The power of representation and interpretation: Doubling statistical reasoning performance with icons and frequentist interpretations of ambiguous numbers

Abstract

Six highly familiar melodies were submitted to three transformations: reduction and two rhythmic group transformations. These three transformations offered the opportunity to compare the role of various means of melody recognition: melodic contour, harmonic structure, local surface cues. If melody recognition relies on melodic contour, an original melody would be easier to recognise after rhythmic group transformation than after reduction; the rhythmic group transformation, but not the reduction, preserves the melodic contour. If melody recognition depends on the harmonic structure, an original melody would be easier to recognise after reduction than after a rhythmic group transformation; the reduction, but not the rhythmic group transformation, respects the underlying harmonic structure. The results of two experiments, one with children and one with adults, showed that recognition was better for rhythmic group transformation but only when local surface cues were preserved, a result that could neither be predicted by the melodic contour hypothesis nor by the harmonic structure hypothesis. The results give support to the cue abstraction hypothesis, which suggests that melody recognition relies on the recognition of certain surface cues abstracted while hearing and which are then memorised. Recognition performances and speed of recognition served as dependent variables.     

Children's perception of certain musical properties: scale and contour

Children's perception of scale and contour in melodies was investigated in five studies. Experimental tasks included judging transposed renditions of melodies (Studies 1 and 3), discriminating between transposed renditions of a melody (Study 2), judging contour-preserving transformations of melodies (Study 4), and judging similarity to a familiar target melody of transformations preserving rhythm or rhythm and contour (Study 5). The first and second studies showed that young children detect key transposition changes even in familiar melodies and they perceive similarity over key transpositions even in unfamiliar melodies. Young children also are sensitive to melodic contour over transformations that preserve it (Study 5), yet they distinguish spontaneously between melodies with the same contour and different intervals (Study 4). The key distance effect reported in the literature did not occur in the tasks of this investigation (Studies 1 and 3), and it may be apparent only for melodies shorter or more impoverished than those used here.     

A bidimensional model of pitch in the recognition of melodies

Pitch can be conceptualized as a bidimensional quantity, reflecting both the overall pitch level of a tone (tone height) and its position in the octave (tone chroma). Though such a conceptualization has been well supported for perception of a single tone, it has been argued that the dimension of tone chroma is irrelevant in melodic perception. In the current study, melodies were subjected to structural transformations designed to evaluate the effects of interval magnitude, contour, tone height, and tone chroma. In two transformations, the component tones of a melody were displaced by octave intervals, either preserving or violating the pattern of changes in pitch direction (melodic contour). Replicating previous work, when contour was violated perception of the melody was severely disrupted. In contrast, when contour was preserved the melodies were identified as accurately as the untransformed melodies. In other transformations, a variety of forms of contour information were preserved, while eliminating information for absolute pitch and interval magnitude. The level of performance on all such transformations fell between the levels observed in the other two conditions. These results suggest that the bidimensional model of pitch is applicable to recognition of melodies as well as single tones. Moreover, the results argue that contour, as well as interval magnitude, is providing essential information for melodic perception.     

Representation and execution of vocal motor programs for expert singing of tonal melodies

Three experiments were conducted to study motor programs used by expert singers to produce short tonal melodies. Each experiment involved a response-priming procedure in which singers prepared to sing a primary melody but on 50% of trials had to switch and sing a different (secondary) melody instead. In Experiment 1, secondary melodies in the same key as the primary melody were easier to produce than secondary melodies in a different key. Experiment 2 showed that it was the initial note rather than key per se that affected production of secondary melodies. In Experiment 3, secondary melodies involving exact transpositions were easier to sing than secondary melodies with a different contour than the primary melody. Also, switches between the keys of C and G were easier than those between C and E. Taken together, these results suggest that the initial note of a melody may be the most important element in the motor program, that key is represented in a hierarchical form, and that melodic contour is represented as a series of exact semitone offsets.     

