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
The Well-Tuned Piano octaves, with nine notes extending the bass of the piano. Young describes the pitches of his tuning as being, "derived from various partials of the overtone series of an inferred low fundamental E-flat reference ten octaves below the lowest E-flat on the Bösendorfer Imperial". Although it might seem that Young is giving a nod to Bach's "The Well-Tempered Clavier" with his title "The Well-Tuned Piano", musical tuning and musical temperament are two very different things. Temperament actually involves the deliberate mistuning of pitches to make the overall octave more or less usable in various different tones. In "The Well-Tuned Piano",