Macroharmonic Progressions through the Discrete Fourier Transform

Abstract

This article examines macroharmony through the lens of the discrete Fourier transform (DFT) using computational analysis. It first introduces the DFT, giving an interpretive framework to understand the theory of chord quality first introduced by Ian Quinn (2007) before extending the theory to macroharmonies. Subsequently, the paper discusses different approaches—including different weighting and windowing procedures—to retrieving pitch data for computational analysis. An analysis of macroharmony in Domine Jesu from Maurice Duruflé’s Requiem, Op. 9 follows. I show that the DFT reflects intuition, reveals form-functional macroharmonies in the movement, and provides us with a perspective to find novel hearings.