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From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture

In: Architecture and Mathematics from Antiquity to the Future

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  • Radoslav Zuk

    (McGill University, School of Architecture)

Abstract

Studies on relationships between music and architecture, inherent in the Renaissance theory of proportions, have focused primarily on comparing length-to-width floor plan ratios to frequency ratios of musical intervals. But since architecture is a volumetric entity, its geometric definition involves three dimensions. Both Alberti and Palladio, in addition to their prescriptions for horizontal dimensional ratios, gave elaborate instructions for determining proportional dimensions of heights of spaces. The length-to-height-to-width proportions resulting from these recommendations, in particular those of Palladio, show striking parallels to frequency ratios of the majority of chords in the system of tonal harmony. Works of architecture, in which spaces are aligned orthogonally, may thus be compared to musical works based on a single tonality, while those, where spaces intersect at several angles, to polytonal compositions, where chords belonging to several tonalities sound simultaneously.

Suggested Citation

  • Radoslav Zuk, 2015. "From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture," Springer Books, in: Kim Williams & Michael J. Ostwald (ed.), Architecture and Mathematics from Antiquity to the Future, edition 127, chapter 0, pages 567-584, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-00137-1_38
    DOI: 10.1007/978-3-319-00137-1_38
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