Tomasacci, David and Benjamin Williams. "Distinguishing Predominant and Subdominant Behavior in Functional Analysis." Confounding Expectations—Inspiring Minds. University of Calgary, Calgary, Alberta (2010).
Plazak, Joseph, David Huron and Benjamin Williams. "Fixed Average Spectra of Orchestral Instrument Tones." Empirical Musicology Review 5.1 (2010).
Abstract: The fixed spectrum for an average orchestral instrument tone is presented based on spectral data from the Sandell Harmonic Archive (SHARC). This database contains non-time-variant spectral analyses for 1,338 recorded instrument tones from 23 Western instruments ranging from contrabassoon to piccolo. From these spectral analyses, a grand average was calculated, providing what might be considered an average non-time-variant harmonic spectrum. Each of these tones represents the average of all instruments in the SHARC database capable of producing that pitch. These latter tones better represent common spectral changes with respect to pitch register, and might be regarded as an "average instrument." Although several caveats apply, an average harmonic tone or instrument may prove useful in analytic and modeling studies. In addition, for perceptual experiments in which non-time-variant stimuli are needed, an average harmonic spectrum may prove to be more ecologically appropriate than common technical waveforms, such as sine tones or pulse trains. Synthesized average tones are available via the web.