reel-to-reel magnetic tape recorders typically have pitch adjustments of up to ±6%, generally used to match the playback or recording pitch to other music sources having slightly different tunings (or possibly recorded on equipment that was not running at quite the right speed). Modern recording studios utilize digital pitch shifting to achieve similar results, ranging from cents up to several half-steps (note that reel-to-reel adjustments also affect the tempo of the recorded sound, while digital shifting does not). History Historically this number was proposed for the first time in relationship to musical tuning in 1580 (drafted, rewritten 1610) by Simon Stevin. In 1581 Italian musician Vincenzo Galilei may be the first European to suggest twelve-tone equal temperament. The twelfth root of two was first calculated in 1584 by the Chinese mathematician and musician Zhu Zaiyu using an abacus to reach twenty four decimal places accurately, calculated circa 1605 by Flemish mathematician Simon Stevin, in 1636 by the French mathematician Marin Mersenne and in 1691 by German musician Andreas Werckmeister. See also Fret Just intonation § Practical difficulties Music and mathematics Piano key frequencies Scientific pitch notation Twelve-tone technique The Well-Tempered Clavier Notes References Further reading Mathematical constants Algebraic numbers Irrational numbers Musical tuning