An on-going account of an experiment

by Dante Rosati

Feb.12, 1999

After playing guitar in standard equal temperament for close to thirty years, I was finally moved to take the frets off an old guitar and see what would happen. What finally convinced me was listening to a recording of Lou Harrison playing his music, "Cinna", on a justly tuned piano. The sounds and harmonies are fascinating and beautiful, as well as strange to ears used to equal temperament. Now, its not like I've never heard anything outside of ET. I've written Csound computer pieces using Phi ratios, prime numbers and frequencies of the sun's spherical harmonics. I play blues on the guitar which uses microtonal pitch bending, as well as sitar which also uses microtones. But I think there is a difference here - in both the blues and indian classical music microtones are heard as intervals, rather than harmonically. In computer music, the pitch continuum is sliced and diced any way imaginable, and the spectra of the sounds themselves can be constructed however you want as well. To me having a harmonic and contrapuntal instrument in an alternate tuning is something different. Here intervals are discrete without having to bend notes across a continuous pitch space, and exactly tuned intervals can be combined harmonically and contrapuntally. In addition, there is something about a flesh and blood (or should I say wood and string) instrument that is lacking in a synth keyboard or computer sound. That is why while I occasionally make forays into digitally synthesized music, I always come back to my box with six strings.

As William Sethares has shown, consonance and dissonance are a function of the spectra of the constituent sounds. When I wrote PHI, I used the same ratios for all parameters: the partials in the sounds, the envelopes of the partials, the ratios between sounds, the durations, volumes and the section lengths. This is only possible on computer, since there are no vibrating bodies in nature that produce only Phi related partials. A guitar string, on the other hand, is a classic vibrating body which produces integer multiple partials, and the consonance or dissonance of various intervals is the result of this.

The frets of an ET guitar impose a tuning which does not completely "resonate" with the sound of the string itself. Without going into the history of tuning and temperament (see here or here) I will only say that equal temperament is an idealized Pythagorean tuning, and tons of great music has been played, and continues to be played, using it. But Lou Harrison's piano gave me a glimpse of something else.....

O.K, so I get a pair of pliers and a screwdriver and pry the frets off of a one-time great classical guitar that I haven't used for a decade or so. Its got a bunch of cracks but maybe I can do something about them too at the same time. The frets come out without too much trouble, although a few fragments of the fingerboard flake off as I pull them out. Next time I will remove frets a little more gently.

After a good cleaning and a little sanding, I fill the grooves with wood putty, and fill in the flaked bits too. After it dries I sand and then put some more putty on. Another sanding produces a nice smooth blank fingerboard. I paint it white with some left over housepaint so that I can put easily seen marks on it with a pencil.

My idea at this point was to leave it fretless - why have to limit yourself to any one tuning? Violinists dont need frets, after all. I put the strings on, tune them up and start playing - thud, thud thud. Instead of nice clear notes, all I hear is muffled thuds produced by stopping the strings with my fingers. Hmmm.. maybe I just have to get used to it. In any case, I find that I can play pretty well even without the frets, it's not so bad. Having experimented alot with harmonics, I can hear the difference between a justly tuned third and an equal tempered one. I try using my fingernail to stop the string, and now the sound is alot better. Sliding around on the strings, I sound like an Indian sarod player. That's cool, but I want to play chords. They are a little harder fretless because on a fretted guitar you can stretch into a fret and get the right note. Now, I have to stretch each finger to its exact position, which is tricky.

Right away I am made aware of the question of the tuning of the open strings. Should I leave the standard tuning? When I improvise Indian style on guitar I usually use low D tuning so the bottom three strings can be a kind of tambour. Sometimes I tune the third string to f# also. So I think what Im moving towards is a open tuning. Then I think, what if I tune the string in fifths and fourths? That is : 1/1, 3/2, 2/1, 3/1, 4/1, 6/1? This is the most general 3-limit tuning which will accomodate other tunings on the strings themselves. I tune the sixth string way down so that the first string is not going to snap. With the sixth tuned to somewhere between C and C#, the first string is high, but holds up. So the guitar is tuned C-G-C-G-C-G. I mark the edge of the fingerboard at 1/2 the scale length, 1/3, 1/4, 1/5, just to orient myself. I use red for 1/2 and 1/4, green for 1/3 and blue for 1/5 and 2/5. The whole guitar resonates powerfully with the open tuning. I like it.

After playing with this set up for awhile I can see that in order to stay fretless I'm going to have to use my fingernail and play sarod style. Otherwise I'm going to have to put some frets on in order to play chords. I decide to go for the frets. But now I have to decide: how many frets and where?

On to "Fretting about Ratios"