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This article is concerned with fluctuations in noise power and with the role that such fluctuations play in the masking of sine signals by noise. Several measures of noise fluctuations are discussed: the fourth moment of the waveform, the fourth moment of the envelope, and the crest factor. Relationships among these quantities are found for cases of equal-amplitude random-phase noise and Rayleigh-distributed-amplitude noise. Of particular interest is a special non-Gaussian noise called low-noise noise in which the fluctuations are small by any of our measures. The results of frozen-noise masking experiments are reported where the noise waveform was fixed for all stimulus presentations. In separate experiments, equal-amplitude random-phase Gaussian noise, with typical fluctuations, and low-noise noise, with almost no fluctuations were used. The data show that for a noise bandwidth less than the critical bandwidth, the masked threshold is about 5 dB lower for low-noise noise than for Gaussian noise. When the noise bandwidth is larger than the critical bandwidth, the masked threshold is the same for both kinds of noise. It is concluded that noise power fluctuations increase masked threshold by about 5 dB and that filtering by the auditory system reintroduces fluctuations into broadband low-noise noise. [ABSTRACT FROM AUTHOR]

This article concerns the generation of waveforms by a digital oscillator in which sampled data in a memory buffer are recycled. The buffer contains a fixed waveform and the output sample rate is also fixed. Despite these constraints, the oscillator is capable of arbitrarily high frequency resolution if the technique of fractional addressing is used. However, fractional addressing introduces distortion. This article gives a theory of fractional addressing, resembling the theory of diffraction in crystal lattices with a basis. The theory shows how the spectrum of the distortion components can be calculated and how the distortion can be minimized. Attention is called to numerous symmetries in the distortion spectrum. These symmetries are especially interesting if the purpose of the system is to make use of the distortion components to create inharmonic signals. Of particular importance is the γp symmetry theorem, which makes it possible to derive simple formulas for the level of the largest distortion component and for the total distortion power. [ABSTRACT FROM AUTHOR]

The steady-state sound field of a sine tone does not provide useful localization information in a room. Nevertheless, listeners can localize a sine tone in a room if it has an onset transient which allows the precedence effect to operate. In the present study, we made a quantitative assessment of onsets and the precedence effect by systematically varying onset duration from 0 s (impulsive), where the precedence effect is maximal, to 5 s, where there is no precedence effect at all. We also assessed listeners' sensitivity to the steady-state sound field under impulsive conditions by varying the total duration of tone pulses. Our experiments were conducted in a room with a single acoustical reflection having various directions and delays, and in an anechoic room. The results for tones of various frequencies (500 and 2000 Hz) and sound-pressure levels (65 and 40 dBA) indicate the following: (1) Localization in rooms is facilitated by onsets even if the onsets are as long as 100 ms. (2) The facilitation depends upon the peak intensity of the tone, as well as the onset duration, suggesting that onset rate is critical for the precedence effect; our results are most consistent with rate expressed as an increase in sound pressure per unit time. (3) The facilitation also depends upon the reflection delay time for a room; gradual onsets take on much more importance for the precedence effect in rooms with long delays. (4) As onsets begin to lose their effectiveness listeners become increasingly ''misdirected'' by invalid cues in the steady-state sound field. The pattern of misdirection suggests a perceptual averaging of cues over an interval more than an order of magnitude longer than previous estimates of the summation window for the precedence effect. (5) The pattern of misdirection varies with the frequency of a tone, due to frequency-dependent interference effects in a room, but it is independent of signal level. (6) Localization of an impulsive sine tone in rooms is very insensitive to the pulse duration; this suggests that binaural inhibition models of the precedence effect must be supplemented by an evaluative component that we term the ''plausibility hypothesis.'' [ABSTRACT FROM AUTHOR]

Experiments were performed to determine the ability of human listeners to discriminate between a sound with a large number of spectral components in a band, of given characteristic frequency and bandwidth, and a sound with a smaller number of components in that band. A pseudorandom placement of the components within the band ensured that no two sounds were identical. The data suggested that discrimination is primarily based upon the perception of temporal fluctuations in the intensity of the sound and secondarily upon resolved structure in the spectrum, perceived as tone color. Experiments using clusters of complex harmonic sounds showed that listeners are able to use the information in upper harmonic bands to discriminate spectral density. [ABSTRACT FROM AUTHOR]

It is shown that a complex tone can be analyzed into its harmonics by adding to it a series of N-1 similar complex tones with uniformly spaced fundamental frequencies. The harmonics appear in a time-ordered sequence, and this is the basis of a computer music effect employed by composer Jean-Claude Risset. The mathematical derivation involves the summing of a geometric progression to form a slowly varying amplitude factor. The effect is directly analogous to the analysis of white light into its constituent colors by a diffraction grating with N slits. The temporal ordering of the sequence does not depend upon the relative phases of the harmonics of the complex tone, nor upon the number of tones which is summed, nor is it sensitive to amplitude changes. The order can be changed by a progressive delay of any harmonic in the summed complex tones. Calculations are made to investigate the stability of the effect against randomness is the tones to explain why the effect does not normally appear in vocal or instrumental choruses. [ABSTRACT FROM AUTHOR]

Auditory localization was studied in a room bounded by a single acoustically reflective surface. The position of that surface was varied so as to simulate a floor, a ceiling, and a left or right side walls. The surface was eliminated in one condition so that we could examine localization in free field for purposes of comparison. Using a source identification method we assessed the influences of these various room configurations on the localization of both slow-onset and impulsive sine tones of low frequency (500 Hz). We also measured the steady-state interaural-time-difference (ITD) and interaural-intensity-difference (IID) cues available to subjects in the different room configurations and compared these data with the perceptual judgments. Our results indicate the following: (1) A sound must include transients if the precedence effect is to operate as an aid to its localization in rooms. (2) Even if transients are present the precedence effect does not eliminate all influences of room reflections. (3) Due to the interference of reflections large interaural intensity differences may occur in a room and these have a considerable influence on localization; this is true even at low frequencies for which IID cues do not exist in a free field. (4) Listeners appear to have certain expectations about the reliability and plausibility of various directional cues and perceptually weight the cues accordingly; we suggest that this may explain, in part, the large variation in time-intensity trading ratios reported in the literature and also the differing reports regarding the importance of onsets for localization. (5) In this study we find that onset cues are of some importance to localization even in free field. [ABSTRACT FROM AUTHOR]

