The ratio of the spacing of two consecutive frets is {\displaystyle {\sqrt[{12}]{2}}} (twelfth root of two). In practice, luthiers determine fret positions using the constant 17.817—an approximation to 1/(1-1/ {\displaystyle {\sqrt[{12}]{2}}} ). 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).[15] 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, allow a dramatic vibrato effect. Fine frets, much flatter, allow a very low string-action, but require that other conditions, such as curvature of the neck, be well-maintained to prevent buzz.
Play each note of the chord one after another (known as playing an arpeggio) to check if any are being accidently muted or need pressing down harder. If you find that you're accidently muting a string with one of your fingers, try lowering your thumb so the tip reaches around half way up the back of the guitar neck. This gives your fingers a better angle to approach the fretboard.
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Russell, George (2001) [1953]. "Chapter 1 The Lydian scale: The seminal source of the principal of tonal gravity". George Russell's Lydian chromatic concept of tonal organization. Volume One: The art and science of tonal gravity (Fourth (Second printing, corrected, 2008) ed.). Brookline, Massachusetts: Concept Publishing Company. pp. 1–9. ISBN 0-9703739-0-2.
A capo (short for capotasto) is used to change the pitch of open strings.[28] Capos are clipped onto the fretboard with the aid of spring tension, or in some models, elastic tension. To raise the guitar's pitch by one semitone, the player would clip the capo onto the fretboard just below the first fret. Its use allows players to play in different keys without having to change the chord formations they use. For example, if a folk guitar player wanted to play a song in the key of B Major, they could put a capo on the second fret of the instrument, and then play the song as if it were in the key of A Major, but with the capo the instrument would make the sounds of B Major. This is because with the capo barring the entire second fret, open chords would all sound two semitones (aka one tone) higher in pitch. For example, if a guitarist played an open A Major chord (a very common open chord), it would sound like a B Major chord. All of the other open chords would be similarly modified in pitch. Because of the ease with which they allow guitar players to change keys, they are sometimes referred to with pejorative names, such as "cheaters" or the "hillbilly crutch". Despite this negative viewpoint, another benefit of the capo is that it enables guitarists to obtain the ringing, resonant sound of the common keys (C, G, A, etc.) in "harder" and less-commonly used keys. Classical performers are known to use them to enable modern instruments to match the pitch of historical instruments such as the Renaissance music lute.
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Guitars have been played since the Renaissance era, after descending from the ancient Greek instrument, the kithara. Or, at least, that's how the theory goes: the only real proof for this is the similarities between the Greek word and the Spanish word, quitarra. Early guitars often had four strings, evolving into the six-string version we know today in the late 1600s. Anton Stradivari, the famous violin-maker, also had a hand in making guitars. There's now only one Stradivarius guitar left in existence.
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