GroupSound

News

• February 25, 2014: Matt Corley will give a talk on our findings thus far at the Pi Mu Epsilon Mathematical Honor Society Induction Ceremony.
• February 14, 2014: Matt Corley adjusted map-reduce convolution to work for small audio samples. You can now listen to audio convolution by downloading the Sage worksheet here
• January 10, 2014: William DeMeo created a map-reduce procedure for convolution over finite groups. Get the Sage worksheet here.
• January 8, 2014: Matt Corley developed Sage/Python routines for creating/playing sound signals and writing them to wav files. Get the Sage worksheet here.
• December 9, 2013: Matt Corley is now a Magellan Scholar and a grant will fund his work on this project. Congratulations, Matt!
• October 18, 2013: Our abstract was accepted; we will present preliminary results of this project at the Joint Math Meetings in Baltimore, Maryland on January 16, 2014 at 10:40am. Event: At the Intersection of Mathematics and the Arts, III.

Abstract

Underlying many digital signal processing (dsp) algorithms, in particular those used for digital audio filters, is the convolution operation, which is a weighted sum of translations f(x-y). Most classical results of dsp are easily and elegantly derived if we define our functions on Z/nZ, the abelian group of integers modulo n. If we replace this underlying "index set" with a nonabelian group, then translation may be written f(y^-1x), and the resulting audio filters arising from convolution naturally produce different effects than those obtained with ordinary (abelian group) convolution.

The aim of this project is to explore the idea of using the underlying finite group (i.e., the index set) as an adjustable parameter of a digital audio filter. By listening to samples produced using various nonabelian groups, we try to get a sense of the "acoustical characters" of finite groups.

Research Team

Matthew Corley -- University of South Carolina (CS major) @corleymj

William DeMeo -- University of South Carolina (Math faculty mentor) @williamdemeo

Reginald Bain -- University of South Carolina (Music faculty mentor) @regbain

Download Instructions

You can download all the materials in our repository using the ZIP or TAR buttons above.

For Git users. If you want to suggest changes to this content, please use the "View on GitHub" button. Then fork the repository, make your changes, and submit a pull request. You can also clone the repository with the following command:

git clone git@github.com:SoundMath/GroupSound.git

Related Resources

1. Programming:
   
   • Main languages: Sage, GAP, Octave, Scala.
   • Others: CSound, Pure Data, Supercollider, Chuck.
2. Books and Notes:
   • Algebraic Signal Processing Theory
   • Music and Computers: a theoretical and historical approach
3. Conferences:
   • We will present a preliminary report on GroupSound at the MAA Session on the Intersection of Mathematics and the Arts III, at the Joint Mathematics Meetings, January 16, 2014.
   • New Interfaces for Musical Expression (NIME)
   • International Symposium on Musical Acoustics (ISMA)
   • International Computer Music Conference (ICMC)