A psychophysical pitch function determined by absolute magnitude estimation and its relation to the musical pitch scale

A psychophysical pitch function, describing the relation of perceived magnitude of pitch to the frequency of a pure tone, was determined by absolute magnitude estimation. Pitch estimates were made by listeners with relative pitch and by absolute pitch possessors for 27 tones spanning a frequency range of 31.5-12,500 Hz in 1/3 octave steps. Results show that the pitch function, plotted in log-log coordinates, is steeper below 200 Hz than at higher frequencies. It is hypothesized that the pitch function's bend may reflect the diversity of neurophysiological mechanisms of pitch encoding in frequency ranges below and above 200 Hz. The variation of the function's slope implies that pitch distances between tones with the same frequency ratios are perceived as larger below 200 Hz than at higher frequencies. It is argued that this implication may apply only to a purely sensory concept of pitch distance and cannot be extended to the perception of musical intervals, a phenomenon governed by musical cognitive principles. The results also show that pitch functions obtained for listeners with relative and absolute pitch have a similar shape, which means that quantitative pitch relations determined for both groups of listeners do not differ appreciably along the frequency scale.     

The effect of amplitude envelope on the pitch of sine wave tones

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 fo: 2.6% at fo = 412 Hz, 1.4% at fo = 825 Hz, 1% at fo = 1650 Hz, and 0.7% at fo = 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.     

The influence of temporal cues on the strength of periodicity pitches

Three different waveforms were generated from the same component frequencies by setting the phase of the components so they were either homophasic (all component sinusoids start at 0 degree), diphasic (sinusoids alternate between -45 degrees and + 45 degrees), or heterophasic (starting phase randomly selected). Listeners were asked to rate the saliency of all periodicity pitches they could detect in stimuli which contained 12 or more components at frequencies above the region where pitches were perceived . A major finding was that the highest ratings of fundamental frequency (f1) pitch "strength" were always obtained for homophasic waveforms, which among the test stimuli have the most abrupt envelope fluctuations. In contrast, diphasic and heterophasic waveforms, which have smoother envelopes, yielded lower pitch strength estimates at f1 and higher ratings two octaves above the fundamental. These data indicate that information concerning the stimulus waveform envelope influences the relative prominence of competing pitches evoked by periodicity pitch stimuli. However, no one-to-one correspondence between pitch and waveform periodicity is apparent.     

The interaction of formant frequency and pitch in the perception of voice category and jaw opening in female singers

This study represents a first step toward understanding the contribution formant frequency makes to the perception of female voice categories. The effects of formant frequency and pitch on the perception of voice category were examined by constructing a perceptual study that used two sets of synthetic stimuli at various pitches throughout the female singing range. The first set was designed to test the effects of systematically varying formants 1 through 4. The second set was designed to test the relative effects of lower frequency formants (F1 and F2) versus higher frequency formants (F3 and F4) through construction of mixed stimuli. Generally, as the frequencies of all four formants decreased, perception of soprano voice category decreased at all but the highest pitch, A5. However, perception of soprano voice category also increased as a function of pitch. Listeners appeared to need agreement between all four formants to perceive voice categories. When upper and lower formants are inconsistent in frequency, listeners were unable to judge voice category, but they could use the inconsistent patterns to form perceptions about degree of jaw opening.     

Absolute pitch among American and Chinese conservatory students: prevalence differences, and evidence for a speech-related critical period

Absolute pitch is extremely rare in the U.S. and Europe; this rarity has so far been unexplained. This paper reports a substantial difference in the prevalence of absolute pitch in two normal populations, in a large-scale study employing an on-site test, without self-selection from within the target populations. Music conservatory students in the U.S. and China were tested. The Chinese subjects spoke the tone language Mandarin, in which pitch is involved in conveying the meaning of words. The American subjects were nontone language speakers. The earlier the age of onset of musical training, the greater the prevalence of absolute pitch; however, its prevalence was far greater among the Chinese than the U.S. students for each level of age of onset of musical training. The findings suggest that the potential for acquiring absolute pitch may be universal, and may be realized by enabling infants to associate pitches with verbal labels during the critical period for acquisition of features of their native language.     

