Quantification of the hierarchy of tonal functions within a diatonic context

Listeners rated test tones falling in the octave range from middle to high C according to how well each completed a diatonic C major scale played in an adjacent octave just before the final test tone. Ratings were well explained in terms of three factors. The factors were distance in pitch height from the context tones, octave equivalence, and the following hierarchy of tonal functions: tonic tone, other tones of the major triad chord, other tones of a diatonic scale, and the nondiatonic tones. In these ratings, pitch height was more prominent for less musical listeners or with less musical (sinusoidal) tones, whereas octave equivalence and the tonal hierarchy prevailed for musical listeners, especially with harmonically richer tones. Ratings for quarter tones interpolated halfway between the halftone steps of the standard chromatic scale were approximately the averages of ratings for adjacent chromatic tones, suggesting failure to discriminate tones at this fine level of division.     

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.     

Pitch chroma discrimination, generalization, and transfer tests of octave equivalence in humans

Octave equivalence occurs when notes separated by an octave (a doubling in frequency) are judged as being perceptually similar. Considerable evidence points to the importance of the octave in music and speech. Yet, experimental demonstration of octave equivalence has been problematic. Using go/no-go operant discrimination and generalization, we studied octave equivalence in humans. In Experiment 1, we found that a procedure that failed to show octave equivalence in European starlings also failed in humans. In Experiment 2, we modified the procedure to control for the effects of pitch height perception by training participants in Octave 4 and testing in Octave 5. We found that the pattern of responding developed by discrimination training in Octave 4 generalized to Octave 5. We replicated and extended our findings in Experiment 3 by adding a transfer phase: Participants were trained with either the same or a reversed pattern of rewards in Octave 5. Participants transferred easily to the same pattern of reward in Octave 5 but struggled to learn the reversed pattern. We provided minimal instruction, presented no ordered sequences of notes, and used only sine-wave tones, but participants nonetheless constructed pitch chroma information from randomly ordered sequences of notes. Training in music weakly hindered octave generalization but moderately facilitated both positive and negative transfer.     

Interference effects in tone memory

Memory for a standard tone in comparison to a subsequent test tone was examined in three experiments with three intervening tones between the standard and test tones. In each trial, the intervening tones were presented from one of seven frequency range and distance from the standard tone conditions. Experiment 1 tone patterns were played at four different presentation rates, and the subjects judged whether the test was higher or lower than the standard. Memory interference effects caused by the different intervening tone conditions could be accounted for by a directional shift in the standard tone memory toward the intervening tones and by a general decrease in the standard tone memory strength with more distant intervening tones. Interference effects were smaller for the rapid presentation rates because the intervening tones formed separate "perceptual streams." Two additional experiments presented the tone patterns in a task requiring the subjects to match a continuously variable tone to their memory of the standard (Experiment 2) and a task requiring them to judge whether the standard and test tones were the "same" or "different" (Experiment 3). These experiments showed large differences in interference effects as a function of the required judgment and the subjects' musical experience.     

Detection and recognition: Concurrent processes in perception

In two experiments, event-related brain potentials (ERPs) were recorded while subjects performed a simultaneous detection and recognition task. Ten subjects listened to pure tones in noise and reported both whether a target tone had occurred (using a four-category confidence rating scale) and whether the target was one of two (Experiment 1) or four (Experiment 2) tones differing in frequency. The amplitudes of three ERP components were found to be differentially related to detection and recognition performance. The early N100 component varied with processing related only to detection, while the late P300 varied with both detection and recognition, and a later slow positive shift varied only with recognition and not with detection. While the latenciee of both N100 and P300 increased for less confident target detections, there were no differences in the latencies of these ERP components between correctly and incorrectly identiffed targets. Recognition performance was above the level expected by chance even when subjects reported that no target had been presented. The results indicate that brain potential components can be used to disclose temporal features of the processing of a stimulus by the nervous system and support the view that detection and recognition are partially independent, concurrent processes in perception.     

The skill of recognizing musical structures

In three experiments, musicians and nonmusicians were compared in their ability to discriminate musical chords. Pairs of chords sharing all notes in common or having different notes were played in succession. Some pairs of chords differed in timbre independent of their musical structures because they were played on different instruments. Musicians outperformed nonmusicians only in recognizing the same chord played on different instruments. Both groups could discriminate between instrument timbres, although musicians did slightly better than nonmusicians. In contrast, with chord structures not conforming to the rules of tonal harmony, musicians and nonmusicians performed equally poorly in recognizing identical chords played on different instruments. Signal detection analysis showed that musicians and nonmusicians set similar criteria for these judgments. Musicians' superiority reflects greater sensitivity to familiar diatonic chords. These results are taken as evidence that musicians develop perceptual and cognitive skills specific to the lawful musical structures encountered in their culture's music. Nonmusicians who lack this knowledge based their judgments on the acoustical properties of the chords.     