A central spectrum explanation of the existence of the binaural edge pitch [Klein and Hartmann, J. Acoust. Soc. Am. 70, 51-61 (1981)] appears to require central lateral inhibition in the human auditory system. We have looked for this effect in central masking experiments. Using the binaural-edge noise, which creates the binaural edge pitch, as a masker (in standard notation: No below and Nπ above a phase boundary frequency), we measured pulsation thresholds for sine tones in two frequency ranges where the binaural edge pitch exists. We also obtained reference data, using the same pulsation threshold technique, for standard binaural conditions NoSo, NoSπ, NπSo, and NπSπ. These data revealed masking level differences. Theoretically the difference between the binaural-edge thresholds and the reference data should show the peak and valley signature of lateral inhibition. No such structure was found. We suggest that this negative result does not exclude the possibility of central lateral inhibition, but that the time course of central lateral inhibition makes the pulsation threshold technique an inappropriate means for observing the effect. [ABSTRACT FROM AUTHOR]

This paper is concerned with the localization of sources of sounds by human listeners in rooms. It presents the results of source-identification experiments designed to determine whether the ability to localize sound in a room depends upon the room acoustics, and how it depends upon the nature of the source signal. The experiments indicate that the localization of impulsive sounds, with strong attack transients, is independent of the room reverberation time, though it may depend upon the room geometry. For sounds without attack transients, localization improves monotonically with the spectral density of the source. Localization of continuous broadband noise does depend upon room reverberation time, and we propose the concept of direct signal to reverberant noise ratio to study that effect. Source identification experiments reveal certain localization biases, invisible to minimum-audible-angle experiments, and of uncertain origin. Appendices to this paper develop the statistics of the source-identification paradigm and show how they relate to the minimum audible angle. [ABSTRACT FROM AUTHOR]

We reopen the question of an appropriate representation to describe the masking of a sine tone midway in frequency between two sine maskers. We suggest that when the maskers are closely spaced in frequency signal detection is mediated by differences in the the stimulus envelope caused by the target signal. We show that in previous two-masker experiments detection threshold was limited by stimulus duration. Our experiments for long stimulus durations find thresholds that are approximately independent of the phase angle between the target and the maskers. Because the different phase angles correspond to very different stimulus envelopes the observed invariance is not easy to understand. For a general phase angle the presence of the signal causes both periodic changes in the envelope and periodic frequency modulation. The experimental detection data do not allow one to distinguish between these two effects. [ABSTRACT FROM AUTHOR]

The Huggins pitch effect is created by dichotic broadband noise with interaural phase varying from 0 to 2π over a narrow frequency region. The sensation of pitch, corresponding to the frequency of the phase shift region, is usually understood as the result of a binaural differencing operation. We report here a pitch effect created by dichotic broadband noise with interaural phase varying from 0 to π over a narrow boundary region, creating an edge in a difference channel. We call this effect Binaural Edge Pitch. For experienced listeners the effect is similar in nature and strength to the Huggins pitch. It is strongest for boundary frequencies in the 350-800 Hz range. Pitch matching experiments in this range find that the spread of matches is 1%-2% of the boundary frequency and that the pitch is 4% higher or lower than the boundary frequency. This shift is identical to the shifts which we find for the pitch of high-pass and low-pass noise bands. The correspondence argues strongly for an explanation of the Binaural Edge Pitch in terms of the Equalization-Cancellation Model of binaural processing, and pitch derived from a central spectrum. [ABSTRACT FROM AUTHOR]

There is general agreement that the frequency difference limen measured in a two-sine-tone frequency discrimination experiment is smaller than that measured in a frequency modulation (FM) experiment. We present a model of frequency modulation detection for low modulation frequencies, within the framework of signal detection theory, which accounts well for the observed difference between frequency discrimination experiments and FM detection experiments. The FM detection model also predicts psychometric functions for detection of FM with different modulation waveforms. FM detection experiments with square, sine, trapezoid, and triangle FM are in reasonable agreement with the model predictions. [ABSTRACT FROM AUTHOR]

Psychophysical experiments show that the pitch of a short sine wave tone depends upon the amplitude envelope of the tone. Subjects find that the pitch of an exponentially decaying tone (1dB/ms) is higher than the pitch of a (20-ms) rectangularly gated tone of equal frequency. The percentage difference in frequency required to produce equal pitches with the two envelopes depends upon frequency f0: 2.6% at f0=412 Hz, 1.4% at f0=825 Hz, 1% at f0=1650 Hz, and 0.7% at f0=3300 Hz. The pitch change is insensitive to the relative intensities of the two tones. The spectra of tones with the two different envelopes suggest no obvious explanation for the pitch change. However, the weighted time-varying spectra for tones with two different envelopes evolve differently with time. Alternatively the pitch change can be derived from a modified version of the auditory phase theory of Huggins. [ABSTRACT FROM AUTHOR]

The Digisound-16 is a two-channel, 16-bit DAC-ADC system with a 32K word buffer. Because of its high performance and low cost it is an attractive signal source for psychoacoustic experiments. The device can be modified to serve as a precision digital oscillator by using the technique of fractional addressing [W. M. Hartmann, J. Acoust. Soc. Am. 82, 1883-1891 (1987)]. The frequency resolution is 0.003 Hz over the audible range and the total distortion approaches the theoretical limit of - 85 dB for single-channel operation. The modification requires that the 15-bit address register be replaced by a 24-bit increment-and-add circuit. Two-way communication between the modified device and the host computer allows the address increment to be changed continuously so that the oscillator can be manually tuned, as in the method of adjustment. The portion of the buffer that is recycled can be reduced by factors of 2, under program control, to as little as 2K words. The reduced buffer length promotes efficiency while compromising frequency resolution and distortion figures. [Work supported by the National Institutes of Health.] [ABSTRACT FROM AUTHOR]

