harmonic division

(mathematics) The division of a line segment externally and internally in the same ratio; that is, the division of a line segment by the harmonic conjugates of its end points.

Relation of successive numbers in a series, the reciprocals of which are in arithmetical progression, the numbers being proportional to the lengths of twanged cords that sound harmonious. Rooms with measurements 1:2, 2:3, and 3:4 were held by Renaissance theorists to be harmonious: some, including Alberti, argued that this was the basis for satisfactory relationships of dimension and form in Classical architecture, and indeed the key to understanding Nature and the Universe. Palladio and others evolved further complex proportions including ratios of 5:6 and others.

Bibliography

• Oxford English Dictionary (1933)
• Wittkower (1988)

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