Article ID: CBB699399259

Propositions VIII.4–5 of Euclid's Elements and the Compounding of Ratios on the Monochord (2015)

unapi

In this article, I try to show how the operation of compounding of ratios as performed with the method of Proposition VIII.4 of Euclid's Elements, has possibly taken shape from experiments on the monochord. This fact, together with the systematic and exclusive use of Proposition VIII.4 in the harmonic field, strengthens the thesis concerning the connection between harmonic theory and Book VIII. A misinterpretation by Zarlino, the most important music theorist of the Renaissance, will help us explain how the musical model may have been partially responsible for the disconnection between compounding and multiplication present in the Elements in spite of the link established by Proposition VIII.5.

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Authors & Contributors
De Young, Gregg
Bromberg, Carla
Zoccola, Martina
Elior, Ofer
Vahabzadeh, Bijan
Ulivi, Elisabetta
Concepts
Mathematics
Geometry
Manuscripts
Ratio and proportion
Arab/Islamic world, civilization and culture
Music
Time Periods
Medieval
16th century
Ancient
9th century
Early modern
Renaissance
Places
Greece
Italy
Mediterranean region
Europe
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