An interval size illusion: the influence of timbre on the perceived size of melodic intervals

In four experiments, we investigated the influence of timbre on perceived interval size. In Experiment 1, musically untrained participants heard two successive tones and rated the pitch distance between them. Tones were separated by six or seven semitones and varied in timbre. Pitch changes were accompanied by a congruent timbre change (e.g., ascending interval involving a shift from a dull to a bright timbre), an incongruent timbre change (e.g., ascending interval involving a shift from a bright to a dull timbre), or no timbre change. Ratings of interval size were strongly influenced by timbre. The six-semitone interval with a congruent timbre change was perceived to be larger than the seven-semitone interval with an incongruent timbre change (interval illusion). Experiment 2 revealed similar effects for musically trained participants. In Experiment 3, participants compared the size of two intervals presented one after the other. Effects of timbre were again observed, including evidence of an interval illusion. Experiment 4 confirmed that timbre manipulations did not distort the perceived pitch of tones. Changes in timbre can expand or contract the perceived size of intervals without distorting individual pitches. We discuss processes underlying interval size perception and their relation to pitch perception mechanisms.     

Expectancies generated by melodic intervals: Perceptual judgments of melodic continuity

The present study tested quantified predictors based on the bottom-up principles of Narmour’s (1990) implication-realization model of melodic expectancy against continuity ratings collected for a tone that followed a two-tone melodic beginning. Twenty-four subjects (12 musically trained, 12 untrained) were presented with each of eight melodic intervals—two successive tones which they were asked to consider as the beginning of a melody. On each trial, a melodic interval was followed by a third tone, one of the 25 chromatic notes within the range one octave below to one octave above the second tone of the interval. The subjects were asked to rate how well the third tone continued the melody. A series of regression analyses was performed on the continuation ratings, and a final model to account for the variance in the ratings is proposed. Support was found for three of Narmour’s principles and a modified version of a fourth. Support was also found for predictor variables based on the pitch organization of tonal harmonic music. No significant differences between the levels of musical training were encountered.     

Expectancies generated by melodic intervals: Evaluation of principles of melodic implication in a melody-completion task

Bottom-up principles of melodic implication (Narmour, 1990) were evaluated in a melody-completion task. One hundred subjects (50 low training; 50 high training in music) were presented each of eight melodic intervals. For each interval, the subjects were asked to compose a short melody on a piano keyboard, treating the interval provided as the first two notes of the melody. For each melody, the first response—the note immediately following the initial interval—was analyzed. Multinomial log linear analyses were conducted to assess the extent to which responses could be predicted by Narmour’s (1990, 1992) bottom-up principles. Support was found for all of Narmour’s principles, and two additional predictors based on implied tonal structure. Responses of low- and high-training groups were similar.     

Comparisons of intervals between subjective numbers

Fifty Ss compared the subjective magnitudes of adjacent, objectively equal intervals between numbers by the method of triads. The numbers investigated were the integers from 1 to 10. For every comparison, the interval between the larger integers was more frequently judged closer, which supported previous findings that, for numbers used in magnitude estimation, subjective number is a negatively accelerated function of objective number. The nature of the psychological and physical variables in a number psychophysical function was discussed.     

The ratio principle holds over a million-to-one range of illumination

Infant sensitivity to kinetic information specifying three-dimensional object shape was assessed using computer-generated random-dot displays. Four-month-old infants were habituated to displays of an object oscillating about two different axes on alternating trials. Following habituation, the infants were tested for recovery from habituation to a display of the same object and a novel object. Both test displays employed a new axis of rotation. The infants generalized habituation to the same object and increased their looking to the new object. These results provide evidence that infants are sensitive to motion-carried information specifying three-dimensional object shape, since the random-dot displays minimized static information that differentiated the two objects. These findings suggest that, at least by 4 months of age, infants can detect subtle differences in shape from purely kinetic information.     

Shortening of subjective tone intervals followed by repetitive tone stimuli

Accumulated evidence shows that a subjective time interval is lengthened by preceding or concurrent presentation of flickers or repetitive tone stimuli that have been hypothesized to increase the frequency of pulse generation by a brain pacemaker. In the present study, we presented a series of repetitive tone stimuli after an interval that started and ended with tone markers. We found that subjective perception of the preceding interval was not lengthened but shortened by the tone stimuli that followed the interval. The perceived duration decreased as the frequency of the repetitive tone stimuli increased. The effect disappeared when the repetitive tone stimuli were delivered with a delay of 500 msec after the test interval or when continuous sound was delivered instead of delivering a rapid series of tones. On the basis of the results, we propose that the pulse count accumulated during a test interval was normalized by the clock frequency just after the test interval in a postdictive manner.     