A consistent finding in our studies of auditory localization in rooms has been that brief tones with abrupt onsets and offsets are localized far more accurately than are sustained tones with slow onsets [W. M. Hartmann, J. Acoust. Soc. Am. 74, 1380-1391 (1983); B. Rakerd and W. M. Hartmann, J. Acoust. Soc. Am. Suppl. 1 75, S88 (1984)]. The purpose of the present study was to explore the contribution of signal onset rate to this effect. In a room with left-wall acoustical reflections of brief delay (mean delay time = 1.5 ms), we assessed localization performance for sustained tones (500 Hz, 60 dB) with onsets of 5000, 1000, 500, 100, 50, 10, 5, and 0 ms. The accuracy of subjects' (n = 4) localization judgments increased monotonically with rate for all onsets less than 100 ms. Testing with a subset of the onset times showed that a similar pattern of results is obtained in rooms with other paths of reflection (ceiling, mean delay = 1.5 ms) and with other delay times (left wall, mean delay = 9 ms). We hypothesize that signal onsets must be shorter than 100 ms if they are to trigger operation of the precedence effect in rooms, and that within that regime their effectiveness increases with increasing rate. [Work supported by NIMH.] [ABSTRACT FROM AUTHOR]

The standard deviation of the distribution of matching frequencies in a two-interval pitch matching experiment and the width of the psychometric function in a two-interval frequency discrimination experiment both measure uncertainties in the perception of pitch. We compared uncertainties as measured by these two methods for tones of short duration, using all nine pairings of 12, 25, and 50 ms, at nominal frequencies of 200, 342, 584, and 1000 Hz. We found that the two experiments gave qualitatively different results. In frequency discrimination, the uncertainty decreased as the duration of either the standard or the comparison tone increased, as expected from statistical decision theory in one dimension. In pitch matching, the uncertainty function had local minima whenever the standard and comparison tones had equal duration. To explain this dichotomy we suggest that a pitch matching experiment permits a multidimensional comparison of two tones, but that a frequency discrimination experiment forces a comparison along a single perceptual dimension. [Work supported by the NIH.] [ABSTRACT FROM AUTHOR]

We have made fine-grained measurements of absolute threshold and of the pitch-intensity relation for sine tones as functions of frequency. For some subjects the measured microstructures have small enough error and are sufficiently stable in time that one can hope to draw conclusions from the data. For some ears, in some frequency ranges, there is little threshold microstructure. In these cases the pitch-intensity relation tends to show a frequency-independent shift. More commonly, however, there is considerable threshold microstructure, as much as 10 dB over one semitone. In those cases there is inevitably appreciable microstructure in the pitch-intensity relation; the pitch shift may change sign six or seven times per octave. We have attempted to exploit the microstructures to test models of pitch perception for sine tones. We made standard assumptions about neural driven firing rate. We also supposed that absolute threshold indicates neural sensitivity. We found that our microstructure data are inconsistent with models in which pitch is derived from either the peak locus or the centroid of an average neural firing rate pattern. This conclusion is in agreement with a previous study of pitch shifts caused by a leading tone. [W. M. Hartmann, J. Acoust. Soc. Am. Suppl. 1 68, S109 (1980)]. [Work supported by the NSF and by the NIH.] [ABSTRACT FROM AUTHOR]

The percent correct responses in a two-interval forced-choice detection experiment can be calculated from the probability density functions for the excitation on the two intervals. This letter introduces an equation which relates the percent correct responses to the characteristic functions of the probability densities. The equation can result in considerable mathematical simplification in the prediction of detection performance in cases of multiple sources of signal or noise. [ABSTRACT FROM AUTHOR]

Courses in elementary acoustics taught at many universities provide introductions to the following six topics: physical acoustics, environmental acoustics, the physiology of hearing, auditory psychophysics, musical acoustics, and the nature of human speech. Electronic demonstrations can be used to enhance instruction in each of the six areas. For example, the modules of an electronic music synthesizer together with an audio system and conventional electronic instrumentation form a versatile laboratory for experiments in sound. Among the demonstrations which can be done are the following. Wave interference can be demonstrated by extracting the separate signals from a stereo recording of signals A + B and A - B. Tone and noise bursts can be used to find the speed of sound, echo and reverberation times. Filter banks, set according to mean audiometric presbycusis data, can show the effects of aging on the frequency response of human hearing. Gently nonlinear electronic devices aid the recognition of combination tones normally generated by the inner ear. Analog delay lines can create repetition pitch from a source of white noise. Sine wave signals from many oscillators can be summed and varied to study the perception of pitch of an inharmonic tone complex like that of a chime. The phase variation of a single rectangular wave with pseudorandom pulse width modulation simulates chorus effect. Much of the effect of nonlinear mode mixing in conventional musical instruments can be simulated by patched of linear electronic components, transient generators and voltage controlled signal processing modules. Three resonant filters allow the synthesis of vowel sounds. Frequency shifted or ring modulated speech sounds can exhibit the importance of vowel formant transitions. Intelligibility experiments with chopped speech serve as an introduction to redundancy, autocorrelation and information theory. We note that one does not pursue this informal experimenting with signal processing equipment for long before one discovers effects which are hard to understand. Further pursuit can lead to new results. For example, our intelligibility experiments with chopped speech suggest that redundancy, measured in spoken English text agrees with that found by Shannon for written text. [ABSTRACT FROM AUTHOR]

