Single Complex Tones Research Articles

The Perception of Multiple Simultaneous Pitches as a Function of Number of Spectral Channels and Spectral Spread in a Noise-Excited Envelope Vocoder.

Cochlear implant (CI) listeners typically perform poorly on tasks involving the pitch of complex tones. This limitation in performance is thought to be mainly due to the restricted number of active channels and the broad current spread that leads to channel interactions and subsequent loss of precise spectral information, with temporal information limited primarily to temporal-envelope cues. Little is known about the degree of spectral resolution required to perceive combinations of multiple pitches, or a single pitch in the presence of other interfering tones in the same spectral region. This study used noise-excited envelope vocoders that simulate the limited resolution of CIs to explore the perception of multiple pitches presented simultaneously. The results show that the resolution required for perceiving multiple complex pitches is comparable to that found in a previous study using single complex tones. Although relatively high performance can be achieved with 48 channels, performance remained near chance when even limited spectral spread (with filter slopes as steep as 144 dB/octave) was introduced to the simulations. Overall, these tight constraints suggest that current CI technology will not be able to convey the pitches of combinations of spectrally overlapping complex tones.

Subspace Approach for Fast and Accurate Single-Tone Frequency Estimation

A new signal subspace approach for estimating the frequency of a single complex tone in additive white noise is proposed in this correspondence. Our main ideas are to use a matrix without repeated elements to represent the observed signal and exploit the principal singular vectors of this matrix for frequency estimation. It is proved that for small error conditions, the frequency estimate is approximately unbiased and its variance is equal to Cramer-Rao lower bound. Computer simulations are included to compare the proposed approach with the generalized weighted linear predictor, periodogram, and phase-based maximum likelihood estimators in terms of estimation accuracy, computational complexity, and threshold performance.

Exploring the acoustic basis of consonance using individual differences.

Despite its central role in music, the origins of the preference for consonant over dissonant intervals remains controversial. We applied an individual differences approach to this question. Subjects were first tested for their aversion to pure‐tone beats, and to inharmonic spectra of single complex tones. Consistent individual differences were observed in the magnitude of subjects’ aversion to beats and inharmonicity, but the two effects were uncorrelated across subjects, suggesting independent factors. Subjects then rated the pleasantness of musical intervals and three‐note chords. If particular acoustic factors determine consonance, stronger sensitivity to those factors should predict stronger musical preferences. In each of two cohorts, only the preference for harmonic spectra was consistently correlated with preferences for consonant over dissonant chords and intervals. Although the strength of a subject’s consonance preference was also correlated with their musical experience, so was their harmonicity preference, which explained most of the effect of experience on consonance ratings. The results suggest that much of consonance perception is rooted in the basic acoustic property of harmonicity. Harmonicity is evidently predictive of important structures in Western music, and with exposure to music, listeners learn to attend to it. [Work supported by NIH grant R01DC05216.]

Pitch representations in the auditory nerve: two concurrent complex tones.

Pitch differences between concurrent sounds are important cues used in auditory scene analysis and also play a major role in music perception. To investigate the neural codes underlying these perceptual abilities, we recorded from single fibers in the cat auditory nerve in response to two concurrent harmonic complex tones with missing fundamentals and equal-amplitude harmonics. We investigated the efficacy of rate-place and interspike-interval codes to represent both pitches of the two tones, which had fundamental frequency (F0) ratios of 15/14 or 11/9. We relied on the principle of scaling invariance in cochlear mechanics to infer the spatiotemporal response patterns to a given stimulus from a series of measurements made in a single fiber as a function of F0. Templates created by a peripheral auditory model were used to estimate the F0s of double complex tones from the inferred distribution of firing rate along the tonotopic axis. This rate-place representation was accurate for F0s greater, similar900 Hz. Surprisingly, rate-based F0 estimates were accurate even when the two-tone mixture contained no resolved harmonics, so long as some harmonics were resolved prior to mixing. We also extended methods used previously for single complex tones to estimate the F0s of concurrent complex tones from interspike-interval distributions pooled over the tonotopic axis. The interval-based representation was accurate for F0s less, similar900 Hz, where the two-tone mixture contained no resolved harmonics. Together, the rate-place and interval-based representations allow accurate pitch perception for concurrent sounds over the entire range of human voice and cat vocalizations.