The detection and tracing of melodic key changes

Adjusting to key changes in music is vital to a listener's understanding of it, although it is unclear when this adjustment occurs. In three experiments, participants heard obscure melodies that sometimes contained key changes. Both the number of notes after the change and the change distance were manipulated. For one task, the participants were explicitly asked to detect a change. For another task, the participants rated probe tones. These ratings allowed us to trace the listeners' multiple representations of keys. Results suggest that old keys were abruptly abandoned but that new keys were accepted gradually. More distant key changes (e.g., C-F#) were associated with more accurate detection of change, as well as with more time being required to adapt to the new key.     

Harmonic structure as a determinant of melodic organization

Musicians and nonmusicians indicated whether a two-note probe following a tonally structured melody occurred in the melody. The critical probes were taken from one of three locations in the melody: the two notes (1) ending the first phrase, (2) straddling the phrase boundary, and (3) beginning the second phrase. As predicted, the probe that straddled the phrase boundary was more difficult to recognize than either of the within-phrase probes. These findings suggest that knowledge of harmonic structure influences perceptual organization of melodies in ways analogous to the influence of clause relations on the perceptual organization of sentences. They also provide evidence that training plays an important role in refining listeners’ sensitivity to harmonic variables.     

Perceptual interference decays over short unfilled intervals

The perceptual interference effect refers to the fact that object identification is directly related to the amount of information available at initial exposure. The present article investigated whether perceptual interference would dissipate when a short, unfilled interval was introduced between exposures to a degraded object. Across three experiments using both musical and pictorial stimuli, identification performance increased directly with the length of the unfilled interval. Consequently, significant perceptual interference was obtained only when the interval between exposures was relatively short (< 500 msec for melodies; < 300 msec for pictures). These results are consistent with explanations that attribute perceptual interference to increased perceptual noise created by exposures to highly degraded objects. The data also suggest that perceptual interference is mediated by systems that are not consciously controlled by the subject and that perceptual interference in the visual domain decays more rapidly than perceptual interference in the auditory domain.     

The subjective size of visual stimuli affects the perceived duration of their presentation

The perception of time spent looking at a stimulus is lengthened or shortened when its physical attributes, such as area, differ from those of a comparison stimulus. We measured the perceived presentation duration of a visual object whose apparent area was altered by the Ebbinghaus illusion while its physical size remained invariant, so that a central circle surrounded by larger inducers appeared smaller than a same-size central circle surrounded by smaller inducers. The results showed that the perceived duration of presentation for apparently larger circles was longer than that of apparently smaller circles, although the actual area remained invariant across all circles. We concluded that the time perception process receives input from later visual processing.     

The influence of melodic context on pitch recognition judgment

Subjects made delayed pitch comparisons between tones that were each preceded by tones of lower pitch. The pitches of these preceding tones were so chosen that in some conditions the melodic intervals formed by the standard (S) and comparison (C) combinations were identical, and in others they differed. A strong effect of melodic relational context was demonstrated. When the S and C combinations formed identical melodic intervals, there was an increased tendency for the S and C tones to be judged as identical. And when the S and C combinations formed different melodic intervals, there was an increased tendency for the S and C tones to be judged as different. These effects occurred both when the S and C tones were identical in pitch and also when these differed, and they occurred despite instructions to attend only to the S and C tones.     

Recognition of transposed melodic sequences

Accuracy of recognition for short (three-note) transposed melodic sequences was measured and compared with accuracy predicted by three models of recognition each of which described a different degree of abstraction and synthesis of the musical intervals contained in the sequence. For subjects with musical training, recognition was best described by a model that assumed abstraction and synthesis of the musical intervals between both adjacent and non-adjacent tones of the sequence. For subjects without musical training, recognition was much less accurate but there was some evidence that intervals between adjacent tones were abstracted. Of major theoretical interest, however, was the finding that none of the models provided a comprehensive account of the data. Not merely the size of the intervals contained in a sequence determines accuracy of recognition of the sequence, but also the order or configuration of the intervals. It is suggested that particular interval configurations facilitate the abstraction of tonal structure.     