Pitch shifts for complex tones with unresolved harmonics and the implications for models of pitch perception

Complex tone bursts were bandpass filtered, 22nd-30th harmonic, to produce waveforms with five regularly occurring envelope peaks ("pitch pulses") that evoked pitches associated with their repetition period. Two such tone bursts were presented sequentially and separated by an interpulse interval (IPI). When the IPI was varied, the pitch of the whole sequence was shifted by between +2% and -5%. When the IPI was greater than one period, little effect was seen. This is consistent with a pitch mechanism employing a long integration time for continuous stimuli that resets in response to temporal discontinuities of greater than about one period of the waveform. Similar pitch shifts were observed for fundamental frequencies from 100 to 250 Hz. The pitch shifts depended on the IPI duration relative to the period of the complex, not on the absolute IPI duration. The pitch shifts are inconsistent with the autocorrelation model of Meddis and O'Mard [J. Acoust. Soc. Am. 102, 1811-1820 (1997)], although a modified version of the weighted mean-interval model of Carlyon et al. [J. Acoust. Soc. Am. 112, 621-633 (2002)] was successful. The pitch shifts suggest that, when two pulses occur close together, one of the pulses is ignored on a probabilistic basis.     

Absolute pitch correlates with high performance on interval naming tasks

Absolute pitch, the rare ability to identify or produce a musical tone without a reference tone, has been shown to be advantageous in some musical tasks; however, its relevance in musical contexts primarily involving relative pitch has been questioned. To explore this issue, 36 trained musicians-18 absolute pitch possessors and 18 non-possessors with equivalent age of onset and duration of musical training-were tested on interval naming tasks requiring only relative pitch. The intervals to be named were either ascending or descending with separation ranging from 1 to 12 semitones and equally involved all 12 pitch classes. Three different conditions were employed; these used brief sine waves, piano tones, and piano tones preceded by a V7-I chord cadence so as to establish a tonal context. The possession of absolute pitch was strongly correlated with enhanced performance on all these tests of relative pitch. Furthermore, no evidence was found that this absolute pitch avantage depended on key, interval size, or musical context.     

Dead regions and pitch perception

The perception of pitch for pure tones with frequencies falling inside low- or high-frequency dead regions (DRs) was examined. Subjects adjusted a variable-frequency tone to match the pitch of a fixed tone. Matches within one ear were often erratic for tones falling in a DR, indicating unclear pitch percepts. Matches across ears of subjects with asymmetric hearing loss, and octave matches within ears, indicated that tones falling within a DR were perceived with an unclear pitch and/or a pitch different from "normal" whenever the tones fell more than 0.5 octave within a low- or high-frequency DR. One unilaterally impaired subject, with only a small surviving region between 3 and 4 kHz, matched a fixed 0.5-kHz tone in his impaired ear with, on average, a 3.75-kHz tone in his better ear. When asked to match the 0.5-kHz tone with an amplitude-modulated tone, he adjusted the carrier and modulation frequencies to about 3.8 and 0.5 kHz, respectively, suggesting that some temporal information was still available. Overall, the results indicate that the pitch of low-frequency tones is not conveyed solely by a temporal code. Possibly, there needs to be a correspondence between place and temporal information for a normal pitch to be perceived.     

The influence of duration on the perception of pitch in single and simultaneous complex tones

The influence of duration on the virtual pitch of complex tones was measured using an absolute identification paradigm. If performance with two-tone complexes is expressed in terms of a single central frequency-coding noise function, this function is found to depend on duration in about the same way as the pure-tone difference limen function. The function is further found to be a reasonably good predictor of pitch identification performance with multitone complexes. Another experimental finding was that subjects tend to switch to the analytic mode of pitch perception when complex tones are shortened (i.e., they tend to hear the spectral pitches instead of the virtual ones). A third finding was that with simultaneous complex tones the degradation of each pitch percept depends not only on duration and harmonic order of the tone but also on the harmonic order of the other tone.     

