Emergence of thematic concepts in repeated listening to music

COGNITIVE

PSYCHOLOGY

Emergence

15,

66-94 (1983)

of Thematic Listening

Concepts to Music

in Repeated

LUCY POLLARD-GOTT Educational

Testing Service

A repeated listening procedure was designed to monitor changes in listener’s appreciation of thematic categories in musical compositions. Subjects listened to a recorded musical composition. Passages selected from the composition were then played in pairs, and listeners rated their similarity. The similarity data were submitted to INDSCAL, a multidimensional scaling procedure, which located the passages in an n-dimensional space. This procedure was repeated in three separate sessions, so that changes in the perceived musical structure could be observed. In Study 1, subjects heard Liszt’s Sonata in b, and target passages were Theme A, Theme B, and three variations of each theme. While extrathematic dimensions dominated early acquaintance, a theme dimension emerged in the second and third sessions. Musicians gave higher weight to the theme dimension than did nonmusicians, and theme was the only dimension for experts on this sonata. Musicians were also more accurate in a final classification test, but only after repeated listening. The effect of repeated exposure on transfer to new theme exemplars was considered in Study 2. It is hoped this work will foster more naturalistic approaches to musical cognition.

INTRODUCTION

Themes and Variations The present research explores listeners’ appreciation of musical themes and their implications in a composition. Western European music has relied heavily on the manipulation of themes and their variations. A theme is a “piece of musical material in a complete, self-contained form, but used in composition for the purpose of development, elaboration, or variation . . . It need not be purely melodic, but may include harmony and texture” (Grove’s Dictionary, 1960, Vol. VIII, p. 409). In variation, one or more musical components of the theme are transformed, while enough of the theme is retained to make it recognizable. “The matter to be varied This paper is based on a dissertation presented to Princeton University in partial fultillment of the requirements for the degree of doctor of philosophy. I am grateful for stimulating discussions of this work with Sam Glucksberg, Ronald Kinchla, Charles Lord, Marilyn Shaw, Nancy Cantor, and Joseph Dubiel. This research was supported, in part, by National Science Foundation Grant BNS 78-27943to Princeton University, Sam Glucksberg, Principal Investigator, and was conducted while the author held a National Science Foundation Predoctoral Fellowship. The author’s address is Educational Testing Service, Research Division, Room 115, Rosedale Road, Princeton, NJ 08541. 66 OOlO-0285/83/010066-29$07.50/O Copyright

0

1983 by Academic

Press. Inc.

THEMATIC

CONCEPTS

IN

MUSIC

67

must not merely proliferate; it must itself persist” (Grove’s Dictionary, 1960, Vol. VIII, p. 671). Copland (1967) discusses four principal classes of variations: (1) harmonic variants, (2) melodic variants, (3) rhythmic variants, and (4) contrapuntal variants. It is useful to summarize them here. In harmonic variation, a melody may be left untouched, but the chords that accompanied it originally are replaced by new chords that give it a different flavor. Alternatively, the composer can create a fuller harmonic texture by using thicker chords. More drastic variation of a theme occurs when the melody is left behind entirely, and only the series of harmonies remains to remind the listener of the theme’s structure. In melodic variation, the contour or shape of a melody is preserved, while its details are manipulated. A melody can be elaborated by adding neighbor notes, or simplified by reducing it to just a few notes that suggest the original contour. A theme can also be varied by changing the position of the melody from the top voice to the bottom, or the bottom voice to the top. In rhythmic variation, the relative duration of the notes in a melody is changed. Changes in meter (from 3/4 to 4/4 time, for example) are a common form of rhythmic variation. Finally, in contrapuntal variation, a new melody or variant is played against the original. The relation of notes played together is crucial to achieving a satisfactory effect. This method is also called fugal development (Grove’s, 1960, Vol. VIII, p. 671). These methods of variation operate on the primary parameters of the music (Meyer, 1973). Secondary parameters of the theme can also be varied. A variation can be faster or slower (tempo), louder or softer (dynamics), and even thicker or thinner (texture) than the original. Finally, transpositions of the theme to other keys and to other modes (major to minor or minor to major) are widely used. Most variations found in real music employ combinations of these devices. Although “theme and variations” is an explicit form, this manner of development is implicit in nearly all major musical forms. In a rondo, for example, the principal theme alternates with other material in the pattern ABACADA. The manipulation of themes and their variations is also crucial to sonata form. It is traditionally divided into three parts: the exposition, where the principal and subordinate themes are introduced; the development, where the themes are varied and combined in new ways; and the recapitulation, where the main themes return and the work is brought to a state of melodic and harmonic closure. The subtleties of chord progressions and other features characteristic of sonata form cannot be taken up here. Newman’s (1963, 1969) volumes on the sonata are an excellent resource. Many symphonies are good examples of sonata form. The variety of