Binaural integration of melodic patterns

It has been argued that there is a limit to the rate at which we can switch attention between ears in monitoring auditory information. Listeners identified melodic configurations formed by rapid sequences of tones. When these sequences were presented binaurally, excellent performance was obtained. Yet when the component tones of the melody were distributed between the ears, performance was largely nullified when a drone (i.e., a lower constantfrequency tone) was presented to the ear opposite that receiving the melody component. This improvement in performance cannot be attributed to processing the harmonic relationships between melody and drone, since when, instead, the drone was presented to the same ear as the melody component, performance was at chance. Onset-offset asynchronies between the drone and melody components resulted in performance levels between those where the drone and melody components were synchronous and those where the melody switched between ears without an accompanying drone. It is argued that difficulties in binaural integration are due not to processing limitations, but to a mechanism that is invoked under certain conditions to prevent confusion in monitoring individual sound sources.     

Controlled attending as a function of melodic and temporal context

Melodic and rhythmic context were systematically varied in a pattern recognition task involving pairs (standard-comparison) of nine-tone auditory sequences. The experiment was designed to test the hypothesis that rhythmic context can direct attention toward or away from tones which instantiate higher order melodic rules. Three levels of melodic structure (one, two, no higher order rules) were crossed with four levels of rhythm [isochronous, dactyl (A U U), anapest (U U A), irregular]. Rhythms were designed to shift accent locations on three centrally embedded tones. Listeners were more accurate in detecting violations of higher order melodic rules when the rhythmic context induced accents on tones which instantiated these rules. Effects are discussed in terms of attentional rhythmicity.     

The generation of temporal and melodic expectancies during musical listening

When listening to a melody, we are often able to anticipate not onlywhat tonal intervals will occur next but alsowhen in time these will appear. The experiments reported here were carried out to investigate what types of structural relations support the generation of temporal expectancies in the context of a melody recognition task. The strategy was to present subjects with a set of folk tunes in which temporal accents (i.e., notes with a prolonged duration) always occurred in the first half of a melody, so that expectancies, if generated, could carry over to an isochronous sequence of notes in the latter half ofthe melody. The ability to detect deviant pitch changes in the final variation as a function of rhythmic context was then evaluated. Accuracy and reaction time data from Experiment 1 indicated that expectancy formation jointly depends on an invariant periodicity of temporal accentuation and the attentional highlighting ofcertain melodic relations (i.e., phrase ending points). In Experiment 2, once these joint expectancies were generated, the temporal dimension had a greater facilitating effectupon melody recognition than did the melodic one. These results are discussed in terms of their implications for the perceptual processing of musical events.     

The effects of illumination level and retinal size on the apparent strength of subjective contours

The apparent strength of subjective contours was investigated as a function of illumination level, figure size, and viewing distance. Magnitude estimation, with a real contour standard as the modulus, was used to measure the perceived strength of the illusory contours. It was found that illumination level and retinal size are both powerful determinants of the apparent strength of subjective contours, generating magnitude estimates varying from 20% to 96% of the strength of the real contour modulus. Particularly strong subjective contours were reported for figures of small retinal size (1.2 to 4.8 deg) under very dim illumination (.10 log lx).     

Preserved spatial memory over brief intervals in older adults

Two studies compared young and older adults' memory for location information after brief intervals. Experiment 1 found that accuracy of intentional spatial memory for individual locations was similar in young and older participants for set sizes of 3 and 6. Both groups also encoded individual locations in relation to the larger configuration of locations. Experiment 2 showed that like young adults, older adults' latency to respond to a test probe in a letter working memory task was negatively influenced by spatial information that was irrelevant to the task. This interference effect indicated preserved incidental memory for spatial information in older adults. Together, these data suggest that initial encoding of spatial information for relatively small numbers of items is largely preserved in healthy older adults and that representations of spatial information persist over short intervals.     

Confidence intervals for the overall effect size in random-effects meta-analysis

One of the main objectives in meta-analysis is to estimate the overall effect size by calculating a confidence interval (CI). The usual procedure consists of assuming a standard normal distribution and a sampling variance defined as the inverse of the sum of the estimated weights of the effect sizes. But this procedure does not take into account the uncertainty due to the fact that the heterogeneity variance (tau2) and the within-study variances have to be estimated, leading to CIs that are too narrow with the consequence that the actual coverage probability is smaller than the nominal confidence level. In this article, the performances of 3 alternatives to the standard CI procedure are examined under a random-effects model and 8 different tau2 estimators to estimate the weights: the t distribution CI, the weighted variance CI (with an improved variance), and the quantile approximation method (recently proposed). The results of a Monte Carlo simulation showed that the weighted variance CI outperformed the other methods regardless of the tau2 estimator, the value of tau2, the number of studies, and the sample size.