The Ten Books on Architecture, 5.4.8

Vitruvius  translated by Joseph Gwilt

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8These names are given them from the number of tones which the voice passes through in going to them, counting that on which the voice begins as one; thus, moving through them to the fourth sound is called diatessarôn; to the fifth, diapente. to the eighth diapasôn, to the eleventh diapasôn with diatessarôn, to the twelfth diapasôn with diapente, to the fifteenth disdiapasôn.

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