ABSTRACT Because the modern concept of number emerged within a quadrivium that included music alongside arithmetic, geometry, and astronomy, musical considerations affected mathematical developments. Michael Stifel embedded the then‐paradoxical term “irrational numbers” (numerici irrationales) in a musical context (1544), though his philosophical aversion to the “cloud of infinity” surrounding such numbers finally outweighed his musical arguments in their favor. Girolamo Cardano gave the same status to irrational and rational quantities in his algebra (1545), for which his contemporaneous work on music (...) suggested parallels and empirical examples. Nicola Vicentino's attempt to revive ancient “enharmonic” music (1555) required and hence defended the use of “irrational proportions” (proportiones inrationales) as if they were numbers. These developments emerged in richly interactive social and cultural milieus whose participants interwove musical and mathematical interests so closely that their intense controversies about ancient Greek music had repercussions for mathematics as well. The musical interests of Stifel, Cardano, and Vicentino influenced their respective treatments of “irrational numbers.” Practical as well as theoretical music both invited and opened the way for the recognition of a radically new concept of number, even in the teeth of paradox. (shrink)

Because of its non-representational nature, music has always had familiarity with computational and algorithmic methodologies for automatic composition and performance. Today, AI and computer technology are transforming systems of automatic music production from passive means within musical creative processes into ever more autonomous active collaborators of human musicians. This raises a large number of interrelated questions both about the theoretical problems of artificial musical creativity and about its ethical consequences. Considering two of the most urgent ethical problems of Musical AI (...) (music job replacement and machine musical authorship), we show in this essay the strict dependence of every form of acknowledgment of a moral and legal status to systems of automatic music production from the theoretical account of musical creativity by turns implicitly or explicitly adopted, arguing, on the basis of pragmatic reasons, for the necessity and the desirability of this acknowledgment. (shrink)