In the pitch step experiment subjects tune an oscillator in three successive adjustments to match the pitch of a 15-msec sine-wave tone of frequency f2 that is immediately preceded by a 4-sec sine-wave tone with frequency f1 (900 f1) the matched tone frequency p2 tends to be greater than f2. This effect, whereby the pitch of tone 1 repels the pitch of tone 2 increases for decreasing |f2-f1|. The effect is reminiscent of the repulsion of a tone by a narrow noise band. [J. C. Webster and D. R. Muerdter, J. Acoust. Soc. Am. 37, 382-383 (1965)]. Therefore, a plot of p2-f1 versus f2-f1 is nonlinear (and possibly discontinuous) near the origin. If p2 is regarded as a description of the state of a pitch perceptor 15 msec after the step then the nonlinearity guarantees that no linear differential equation can describe the time-dependent response of the pitch perceptor. Dichotic experiments with tones 1 and 2 in different ears suggest that a repulsive-type nonlinearity is still present, though reduced in size. For downward pitch steps two of our subjects exhibit a repulsive effect (p2

Professor A. H. Benade frequently remarked on the paradox involved in listening to musical sounds in rooms. He noted that the transmission path from the sound source to the listener is unreliable; its impulse response and its corresponding frequency response, are irregular, unpredictable, and unstable. Nevertheless, the listener obtains reliable information about the location of the source, about the tone color, and about the transient character. The paradox may be resolved in principle by postulating that the listener's nervous system performs certain temporal summation and differencing operations as well as binaural summation and differencing operations on the internal representation of the sound field. The present talk will review what is known from psychoacoustical experiments concerning these parallel summation and differencing operations with the goal of distinguishing between plausible and implausible models. Most striking has been recent progress on binaural processing where psychoacoustics and electrophysiology appear to be converging on a single model, based upon crosscorrelation in tuned channels. Of particular importance is the precedence effect, which, after 100 years of study, still creates surprises but still wants an adequate definition. [Work supported by the National Institutes of Health.] [ABSTRACT FROM AUTHOR]

The central spectrum model of Raatgever and Bilsen [J. Acoust. Soc. Am. 80, 429-441 (1986)] successfully accounts for a number of dichotic-noise pitch effects and for the lateralization of the pitches. The model is, however, physiologically implausible. An improved model, based upon a neural delay line having coincidence cells that obey the statistical rules of Stem and Colburn [J. Acoust. Soc. Am. 64, 127-140 (1978)], retains the predictive power of the Raatgever-Bilsen model. It also successfully predicts the results of new experiments where the Raatgever-Bilsen model fails. New experiments measure the relative strengths of Huggins pitches HP + and HP -, the lateralization of the binaural-edge pitch (BEP), the spectral density dependence of the BEP, and the strength of generalized BEP, where the interaural phase shift may have any magnitude. [Work supported by the NIH.] [ABSTRACT FROM AUTHOR]

The technique of fractional addressing permits one to construct a digital oscillator with arbitrarily high frequency resolution. However, the technique introduces distortion. The distortion power spectrum may be calculated exactly by borrowing mathematical methods from crystallography, such that the crystallographic unit cell length equals the denominator of the irreducible fractional part of the address increment. The calculation exhibits remarkable mathematical symmetries, which lead to simple closed-form expressions for the levels of the components in the distortion spectrum and for the total rms distortion. The expressions show how the distortion may be minimized or possibly employed as an alternative to digital FM in the synthesis of complex tones. [Work supported by the NIH.] [ABSTRACT FROM AUTHOR]

The ability of human listeners to localize sound sources can be measured by discrimination experiments, such as the minimum audible angle (MAA) paradigm, or by source identification experiments. In principle, these two kinds of experiments can be unified by a statistical decision theory model, incorporating a process whereby a sensory scale is referenced to an absolute scale. To test this idea we performed several kinds of free field discrimination and source identification experiments, both in the light and in the dark. Among our conclusions are the following: (1) The variance of the referencing process depends upon the width of the absolute scale required by the experiment. It doubles as the width increases from 2°-33°. (2) The MAA experiment, nominally a measurement of discrimination, probably includes a source identification component as well. In fact, our data in the light are consistent with a model in which the MAA experiment is treated exclusively as a source identification task. [Work supported by the NIH and NIMH.] [ABSTRACT FROM AUTHOR]

Listeners adjusted the frequency of a sine tone to match the pitch of a single mistuned harmonic in a complex tone consisting of 16 harmonics. Fundamental frequencies were 200, 400, or 800 Hz, and mistunings ranged from 0.5% to 8.0%. The successful matches, those close to the actual mistuned harmonic, show highly consistent and unexpected pitch shift effects; the pitch shifts can be twice as large as the frequency shifts, for both positive and negative frequency shifts. The percentage of matches which are successful provides an estimate of a listener's ability to segregate the mistuned component from the complex tone. Best performance occurs for mistuned harmonics in the region of spectral dominance. The highest frequency which can be segregated is a decreasing function of the fundamental frequency. The latter result suggests that the segregation operation depends upon both place and time coding in the auditory system. [Work supported by the NIH, the NSF, and the CHRS-France.] [ABSTRACT FROM AUTHOR]

The psychological attribute of pitch is the most important organizing element by which the human auditory system reduces a steady-state complex signal to one or more perceptual entities. Historically both experimental and theoretical studies of pitch perception have been primarily concerned with the synthetic listening mode and the pitch of a single entity. However, there are experiments which test the analytic mode and the ability to segregate several entities. The mistuned harmonic experiment, in which the task is to hear out a mistuned partial in a complex tone, is a promising approach of this kind, though it demands that the experimenter try to distinguish those effects which are due to beats of mistuned consonances or nonlinear combination tones from those due to perceptual reorganization into segregated entities. The results of mistuned harmonic experiments suggest that the most sensitive segregation operation is mediated by neural processes which are tonotopically local, though they are tuned more broadly than a critical band. Therefore, appropriate models are not based upon pattern matching in a central spectrum but upon cross correlation between the firing patterns in neighboring sharply tuned neural elements or upon autocorrelation of the pattern in a more broadly tuned element. Such models are supported and constrained by physiological observations of the temporal response to complex tones in single cells of the eighth nerve, the cochlear nucleus, the inferior colliculus and the cortex. [ABSTRACT FROM AUTHOR]