Pitch strength and pitch dominance of iterated rippled noises in hearing-impaired listeners.

Reports using a variety of psychophysical tasks indicate that pitch perception by hearing-impaired listeners may be abnormal, contributing to difficulties in understanding speech and enjoying music. Pitches of complex sounds may be weaker and more indistinct in the presence of cochlear damage, especially when frequency regions are affected that form the strongest basis for pitch perception in normal-hearing listeners. In this study, the strength of the complex pitch generated by iterated rippled noise was assessed in normal-hearing and hearing-impaired listeners. Pitch strength was measured for broadband noises with spectral ripples generated by iteratively delaying a copy of a given noise and adding it back into the original. Octave-band-pass versions of these noises also were evaluated to assess frequency dominance regions for rippled-noise pitch. Hearing-impaired listeners demonstrated consistently weaker pitches in response to the rippled noises relative to pitch strength in normal-hearing listeners. However, in most cases, the frequency regions of pitch dominance, i.e., strongest pitch, were similar to those observed in normal-hearing listeners. Except where there exists a substantial sensitivity loss, contributions from normal pitch dominance regions associated with the strongest pitches may not be directly related to impaired spectral processing. It is suggested that the reduced strength of rippled-noise pitch in listeners with hearing loss results from impaired frequency resolution and possibly an associated deficit in temporal processing.     

Comparative learning of pitch and loudness identification

This study investigated possible similarities between the ability to identify pitches and the ability to identify loudnesses. Systematic training of musically naive subjects indicated that frequency identification performance improves at about the same rate as intensity identification performance. Examination of frequency and intensity identification behavior of musically trained subjects showed that their ability to code pitch information efficiently does not generalize to an ability to encode loudness information more efficiently than untrained subjects. Intensity identification training curves of musically trained and untrained subjects are similar, but final performance levels are below frequency identification performance levels exhibited by musically trained subjects, especially those with absolute pitch.     

Effects of signal envelope on the pitch of short complex tones

Envelope-induced pitch shifts were measured for exponentially decaying complex tones consisting of two sinusoidal components with frequencies f1 = nf0 + 50 Hz and f2 = (n + 1) f0 + 50 Hz, where n equals 3, 4, or 5 and exponential decay rates were 0, 0.5, 1, and 2 dB/ms. Four subjects adjusted a sinusoidal comparison tone to match the virtual pitch of the (missing) fundamental and the pitches of the lower and upper partials f1 and f2. Pitch shifts for f1 are generally less, and pitch shifts for f2 always greater, than envelope-induced shifts observed in isolated sinusoidal tones of comparable frequency and envelope decay rate. Pitch-shift functions for virtual pitch are similar in magnitude and shape to average pitch-shift functions of the partials, which supports the idea that virtual pitch depends on spectral pitch.     

Perceived continuity and pitch shifts for complex tones with unresolved harmonics

Brief complex tone bursts with fundamental frequencies (F0s) of 100, 125, 166.7, and 250 Hz were bandpass filtered between the 22nd and 30th harmonics, to produce waveforms with five regularly occurring envelope peaks ("pitch pulses") that evoked pitches associated with their repetition period. Two such tone bursts were presented sequentially and separated by a silent interval of two periods (2/F0). When the relative phases of the two bursts were varied, such that the interpulse interval (IPI) between the last pulse of the first burst and the first pulse of the second burst was varied, the pitch of the whole sequence was little affected. This is consistent with previous results suggesting that the pitch integration window may be "reset" by a discontinuity. However, when the interval between the two bursts was filled with a noise with the same spectral envelope as the complex, variations in IPI had substantial effects on the pitch of the sequence. It is suggested that the presence of the noise causes the two tones bursts to appear continuous, hence, resetting does not occur, and the pitch mechanism is sensitive to the phase discontinuity across the silent interval.     

The speed of pitch resolution in a musical context.

