Perception of the missing fundamental in nonhuman primates

In preparation for neurophysiological experiments aimed at mechanisms of pitch perception, four rhesus monkeys were trained to press a button when the fundamental frequencies (missing or present) of two complex tones in a tone pair matched. Both tones were based on a five-component harmonic series. Zero to three of the lowest components could be missing in the first tone, while the second (comparison) tone contained all five harmonics. The range of fundamentals tested varied from 200 to 600 Hz. Three monkeys learned to match tones missing their fundamentals to comparison harmonic complexes with the same pitch, whereas the fourth monkey required the physical presence of the fundamental. Consideration of several cues available to the monkeys suggests that the animals could perceive the missing fundamental.     

Infant pitch perception: evidence for responding to pitch categories and the missing fundamental

While numerous studies on infant perception have demonstrated the infant's ability to discriminate sounds having different frequencies, little research has evaluated more sophisticated pitch perception abilities such as perceptual constancy and perception of the missing fundamental. In the present study 7-8-month-old infants demonstrated the ability to discriminate harmonic complexes from two pitch categories that differed in pitch by approximately 20% (e.g., 160 vs 200 Hz). Using a visually reinforced conditioned head-turning paradigm, a number of spectrally different tonal complexes that contained varying harmonic components but signaled the same two pitch categories were presented. After learning the basic pitch discrimination, the same infants learned to categorize spectrally different tonal complexes according to the pitches signaled by their fundamental frequencies. That is, the infants showed evidence of perceptual constancy for the pitch of harmonic complexes. Finally, infants heard tonal complexes that signaled the same pitch categories but for which the fundamental frequency was removed. Infants were still able to categorize the harmonic complexes according to their pitch categories. These results suggest that by 7 months of age infants show fairly sophisticated pitch perception abilities similar to those demonstrated by adults.     

How we hear what is not there: a neural mechanism for the missing fundamental illusion

How the brain estimates the pitch of a complex sound remains unsolved. Complex sounds are composed of more than one tone. When two tones occur together, a third lower pitched tone is often heard. This is referred to as the "missing fundamental illusion" because the perceived pitch is a frequency (fundamental) for which there is no actual source vibration. This phenomenon exemplifies a larger variety of problems related to how pitch is extracted from complex tones, music and speech, and thus has been extensively used to test theories of pitch perception. A noisy nonlinear process is presented here as a candidate neural mechanism to explain the majority of reported phenomenology and provide specific quantitative predictions. The two basic premises of this model are as follows: (I) The individual tones composing the complex tones add linearly producing peaks of constructive interference whose amplitude is always insufficient to fire the neuron (II): The spike threshold is reached only with noise, which naturally selects the maximum constructive interferences. The spacing of these maxima, and consequently the spikes, occurs at a rate identical to the perceived pitch for the complex tone. Comparison with psychophysical and physiological data reveals a remarkable quantitative agreement not dependent on adjustable parameters. In addition, results from numerical simulations across different models are consistent, suggesting relevance to other sensory modalities.     

Acoustic pursuit of invisible moving targets by cats.

Head movements evoked by an invisible acoustic target were used as a metric to analyze localization of moving sources of sound in naive cats. The target was presented in the lateral sound field and moved along an arc at constant angular speeds. Head-movement trajectories were characterized by a large-magnitude orienting component that undershot the target, and a tracking component elicited by the target during acoustic pursuit. The tracking component was characterized by a succession of stepwise head movements that maintained a relatively close alignment of the median plane of the head with the moving acoustic target.     

Transitions driven by a missing frequency

We demonstrate an intricate combination of strong and weak interactions of a broadband half-cycle pulse with Rydberg atoms. A transition, which is resonant with a frequency that was taken out of the frequency spectrum, can be enhanced. In the experiment, the broadband ultrashort terahertz half-cycle pulse propagates through water vapor, which absorbs on discrete lines in the spectrum, thus removing frequencies from the spectrum. The resulting pulse interacts with a rubidium Rydberg atom, which has a resonant transition with one of the missing frequencies. Under certain conditions, the transition probability is enhanced although the associated frequency was missing in the spectrum.     