Experiments were performed to determine the ability of human listeners to discriminate between a sound with a large number of spectral components in a band, of given characteristic frequency and bandwidth, and a sound with a smaller number of components in that band. A pseudorandom placement of the components within the band ensured that no two sounds were identical. The data suggested that discrimination is primarily based upon the perception of temporal fluctuations in the amplitude envelope of the sound and secondarily upon a steady-state tone color. Experiments using clusters of complex sounds showed that listeners are able to use the information in harmonic bands to discriminate spectral density. [Work partially supported by NIH, the NSF, and the CNRS.] [ABSTRACT FROM AUTHOR]

We investigated room-reflection effects on auditory localization by conducting experiments in a room bounded by a single, manipulable, sound-reflecting surface. Across experimental conditions this surface alternatively served as a wall, floor, or ceiling. Previously we have reported that the azimuthal localization of slow-onset tones of low frequency (500 Hz) is extremely poor for most configurations of the room, and that the azimuthal localization of impulsive tones is adversely affected by reflections from side walls [B. Rakerd and W. M. Hartmann, J. Acoust. Soc. Am. Suppl. I 75, S88 (1984)]. In the present study we compare those perceptual data to physical measurements of the interaural-time-difference (ITD) and interaural-intensity-difference (IID) cues available to listeners in each room condition. In a room there can be very large values of IID, even at low frequencies, and we find that these significantly influence localization decisions. Results for both the slow-onset and impulsive tones suggest the hypothesis that listeners weight ITD cues according to their plausibility. Plausibility is established with reference to both 90-deg azimuth and the angle of sources as observed visuality. [Work supported by NIH and NIMH.] [ABSTRACT FROM AUTHOR]

The dynamically shifted oscillator is a nonlinear system described by a differential equation of motion which includes a Hooke's law restoring force plus a stiffness force which depends only upon the sign of the displacement. The natural frequency of the oscillator is a function of the displacement amplitude; for positive stiffness it increases as the amplitude decreases. Because of the special nature of the nonlinearity it is possible to find an exact expression for the displacement waveform as a function of time. In the limits of zero Hookian force or zero stiffness, the waveform becomes, respectively, a cosine wave or a parabola wave. Conservation of energy leads to an integral equation which can be solved to find an exact expression for the amplitude-dependent frequency. If the model equation is extended to include damping then the model predicts the time dependence of the frequency. The latter is compared with the measured time-dependent frequencies of two systems to which the dynamically shifted oscillator theory can be applied, the spring doorstop and the two-point librator. [ABSTRACT FROM AUTHOR]

It is shown that a complex tone can be analyzed into its harmonics by adding to it a series of N - 1 similar complex tones with uniformly spaced fundamental frequencies. The harmonics appear in a time ordered sequence, and this is the basis of the computer music effect employed by composer Jean-Claude Risset. The mathematical derivation involves the summing of a geometric series to form a slowly varying amplitude factor. The effect is directly analogous to the analysis of white light into its constituent colors by a diffraction grating with N slits. The temporal ordering of the sequence does not depend upon the relative phases of the harmonics of the complex tone, nor is it altered if any harmonic(s) of the summed complex tones are successively attenuated by a common factor. The order can be changed by a progressive delay of any harmonic in the summed complex tones. Calculations are made to investigate the stability of the effect against nonuniform frequency spacing and modulation to explain why the effect does not normally appear in instrumental choruses. [ABSTRACT FROM AUTHOR]

Numerous experiments have studied pitch discrimination for sine tones as a function of the duration T of the two tones to be discriminated. All the data agree that as T decreases the uncertainty in pitch discrimination becomes larger, and the functional dependence of the uncertainty on T has been used to test various models of pitch perception. However, all simple models, whether temporal or spectral, predict that if the two tones have different durations, T1 and T2, then the uncertainty should lie between the uncertainty obtained when both tones have duration T1 and the uncertainty obtained when both tones have duration T2. To find out whether this is so we measured the variability in a pitch matching task where the tones to be matched had different durations. The matching task provides data on pitch uncertainty in the presence of large duration-dependent pitch shifts whereas a standard discrimination experiment does not. We studied seven different frequencies between 200 and 7000 Hz and all combinations of 12, 25, and 50 ms for T1, and T2. Ninety percent of the data with T1 ≠ T2 show a variability which is larger than would be expected based upon the variability in the data with T1 = T2. We believe that it is possible to understand these results in terms of an improved statistical decision theoretic model of pitch perception. [Work supported by the National Institutes of Health Grant 17917.] [ABSTRACT FROM AUTHOR]

A low-pass noise band with a sharp spectral edge produces a sensation of pitch, noise edge pitch (NEP), which matches a sine tone having a frequency below the noise edge frequency. Similarly a high-pass noise band results in a NEP above the edge frequency. Dichotic noise with an interaural phase shift varying rapidly with frequency at an edge frequency produces the binaural edge pitch (BEP). The BEP is bimodal and is normally equal to both the low-pass and the high-pass NEP. We performed pitch matching experiments to study both NEP and BEP as functions of the width of the edge. Edge center frequencies were between 150 and 1500 Hz, and the edge widths were 0%, 10%, 20%, and 40% of the edge center frequencies. Experimental variance increased with increasing edge width, but less than proportionally. The low-pass NEP increased systematically with increasing width, especially for edge frequencies above 300 Hz, where the NEP exceeded the edge center frequency for 30% and 40% widths. The high-pass NEP changed less predictably and it usually remained above the edge center frequency. The two modes of the BEP distribution changed less with increasing edge width than did either NEP. This difference in dependence challenges dichotic pitch perception models in which the BEP and the NEP have a common central origin. [Work partially supported by the NIH Grant 17917.] [ABSTRACT FROM AUTHOR]