Rhythm and Melody in Children and Adolescents after Left or Right Temporal Lobectomy

Rhythm (a pattern of onset times and duration of sounds) and melody (a pattern of sound pitches) were studied in 22 children and adolescents several years after temporal lobectomy for intractable epilepsy. Left and right lobectomy groups discriminated rhythms equally well, but the right lobectomy group was poorer at discriminating melodies. Children and adolescents with right lobectomy, but not those with left temporal lobectomy, had higher melody scores with increasing age. Rhythm but not melody was related to memory for the right lobectomy group. In neither group was melody related to age at onset of non-febrile seizures, time from surgery to music tests, or the linear amount of temporal lobe resection. Pitch and melodic contour show different patterns of lateralization after temporal lobectomy in childhood or adolescence.     

Recognition of melodic transformations: Inversion,retrograde, and retrograde inversion

The melodic transformations of inversion, retrograde, and retrograde inversion occur in pieces of music. An important question is whether such manipulations of melodic material are perceptually accessible to the listener. This study used a short-term recognition-memory paradigm and found that in the easier conditions all these transformations were recognized with better than chance accuracy. The ascending order of difficulty was: inversion, retrograde, retrograde inversion. There was no evidence that listeners distinguish between transforms that preserve the exact interval relationships of the standard stimulus and those that merely preserve its contour (pattern of ups and downs). In view of the order of difficulty of the transforms, two theoretical explanations of performance are possible (1) Listeners may perform the mental transformation required by the recognition task on a representation of the vector of pitches in the standard—an operation that is very like transforming a mental image of the written notation. (2) Listeners may handle inversions differently from the other transformations, comparing the standard and the comparison contour element by contour element, in temporal order. In this view, the temporal dimension would appear to have precedence over the pitch dimension in the musical structure, in consideration of the consequences of disturbing it.     

Postrecognition of interleaved melodies as an indirect measure of auditory stream formation

Primitive processes involved in auditory stream formation are measured with indirect, objective method. A target melody interleaved with a distractor sequence is followed by a probe melody that was identical to the target or differed by 2 notes. Listeners decided whether the probe melody was present or not in the composite sequence. Interleaved melody recognition is not possible when distractor sequences have the same mean frequency and maximum contour crossover with target melodies. Performance increases with mean frequency separation and timbral dissimilarity and is unaffected by the duration of the silent interval between composite sequence and probe melody. The relation between this indirect task measuring the interleaved melody recognition boundary and direct judgments measuring the fission boundary is discussed.     

A strong test of exposure effects

A strong test of exposure effects was made by eliminating confounding demand characteristics through the use of a between-subject design. Each subject viewed novel stimuli at a single frequency level, and then rated them on several affective scales. Frequency of stimulus exposure was systematically varied across subjects. Stimuli were rated more positively with increasing exposure, despite the fact that subjects were unaware of any differences in exposure frequencies, and clearly unable to identify the experimental hypothesis. An awareness of the relationship between repeated exposure and affect was thus shown to be an unnecessary condition for the occurrence of exposure effects.     

The effects of auditory and visual interference on the immediate recall of melody

College-age subjects recalled melodies or spoken sentences immediately after hearing them, by either pointing on a chart designed to interfere with a visual memory code orsaying the equivalent responses, which should interfere with an auditory code. Pointing took significantly longer than saying for melodies, but not for sentences. A second experiment showed that this task x materials interaction could be due to interference with contour per se rather than with visual coding of melody, because a similar effect was found for spoken contours consisting simply of the words “up” or “down.” In a third experiment, pointing and saying tasks were modified both to control and to manipulate the amount of contour interference. Visual control stimuli for melodies were introduced, employing a marker that moved up or down. This time the task x materials interaction could be explained in terms of an auditory memory code for melody, but there were some problems with this interpretation. Interference related to contour, rather than to a specific modality, appeared to account best for the results of all three experiments.     