Influence of fundamental frequency and source elevation on the vertical localization of complex tones and complex tone pairs

This study investigates the vertical localization of single complex tones (monads) and simultaneous complex tone pairs (dyads), especially as it is affected by their fundamental frequency and source elevation. Two complex tone timbres are considered: one consisting of five low-order harmonics, and the other of all odd harmonics (a square wave). Sound sources were at -15, 0, 15, and 30 deg from the horizontal plane at ear height. For eight subjects, this source array was in the median plane, and for a further nine subjects, it was directly to the subject's left (lateral plane). The subjects localized the angle of the auditory image(s) of one or two complex tones around the vertical plane containing the sound sources. Mean responses for the five-harmonic complex tones show a systematic effect (referred to as Pratt's effect) of fundamental frequency on vertical localization--whereby high-frequency complex tones are localized to positions higher than low-frequency complex tones for equivalent source positions. For the square wave, the sound-source position dominates localization, although some effect of fundamental frequency is evident for median plane sources.

Characterization of threshold for single tone maximum likelihood frequency estimation

This paper presents a simple and direct approach to understanding the threshold effect associated with maximum likelihood estimation of the frequency of a single complex tone. Motivation for the approach, stemming from known results in the field of phase locked loops, is given. It is shown both theoretically and experimentally that the onset of threshold can be directly characterized by a single, easily computed parameter, namely the Cramer-Rao bound on the phase estimation error variance.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Central processes in the perception of pitch in simultaneous complex tones

Pitch identification of two simultaneous complex tones is more difficult than pitch identification of a single complex tone. In this talk, the more central processes that are involved in the perception of simultaneous complex tones will be discussed. Experiments are reported in which subjects had to identify two missing fundamental frequencies. A first set of experiments uses simultaneous two‐tone complexes with different distributions of the four partial over the ears. It is shown that subjects can identify the two missing fundamental frequencies and that the identification results only weakly depend on the manner of distributing the four partials over the ears. For some subjects, the identification results showed that the more salient pitch can inhibit to some extent the identification of the less salient one. This “central interference” is most prominent when the partials of the two complex tones are widely separated. In a second set of experiments, the influence of signal duration on the virtual pitch of single and simultaneous complex tones is investigated. The results for single complex tones allow the formulation of a stochastic pitch model in which a central processor derives noisy subharmonics from noisy representation of the partials. For simultaneous complex tones, the behavior is more difficult to model because of the more central processes that are involved.

Thresholds for hearing mistuned partials as separate tones in harmonic complexes.

When a low harmonic in a harmonic complex tone is mistuned from its harmonic value by a sufficient amount it is heard as a separate tone, standing out from the complex as a whole. This experiment estimated the degree of mistuning required for this phenomenon to occur, for complex tones with 10 or 12 equal-amplitude components (60 dB SPL per component). On each trial the subject was presented with a complex tone which either had all its partials at harmonic frequencies or had one partial mistuned from its harmonic frequency. The subject had to indicate whether he heard a single complex tone with one pitch or a complex tone plus a pure tone which did not "belong" to the complex. An adaptive procedure was used to track the degree of mistuning required to achieve a d' value of 1. Threshold was determined for each ot the first six harmonics of each complex tone. In one set of conditions stimulus duration was held constant at 410 ms, and the fundamental frequency was either 100, 200, or 400 Hz. For most conditions the thresholds fell between 1% and 3% of the harmonic frequency, depending on the subject. However, thresholds tended to be greater for the first two harmonics of the 100-Hz fundamental and, for some subjects, thresholds increased for the fifth and sixth harmonics. In a second set of conditions fundamental frequency was held constant at 200 Hz, and the duration was either 50, 110, 410, or 1610 ms. Thresholds increased by a factor of 3-5 as duration was decreased from 1610 ms to 50 ms. The results are discussed in terms of a hypothetical harmonic sieve and mechanisms for the formation of perceptual streams.