The binaural coherence edge pitch (BICEP) is a dichotic broadband noise pitch effect similar to the binaural edge pitch. The noise is made by summing sine waves with equal amplitudes and random phases. The interaural phase angle is a constant for sine wave components with frequencies below a chosen frequency, and it is a random variable for components with frequencies above that frequency. The chosen frequency is a coherence edge because the signals to the two ears are mutually coherent within any band of frequencies below the edge and they are mutually incoherent in any band above the edge. Sine tone pitch matching experiments show that the BICEP exists for coherence edge frequencies between 300 and 1000 Hz and that it is always matched by a frequency above the edge frequency, by 5%-10%. The effect can be extended to higher edge frequencies, at least 2000 Hz, if the listener is appropriately cued. The results do not depend upon whether the coherent components are presented in phase or completely out of phase to the two ears. For the opposite case, coherence above the edge frequency and incoherence below, the BICEP can be reliably matched only for coherence edge frequencies between 300 and 600 Hz, and the matching frequency is invariably below the coherence edge frequency, by 10%-20%. [Work supported by the National Institutes of Health Grant 17917.] [ABSTRACT FROM AUTHOR]

When localizing sounds in a room, listeners must overcome interference from numerous echoes. We created a simple limiting case of this situation by conducting experiments in an anechoic chamber in which a heavy 4 × 8 ft panel provided a single early reflection. The panel alternatively served as a left wall, right wall, floor, or ceiling. Localization accuracy was assessed with the source identification method [W. M. Hartmann, J. Acoust. Soc. Am. 74, 1380-1391 (1983)] for eight loudspeakers separated in azimuth by three degrees of arc. The stimuli were 500-Hz tones which were either pulsed for 50 ms or turned on with a slow (7 s) envelope and left on to deprive the listener of any transient information. For pulses, performance was significantly poorer with side wall reflections than with reflections from the floor or ceiling, or with no reflections at all. There was no evidence that responses systematically deviated to the left or right of targets in any condition. Together, these findings indicate that the precedence effect [H. Wallach et al., Am. J. Psychol. 62, 315-336 (1949)] can break down over short intervals and that when it does so the result is simply increased uncertainty in localization. For tones with no transients, performance was very much poorer for side walls and ceiling than for the floor and no-wall conditions. Physical measurements indicate that these judgments were determined jointly by the binaural time and intensity differences that resulted from interference between the source and its reflection. [Work partially supported by NIH and the Department of Audiology and Speech Sciences, Michigan State University.] [ABSTRACT FROM AUTHOR]

To understand the existence of the binaural edge pitch [Klein and Hartmann. J. Acoust. Soc. Am. 70, 51-61 (1981)] appears to require central lateral inhibition in the human auditory system. We have looked for this effect in central masking experiments. Using the binaural-edge noise, which creates the binaural edge pitch, as a masker, we found pulsation thresholds for sine tones in two frequency ranges where the binaural edge pitch exists. We further found masking level differences using the same pulsation threshold technique. Theoretically the difference between the binaural-edge thresholds and the MLD thresholds should show the peak and valley signature of lateral inhibition. No such structure was found. We suggest that this negative result does not exclude the possibility of central lateral inhibition, but that the time course of central lateral inhibition makes the pulsation threshold technique an inappropriate means for observing the effect. [Work partially supported by the NIH, grant NS 17917.] [ABSTRACT FROM AUTHOR]

We have studied the ability of human listeners to locate the origin of a sound in a room in a series of source azimuth identification experiments. All experiments were done in a small rectangular concert hall with variable geometry and acoustical properties. Subjects localized a 50-ms, 500-Hz sine pulse with an rms error of 3.3° (±0.6°) regardless of room reverberation time. Lowering the ceiling from 11.5 to 3.5 m decreased the error to 2.8° (±0.6°). Subjects localized broadband noise without attack transients with an rms error of 2.3° (±0.6°) if the reverberation time was 1 s. The error increased to 3.2° (±0.7°) if the reverberation time was 5 s. For complex tones without attack transients the localization error continuously increased as the intensity of spectral components decreased. Performance was nearly random for a 500-Hz sine tone, but was significantly better than random for a 5000-Hz sine tone. Our azimuth identification experiments revealed significant biases, as much as 2°; such biases are, of course, invisible in minimum audible angle experiments. [ABSTRACT FROM AUTHOR]

The noise stimulus for repetition pitch has a spectral envelope consisting of an unlimited number of identical broad peaks. The frequency spacing between the peaks is 1/τ, the reciprocal of the repetition time. With appropriate digital techniques it is possible to cause the spectral envelope to glide slowly and indefinitely along the frequency axis, while maintaining a constant envelope shape and peak spacing. The pitch generated by this stimulus does not ascend or descend indefinitely, as in the illusions of Risset and Burns. Instead, there are several pitches, which follow repetitive sawtooth patterns. One pitch glide follows the pattern conjectured by F. A. Bilsen [Acustica 17, 295-300 (1966)], with a discontinuity from about 1/τ, ± 12% to 1/τ ∓ 12% near the cos- condition. Another pitch, heard for some positive spectral glides, has a discontinuity near the cos+ condition, beginning at 1/2τ and rising to 1/τ. There are sometimes other gliding pitches, not necessarily weaker than the above, for which we have no ready explanation. [Work partially supported by the NSF and the NIH.] [ABSTRACT FROM AUTHOR]

The sonorous twang of the spring doorstop is known and beloved throughout the United States. The waveform consists of a series of impulses of partly random character with significant spectral energy up to 8 kHz. The inverse of the impulse spacing is the fundamental frequency and the waveform exhibits well-developed harmonics at least up to the 20th. Two polarizations of spring vibrations may be excited, but there is a preferred orientation. As the doorstop vibration decays the polarization rotates into the preferred orientation. The fundamental frequency rises by more than an octave (16 to 40 Hz is typical). The fundamental frequency increases linearly with the number of cycles therefore it increases exponentially with time. Stroboscopic observation reveals no indication of wave motion along the spring axis. Therefore it is possible to model the system as two coupled, damped oscillators. The nonlinearity presumably arises from the compression of the spring, which produces a force discontinuity at the origin. Numerical solution of the coupled nonlinear differential equations reproduces most of the features of the spring vibrations, but as of this writing the computed frequency increase with increasing cycle number is not linear, as observed experimentally, but has positive curvature. [ABSTRACT FROM AUTHOR]

