My 31-tone guitar John S. Allen When I studied musical tunings in the 1970's, I found the 31-tone equal temperament one of the most interesting tunings. It falls within the Fibonacci series 2, 5, 7, 12,19, 31, 50 ... which is the basis of musical scales of cultures all around the world. It provides very good approximations to all terms of the harmonic series up to the 11th. And it is almost identical to the standard Baroque mean-tone temperament -- but with a full circle of fifths, eliminating the discordant "wolf fifths." Around 1979, I built an experimental guitar neck to try out the 31-tone temperament. I made a template from angle iron, measuring off the fret spacing on a Bridgeport milling machine. Other than that, the design of the neck was fairly conventional. I mated the neck to a Framus steel-string acoustic guitar body, which, unlike most acoustic guitar bodies, holds the neck in place with screws rather than glue. I built a fully-adjustable bridge saddle, to assure tuning accuracy. When I tried out the guitar, I arrived at the following conclusions: On a guitar, 31-tone equal temperament sounds very pleasant -- and not only for diatonic music. Chords using the natural 7th and 11th sound completely normal and in tune, even though these intervals are far from standard scale degrees in Western music. Chords played on this guitar have a harmonious throb like that of a good barbershop quartet.

Chording is made much more difficult by the need for greater accuracy in finger placement (similar to the problem in playing chords high on the neck of a conventional guitar)

There is little problem in playing single-note melodic lines. A 31-tone neck would be practical on a melody instrument or electric bass.