For the musical (rather than instrumental) scale, see Pythagorean tuning. When referring to stringed instruments, the scale length (often simply called the “scale”) is considered to be the maximum vibrating length of the strings to produce sound, and determines the range of tones that string is capable of producing under a given tension. In the classical community, it may be called simply “string length.” On instruments in which strings are not “stopped” or divided in length (typically by frets, the player’s fingers, or other mechanism), such as the piano, it is the actual length of string between the nut and the bridge. String instruments produce sound through the vibration of their strings. The range of tones these strings can produce is determined by three primary factors: the mass of the string (related to its thickness as well as other aspects of its construction: density of the metal/alloy etc.), the tension placed upon it, and the instrument’s scale length. On many, but not all, instruments, the strings are at least roughly the same length, so the instrument’s scale can be expressed as a single length measurement, as for example in the case of the violin or guitar. On other instruments, the strings are of different lengths according to their pitch, as for example in the case of the harp or piano. On most modern fretted instruments, the actual string length is a bit longer than the scale length, to provide some compensation for the “sharp” effect caused by the string being slightly stretched when it is pressed against the fingerboard. This causes the pitch of the note to go slightly sharp (higher in pitch). Another factor in modern instrument design is that, at the same tension, thicker strings are more sensitive to this effect, which is why saddles on acoustic (and often electric) guitars are set on a slight diagonal. This gives the thicker strings slightly more length. All other things being equal, increasing the scale length of an instrument requires an increase in string tension for a given pitch. A musical string may be divided by the twelfth root of two , approximately 1.059463094 and the result taken as the string-length position at which the next semitone pitch (fret position) should be placed from the previous fret (or, in case this is the first calculation, the nut (instrumental) or zero fret) of the instrument. This quotient is then divided again by itself to locate the next semitone higher, and so on. Alternatively, the string may be divided by , approximately 17.817154, and the quotient taken as the location of the next semitone pitch from the nut of the instrument. The remainder is again divided by 17.817154 to locate the next semitone pitch higher, and so on. For centuries the divisor 18 was used instead; this “Eighteen Rule” produced a sort of rough compensation. Actual fret spacing on the fretboard was often done by trial and error method (testing) over the ages. However, since the nineteenth century the availability of precision measuring instruments has allowed frets to be laid out with mathematical accuracy. In many instruments, for example the violin, the scale of a full-sized instrument is very strictly standardised. Smaller scale instruments are still often used: By younger players. By smaller advanced players. To obtain a particular tone or effect. For convenience when travelling. Larger scale instruments are rare, but may be used by experimental and avant-garde players, or specially made for soloists with particularly extended reach. In other instruments, for example the viola and the electric guitar, the scale of a full-sized instrument varies a great deal.
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