68

LUCY

POLLARD-GOTT

structure found in symphonies tells us that sonata form is not rigid, but very flexible in the hands of great composers. The Sonata in B-minor by Liszt will be played for subjects in Experiments 1 and 2. Appreciation of Thematic Categories A theme and its associated variations can be seen as a conceptual category within a given composition. Appreciation of a piece of music depends in part, then, on the acquisition of one or more of its thematic categories. Themes function as prototypes and variations as instances that bear greater or lesser family resemblance (Rosch & Mervis, 1975) to their prototype. Welker (Note 1) reports a study consistent with this view. He constructed short melodies and variations for each. When he played only the variations for subjects, they were able to draw the contour of the original prototype melody, which they had never heard. They also made false recognitions to the prototype when it was played among a new set of variations. (This study is analogous to the abstraction paradigm devised by Bransford and Franks (1971) for sentences.) In a natural setting, listeners may sometimes need to abstract a theme from a welter of its variations. Often, however, natural musical appreciation proceeds in the opposite direction. Composers usually state their themes near the beginning of the work and then develop them. The astute listener must detect the principal themes as they unfold in each new variation. There are very few studies that have explored theme recognition under natural conditions. In one (Duerksen, 1968), a large group of college and high school students listened to 15 selection of Western music that made use of themes and variations. Subjects were required to distinguish between an exact repetition of a theme and a variation. Not surprisingly, it was found that college music majors were more successful at indicating theme occurrences than the other groups of less experienced listeners. Frances (1958, trans. 1972) reports a series of studies that pursue theme recognition a bit further. He studied people’s ability to pick out themes and variations in compositions under two conditions, guided and unguided. In the guided condition, subjects were told to expect to hear a rondo and a sonata, and these theme structures were explained to them in advance by the experimenter. The nonmusicians in the group performed adequately with the simple rondo, but could not discriminate the themes in the more difficult sonata-form work, Beethoven’s Archduke Trio. Music conservatory students succeeded in detecting the themes in either composition. The unguided condition included only nonmusicians, who, in this case, did poorly even with the rondo. Without guidance, they failed to note six

THEMATIC

CONCEPTS

IN MUSIC

69

out of the 10 instances of the theme. Frances did not include any musicians in his unguided condition, judging that their prior knowledge of sonata form disqualified them. It would have been interesting to observe their performance without guidance on the more difficult Beethoven trio. Even sophisticated listeners may have some uncertainty during the initial period of acquaintance with a piece of music. Normally, listeners need to hear a piece several times before they are willing to say that they have really appreciated it. Thus, performance in an experiment requiring theme detection should depend on the number of opportunities to hear the music. Frances reports one experiment where subjects had two listening trials. The test music was a Bach fugue (where a subject and countersubject undergo contrapuntal variation). The addition of a second chance to listen and detect the themes was very important, especially for nonmusicians who showed a substantial increase in accuracy. Repeated Listening

Experiment

This paper presents new research on thematic appreciation in music. The procedures are designed to approximate the natural conditions under which people come to appreciate a composition, while also permitting the collection of data on the progress of that learning process. First, listeners heard natural music by a master composer, rather than artificial materials constructed for the purpose of an experiment. In this way, it was safer to generalize from experimental results to real-world appreciation of music. Second, the listening situation was unguided. Unless they are in a music class, listeners ordinarily confront a musical piece alone, without any instruction on its particular structure. Of course, we will take into account the different musical backgrounds that listeners bring to a piece. Third, subjects had the opportunity for repeated listening. In this way, we could investigate the growth of appreciation by comparing people’s impression of a composition’s structure when they first encountered it with the more mature impressions gained through familiarization. The concept-learning literature offers an intriguing method for measuring progress in concept learning that can be adapted nicely to music. Homa, Rhoads, and Chambliss (1979) created three different categories of dot patterns generated by random walk from one of three prototype dot patterns. Subjects’ task was to learn to distinguish the three categories. Different groups of subjects received different amounts of categorization training with feedback: 0, 1, or 2 trials. Categorization performance was measured by collecting similarity judgments for all pairs of dot patterns. If subjects were learning the categories, they should rate dot patterns in the same category as more similar to each other than they were to members of

