Explanation
Pressing the string against the fret reduces the vibrating length of the string to that between the bridge and the next fret between the fretting finger and the bridge. This is damped if the string were stopped with the soft fingertip on a fretless fingerboard.
An advantage of frets is that they make it much easier to achieve an acceptable standard of intonation since the positions for the correct notes are given by the frets. Furthermore, playing chords are much easier on a fretted fingerboard.
A disadvantage of using frets is that the player is restricted by the temperament given by the position of the frets. Some influence on the intonation is still possible, however. The string can be pulled to the side to increase the string tension and the pitch. This technique (commonly called 'bending') is often used by electric guitarists of all genres and is a very important part of sitar playing. On instruments with thicker frets, the string tension and pitch will vary with the pressure of the finger behind the fret. Sometimes it is also possible to pull the string toward the bridge or nut, thus lowering or raising the string tension and pitch, respectively. However, with the exception of instruments like the sitar, where extensive pulling of the string is possible, much less influence on the intonation is possible than on unfretted instruments.
Since the intonation of most modern western fretted instruments is equal tempered, the ratio of the distances of two consecutive frets to the bridge is, or approximately 1.059463. Theoretically, the twelfth fret should divide the string in two exact halves. To compensate for the increase in string tension when the string is pressed against the frets, the bridge position can be adjusted slightly so that the 12th fret plays exactly in tune.
Many instruments' frets are not spaced according to the semitones of equal temperament, including the Appalachian dulcimer (with frets in a diatonic scale), the Turkish Saz (with frets spaced according to the Makam system of Turkish folk music), the Arabic Buzuq (with frets spaced according to the Arabic maqam system), and the Persian setar and tar (with frets spaced according to the Persian Dastgah system), and the Turkish tanbur (with as many as 5 frets per semitone, to cover all of the commas of the Turkish Makam system).
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