Irida Altman

There is a tradition of Mathematics contributing to the understanding of Music. This article sets out to contribute in the other direction. It uses musical sensibilities to feel its way through a piece of mathematics called the Urysohn Lemma, suggesting the presence of rhythmic, melodic, and harmonic elements within standard proving practices of contemporary Western mathematics. This article employs a literary-philosophical technique of viewing a text in one discipline (mathematics) through the conceptual lens of another (music). As such, this article reports on no experiments—reading the article is the experiment. Each reader performs it for themselves.

There is a tradition of Mathematics contributing to the understanding of Music. This article sets out to contribute in the other direction. It uses musical sensibilities to feel its way through a piece of mathematics called the Urysohn Lemma, suggesting the presence of rhythmic, melodic, and harmonic elements within standard proving practices of contemporary Western mathematics. This article employs a literary-philosophical technique of viewing a text in one discipline (mathematics) through the conceptual lens of another (music). As such, this article reports on no experiments—reading the article is the experiment. Each reader performs it for themselves.

We develop a new theoretical approach to musical hermeneutics founded on translation as a concept of significant philosophical interest. Our framework locates musical ontology in an ongoing unfurling of the contextualized performative event, thought of as a skein of translation processes mediated by the translators’ gestures happening against the socio-historical and cultural understanding of a particular interpreter. We work with presentation systems, structured collections of iterable material marks that organize musical notation, gesture, and sound in the (post)structuralist tradition. Between the systems, agents of translation operate in accordance with the gestural script, an interpretative approach that encompasses gestural conventions of performance, inscribed and prescribed by the score. Our approach adds to recent scholarship on music as a multimodal translation process, highlighting the importance of gesture and giving renewed emphasis to materiality, including that of the instrument as contributor to ontological identity and difference of the performative event.