Fret positions and string parameters for fretted stringed instruments

A serious problem with exact intonation on most fretted string instruments is caused by the fact that each string is used to produce many notes, undergoing changes in effective length and in tension, and that one and the same fret is used to stop more than one string. To compensate for the increased tension when a string is stopped, the effective string length must always be a little larger than what one would expect from an inversely proportional relation to pitch. The optimum amount of compensation, however, is usually not the same for each string but depends on action height, string tension, and string elasticity. Optimum compensations were computed for nylon and steel guitar strings and results were compared with both a simple logarithmic fret layout and the more traditional “rule of 18.” Fretboard and string designs, securing exact intonation over the entire range of the instrument, are discussed. [Work supported by a grant from Norlin Music, Inc.]