Discrimination of simultaneous and successive tones

A series of discrimination tasks involving simultaneous and successive presentation of pairs of piano notes was given to 27 Ss. The listeners exhibited less-than-perfect ability to “hear out” the component notes in simultaneous presentations. This finding, in agreement with the results of previous investigators, demonstrated the limitation of Ohm’s law of acoustical analysis. It was also found that changes in successive notes fOllowing simultaneous notes were discriminated more accurately than changes in simultaneous notes following successive notes. This was interpreted as suggesting that listeners are better able to analyze than to synthesize the components of complex tones.     

Perception of structure in novel music

Two experiments demonstrated the way in which musicians and nonmusicians process realistic music encountered for the first time. A set of tunes whose members were related to each other by a number of specific musical relationships was constructed. In Experiment 1, subjects gave similarity judgments of all pairs of tunes, which were analyzed by the ADDTREE clustering program. Musicians and nonmusicians gave essentially equivalent results: Tunes with different rhythms were rated as being very dissimilar, whereas tunes identical except for being in a major versus a minor mode were rated as being highly similar. In Experiment 2, subjects learned to identify the tunes, and their errors formed a confusion matrix. The matrix was submitted to a clustering analysis. Results from the two experiments corresponded better for the nonmusicians than for the musicians. Musicians presumably exceed nonmusicians in the ability to categorize music in multiple ways, but even nonmusicians extract considerable information from newly heard music.     

Perceptual grouping in audition

The present experiments evaluated the effect of relative frequency as a determinant of the figure-ground organization of sequences of auditory tones. Observers counted sequences of 20 ms tones that were presented at the same frequency or that alternated between two different frequencies. The alternating tones differed in frequency by one whole tone, seven tones, or nineteen tones. Counting accuracy increased with increases in the silent interval between the tones. When the alternating tones differed by seven or nineteen tones, counting was disrupted at rates of presentation of eight tones per second or slower. In contrast to this decrement in the counting of tones that alternated by over an octave, very little decrement was observed when the tones alternated by just one whole tone. The best subjects counted these alternating tones more accurately than the tones presented at the same frequency. The poorest subjects showed a small decrement even when the tones alternated by just one whole tone. The results were discussed in terms of determinants of figure-ground organization in auditory information processing.     

The psychological representation of musical pitch in a tonal context

In this series of experiments, evidence was found for a complex psychological representation of musical pitch. The results of a scaling study, in which subjects judged the similarities between pairs of tones presented in an explicitly tonal context, suggest that musical listeners extract a pattern of relationships among tones that is determined not only by pitch height and chroma, but also by membership in the major triad chord and the diatonic scale associated with the tonal system of the context. Multidimensional scaling of the similarity ratings gave a three-dimensional conical structure around which the tones were ordered according to pitch height. The major triad components formed a closely related cluster near the vertex of the cone; the remaining diatonic scale tones formed a less closely related subset farther from the vertex; and, the nondiatonic tones, still farther from the vertex, were widely dispersed. The results also suggest that, in the psychological representation, tones less closely related to the tonality are less stable than tones closely related to the tonality, and that the representation incorporates the tendency for unstable tones to move toward the more stable tones in time, reflecting the dynamic character of musical tones. In the similarity ratings of the scaling study, tones less related to the tonality were judged more similar to tones more related to the tonality than the reverse temporal order. Furthermore, in a delayed recognition task memory performance for nondiatonic tones was less accurate than for diatonic tones, and nondiatonic tones were more often confused with diatonic tones than diatonic tones were confused with nondiatonic tones. These results indicate the tonality-specific nature of the psychological representation and argue that the perception of music depends not only on psychoacoustic properties of the tones, but also on processes that relate the tones to one another through contact with a well-defined and complex psychological representation of musical pitch.     

The interdependence of pitch and temporal judgments by absolute pitch possessors

The auditory tau and the kappa effects show that there is time-pitch interdependence in our perception. Our judgments of pitch separation between two tones depend on the temporal interval between them (the auditory tau effect), and our judgments of the tones’ temporal interval depend on their pitch separation (the kappa effect). The mechanisms underlying this interdependence were investigated by studying the auditory tau and the kappa effect in three experiments. Comparisons were made between results obtained from subjects with absolute pitch and those who did not have absolute pitch, and two frequency ranges of pure tones (octave and whole-tone conditions) were selected. The procedures had been used in previous experiments (Shigeno, 1986), in which the auditory tau and the kappa effects were compared in speech and nonspeech stimuli. The present results demonstrate that the auditory tau effect does not occur when possessors of absolute pitch judge the closeness of stimuli in pitch, except when the stimulus continuum consists of tones that do not correspond to musical notes in the whole-tone condition. The kappa effect was obtained in the judgment of possessors of absolute pitch in both the octave and the whole-tone conditions. These findings suggest that the interaction between temporal interval and pitch judgment might be explained in terms of the two different memory modes for retaining the pitch of tones, and that these effects occur at the precategorical level.     

