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
Appalachian dulcimer half," "6½" or "6+" fret a half step below the octave. This enables one to play in the Ionian mode when tuned to D3-A3-D4 (the traditional tuning for the Mixolydian mode), where the scale starts on the open (unfretted) string. This arrangement is often found to be more conducive to chord-melody play. It also became common to add a fret one octave up from the 6+ fret, called the "13+" fret, and by the late 1970s these additional frets had become standard. Eventually, some builders began to offer further additional frets at the "1+" and "8+" positions or (as an