70

LUCY

POLLARD-GOTT

the other dot categories. Multidimensional scaling was used to analyze the similarities. The degree of separation of the categories in the spatial solution was a function of the number of categorization trials. In the present study, themes and their variations function like the dot categories. After listening to a composition, subjects heard excerpted passages representing its two themes and their variations. They rated the similarity of all pairs of passages for multidimensional scaling analysis. The power of multidimensional scaling lies in its capacity to represent multiple features of structure in people’s responses to complex stimuli. When we use it to locate the musical passages in an n-dimensional space, we can observe which passages listeners hear as most related, and we can infer which musical dimensions played the greatest role in generating the observed pattern of relations. INDSCAL (Carroll & Chang, 1970) was selected because it permits analysis of individual differences, a feature important for listeners with differing musical backgrounds. Although it carries with it the strong assumptions of a metric scaling procedure, it has been found to perform well with musical stimuli (Gabrielsson, 1973; Berlyne, 1977; Hare, 1977; Shaw, Note 2). A spatial representation of relationships among the thematic passages was generated after the first and subsequent listening sessions. In this way, we could chart the progress of conceptual differentiation of the themes among a group of listeners. It was expected that theme categorization would appear gradually. Listeners may tend to group musical passages according to their common secondary characteristics (loudness, tempo, texture) at first. As they begin to appreciate the primary structural parameters of harmony, melody, and rhythm, their similarity judgments should increasingly reflect the thematic category structure. This change may manifest itself in the relative salience of the musical dimensions listeners focus on at different points in the acquaintance process. It was also expected that this process would be accelerated for experienced musicians. EXPERIMENT

1

In the first experiment, we show how the repeated listening procedure can be used to study musical appreciation. A group of listeners become well-acquainted with the Sonata in B-minor by Liszt, and they provide several kinds of data which can be used to monitor their progress in appreciating the sonata’s theme categories. Method

Subjects Fifty subjects were recruited from notices posted in the departments of psychology of music at Princeton. There were 24 participants in Condition III, repented listening,

and and

THEMATIC

CONCEPTS

IN

MUSIC

71

another 24 in Condition I, sing/e listening. All subjects provided musical background data on a preliminary questionnaire. About two-thirds of the subjects in Condition I and III were experienced musicians. An expert condition was created by two additional subjects, one of whom had studied and performed the sonata, and another who had written a critical analysis of it.