The dimensions of tonal experience: A nonmetric multidimensional scaling approach

Subjects were required in each trial to directly compare two pairs of tones and indicate which pair of tones had the greater subjective difference or dissimilarity. Eleven tones differing in both intensity and frequency were employed. Subjects made binary comparisons among the 55 tone pairs which can be formed from the set of 11 tones. These paired comparisons of tonal intervals were used to determine a two-dimensional Euclidean representation for tonal experience. Loudness and pitch appeared as orthogonal dimensions in this representation. However, a 45-deg rotation of loudness and pitch axes produced axes which could be identified as volume and density. This relationship suggested that volume and density were simple functions of pitch and loudness. Volume and density predictions based on this two-dimensional representation were shown to provide a good account of the data from three experiments on volume and density.     

Duplex perception with musical stimuli

Duplex perception, a phenomenon previously demonstrated for speech stimuli, is demonstrated here for musical stimuli. In the first experiment, major and minor chords are produced by dichotic fusion of two simultaneous piano notes presented to one ear (perfect fifth) with a “natural” or “flat” single note presented to the opposite ear. Musically trained subjects perceive simultaneously both the single tone and a fused (major or minor) chord. The chords are labeled more consistently than the single notes, even though the fused chords differ solely in terms of the contralateral notes. In a second experiment, using pure tones in place of piano notes, other musically trained subjects individually exhibited categorical perception for either the fused chord or the single tones, but never for both types of stimuli. The duplex phenomenon is discussed in terms of its implications for its specific component modes of perception.     

“Octave illusion” or “Deutsch’s illusion”?

The “Deutsch’s illusion” occurs in most people when a dichotic pair of tones spaced an octave apart is presented repeatedly in alternation, so that when the right ear receives the high tone, the left ear receives the low tone, and vice versa. The illusory percept consists typically in a single low tone heard at one ear alternating with a single high tone heard at the other ear. Here, we investigate whether the frequency interval between the tones and their duration play a role in the perception of the illusion. By testing 74 subjects we demonstrate that the illusion is not confined to tones spaced an octave apart but it is perceivable also with tones separated by a major seventh, a minor ninth, a major ninth, and a minor tenth. Regarding duration, the present results show that the illusion is stronger with tones lasting 500 than 200 ms. The present results suggest that the perceptual mechanisms at the basis of the illusion are not strictly linked to the frequency relationships between the dichotic tones.     

Cross-octave masking of single tones and musical sequences: The effects of structure on auditory recognition

A series of experiments explored the role of structural information in the auditory recognition process, within the context of a backward recognition masking paradigm. A masking tone presented after a test tone has been found to interfere with the perceptual processing of the test tone, the degree of interference decreasing with increased durations of the silent intertone interval between the test and masking tones. In the current studies, the task was modified to utilize three-tone sequences as the test stimuli. Six test sequences were employed (LMH, LHM, MLH, MHL, HLM, HML), where L, M, and H represent the lowest, middle, and highest frequencies in the melody. The observers identified these six possible sequences when the three tones of the test sequence were interleaved with three presentations of a single masking tone. All three tones of the test sequence were drawn from the same octave, while the masking tones could be drawn from any of three octaves, symmetrical around the octave containing the test tones. Under these conditions, interference occurred primarily from masking tones drawn from the same octave as the test tones. Masking tones drawn from other octaves were found to produce little, if any, interference with perception of the test tones. This effect was found to occur only for the identification of tonal sequences. Substantial masking of single-tone targets occurred with masking tones drawn from octaves other than that containing the targets. The results make apparent the use of structural information during auditory recognition. A theoretical interpretation was advanced which suggests that, while single tones are perceived on the basis of absolute pitch, the presence of auditory structure may allow relational information, such as exact pitch intervals or melodic contour, to facilitate perception of the tonal sequence.     

Acquisition of the hierarchy of tonal functions in music

The acquisition of the hierarchy of tonal stabilities in music is investigated in children of elementary school age. Listeners judge how good short tone sequences sound as melodies. The ratings show a pattern of increasing differentiation of the pitches in an octave range. The youngest listeners distinguish between scale and nonscale tones; older listeners distinguish between the tonic triad tones and other scale components. A group of adult listeners show octave equivalence and temporal asymmetries, with a preference for sequences ending on the more stable tones within the hierarchy. Pitch height effects do not interact with the age of the listener. These results are discussed in terms of the primacy of physical variables, novice-expert differences, and general cognitive principles governing the acquisition and development of internal representations of pitch relationships.     