Developmental changes in infants' sensitivity to octave-band noises

Localization responses to octave-band noises with center frequencies at 200, 400, 1000, 2000, 4000, and 10,000 Hz were obtained from infants 6, 12, and 18 months of age. During an experimental trial, an octave-band noise was presented on one of two speakers located 45° to each side of the infant. A head turn to the noise (correct response) was rewarded by activating an animated toy on top of the speaker. The intensity of the noise was varied over trials (method of constant stimuli) to determine thresholds at each center frequency. Thresholds for the lower frequencies were approximately 5–8 db higher in the 6-month-old infants compared to the older infants. However, there were no consistent differences among groups at the higher frequencies. Infant thresholds were found to be 20–30 db higher than adult thresholds at the lower frequencies. At the higher frequencies thresholds for infants were approaching those of adults.     

Number Versus Contour Length in Infants' Discrimination of Small Visual Sets

This study examined infants' use of contour length in number discrimination tasks. We systematically varied number and contour length in a visual habituation experiment in order to separate these two variables. Sixteen 6- to 8-month-old infants were habituated to displays of either two or three black squares on a page. They were then tested with alternating displays of either a familiar number of squares with a novel contour length or a novel number of squares with a familiar contour length. Infants dishabituated to the display that changed in contour length, but not to the display that changed in number. We conclude that infants base their discriminations on contour length or some other continuous variable that correlates with it, rather than on number.     

Shared processes in spatial rotation and musical permutation

An experiment was conducted in which subjects performed a three-dimensional spatial rotation test (24 trials) and a new test involving judgments of musical permutations (64 trials). Two types of musical permutations were used, including retrograde and inverse. In a retrograde permutation, the criterion melody was played backward in the test melody, and in an inverse permutation, an ascending or descending interval in the criterion melody became an opposite in the test melody. Subjects included 32 male and 64 female undergraduates at the University of Toronto. Regression analysis clearly showed that it was easiest to compare short retrograde permutations and that accuracy at discerning retrograde permutations predicted accuracy at judging spatial rotations. The implication is that a higher order ability to discriminate contour underlies both kinds of judgments.     

Harmonic,melodic, and frequency height influences in the perception of multivoiced music

Two experiments addressed the influences of harmonic relations, melody location, and relative frequency height on the perceptual organization of multivoiced music. In Experiment 1, listeners detected pitch changes in multivoiced piano music. Harmonically related pitch changes and those in the middle-frequency range were least noticeable. All pitch changes were noticeable in the high-frequency voice containing the melody (the most important voice), suggesting that melody can dominate harmonic relations. However, the presence of upper partials in the piano timbre used may have accounted for the harmonic effects. Experiment 2 employed pure sine tones, and replicated the effects of Experiment 1. In addition, the influence of the high-frequency melody on the noticeability of harmonically related pitches was lessened by the presence of a second melody. These findings suggest that harmonic, melodic, and relative frequency height relationships among voices interact in the perceptual organization of multivoiced music.     

Auditory feedback in music performance: the role of transition-based similarity

Past research has suggested that the disruptive effect of altered auditory feedback depends on how structurally similar the sequence of feedback events is to the planned sequence of actions. Three experiments pursued one basis for similarity in musical keyboard performance: matches between sequential transitions in spatial targets for movements and the melodic contour of auditory feedback. Trained pianists and musically untrained persons produced simple tonal melodies on a keyboard while hearing feedback sequences that either matched the planned melody or were contour-preserving variations of that melody. Sequence production was disrupted among pianists when feedback events were serially shifted by one event, similarly for shifts of planned melodies and tonal variations but less so for shifts of atonal variations. Nonpianists were less likely to be disrupted by serial shifts of variations but showed similar disruption to pianists for shifts of the planned melody. Thus, transitional properties and tonal schemata may jointly determine perception-action similarity during musical sequence production, and the tendency to generalize from a planned sequence to variations of it may develop with the acquisition of skill.     