The Institute for Research and Coordination of Acoustics and Music, directed by Pierre Boulez, pursues new ideas and techniques in music with the aid of acoustic and information science. IRCAM has personnel and facilities in place throughout the large terrain that concerns itself with the creation of musical sounds. There is research in psychoacoustics and in the acoustics of the human voice, of musical instruments and of rooms. Much of this research is of an applied nature, addressing the needs of particular compositions or performance situations. Acousticians often collaborate closely with individual musicians from the Ensemble Intercontemporain, an ensemble of professional musicians dedicated to comtemporary music, allied with the Institute. IRCAM contributes significantly to the continuing development of digital hardware and software for the analysis and synthesis of sounds. Most notable are IRACAM's high-speed digital synthesizers, which permit real-time control in the creation and modification of musical sounds. Musical acitivity at IRCAM extends from composition to performance and commercial recording. The Institute is host to composers from many countries, who employ its facilities to create electronic music. Performance and recording capabilities are greatly enhanced, by the Espace de Projection, an acoustically variable room of unparalleled flexibility. The present talk is a guided tour of IRCAM's unique laboratories and studios, with recorded examples of recent compositions. [ABSTRACT FROM AUTHOR]

We reopen the question of an appropriate representation to describe the masking of a sine tone midway in frequency between two maskers [A. R. Phipps and G. B. Henning, J. Acoust. Soc. Am. 59, 442-447 0976)]. We argue that when the maskers are closely spaced in frequency, signal detection is mediated by recognizable differences in the stimulus envelope. For unit maskers, separated in angular frequency by δ, and for signal amplitude a, the square of the envelope is given by |E|2 = 2 + 2 cos (δt) + a2 + 4a cos [lowercase_phi_synonym] cos (δt/2), where [lowercase_phi_synonym] is the signal phase relative to the mean of the masker phase angles. Rhythmic envelope variations caused by the signal occur at a rate of δ/(4π) Hz. Our 2IFC detection experiments find that for sufficiently long signal durations the large dependence on signal phase reported by Phipps and Henning is greatly reduced. [Work supported by NSF grant BNS 79-14155.] [ABSTRACT FROM AUTHOR]

Periodic modulation of a signal may be perceived by a spectral process or by a temporal process. R. M. Warren, J. M. Wrightson, and H. E. Storck [J. Acoust. Soc. Am. Suppl. 1 67, S21 (1980)] have performed an interesting experiment exploring the transition between these two perceptual regimes. They determined the perceived periodicity of repeated noise segments having alternating polarity; they found a transition at a repetition frequency of about 70 Hz. We have analyzed this experiment with a model of the auditory system consisting of frequency analysis, square-law detection and leaky integration. The model provides a time-variant spectral analysis of an arbitrary signal. It interpolates between long-term and short-term spectral representations. Using model parameters for spectral resolution and minimum integration time taken from other psycho-acoustical experiments we obtained model predictions in good agreement with the data of Warren et al. The calculations imply that the perception of low-frequency periodicity in this experiment is not properly an aspect of pitch perception. [Supported by NSF grant BNS 79-14155.] [ABSTRACT FROM AUTHOR]

The pitch of a brief sine tone is increased if the tone is preceded by a sine tone of the same frequency and higher intensity. This effect was observed in a pitch matching experiment with the following sequence: 500-ms leading tone of 60 dB SPL and frequency f1 around 1000 Hz, silent gap of variable duration, 50-ms target tone with intensity I2 and frequency f1 500-ms silent interval, 50-ms matching tone with intensity I2 and frequency adjusted by the subject. This experiment measures the pitch shift caused by the leading tone; the results are unaffected by pitch changes with intensity. For I2 > 60 dB no significant pitch shift was observed. As I2 decreased from 60 to 35 dB, increasing positive pitch shifts were found. For a silent gap duration of 5 ms, maximum shift was 2%-4% of f1. For a 25-ms gap, the shift was about 1%. For a 50-ms gap, the shift was almost insignificant. When the leading tone was replaced by octave band noise (76 dB SPL, 57 dB maximum spectral level) much smaller shifts, with quite a different form, were observed. The experimental data together with the results of neurophysiological experiments on pure tone adaptation can be used to constrain the form of allowable place theories of pitch perception. [Supported by NSF Grant BNS 79-14155.] [ABSTRACT FROM AUTHOR]

The binaural edge pitch is created by dichotic, broadband noise with an interaural phase spectrum which changes abruptly. [M. A. Klein and W. M. Hartmann, J. Acoust. Sec. Am. Suppl. 1 67, S20 (1980)]. We employed dichotic noise with Fourier components in phase below frequency f0 and out of phase above f0. The pitch of this noise corresponds to a frequency which is about 4% above or below f0 for 250 < f0 < 1000 Hz. For f0 < 250 Hz the deviation f0 increases rapidly with decreasing f0. We performed auxiliary experiments to find the pitches of high-pass and low-pass noise bands with sharp cutoffs at f0. The pitches deviate from f0 in the same way as for the binaural edge pitch. The correspondance supports the Equalization Cancellation model of binaural processing; it provides stronger support than does the Huggins pitch effect. Further experiments, with interaural phase changes from -π/2 to +π2, or changes superimposed upon a slowly varying phase shift show that the binaural processing must be a flexible system capable of enhancing local spectral features. Generally any abrupt change in interaural phase provides some pitch cue. [Work supported by NSF Grant BNS 79-14155.] [ABSTRACT FROM AUTHOR]

