The title page of Jost Buergi’s Progress-Tabulen (1620) is not only an eye catching masterpiece of the art of printing and a substrate of the tables inside, it also reveals fundamental insights into the nature of numbers and number systems.
The circular arrangement of the two number sequences links algebra with geometry by mapping the exponential function on an angular scale of red numbers to black numbers in the logarithmic place value system. In retrospect, the step from Buergi's diagram to the circular slide rule for multiplication seems a small one.
The lecture is intended as a contribution to the history of circular diagrams and volvelles – paper constructs with rotating parts – that emerged during the Renaissance. In particular, we will take a look at visualisations in contemporary music theory, which deal with closely related questions.
Opportunities to historically underpin and unconventionally motivate topics in mathematics education – geometric sequences, inverse functions, modulo arithmetic and number systems – emerge casually. Making calculating discs for music theory will sensitise learners for the fundaments of calculation techniques and number systems, and it promotes historically anchored, discovery-based learning. The transfer achievements to be made will sharpen the view for interdisciplinary topics.
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
Rechteinhaber/in
Zürcher Hochschule der Künste
Es sind keine Metadaten zu diesem Kontext bereitgestellt.
Importiert am
26.06.2021
Übergeordnete Sets
3
Zarlino digital: The Art of Diagram
Name that can easily go onto 2 lines
Author that can easily go onto 2 lines as well
Untertitel
Referat: Musik und Musikforschung im digitalen Wandel, Formum der Fakultät III, HMT Leipzig
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.
Rechteinhaber/in
Zürcher Hochschule der Künste
Es sind keine Metadaten zu diesem Kontext bereitgestellt.