In five experiments, we investigated the speed of pitch resolution in a musical context. In experiments 1-3, listeners were presented an incomplete scale (doh, re, mi, fa, sol, la, ti) and then a probe tone. Listeners were instructed to make a rapid key-press response to probe tones that were relatively proximal in pitch to the last note of the scale (valid trials), and to ignore other probe tones (invalid trials). Reaction times were slower if the pitch of the probe tone was dissonant with the expected pitch (i.e., the completion of the scale, or doh) or if the probe tone was nondiatonic to the key implied by the scale. In experiments 4 and 5, listeners were presented a two-octave incomplete arpeggio, and then a probe tone. In this case, listeners were asked to make a rapid key-press response to probe tones that were relatively distant in pitch from the last note of the arpeggio. Under these conditions, registral direction and pitch proximity were the dominant influences on reaction time. Results are discussed in view of research on auditory attention and models of musical pitch.     

Relating binaural pitch perception to the individual listener's auditory profile

The ability of eight normal-hearing listeners and fourteen listeners with sensorineural hearing loss to detect and identify pitch contours was measured for binaural-pitch stimuli and salience-matched monaurally detectable pitches. In an effort to determine whether impaired binaural pitch perception was linked to a specific deficit, the auditory profiles of the individual listeners were characterized using measures of loudness perception, cognitive ability, binaural processing, temporal fine structure processing, and frequency selectivity, in addition to common audiometric measures. Two of the listeners were found not to perceive binaural pitch at all, despite a clear detection of monaural pitch. While both binaural and monaural pitches were detectable by all other listeners, identification scores were significantly lower for binaural than for monaural pitch. A total absence of binaural pitch sensation coexisted with a loss of a binaural signal-detection advantage in noise, without implying reduced cognitive function. Auditory filter bandwidths did not correlate with the difference in pitch identification scores between binaural and monaural pitches. However, subjects with impaired binaural pitch perception showed deficits in temporal fine structure processing. Whether the observed deficits stemmed from peripheral or central mechanisms could not be resolved here, but the present findings may be useful for hearing loss characterization.     

Grouping in pitch perception: effects of onset asynchrony and ear of presentation of a mistuned component.

Three experiments investigated how the onset asynchrony and ear of presentation of a single mistuned frequency component influence its contribution to the pitch of an otherwise harmonic complex tone. Subjects matched the pitch of the target complex by adjusting the pitch of a second similar but strictly periodic complex tone. When the mistuned component (the 4th harmonic of a 155 Hz fundamental) started 160 ms or more before the remaining harmonics but stopped simultaneously with them, it made a reduced contribution to the pitch of the complex. It made no contribution if it started more than 300 ms before. Pitch shifts and their reduction with onset time were larger for short (90 ms) sounds than for long (410 ms). Pitch shifts were slightly larger when the mistuned component was presented to the same ear as the remaining 11 in-tune harmonics than to the opposite ear. Adding a "captor" complex tone with a fundamental of 200 Hz and a missing 3rd harmonic to the contralateral ear did not augment the effect of onset time, even though the captor was synchronous with the mistuned harmonic, the mistuned component was equal in frequency to the missing 3rd harmonic of the captor complex tone and it was played to the same ear as the captor. The results show that a difference in onset time can prevent a resolved frequency component from contributing to the pitch of a complex tone even though it is present throughout that complex tone.     

Pitch and pitch discrimination of broadband signals with rippled power spectra

A random-interval pulse train or wide-band noise when delayed (tau) and added back to itself (cos+) produces a stimulus with a consinusoidally varying (or trippled) power spectrum. The spacing between the peaks in the spectrum is equal to the reciprocal of the delay (1/tau). If the stimulus is delayed and added back at 180 degrees phase reversal (cos-), then a cosinusoidally varying power spectrum is generated whose spectral peaks are separated by 1/tau, but whose peaks are displaced by 1/2tau relative to the power spectrum of the cos+ stimulus generated with the same day, tau. These stimuli yield a pitch, such that the pitch of the cos+ stimulus is equal to approximately 1/tau and the pitches of the cos- stimuli are equal to approximately 0.9/tau and 1.1/tau. These pitch matching results were studied using a variety of matching stimuli and conditions. Following the identification of the pitches, a method of limits and a same-different procedure were used to study the pitch discriminability of both the cos+ and cos- stimuli. Delays (tau) ranging from 1 to 10 ms were studied covering a pitch range of 90-1100 Hz. The pitch discriminations associated with the cos+ and cos- stimuli were essentially the same for both the random-interval pulse train and the wide-band stimuli. These pitch-discrimination results are compared to those associated with a periodic pulse train. The research is also discussed in terms of discriminations of delayed sounds in reverberant environments. These are consistent with assumptions concerning the autocorrelation of the rippled stimuli within the dominant frequency region for pitch perception.     

