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Douglas Leedy

revised by 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.

Until about 1850 many organs in New England were tuned to some practical variant of meantone temperament, while in areas of German influence (such as the Moravian communities) equal temperament prevailed. The universal acceptance of 12-tone equal temperament as standard from the mid-19th century nearly silenced discussion of alternative systems; only a few isolated composers and theorists advocated or experimented with non-standard tuning systems before about ...

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J. Richard Haefer

Five-stringed small guitar of Mexico. Commonly known as the vihuela, it is played in the mariachi ensemble as a harmony and rhythm instrument, and should not be confused with the Spanish vihuela de mano. It has a loud, crisp, rapid-decay sound. The soundbox is typically 39 cm long with a 29 cm maximum width, a 28 cm neck with four to six movable nylon frets, and 50 cm string length. The maximum depth of the sides is 10.5 cm plus an additional 6 cm depth to the apex of the vaulted, angled back. Wooden pegs inserted from the rear of the pegboard are traditional but nowadays most vihuelas have mechanical tuners. The tuning is a-d′-g′-b-e′ but sometimes the lowest three strings are tuned an octave higher. The soundhole (boca) is surrounded by nácar (mother of pearl) and wood inlay in a starburst pattern, and the purfling has intricate ...

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