Frets

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. Standard classical guitars have 19 frets and electric guitars between 21 to 24 frets, although guitars have been made with as many as 27 frets.
Frets are laid out to accomplish an equal tempered division of the octave. Every twelve frets represents one 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 (twelfth root of two). In practice, luthiers determine fret positions using the constant 17.817---an approximation to 1/(1-1/). 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 several different gauges and 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 to prevent buzz.
On steel-string guitars, frets are eventually bound to wear down; when this happens, frets can be replaced or, to a certain extent, leveled, polished, recrowned, or reshaped as required.