Taming the Irrational Through Musical Diagrams – from Boethius to Oresme and Nemorarius

Boethius and his followers used diagrammatic methods to estimate musical intervals with epimoric ratios, they determined geometric number sequences with triangular tables, and they treated the converse problem of dividing musical intervals equally. The collection of mathematical manuscripts Codex Basel F II 33 (ca. 1360) contains treatises by Nicolaus Oresme, Jordanus Nemorarius and others. Images in Nemorarius' treatise combine number triangles into complex spider webs and they display recursive algorithms. Oresme diagrams make use of irrational ratios. These little known images and their relationship to music theory are the focus of this paper.
+ ID: 590951 + PeerReviewed