Estimating missing information by maximum likelihood deconvolution

The ability of iteratively constrained maximum likelihood (ML) deconvolution to reconstruct out-of-band information is discussed and exemplified by simulations. The frequency dependent relative energy regain, a novel way of quantifying the reconstruction ability, is introduced. The positivity constraint of ML deconvolution allows reconstructing information outside the spatial frequency bandwidth which is set by the optical system. This is demonstrated for noise-free and noisy data. It is also shown that this property depends on the type of object under investigation. An object is constructed where no significant out-of-band reconstruction is possible. It is concluded that in practical situations the amount of possible out-of-band reconstruction depends on the agreement between reality and the model describing "typical objects" incorporated into the algorithm by appropriate penalty functions.     

Transforming NMR data despite missing points.

Some NMR experiments produce data with several of the initial points missing. The inverse discrete Fourier transform (IDFT) assumes these points are present so the data cannot be so transformed without artifact-ridden results. This problem is often particularly severe when projection imaging with free-induction decays (FIDs). This paper compares recent methods for obtaining a projection from incomplete data and elaborates on their strengths and limitations. One method is to write the transform that would take the desired projection to the truncated data set, and then solve the matrix equation by singular value decomposition. A second replaces the missing data with zeros, so that an IDFT produces a projection with unwanted artifacts. Then one solves the matrix equation that takes the desired projection to the artifact-ridden projection. A third uses the same artifact-ridden projection, but fits the region outside the bandwidth of the sample with as many sinusoidal functions as there are missing data. The coefficients of these functions are estimates of the missing data, and the projection is obtained by transforming the completed FID or subtracting the extrapolation of the fitted curve from the region containing the object. We show that when all three methods are applicable, they theoretically produce the same result. They differ by ease of implementation and possibly by computational errors. They give a result similar to that of the previous method that iteratively corrects the FID and projection after repeated IDFTs and DFTs. We find that one can obtain a projection despite missing a substantial number of data.     

Perception of syllable timing by prebabbling infants

Adults hear alternating syllables with isochronous syllable onset-onset times as having a long-short, alternating rhythm when the syllables differ in initial consonant. This occurs because adults attend to syllable-internal events, called the "P centers" or "stress beats", rather than to syllable onsets. Thus they report that stress-beat aligned speech is isochronous and stress-beat aligned clicks are synchronized with the speech. The question asked here is whether, like adults, infants attend to the timing of syllable stress beats. In experiment 1, infants showed differences in time to habituate to sequences of alternating monosyllables, [bad] and [strad], having two different onset-onset times (onset- and stress-beat-timed) and two different placements of clicks on the syllables (on syllable onsets and on stress beats). Infants habituated more slowly to sequences with clicks on the stress beats than to sequences with clicks on syllable onsets and most slowly of all to stress-beat-timed speech with clicks on the stress beats. To interpret these findings, a second experiment was run using sequences only of the syllable [strad] so that speech timing measured according to onsets and stress beats was the same. Syllables had isochronous timing or a long-short alternating rhythm, corresponding to two possible ways of hearing the stress-beat-timed speech of experiment 1. In addition, two patterns of click placement were compared, uniform and syncopated, corresponding to two ways of hearing the stress-beat aligned clicks of experiment 1. The patterns of sucking times in the two experiments match exactly if stress-beat aligned speech in experiment 1 is identified with the isochronous speech of experiment 2 and the stress-beat aligned clicks of experiment 1 match with the uniformly timed clicks of experiment 2. It is inferred from this correspondence that infants perceive stress beats and stress-beat timing of syllables as adults do.     

Modeling the identification of concurrent vowels with different fundamental frequencies.

Human listeners are better able to identify two simultaneous vowels if the fundamental frequencies of the vowels are different. A computational model is presented which, for the first time, is able to simulate this phenomenon at least qualitatively. The first stage of the model is based upon a bank of bandpass filters and inner hair-cell simulators that simulate approximately the most relevant characteristics of the human auditory periphery. The output of each filter/hair-cell channel is then autocorrelated to extract pitch and timbre information. The pooled autocorrelation function (ACF) based on all channels is used to derive a pitch estimate for one of the component vowels from a signal composed of two vowels. Individual channel ACFs showing a pitch peak at this value are combined and used to identify the first vowel using a template matching procedure. The ACFs in the remaining channels are then combined and used to identify the second vowel. Model recognition performance shows a rapid improvement in correct vowel identification as the difference between the fundamental frequencies of two simultaneous vowels increases from zero to one semitone in a manner closely resembling human performance. As this difference increases up to four semitones, performance improves further only slowly, if at all.     

