Frets are metal strips (usually nickel alloy or stainless steel) embedded along the fretboard and located at exact points that divide the scale length in accordance with a specific mathematical formula. Pressing a string against a fret determines the strings' vibrating length and therefore its resultant pitch. The pitch of each consecutive fret is defined at a half-step interval on the chromatic scale. Frets worn down from heavy use can be replaced or, to a certain extent, re-shaped as required. Frets are available in different gauges.
Frets are laid out to a mathematical ratio that results in equal tempered division of the octave. The ratio of the spacing of two consecutive frets is the twelfth root of two , whose numeric value is about 1.059463. The twelfth fret divides the scale length in two exact halves and the 24th fret position divides the scale length in half yet again. Every twelve frets represents one octave. In practise, luthiers determine fret positions using the constant 17.817, which is derived from the twelfth root of two. The scale length divided by this value yields the distance from the nut to the first fret. That distance is subtracted from the scale length and the result is divided in two sections by the constant to yield the distance from the first fret to the second fret. Positions for the remainder of the frets are calculated in like manner.
There are several different fret gauges, which can be fitted according to player preference. Among these are "jumbo" frets, which have much thicker gauge, allowing for use of a slight vibrato technique from pushing the string down harder and softer. "Scalloped" fretboards, where the wood of the fretboard itself is "scooped out" between the frets allows a dramatic vibrato effect. Fine frets, much flatter, allow a very low string-action but require other conditions such as curvature of the neck to be well maintained in order to prevent buzz.