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Douglas Leedy and Charles Corey

Systems of organization of the pitch scale. Such systems are either “just” or “tempered.” Just systems consist entirely of pure intervals, and though literal transposition of patterns or scales may be very limited, other musically useful symmetries are available. Tempered systems are those in which the purity of some or all intervals is deliberately compromised in order to render other intervals less impure, and thus increase the number of musically serviceable intervals. Over the course of centuries countless tunings and temperaments have been proposed, but few have been of practical importance; of these, 12-tone equal temperament has become the standard in Western music since the 19th century....