Hearing the Irrational
Music and the Development of the Modern Concept of Number
Bibliographic Data
| ID | 4175783 |
|---|---|
| Authors | Peter Pesic (0000-0001-5539-0518, St. John's College of Nursing, corresponding author) |
| Year | 2010 |
| Volume | 101 |
| Issue | 3 |
| Pages | 501-530 |
| Publication date | 2010-09-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Isis (JOURNAL) |
| Journal identifiers | ISSN: 0021-1753 • E-ISSN: 1545-6994 |
| Publisher | University of Chicago Press (PUBLISHER • US) |
| DOI | 10.1086/655790 |
| PMID | 21077550 |
| OpenAlex | W2171240957 |
| Language | EN |
| Citations received | 4 |
| References cited | 17 |
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
Aesthetics · Archaeology · Art · Context (archaeology · Epistemology · Geometry · Irrational number · Literature · Musical · Parallels · Period (music · Architecture and Art History Studies · Historical and Literary Studies · History · Mathematics · Musicology and Musical Analysis · Philosophy
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,31 |
| Citation span | 2013 - 2024 (12) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 4 |