, I do it based on beats in the harmonics.) In contrast, changing fingerboards is pretty quick and easy. So for me, the idea of using one tuning for more than one fingerboard seems attractive.
But a natural approach is to tune the strings to the scale. For those that do a lot with open strings, this makes good sense. (I'm not a very good guitarist, but I like to play melodies all over the neck and don't always use open strings.) Of course, the choices of scale and string tuning determine fret positions, which affects the playability (and navigability too!).
For my first interchangeable fingerboard, I used standard EADGBE tuning, but all pure fourths (3/2 1/1 4/3 16/9 9/8 3/2, to A440), even though the G in the scale is 7/4, not 16/9. This means I can never play an open G with a fretted G (unless I'm into ugly). But had I instead chosen an open G 7/4, the frets on the G string would all have to go up a bit, resulting in many more partial frets for just the one string. Not only would the fingerboard be harder to make, but a bit harder to play as well. Having all my open fourths perfect makes the frets simpler, and when they go straight across several strings I know those fourths are perfect too, which helps in understanding which frets are which in the scale. (I may use the same tuning for my next fingerboard as well, for harmonic scales 8-16.)
Using "dofrets.eps" to visualize the frets helps in exploring the possibilities...
last updated 1999 Oct 10