The Ten Books on Architecture, 5.4.7

Vitruvius  translated by Joseph Gwilt

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7There are five tetrachords. The Greeks call the lowest ὕπατον (hypaton); the second, which is in the middle, μέσον (meson). The third, which is joined to the two preceding, is called συνημμένον (synèmmenon). The fourth, which is disjoined, called διεζευγμένον (diezeugmenon). The fifth, which is the highest, the Greeks call ὑπερβόλαιον(hyperbolæon). The natural consonances, which the Greeks call συμφωνίαι (symphoniæ), are six in number; diatessarôn (fourth), diapente (fifth), diapasôn (octave), diapasôn with diatessarôn(eleventh), diapasôn with diapente (twelfth), and disdiapasôn (fifteenth).

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