Materials Music for fistening tasks. Music materials for this study were drawn from the Sonata in B-minor by Franz Liszt. It is a work for piano solo in one movement, structured around two principal themes and three minor themes (Hopkins, 1971; Newman, 1969). The usual divisions of a sonata into exposition, development, and recapitulation are united into one closely structured movement. A performance by Vladimir Horowitz on disk served as the master recording from which stimulus materials were constructed. The reader is also referred to the score (Kalmus piano series, Belwin Mills Pub.). Subjects in the experiment heard the first 12 min of the sonata ending on measure 328. The selection has a natural break at that point, where a subsection of the composition ends and a new section begins, marked by the instructions “andante sostenuto” and the entrance of a subsidiary theme. This latter portion of the piece was not played for subjects. Eight target passages were selected and recorded separately. They represented four examples of each of the two principal themes, which shall be called Themes A and B. Passage Al (measures 8-13) and passage Bl (measures 13-17) are the initial expositions of these themes. Theme Al is a gap-fill melody (see Rosner & Meyer, 1982) which takes several large leaps at the beginning and moves up and down the scale filling those gaps. Hopkins (1971) calls it the “octave theme” because both hands play it in octaves. He calls Theme Bl the “knocking theme” because it raps out five staccato notes on the same pitch and then ends with a changing-note tag. The other passages are three variations each on Al and Bl. Passage A2 (measures 18-23) is a subtle variation which manipulates the melody by breaking it up into parts and distributing these parts in a new way. All the elements of the melody are still there, although the rhythm and accompanying harmonies change. A2 is faster and more varied in texture than Al. It also builds to a crescendo where Al was uniformly loud. Passage A3 (measures 123- 139) is primarily a transposition of the melody to the relative major key (D) with some additional melodic ornamentation. This variation should be a challenge, since Frances (1958) found that changing mode from minor to major (or vice versa) made the theme more difficult to detect. The slowing of tempo and drastic reduction in loudness also contribute to its new flavor. In passage A4 (measures 177- 184), the melody is moved to the lower voice, with an interesting flurry of harmony above it. Listeners will have to be alert to hear the melody in the left hand. Again the tonal center is D-major. Passage B2 (measures 140- 147) is basically a tonal answer to Bl. That is, the melody is transposed, but all within the same scale, B-minor. B2 is very close to Bl and should be easy to associate with it. Passage B3 (measures 152-158) occurs in the same section of the piece as A3 and is correspondingly slow and quiet. The theme has been in the lower voice up to now. In this variation, it is transposed to a lilting D-major and raised to the upper register. The accompanying harmonies are manipulated and the melody embellished for a truly fresh variation. In passage B4 (measures 261-266), the theme is still in the upper voice, but with a new and sonorous accompaniment. The theme is repeated in two rapid bursts and builds to a loud climax. Passages B3 and B4 should be hard to associate with the parent theme Bl if its low pitch is taken to be a criteria1 feature. The melody is preserved over changes in register, and listeners’ skill in detecting such invariance is tested here.

72

LUCY POLLARD-GOT7

The selection of the eight passages was governed by the desire to provide a test of the emergence of thematic concepts, the growth of discrimination between the two themes and their variations. To produce such a test, it is necessary to find themes that are similar enough and variations subtle enough that the task of theme discrimination is not trivial. The theme structure should not be obvious at first hearing, but should require a real learning process that takes place with repetition, The Liszt sonata had just these desirable attributes. Specific passages were selected in order to eliminate or at least minimize the presence of “redundant relevant cues” (Trabasso & Bower, 1968),which might give the illusory appearance of theme discrimination. For example, if all of the A passages were loud and all the B passages were soft, we might find that the passages were grouped with their respective themes. But this could not be attributed solely to thematic discrimination, since dynamics can serve as a redundant relevant cue. To prevent this, an effort was made to balance some important dimensions across themes. For each theme, two passages were loud (Al A2; Bl B4) and two were soft (A3 A4; B2 B3). Two were in the key of B-minor (Al A2; Bl B2) and two were in D-major (A3 A4; B3 B4). The voice in which the theme was presented was also varied. Theme Al is played in unison by both hands. It occurs primarily in the lower voice in A2, back to the upper voice in A3, and in the lower in A4. Theme B occurs in the lower voice in Bl and B2 and in the upper voice in B3 and B4. We can also check how well the theme categories are balanced by using the final adjective scale ratings. Listeners will be rating the target passages on scales such as Loud-Soft, Fast-Slow, Happy-Sad. We wanted the values for passages from both Theme A and Theme B categories to be spread over these scales. We also made sure that the combined values on all these scales did not discriminate between theme categories. The eight passages were recorded on cassette in the order of their occurrence (Al, B 1, A2, A3, B2, B3, A4, B4) and in all possible pairs for the similarity judgment task. (See design for details of list construction.) Cfassijhtion test. In addition to the eight target passages, there were eight new passages, four new variations each of the A and B themes. These were selected from the second half of the composition that subjects had not heard and served as new transfer items. There were an additional eight passages that were designated as instances of neither the A nor the B theme. Four were old, from the sonata selection played to subjects, and four were new. The neither passages included the three subsidiary motives and variations on them. Adjective rating tusk. A set of fifteen 11-point, bipolar adjective scales were prepared to obtain ratings of the target passages. They fell under a list of headings derived chiefly from Getz (1966) and Gabrielsson (1973). They are tempo (Fast-Slow); dynamics (Loud-Soft); rhythm (Firm-Flowing); melody (Melodious-Unmelodious, Smooth-Jumpy); pitch (High-Low); sonority (Thin Sound-Rich Sound); mode (Major-Minor); mood (HappySad, Light-Heavy, Strong-Weak, Playful-Assertive); form (Simple-Complex); and activity (Active-Passive, Calm-Energetic). While no list is exhaustive, these scales were intended to tap many of the important primary and secondary parameters of music. In addition, they covered the characteristics mentioned by listeners in their written observations about the music.

