Pitch Of Harmonic Complex Tones Research Articles

In search of the missing resolved harmonics: Neural and behavioral studies of pitch discrimination

The pitch of harmonic complex tones (HCT) plays important roles in speech and music perception and in the perceptual organization of sound. Human listeners rely primarily on the spectral pattern of harmonics individually resolved by the frequency analysis in the cochlea to derive a pitch percept. Yet, evidence for a robust neural representation of resolved harmonics in animal models has been elusive, and some species appear to rely on temporal envelope cues rather than on resolved harmonics to discriminate pitch. We performed both behavioral experiments on pitch discrimination by rabbits and single-unit recordings from the auditory nerve (AN) and inferior colliculus (IC) using HCTs with equal-amplitude harmonics in which the fundamental frequency (F0) was varied over a wide range. We found that rabbits can discriminate the pitch of HCT using the spectral pattern of resolved harmonics for F0s within the range of conspecific vocalizations. Correspondingly, many IC neurons contribute to a rate-place code for the frequencies of resolved harmonics for F0s >500 Hz, and this code is more robust to variations in stimulus level than that found in the AN. A remaining challenge is to identify the neural mechanisms underlying enhanced rate-place coding in IC. [Work supported by NIH-NIDCD DC002258.]

Pitch of harmonic complex tones: rate and temporal coding of envelope repetition rate in inferior colliculus of unanesthetized rabbits.

Harmonic complex tones (HCTs) found in speech, music, and animal vocalizations evoke strong pitch percepts at their fundamental frequencies. The strongest pitches are produced by HCTs that contain harmonics resolved by cochlear frequency analysis, but HCTs containing solely unresolved harmonics also evoke a weaker pitch at their envelope repetition rate (ERR). In the auditory periphery, neurons phase lock to the stimulus envelope, but this temporal representation of ERR degrades and gives way to rate codes along the ascending auditory pathway. To assess the role of the inferior colliculus (IC) in such transformations, we recorded IC neuron responses to HCT and sinusoidally modulated broadband noise (SAMN) with varying ERR from unanesthetized rabbits. Different interharmonic phase relationships of HCT were used to manipulate the temporal envelope without changing the power spectrum. Many IC neurons demonstrated band-pass rate tuning to ERR between 60 and 1,600 Hz for HCT and between 40 and 500 Hz for SAMN. The tuning was not related to the pure-tone best frequency of neurons but was dependent on the shape of the stimulus envelope, indicating a temporal rather than spectral origin. A phenomenological model suggests that the tuning may arise from peripheral temporal response patterns via synaptic inhibition. We also characterized temporal coding to ERR. Some IC neurons could phase lock to the stimulus envelope up to 900 Hz for either HCT or SAMN, but phase locking was weaker with SAMN. Together, the rate code and the temporal code represent a wide range of ERR, providing strong cues for the pitch of unresolved harmonics.NEW & NOTEWORTHY Envelope repetition rate (ERR) provides crucial cues for pitch perception of frequency components that are not individually resolved by the cochlea, but the neural representation of ERR for stimuli containing many harmonics is poorly characterized. Here we show that the pitch of stimuli with unresolved harmonics is represented by both a rate code and a temporal code for ERR in auditory midbrain neurons and propose possible underlying neural mechanisms with a computational model.

Pitch of Harmonic Complex Tones: Rate Coding of Envelope Repetition Rate in the Auditory Midbrain.

SummaryEnvelope repetition rate (ERR) is an important cue for the pitch of harmonic complex tones (HCT), especially when the tone consists entirely of unresolved harmonics. Neural synchronization to the stimulus envelope provides a prominent cue for ERR in the auditory periphery, but this temporal code becomes degraded and gives way to rate codes in higher centers. The inferior colliculus (IC) likely plays a key role in this temporal-to-rate code transformation. Here we recorded single IC neuron responses to HCT at varying fundamental frequencies (F0). ERR was manipulated by applying different inter-harmonic phase relationships. We identified a subset of neurons that showed a ‘non-tonotopic’ rate tuning to ERR between 160 and 1500 Hz. A comparison of neural responses to HCT and sinusoidally amplitude modulated (SAM) noise suggests that this tuning is dependent on the shape of stimulus envelope. A phenomenological model is able to reproduce the non-tonotopic tuning to ERR, and suggests it arises in the IC via synaptic inhibition.

Dual rate codes for the pitch of harmonic complex tones in the auditory midbrain

Harmonic complex tones contained in speech and music evoke a pitch at their fundamental frequency (F0). This pitch can be produced through either patterns of harmonics individually resolved by the cochlear frequency analysis or periodicity in the amplitude envelope resulting from beating between neighboring harmonics. To investigate how these two pitch cues are coded in the auditory midbrain, we recorded from single units in unanesthetized rabbits in response to harmonic complex tones with varying F0 so as to create conditions where harmonics were likely resolved or unresolved. For F0 above 600 Hz, some neurons showed local maxima in firing rate when a low-order (<6-8) harmonic of F0 coincided with the neuron’s best frequency (BF), thereby providing a rate-place code to resolved harmonics similar to that found in the auditory nerve. For F0 below 800 Hz, some neurons showed rate tuning to a particular F0 unrelated to the BF. Altering the phase relationships among the harmonics showed that this nontonotopic...

