fairfolio
Saved Projects

Musical Homotopy: A Topological Study of Voice Leading Groups and Its Application to Contrapuntal Music Genres

ISEF · 2018 Mathematics

Sivakumar, Aditya · Franklin High School

Is this your project?

Overview

Voice leading in music is a key element of the Western tradition. It is closely associated with homotopy, the exploration of chordal paths in higher dimensional configuration spaces. Musicians intuitively explored these spaces centuries ago and developed simple rules to ensure musical quality, long before mathematicians developed the concepts needed to describe them. This work develops the formal mathematical framework for analyzing voice leading, making explicit the musician's implicit knowledge and allowing the appreciation of the deep and inherently mathematical knowledge of the practical musician. For the first time, a software package has been developed that uses the mathematics and music theory to perform a comprehensive analysis of bijective and non-bijective voice leadings and classify them for performability. This tool is immensely useful for composers to quickly identify the performable voice leadings from among all the theoretical contrapuntal possibilities, and is being productized for general use.

Working on something like this? See what's been done and what's still open.

Competition history

Resources

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

Report a problem

Source: Regeneron International Science and Engineering Fair

Save projects to your library

Sign in with Google to keep track of projects you find interesting, organized into folders. An account also raises your daily allowance for “Has this been done?”, and lets you create a key for the MCP server with a much higher limit than anonymous use. Browsing stays public.

Continue with Google