Procedure Listening tusks. In the first session, the participants, who were tested in groups of four or less, were introduced to the purposes of the experiment. It was explained that they would be hearing a piece of music and that their job was to learn as much as possible about it through careful listening. Listeners were not informed of the name of the selection or its composer. It was largely

THEMATIC

CONCEPTS

IN

MUSIC

73

unfamiliar to subjects. They were not alerted to the presence of themes and variations, nor were they instructed in any way on sonata form. It was emphasized that they should make an active effort to understand the structure and properties of the piece. A number of tasks had been devised to facilitate this process. The first of these was listening and notetaking. The selection from the Liszt sonata was played (lasting about 12 min). Then the eight target passages were played in their order of occurrence in the piece, and subjects wrote observations about each passage on an index card. It was suggested that they write down comments which might help them to remember or identify that passage later, just as one would jot down the important ideas from a lecture to help organize and remember it later. (Analysis of these protocols will not be taken up in this paper. The major finding was that nonmusicians tended to discuss each passage in isolation, whereas musicians made comments which related one passage to another.) After this initial acquaintance process, it was suggested to subjects that they could now improve their understanding of the music by thinking about the relations among the passages. They would do this by comparing pairs of passages and judging their similarity on an 1l-point scale (l-extremely dissimilar, 1l-extremely similar). Similarity data were collected for all pairs of passages (see design details). This ended the first phase of the experiment. When subjects returned for the second and third sessions (all within a week), they followed the same basic procedure. However, they were encouraged to take advantage of the opportunity to hear the composition again by writing new observations about each selected passage. Further, when pairs of passages were played again, subjects were instructed to base their similarity judgments on their current understanding of the composition, as reflected in their new observations. The repeated listening procedure is summarized in Table 1. The repeated listening subjects (Condition III) performed these tasks in hour-long sessions on 3 separate days within a period of a week. The single listening subjects (Condition I) went through the process only once. Chssifcation test. The classification test was administered after all the similarity data had been collected at the end of either one or three sessions. The participants were told for the first time that the music they had been hearing contained two themes that were developed throughout the composition. They were informed that the themes were among the passages they had been working on. At this point, Passages Al and Bl were played and labeled as Themes A and B. The subjects were briefly instructed on the nature of themes and variations. Then subjects were told that a set of passages would be played, some old, and some new from the second half of the composition. They were to decide whether the passage was best described as an example of Theme A, Theme B, or neither, and check one of these on their answer sheet. They were told to expect about an equal proportion of each type. Before the classification test began, Themes A and B were played again and the subject was asked to identify them (B came first this time). Testing began after subjects demonstrated that they knew which was which. The last two items in the list of 24 passages were always Theme B and Theme A. They were included as a check on whether the subject still knew which was which at the end of the test. If the subject got either of these mixed up, then that subject’s classification data were invalidated. Adjective rating tusk. After the classification test, subjects were given a questionnaire with the 15bipolar adjective scales, a new set for each of the eight passages to be rated. The subjects were instructed to circle 1 point on each scale. They were not required to answer the Major-Minor scale if they did not feel sure of their knowledge on that dimension. The eight target passages were played in one of four random orders. Subjects answered all the rating scales for one passage before going on to the next one.

74

LUCY

POLLARD-GOTT

TABLE 1 Outline of Repeated Listening Procedure Session 1 Listen to entire musical selection. Write observations about each selected passage. Rate the similarity of pairs of passages. Sessions 2 and 3 Listen to entire musical selection again. Write something NEW about each passage. Rate the similarity of passages again. At the conclusion of data collection, the name and composer of the music were revealed. The purpose of the study was explained more fully, and questions and comments were solicited from the participants.