Schema-based processing in auditory scene analysis

What is the involvement of what we know in what we perceive? In this article, the contribution of melodic schema-based processes to the perceptual organization of tone sequences is examined. Two unfamiliar six-tone melodies, one of which was interleaved with distractor tones, were presented successively to listeners who were required to decide whether the melodies were identical or different. In one condition, the comparison melody was presented after the mixed sequence: a target melody interleaved with distractor tones. In another condition, it was presented beforehand, so that the listeners had precise knowledge about the melody to be extracted from the mixture. In the latter condition, recognition performance was better and a bias toward same responses was reduced, as compared with the former condition. A third condition, in which the comparison melody presented beforehand was transposed up in frequency, revealed that whereas the performance improvement was explained in part by absolute pitch or frequency priming, relative pitch representation (interval and/or contour structure) may also have played a role. Differences in performance as a function of mean frequency separation between target and distractor sequences, when listeners did or did not have prior knowledge about the target melody, argue for a functional distinction between primitive and schema-based processes in auditory scene analysis.     

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.     

Tonal strength and melody recognition after long and short delays.

In a continuous-running-memory task, subjects heard novel seven-note melodies that were tested after delays of 11 sec (empty) or 39 sec (filled). Test items were transposed to new pitch levels (to moderately distant keys in the musical sense) and included exact transpositions (targets), same-contour lures with altered pitch intervals, and new-contour lures. Melodies differed in tonal strength (degree of conformity to a musical key) and were tonally strong, tonally weak, or atonal. False alarms to same-contour lures decreased over the longer delay period, but only for tonal stimuli. In agreement with previous studies, discrimination of detailed changes in pitch intervals improved with increased delay, whereas discrimination of more global contour information declined, again only for tonal stimuli. These results suggest that poor short-delay performance in rejecting same-contour lures arises from confusion that is based on the similarity of tonality between standard stimuli and lures. If a test item has the same contour and a similar tonality to a just-presented item, subjects tend to accept it. After a delay filled with melodies in other tonalities, the salience of key information recedes, and subjects base their judgments on more detailed pattern information (namely, exact pitch intervals). The fact that tonality affects judgments of melodic contour indicates that contour is not an entirely separable feature of melodies but rather that a melody with its contour constitutes an integrated perceptual whole.     

Tonal strength and melody recognition after long and short delays

In a continuous-running-memory task, subjects heard novel seven-note melodies that were tested after delays of 11 sec (empty) or 39 sec (filled). Test items were transposed to new pitch levels (to moderately distant keys in the musical sense)and included exact transpositions (targets), same-contour lures with altered pitch intervals, and new-contour lures. Melodies differed in tonal strength (degree of conformity to a musical key) and were tonally strong, tonally weak, or atonal. False alarms to same-contour lures decreased over the longer delay period, but only for tonal stimuli. In agreement with previous studies, discrimination of detailed changes in pitch intervals improved with increased delay, whereas discrimination of more global contour information declined, again only for tonal stimuli. These results suggest that poor short-delay performance in rejecting same-contour lures arises from confusion that is based on the similarity of tonality between standard stimuli and lures. If a test item has the same contour and a similar tonality to a just-presented item, subjects tend to accept it. After a delay filled with melodies in other tonalities, the salience of key information recedes, and subjects base their judgments on more detailed pattern information (namely, exact pitch intervals). The fact that tonality affects judgments of melodic contour indicates that contour is not an entirely separable feature of melodies but rather that a melody with its contour constitutes an integrated perceptual whole.     

The perception of interleaved melodies

If the notes of two melodies whose pitch ranges do not overlap are interleaved in time so that successive tones come from the different melodies, the resulting sequence of tones is perceptually divided into groups that correspond to the two melodies. Such “melodic fission” demonstrates perceptual grouping based on pitch alone, and has been used extensively in music.Experiment I showed that the identification of interleaved pairs of familiar melodies is possible if their pitch ranges do not overlap, but difficult otherwise. A short-term recognition-memory paradigm (Expt II) showed that interleaving a “background” melody with an unfamiliar melody interferes with same-different judgments regardless of the separation of their pitch ranges, but that range separation attenuates the interference effect. When pitch ranges overlap, listeners can overcome the interference effect and recognize a familiar target melody if the target is prespecified, thereby permitting them to search actively for it (Expt III). But familiarity or prespecification of the interleaved background melody appears not to reduce its interfering effects on same-different judgments concerning unfamiliar target melodies (Expt IV).