The purpose of this research is to reduce inharmonicity in fretted instruments. It has long been known that the notes on fretted instruments are too sharp at high fret positions unless some sort of adjustment is made to the instrument. The deviation of the fundamental frequencies from the harmonic ideal is called inharmonicity. The universal solution has been to offset the saddle(s) so that the actual distance from nut to saddle is slightly more than the scale length. This approach, called intonation, greatly reduces inharmonicity, but errors remain and they are sometimes noticeable, especially to skilled musicians. There have been some attempts to adjust both nut position (intonating the nut) and fret positions, and some of them appear to be very effective. However, they are often difficult to implement. There is a much simpler approach to the problem that makes use of trends identified in a mathematical model of a vibrating string. The vibrating string behavior is clearly shown using a mathematical model of a single ideal string, that is, a plain string with no bending stiffness. With some basic assumptions about string height above the frets, frequency shift can be calculated for the different fret positions. We modified an electric guitar and measured string frequencies along the neck. Measured data was used to fine tune the saddle positions and intonation at the nut. The result was an instrument that has less frequency error at most frets along the neck.
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