Apparent equivalence between perception and imagery in the production of various visual illusions

The ability of high and low imagers (as assessed by the Vividness of Visual Imagery Questionnaire) to utilize imagery in the production of a visual illusion was examined in three experiments. In Experiment 1, subjects were to imagine noninducing elements oi the Ponzo figure. In Experiment 2, subjects were asked to imagine the inducing angle of the Ponzo figure. Subjects were requested to imagine the inducing diagonals of the Hering and Wundt figures in Experiment 3. Regardless of which figure was presented, high imagers consistently reported an illusion whether it was produced by real or imagined lines. Also, the imagery-produced illusion was equivalent in magnitude to the actual illusion (when all lines are physically present). Low imagers reported an illusion only when lines were physically present. These results were interpreted in terms of Finke’s (1980) equivalence theory.     

Responsiveness of Western adults to pitch-distributional information in melodic sequences

Responsiveness of musically trained and untrained adults to pitch-distributional information in melodic contexts was assessed. In Experiment 1, melodic contexts were pure-tone sequences, generated from either a diatonic or one of four nondiatonic tonesets, in which pitch-distributional information was manipulated by variation of the relative frequency of occurrence of tones from the toneset. Both the assignment of relative frequency of occurrence to tones and the construction of the (fixed) temporal order of tones within the sequences contravened the conventions of western tonal music. A probe-tone technique was employed. Each presentation of a sequence was followed by a probe tone, one of the 12 chromatic notes within the octave. Listeners rated the goodness of musical fit of the probe tone to the sequence. Probe-tone ratings were significantly related to frequency of occurrence of the probe tone in the sequence for both trained and untrained listeners. In addition, probe-tone ratings decreased as the pitch distance between the probe tone and the final tone of the sequence increased. For musically trained listeners, probe-tone ratings for diatonic sequences tended also to reflect the influence of an internalized tonal schema. Experiment 2 demonstrated that the temporal location of tones in the sequences could not alone account for the effect of frequency of occurrence in Experiment 1. Experiment 3 tested musically untrained listeners under the conditions of Experiment 1, with the exception that the temporal order of tones in each sequence was randomized across trials. The effect of frequency of occurrence found in Experiment 1 was replicated and strengthened.     

Perceptual hysteresis in the judgment of auditory pitch shift

Perceptual hysteresis can be defined as the enduring influence of the recent past on current perception. Here, hysteresis was investigated in a basic auditory task: pitch comparisons between successive tones. On each trial, listeners were presented with pairs of tones and asked to report the direction of subjective pitch shift, as either “up” or “down.” All tones were complexes known as Shepard tones (Shepard, 1964), which comprise several frequency components at octave multiples of a base frequency. The results showed that perceptual judgments were determined both by stimulus-related factors (the interval ratio between the base frequencies within a pair) and by recent context (the intervals in the two previous trials). When tones were presented in ordered sequences, for which the frequency interval between tones was varied in a progressive manner, strong hysteresis was found. In particular, ambiguous stimuli that led to equal probabilities of “up” and “down” responses within a randomized context were almost fully determined within an ordered context. Moreover, hysteresis did not act on the direction of the reported pitch shift, but rather on the perceptual representation of each tone. Thus, hysteresis could be observed within sequences in which listeners varied between “up” and “down” responses, enabling us to largely rule out confounds related to response bias. The strength of the perceptual hysteresis observed suggests that the ongoing context may have a substantial influence on fundamental aspects of auditory perception, such as how we perceive the changes in pitch between successive sounds.     

Binaural summation of loudness: Noise and two-tone complexes

A series of six experiments used the method of magnitude estimation to assess how the two ears sum the loudness of stimuli with various spectra. The results showed that the binaural system sums loudnesses by at least two distinct sets of rules, one applicable to narrow-band stimuli (complete loudness summation), another to wide-band noises (partial summation, dependent on level). The main findings were: (1) Narrow-band noise (Vi-octave bands at 1,000 Hz) showed complete binaural loudness summation, like that previously reported for pure tones (Marks, 1978a). At all but low SPL, a monaural stimulus must be 10 dB greater than a binaural stimulus to be equally loud; a stimulus ratio of 10 dB corresponds to a loudness ratio of 2:1 on Stevens’ sone scale. (2) Wide-band noise (300-4,800 Hz) showed only partial summation, the subadditivity being confined largely to levels below about 60 dB SPL. This result obtained both with bands of white noise (flat spectrum) and pink noise (—3 dB/ octave). (3) Binaural summation of two-tone complexes depended slightly on frequency spacing. Narrow spacing (860 and 1,160 Hz) gave summation equal to about 10 dB, like that of narrowband noises and single tones, whereas wider spacing (675 and 1,475 Hz) gave less summation, equal to about 9 dB, and more like wide-band noise; however, a very wide spacing (300 and 4,800 Hz) gave summation like that of narrow-band noises and single pure tones.