Effects of musical training and absolute pitch ability on event-related activity in response to sine tones.

The neural correlates of music perception have received relatively little scientific attention. The neural activity of listeners without musical training (N = 11), highly trained musicians (N = 14), and musicians possessing "absolute pitch" (AP) ability (N = 10) have been measured. Major differences were observed in the P3, an endogenous event-related potential (ERP), which is thought to be a neurophysiological manifestation of working memory processing. The P3 was elicited using the classical "oddball" paradigm with a sine-tone series. Subjects' musical backgrounds were evaluated with a survey questionnaire. AP ability was verified with an objective pitch identification test. The P3 amplitude, latency and wave shape were evaluated along with each subjects' performance score and musical background. The AP subjects showed a significantly smaller P3 amplitude than either the musicians or nonmusicians, which were nearly identical. The P3 latency was shortest for the AP subjects, and was longer for the nonmusicians. Performance scores were uniformly high in all three groups. It is concluded that AP subjects do indeed exhibit P3 ERPs, albeit with smaller amplitudes and shorter latencies. The differences in neural activity between the musicians and AP subjects were not due to musical training, as the AP subjects had similar musical backgrounds to the musician group. It is also concluded that persons with the AP ability may have superior auditory sensitivity at cortical levels and/or use unique neuropsychological strategies when processing tones.     

A nonmusical paradigm for identifying absolute pitch possessors

The ability to identify and reproduce sounds of specific frequencies is remarkable and uncommon. The etiology and defining characteristics of this skill, absolute pitch (AP), have been very controversial. One theory suggests that AP requires a specific type of early musical training and that the ability to encode and remember tones depends on these learned musical associations. An alternate theory argues that AP may be strongly dependent on hereditary factors and relatively independent of musical experience. To date, it has been difficult to test these hypotheses because all previous paradigms for identifying AP have required subjects to employ knowledge of musical nomenclature. As such, these tests are insensitive to the possibility of discovering AP in either nonmusicians or musicians of non-Western training. Based on previous literature in pitch memory, a paradigm is presented that is intended to distinguish between AP possessors and nonpossessors independent of the subjects' musical experience. The efficacy of this method is then tested with 20 classically defined AP possessors and 22 nonpossessors. Data from these groups strongly support the validity of the paradigm. The use of a nonmusical paradigm to identify AP may facilitate research into many aspects of this phenomenon.     

Musical pitch of two-tone complexes and predictions by modern pitch theories.

Most studies of the musical pitch of harmonic tone complexes have utilized signals comparing two or more successive harmonics. The present study provides systematic data on melodic interval recognition by three musically experienced subjects with sounds whose missing fundamentals were represented by two nonsuccessive harmonics nf0,(n + m)f0, delivered to separate ears. Data were obtained in the ranges 1 less than or equal to n less than or equal to 9, 2 less than or equal to m less than or equal to 4, and 200 Hz less than or equal to f0 less than or equal to 1000 Hz. The data are interpreted in the light of three theories, the "optimum processor theory," the "virtual pitch theory," and the "pattern transformation theory." For each theory, a constraint on preformance is proposed based on interference between the "analytic" and "synthetic" pitch perception modes. The former is obtained with large spacings between harmonics, where listeners are more likely to perceive harmonics as individual tones, each having their own pitch. This degrades the listener's ability to hear the fundamental pitch.