The Huggins pitch effect is created by dichotic broadband noise with interaural phase varying from 0 to 2&;pgr; over a narrow frequency range. The sensation of pitch, corresponding to the frequency of the phase shift region, is usually understood as the result of a binaural differencing operation. We report here a pitch effect created by dichotic broadband noise with interaural phase varying from 0 to π over a narrow range, creating an edge in a difference channel. This stimulus produces a pitch close to the phase shift region. It requires practice, alternating the dichotic noise with a probe tone, to hear the effect. For experienced listeners the pitch sensation is similar in nature and strength to the Huggins pitch. It is strongest for shift frequencies in the 350-800 Hz range. It is present for noise at 40 to 60 dB and for shift region widths which are 10%, 5%, or 12% of the center shift frequency. Pitch matching experiments find that the spread of matches is 1%-2% of the shift frequency, as for Huggins pitch, and that the pitch does not depend upon the direction of the shift. [Supported by the NSF.] [ABSTRACT FROM AUTHOR]

According to Goldstein's 1967 theory [J. Acoust. Soc. Am. 41, 458-479 (1967)] modulation is detected by the detection of energy fluctuations in a critical band filter centered on the lower modulation sideband. This theory predicts the relative detectabilities of AM and FM. We have generalized the theory to the detection of mixed modulation, MM, viz., combined AM and FM. The parameter space of MM is rich; AM and FM may be combined in any proportion and with any relative phase; the ratio of upper to lower sideband levels may take on any value. Therefore, MM experiments provide a stringent test of the general detection theory. In particular, as the upper sideband level is increased relative to the lower it becomes advantageous to the listener to change to a critical band filter centered on the upper sideband. The conditions for this transition can be predicted from pure tone masking data. We performed parallel AM, FM, MM, and masking experiments. Although most data support the theory, thresholds at the transitions are anomalously high in some conditions in disagreement with theory. [Supported by the NSF.] [ABSTRACT FROM AUTHOR]

Experiment I estimated the point of subjective equality (PSE) for the perceived width of a complex waveform FM compared to a standard 4-Hz sine waveform FM with excursions, Δfs = ±2.5, ±5, and ±10 Hz. The complex FM was the sum of a 4-Hz fundamental and its third harmonic with 13 the fundamental amplitude. The phase [lowercase_phi_synonym] between the two components varied from 0 to 7π/4 in steps of π/4. A 2IFC up-down staircase procedure was used. Experiment II was a 2IFC identification task in which subjects distinguished sine FM from complex FM at PSE, with Δfs and [lowercase_phi_synonym] from experiment I. Results of experiments I and II show similar dependences on Δfs and [lowercase_phi_synonym]. The complex wave excursion at PSE relative to the sine excursion (I) and the identification error rate (II) both decrease with increasing Δfs and with increasing |[lowercase_phi_synonym] - π|. The dependences on Δfs support an independent channels model for FM perception, but the dependences on [lowercase_phi_synonym] argue against this model and favor a model based upon the perception of FM waveform features. [Work supported by the NSF.] [ABSTRACT FROM AUTHOR]

The pitch of a brief target sine tone is changed by a preceding tone. The pitch of the target tone is shifted away from the pitch of the preceding tone [A. Jaroszewski and A. Rakowski, Acustica 34, 220 (1976); W. M. Hartmann and B. J. Blumenstock. J. Acoust. Soc. Am. 60, S40 (A) (1976)]. Recent experiments on this effect show the following: (1) The shift is present for tones near 1000 Hz and near 200 Hz and for tones heard at 80 dB and at 40 dB. (2) Smaller shifts exist when 40 dB preceding and target tones are in opposite ears, and for preceding tones 40 dB less intense than the target tones. (3) The shift tends to vanish for missing-fundamental preceding tones with no spectral energy near the target tone. These experiments support a model of pitch perception based upon a central neural excitation pattern which is an intensity-compressed representation of the stimulus spectrum. The results can be understood from a model of short-term neural adaptation and a model for the extraction of pitch from a neural excitation pattern. [Supported by the NSF.] [ABSTRACT FROM AUTHOR]

The detection of frequency modulation at high modulation frequencies seems to be based upon detection of the first lower modulation sideband in the presence of the carrier as masker. This conclusion followed from a series of interleaved experiments on modulation detection and sine tone masking. [W. M. Hartmann, J. Acoust. Soc. Am. 63, S66(A) (1978)]. The present paper reports a similar combined study of amplitude modulation detection and masking. The AM detection experiment used an 80 dB. 1000 Hz carrier with high and low modulation frequencies. The masking experiment used an 80 dB, 1000 Hz masker and a target tone with frequency equal to a sideband frequency from the AM experiment. Each experimental run consisted of an AM detection half and a masking half. Both halves employed a 2IFC staircase method. The results for three subjects show that for modulation frequencies of 200, 150, and 100 Hz, AM detection threshold occurs when the lower modulation sideband is at masked threshold. For modulation frequencies of 50, 25, and 12 Hz, AM is detected when the lower sideband is 5.2 dB (±1.3 dB) below masked threshold. These results agree with a duplex model of AM detection. In this model AM detection is based upon lower sideband detection for high modulation frequencies and upon detection of intensity fluctuations for low modulation frequencies. [Supported by the NSF.] [ABSTRACT FROM AUTHOR]

We describe a psychoacoustics laboratory with microcomputer control of stimulus generation and data acquisition. The control hardware is based on a MOS Technology 6502 microprocessor with 6 K of ROM and 13 K of RAM. Interfacing is through programmable circuitry using MOS Technology 6532 chips. Analog signal generating equipment is controlled by 16 logic lines and eight 12-bit DAC's. Interaction with subjects is through 48 input/output logic lines and a 16-channel 12-bit ADC. Experimental data is stored in a fixed, standard format; it can be displayed on a video screen, printed on paper, and/or stored on standard audio cassettes. Software is based around the KIM operating system using subroutine calls rather than a high-level language. The software control package is specialized for counting, timing, and sequencing stimuli and interacting with subjects. The system presently runs forced choice, method of adjustment, and up-down tracking routines. Logical construction of experimental programs from the modular subroutines can be simpler and faster (though less flexible) than FORTRAN programming of a large system. [ABSTRACT FROM AUTHOR]