In the series of auditory list comments on “harmonic extraction,” there has been some speculation concerning the basis for the distinctive properties of odd-harmonic tones. To start with, all tones lacking even harmonics have alternating polarity waveforms, and all tones with alternating polarity waveforms (e.g., square waves, symmetrical triangular waves, and alternating polarity pulse trains) have odd-harmonic spectra. Long years ago, Warren and Wrightson (1981) used iterated alternating polarity randomly determined waveforms (i.e., frozen noise segments) as representative odd-harmonic tones. It was found that these tones can produce a dominant pitch of 2F0 with repetition frequencies up to about 100 Hz and a pitch of F0 at repetition frequencies above roughly 200 Hz. Simultaneous pitches were heard between these frequencies. Further experiments have shown that in the ambiguous range of fundamental frequencies between roughly 100 and 200 Hz, unresolved harmonics produced pseudoperiodicities, one slightly more and the other slightly less than 2F0. The bases for these pitches were described concisely in the abstract by Bashford and Warren (1990):
Previous studies have shown that tones consisting solely of odd harmonics can produce two types of low pitch, one matching the fundamental frequency and another approximately 1 octave higher. The present study examined the bases of these pitches. Musicians provided matches for odd-harmonic triads (3rd, 5th, and 7th; 5th, 7th, and 9th;...; 17th, 19th, and 21st) having a common, missing fundamental ranging from 100 to 200 Hz. Low-order triads were matched to the fundamental, whereas high-order triads produced pitches approximately 1 octave higher, but deviating from exact doubling of the fundamental by an amount consistent with the waveform pseudoperiodicities. Interestingly, the change from fundamental to pseudoperiod matching occurred with triads centered at about the 9th or 11th harmonic, which have frequency separations approximating those of the dominant partials in an “all-harmonic” signal. These results, together with neurophysiological evidence in the literature, indicate that harmonics within the dominant region interact sufficiently to provide a temporal basis for pitch. It appears that the dominant region is a transition zone where two modes of pitch analysis overlap.
The pitches of odd-harmonic tones are discussed at greater length in Warren (2008).
R.M. Warren and J.M. Wrightson, “Stimuli producing conflicting temporal and spectral cues to frequency,” JASA, 1981, 70 (4), 1020-1024.
J.A. Bashford, Jr. and R.M. Warren, “The pitch of odd-harmonic tones: Evidence of temporal analysis in the dominance region,” JASA, 1990, 88, S48.