Mandolin are used. Usually, courses of 2 adjacent strings are tuned in unison. By far the most common tuning is the same as violin tuning, in scientific pitch notation G–D–A–E, or in Helmholtz pitch notation: g–d′–a′–e″. Note that the numbers of Hz shown above assume a 440 Hz A, standard in most parts of the western world. Some players use an A up to 10 Hz above or below a 440, mainly outside the United States. Other tunings exist, including "cross-tunings", in which the usually doubled string runs are tuned to different pitches. Additionally, guitarists may sometimes tune a mandolin to
String instrument ways to change the pitch of a vibrating string. String instruments are tuned by varying the strings' tension because adjusting length or mass per unit length is impractical. Instruments with a fingerboard are then played by adjusting the length of the vibrating portion of the strings. The following observations all apply to a string that is infinitely flexible (a theoretical assumption, because in practical applications, strings are not infinitely flexible) strung between two fixed supports. Real strings have finite curvature at the bridge and nut, and the bridge, because of its motion, are not exactly nodes of vibration. Hence the