Further simplifications occur for the regular tunings that are repetitive, that is, which repeat their strings. For example, the E-G♯-c-e-g♯-c' M3 tuning repeats its octave after every two strings. Such repetition further simplifies the learning of chords and improvisation;[71] This repetition results in two copies of the three open-strings' notes, each in a different octave. Similarly, the B-F-B-F-B-F augmented-fourths tuning repeats itself after one string.[73]

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All-fourths tuning replaces the major third between the third and second strings with a fourth, extending the conventional tuning of a bass guitar. With all-fourths tuning, playing the triads is more difficult, but improvisation is simplified, because chord-patterns remain constant when moved around the fretboard. Jazz guitarist Stanley Jordan uses the all-fourths tuning EADGCF. Invariant chord-shapes are an advantage of other regular tunings, such as major-thirds and all-fifths tunings.[20]
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.
The history of stringed instruments dates back thousands of years, while the modern guitar can be traced back to the oud and the lute of the 8th and 9th centuries. Today's guitars come in countless variations and at JustStrings.com, we have a dazzling variety of guitar strings and other types of strings for many different instruments. Advanced technology combined with traditional craftsmanship produces some of the finest strings that boast long-lasting durability and exceptional tonal quality. Whether you're looking for rugged, great-sounding electric guitar strings to take on tour with you, or the perfect set of strings for your lap steel, we're bound to have exactly what you need. We take great pride in bringing you the best quality strings from the world's leading innovators. Our acoustic guitar strings, from manufacturers like Ernie Ball, GHS, Thomastik-Infeld and Fender, are available in many varieties, from silver-plated copper flat wound to 80/20 bronze round-wound. You'll find plain uncoated strings and coated strings that improve longevity. Classical guitar strings, traditionally made from gut, are now strung with nylon or advanced synthetic materials for better performance. Electric guitar strings are available in nickel-plated steel, pure nickel or stainless steel. We also have strings for resophonic guitars (also known as Dobros), Steinberger guitars and pedal steel guitars. Browse our bass guitar strings, and find 7-string, 8-string or 12-string guitar strings. We also carry banjo strings, harp strings, and strings for octave, tenor, baritone and Renaissance guitars. We are the leading source of premium strings for nearly every type of instrument.

In major-thirds tuning, the interval between open strings is always a major third. Consequently, four frets suffice to play the chromatic scale. Chord inversion is especially simple in major-thirds tuning. Chords are inverted simply by raising one or two notes by three strings. The raised notes are played with the same finger as the original notes.[22][23] In contrast, in standard tuning, the shape of inversions depends on the involvement of the irregular major-third.[24]
As already stated, the perfect-fifths (P5) interval is the most harmonious, after the unison and octave intervals. An explanation of human perception of harmony relates the mechanics of a vibrating string to the musical acoustics of sound waves using the harmonic analysis of Fourier series. When a string is struck with a finger or pick (plectrum), it vibrates according to its harmonic series. When an open-note C-string is struck, its harmonic series begins with the terms (C,C,G,C,E,G,B♭,C). The root note is associated with a sequence of intervals, beginning with the unison interval (C,C), the octave interval (C,C), the perfect fifth (C,G), the perfect fourth (G,C), and the major third (C,E). In particular, this sequence of intervals contains the thirds of the C-major chord {(C,E),(E,G)}.[4]

### The Spanish vihuela, called in Italian the "viola da mano", a guitar-like instrument of the 15th and 16th centuries, is widely considered to have been the single most important influence in the development of the baroque guitar. It had six courses (usually), lute-like tuning in fourths and a guitar-like body, although early representations reveal an instrument with a sharply cut waist. It was also larger than the contemporary four-course guitars. By the 16th century, the vihuela's construction had more in common with the modern guitar, with its curved one-piece ribs, than with the viols, and more like a larger version of the contemporary four-course guitars. The vihuela enjoyed only a relatively short period of popularity in Spain and Italy during an era dominated elsewhere in Europe by the lute; the last surviving published music for the instrument appeared in 1576.[9]

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