Although chords are often represented by pitch-class (chroma) content in
computational research, chord spacing is often a more salient feature. This
paper addresses this disparity between models and cognition by extending
the discrete Fourier transform (DFT) theory of chord quality from
pitch-classes to pitches. In doing so, we note a structural similarity
between music theory’s chord quality and audio engineering’s timbral
cepstrum: both are DFTs, performed in the pitch or frequency domains,
respectively. We thus treat chord spacing as a hybrid of pitch-class and
timbre.
To investigate the potential benefits of the DFT on pitch space (P-DFT), we
perform two computational experiments. The first explores the P-DFT model
theoretically by correlating chord distances calculated with a pitch-class
model against those calculated with spacing. The second compares P-DFT
estimations of chord distances against listener responses (Kuusi 2005). Our
results show that spacing is a salient feature of chords, and that it can
be productively described by timbre-influenced methods.