Abstract: The aim of this essay is to create a geometrical link between the music theory and the mathematics of the early 17th century by studying and comparing diagrams which directly or indirectly refer to mathematical logarithms.The focus is on the relationships between ratios of numbers referring to sounds and related concepts of perception. The relationship between frequency and pitch is a paradigmatic case of the Weber-Fechner law of psychophysics, stating that equal frequency ratios are perceived as equally sized musical intervals. The Weber-Fechner law maintains that many perceptual phenomena are logarithmic by their very nature.The circular diagrams studied here are by Descartes (1618), Robert Fludd (1618) and Jost Bürgi (1620). Descartes’s diagrams have recently attracted the attention of authors from different fields. A second type of geometric diagrams related to musical arithmetic is looked at in the final section of this article.
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Daniel Muzzulini
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30.12.2016
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1
"Art of Diagram"-Meeting Nr. 4
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Michael Dodds: Circular Diagrams and Volvelles in Early Modern Music Theory
The epistemic shift underlying the Scientific Revolution may be traced in parallel developments in the mapping of musical and physical space. Circular diagrams in music theory texts reveal the influence of spatial and temporal disciplines, including astronomy, chronometry, geography, and navigation. If these sister disciplines had always been tied to music through musica mundana, their influence on the mapping of tonal space only intensified in the early 17th century, exhibiting a concurrent shift from symbolic to empirical representations. Zarlino's circular illustration of the senario, for example, legitimates the syntonic diatonic scale; its circular organization has nothing to do with tonal circularity, but rather with graphical logic and rhetoric. In contrast, circles by René Descartes, Quirinus van Blankenburg (based on work by Christian Huygens) and Isaac Newton present logarithmic circular divisions of the scale—approaches made possible by recent innovations by Simon Stevin and John Napier.
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Zürcher Hochschule der Künste
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09.12.2020
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3
Musical Proportions and Complete Graphs
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Visualizing and Operationalizing Early Music Theory through Diagrams: From Guido to Zarlino and Beyond
Preparation meeting of the panel presentation at the annual conference of the Renaissance Society of America (2021). Changes in Visual and Material Culture as Revealed in Early Modern Printed Music Treatises
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Zürcher Hochschule der Künste
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