Set-Class Similarity, Voice Leading, and the Fourier Transform

Abstract

In this article, I consider two ways to model distance (or inverse similarity) between chord types, one based on voice leading and the other on shared interval content. My goal is to provide a contrapuntal reinterpretation of Ian Quinn's work, which uses the Fourier transform to quantify similarity of interval content. The first section of the article shows how to find the minimal voice leading between chord types or set-classes. The second uses voice leading to approximate the results of Quinn's Fourier-based method. The third section explains how this is possible, while the fourth argues that voice leading is somewhat more flexible than the Fourier transform. I conclude with a few thoughts about realism and relativism in music theory.