Hadamard transforms of pure-duple rhythms

Abstract

Recent research has demonstrated a number of applications of the discrete Fourier transform to cyclic rhythms, addressing amongst other issues questions about conceptualizations of metre. One can apply a similar operation, the Hadamard transform, when the rhythmic cycle is a power of two. This paper explores some analytical applications of the Hadamard transform to repertoires where pure-duple metrical settings are the norm, such as American ragtime and Balinese gamelan. I compare it to the Fourier transform and highlight special features of the Hadamard transform of particular theoretical value, such as its sorting of rhythmic information into metrical levels, which leads to methods of classifying and quantifying syncopation.