The pitch of short-duration fundamental frequency glissandos.

Pitch perception for short-duration fundamental frequency (F0) glissandos was studied. In the first part, new measurements using the method of adjustment are reported. Stimuli were F0 glissandos centered at 220 Hz. The parameters under study were: F0 glissando extents (0, 0.8, 1.5, 3, 6, and 12 semitones, i.e., 0, 10.17, 18.74, 38.17, 76.63, and 155.56 Hz), F0 glissando durations (50, 100, 200, and 300 ms), F0 glissando directions (rising or falling), and the extremity of F0 glissandos matched (beginning or end). In the second part, the main results are discussed: (1) perception seems to correspond to an average of the frequencies present in the vicinity of the extremity matched; (2) the higher extremities of the glissando seem more important; (3) adjustments at the end are closer to the extremities than adjustments at the beginning. In the third part, numerical models accounting for the experimental data are proposed: a time-average model and a weighted time-average model. Optimal parameters for these models are derived. The weighted time-average model achieves a 94% accurate prediction rate for the experimental data. The numerical model is successful in predicting the pitch of short-duration F0 glissandos.     

A unified theory of matter. II. Derivation of the fundamental physical law

The equation for the fundamental field quantity ? is obtained. It is Div \(\rho ^\mu (\Omega _1 ) = \operatorname{h} \int {[\rho _\mu (\Omega _1 ),\rho ^\mu (\Omega _2 )]_ - \operatorname{d} \Omega _2 } \) ,where h is an arbitrary function oft andr, and [,]_? is the commutator. The derivation requires the following hypotheses:(1) All of physical reality is completely described by the field ?.(2) Relativistic covariance of the equations governing ?.(3) Principle of continguous action.(4) Conservation of total amount of ?. The equation appears to be unique. It is suggested that the physical world corresponds to ? being a2×2 matrix. A close correspondence between the basic equation and Maxwell's equation is displayed. The electromagnetic vector potential A^μ is identified with ε ρ^μ dΩ. Conservation laws on various measures of ? are obtained. The symmetry groups of the basic equation are derived. A preliminary attempt to connect the field ? to the metric is made via Einstein's gravitational equation G_μυ =_KT_μυ.     

Detection versus discrimination of brief tones by cats with auditory cortex lesions.

In recent years, a number of investigators have provided evidence that the auditory cortex has a critical role in both the detection and discrimination of brief sounds. Dogs and humans with lesions of the neocortical auditory centers have been reported to exhibit significantly elevated detection thresholds for signals shorter than 16 ms in duration. In tests of frequency discrimination, the same subjects also exhibited severe deficits whenever tonal signals were less than 20--40 mn in lengths. In the present report, we present evidence brief tones. Operated cats, while exhibiting normal difference limens for 1-kHz tones of 100-ms duration, have significantly elevated limens for discriminating tones of 8- and 2-ms duration. With further testing, the same operated cats can be shown to have normal absolute thresholds for detecting brief tones.     

A unified theory of matter. I. The fundamental idea

The Lorentz transformation is derived without assuming that the velocity of light is a constant. This suggests that the constantc which appears in the transformation has a deeper significance than heretofore commonly assumed. It is hypothesized that there exists, in all of physical reality, velocities of only one magnitude. The magnitude isc, the speed of light in vacuum. This hypothesis forces us to view a fundamental particle as an extended object and matter in general as a field (t, r, ), which we give the generic name stuff. An important feature of the field is that at each spacetime point(t, r) stuff travels in all directions with speedc. In order to elucidate the nature of (t, r, ), the equations determining for a one-dimensional world are derived and solved. Fundamental particles are shown to exist and their structure is obtained.A private communication; not an official publication of the National Bureau of Standards.