Frequency discrimination in the common marmoset (Callithrix jacchus)

The common marmoset (Callithrix jacchus) is a highly vocal New World primate species that has emerged in recent years as a promising model system for studies of auditory and vocal processing. Our recent studies have examined perceptual mechanisms related to the pitch of harmonic complex tones in this species. However, no previous psychoacoustic work has measured marmosets' frequency discrimination abilities for pure tones across a broad frequency range. Here we systematically examined frequency difference limens (FDLs), which measure the minimum discriminable frequency difference between two pure tones, in marmosets across most of their hearing range. Results show that marmosets' FDLs are comparable to other New World primates, with lowest values in the frequency range of ∼3.5–14 kHz. This region of lowest FDLs corresponds with the region of lowest hearing thresholds in this species measured in our previous study and also with the greatest concentration of spectral energy in the major types of marmoset vocalizations. These data suggest that frequency discrimination in the common marmoset may have evolved to match the hearing sensitivity and spectral characteristics of this species’ vocalizations.

Spatiotemporal Representation of the Pitch of Harmonic Complex Tones in the Auditory Nerve

The pitch of harmonic complex tones plays an important role in speech and music perception and the analysis of auditory scenes, yet traditional rate-place and temporal models for pitch processing provide only an incomplete description of the psychophysical data. To test physiologically a model based on spatiotemporal pitch cues created by the cochlear traveling wave (Shamma, 1985), we recorded from single fibers in the auditory nerve of anesthetized cat in response to harmonic complex tones with missing fundamentals and equal-amplitude harmonics. We used the principle of scaling invariance in cochlear mechanics to infer the spatiotemporal response pattern to a given stimulus from a series of measurements made in a single fiber as a function of fundamental frequency F0. We found that spatiotemporal cues to resolved harmonics are available for F0 values between 350 and 1100 Hz and that these cues are more robust than traditional rate-place cues at high stimulus levels. The lower F0 limit is determined by the limited frequency selectivity of the cochlea, whereas the upper limit is caused by the degradation of phase locking to the stimulus fine structure at high frequencies. The spatiotemporal representation is consistent with the upper F0 limit to the perception of the pitch of complex tones with a missing fundamental, and its effectiveness does not depend on the relative phase between resolved harmonics. The spatiotemporal representation is thus consistent with key trends in human psychophysics.

Listeners’ spectral weighting functions for pitch judgment

Two experiments were carried out to determine how listeners use spectral information in judging the pitch of harmonic complex tones. In particular, spectral weighting functions were obtained using a correlation technique in which random, independent perturbations were added to the frequencies of the spectral components. The correlation coefficient between the perturbations applied to a given frequency component and listeners’ responses provides an estimate of the weight associated with that component. In the first experiment, all complex tones had the first 12 partials; the fundamental frequency was varied from 100 to 800 Hz. The obtained weighting function tended to show a peak for partials close to 600 Hz regardless of their harmonic numbers. In the second experiment, the fundamental was fixed at 200 Hz, and the number of partials was reduced by omitting the first two, four, or six partials. As these partials were excluded, the weights redistributed, with the maximum weight consistently going to the lowest partial present in the stimulus, i.e., at 600, 1000, or 1400 Hz. Overall, these spectral weighting functions reaffirmed the presence of a frequency dominance region, showing prominent influences on pitch judgment from low-ranked partials. [Work supported by NIH/NIDCD.]

Difference limens for pitch of harmonic complex tones comprising higher harmonics.

Difference limens for pitch of harmonic complex tones comprising higher harmonics.

Edge pitches of complex tones obtained at high frequencies

The upper edge pitch of harmonic complex tones was matched by adjusting the frequency of a sinusoidal comparison tone. Complexes with upper-edge frequencies between 2 and 8 kHz and fundamental frequencies of 50, 100, and 200 Hz were synthesized by adding all harmonics with equal amplitudes and with zero phases. Tones and intertone gaps had durations of 500 ms. Stimuli were presented diotically through Etymotic ER-2 insert earphones at a sound-pressure level of 60 dB. Five subjects performed ten matches for each complex, from which the standard deviation (s.d.) was calculated and expressed as percentage of the edge frequency. The s.d. generally increased with the edge frequency and with the fundamental frequency. For 50-Hz fundamental, the s.d. was only a factor two larger than in a sine-on-sine match, and four of the five subjects could perceive the edge pitch up to 8 kHz. For higher fundamental frequencies, more and more subjects lost the pitch percept at high edge frequencies, and for 200 Hz only one subject consistently matched the edge pitch at 8 kHz. The results emphasize the role of temporal processes in the perception of edge pitch as well as the importance of phase locking at the frequency of the edge component.

Pitch of complex signals according to virtual-pitch theory: Tests, examples, and predictions

The pitch-extraction algorithm described by Terhardt et al. [J. Acoust. Soc. Am. 71, 679–688 (1982)] is used to compute a number of examples to test the procedure’s validity, and to illustrate its applicability. The following subjects are considered: (a) pitch of harmonic complex tones (with and without fundamental); (b) existence region of virtual pitch; (c) Shepard pitch phenomenon; (d) virtual pitch of inharmonic complex tones; (e) spectral dominance; (f) effect of amplitude spectrum on pitch; (g) pitch of bell sounds; and (h) tonal evaluation of musical chords. The algorithm’s predictions agree well with psychoacoustic observations and it is concluded that it can be useful in audio-engineering and psychoacoustic research.