Towards A Topology of Music

Year: 1999 Authors: Isaiah Jackson; Nathan P. Ritchey

Core claim

Mathematics can clarify music, but overly precise systems and “topologies” can obscure subjectivity and diminish musical value.

Topics

music theory, topology, fuzzy logic, musical notation

Domains

topology, fuzzy logic, mathematical mapping, music, Western art music, musical interpretation

Methods

conceptual analysis, notation comparison, repertoire examples

Media

musical notation, Western art music repertoire, J. S. Bach’s A Musical Offering

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

BRIDGES Mathematical Connections in Art, Music, and Science

Towards A Topology of Music

Isaiah Jackson, DMA Music Director Youngstown Symphony Orchestra Youngstown, OH 44503 E-mail: i.jackson@udayton.edu

Nathan P. Ritchey, PhD Department of Mathematics Youngstown State University Youngstown, OH 44555 E-mail: nate@math.ysu.edu

Music, that most mathematical of all arts! How can two disciplines continue to enjoy such an uncomfortable intimacy after so many centuries? For the Ancients, after all, music was a branch of mathematics; and, for our exquisitely quantified society, one would assume the comprehensive topology of music to be near completion. Why are we, in fact, still unable to agree on so much?

We begin by exploring four relatively straightforward notions, areas where the mapping ought to be complete: intonation, rhythm, dynamics, and articulation. We explore the notation of these qualities, tracing the increasing precision with which they can be indicated. We then introduce the elements of fuzzy logic to demonstrate the deficiencies of excessively precise topologies. In addition, we chart some of the exceeding subjectivity that exists in systems commonly held to be objective.

When Gerard Manley Hopkins wrote “Glory be to God for dappled things…All things counter, original, spare, strange”, he was talking about music, too. We aim to show how mathematics can enhance music, and how it can hurt it. Why is it that if you make a piece of music perfect, people might not like it?

Our closing draws examples from the Western art music repertoire, starting with the canons of J. S. Bach’s A Musical Offering in honor of the upcoming Bach Year, and ending in our own time.