Guitar Frets are laid out to accomplish an equal tempered division of the octave. Each set of twelve frets represents an octave. The twelfth fret divides the scale length exactly into two halves, and the 24th fret position divides one of those halves in half again. The ratio of the spacing of two consecutive frets is formula_1 (twelfth root of two). In practice, luthiers determine fret positions using the constant 17.817—an approximation to 1/(1-1/formula_1). If the nth fret is a distance x from the bridge, then the distance from the (n+1)th fret to the bridge is x-(x/17.817). Frets are available in
Scale length (string instruments) All other things being equal, increasing the scale length of an instrument requires an increase in string tension for a given pitch. A musical string may be divided by the twelfth root of two formula_1, approximately 1.059463094 and the result taken as the string-length position at which the next semitone pitch (fret position) should be placed from the previous fret (or, in case this is the first calculation, the nut or zero fret) of the instrument. This quotient is then divided again by itself to locate the next semitone higher, and so on. Alternatively, the string may be divided by