Design Simifurity judgments. Each subject received a list of 28 paired comparisons in the similarity task. This is the number of pairs in a lower-half 8 x 8 matrix (minus the diagonal). Thus, each passage occurred once with each of the seven remaining passages. Balancing of the order of passages within a pair was achieved in the following way. In a given list, half the A passages and half of the B passages occurred three times in first position and four times in second position. The other A and B passages occurred four times in first position and three times in second position. Then, a mirror-image list was constructed in which the pair orders were reversed. Half the subjects in a condition received one pair order and the other half the reverse pair order. Three random orders of the list of pairs were generated. With the mirror-image lists, this makes a total of six lists: 1,2, 3, la, 2a, 3a. In Condition I, four subjects received each of the six lists for a total of 24 subjects. In Condition III, the orders were rotated through the three sessions according to a 3 x 3 Latin square. There were six different combinations of the three presentation orders by two pair orders. Each of the six combinations were given to four subjects for a total of 24 subjects in Group III. ChssificatiOn test. The set of 24 passages that was used in the classification test included eight of Theme A, eight of Theme B, and eight of neither. In each category, four were old and four were new. The old A and B passages were the targets in the similarity task. The new passages were drawn from the second half of the sonata, not played for subjects. Three list orders were generated by randomizing these passages with the exception of Themes Al and Bl. They always occurred at the end of the list to check memory for the standards. One-third of the subjects received each of the three list orders. This was balanced between groups of subjects who had received the original pair order in the similarity task (Lists 1, 2, or 3) and those who had received the mirror-image lists (la, 2a, or 3a). Adjective rating tusk. Six versions of the listener questionnaire were prepared by randomizing the 10 headings representing various musical dimensions. Four orders of the eight target passages were recorded on tape for presentation. Each of the 24 subjects in Conditions I and III were given a unique combination of passage presentation order and questionnaire version (4 x 6 = 24). In this way, the questionnaire results for Condition III serve as a replication of Condition I. This may be useful, because ratings on some of the dimensions might be affected by the number of exposures to the music.

THEMATIC

Results

CONCEPTS

IN

MUSIC

75

and Discussion

We wanted to know to what extent subjects acquired the main conceptual categories of the composition, that is, to what extent had they appreciated its two major themes. We had two kinds of data to answer this question: (1) judgments of similarity among thematic passages, and (2) performance on the explicit classification test. A third source of data, ratings of the passages on 15 bipolar adjective scales, was useful in interpreting the similarity data. We also wanted to determine the effect of repeated listening on the acquisition of theme categories. Before turning to the major results we should consider the musical background of the participants. Results of Musical Background Questionnaire The average experience of the participants was calculated for four indices: number of music courses taken, years of performing experience, years of piano instruction, and maximum years of instruction on any instrument. The means were 2.79, 6.58, 3.96, and 6.67, respectively, for single listening subjects (Condition I) and 2.12, 6.50, 3.33, and 7.29 for repeated listening subjects (Condition III). None of the differences between Groups I and III was significant (t < l), nor were they all in the same direction. Subjects in these two conditions can be treated as roughly equivalent in musical background. The two experts were both very experienced on each of these indices. One of the experts, who had played the sonata, had 13 years of piano instruction and 10 years of performing experience. The other expert listener had studied and performed on the flute for 11 years. She had taken three music courses, and for one of these she had written a critical analysis of the Liszt sonata for her term paper. Adjective Scale Data The mean rating of each passage on each of the 15 bipolar adjective scales (Loud-Soft, Fast-Slow, etc.) was computed for the data obtained in the single and repeated listening conditions. The two listening groups were largely in agreement on the placement of the passages on each scale. For 11 out of the 15 scales, both the Pearson and Spearman correlations of passage means are .97 to .99 and highly significant (p < .OOl). Three of the remaining scales achieve correlations of .90 or better (p < .002). The Simple-Complex scale falls somewhat short of this with a Pearson correlation of .88 (p < .004) and a rank-order correlation of .85 (p < .Ol). On none of these scales do all of the A passages appear on one end of the scale and all the B passages on the other. None of the scales, taken singly, permitted complete discrimination of the themes. But we also

76

LUCY POLLARD-GOTT

checked to see whether passages in the same theme category shared similar values on a number of different scales at once. Each passage has associated with it a mean value on each of the 15 adjective scales. These mean values can serve as clustering variables in Johnson’s (1967) hierarchical clustering program (complete link method). (The program was run on the Statistical Analysis System (SAS). Its CLUST program accepts a list of stimulus values, such as these adjective scale means, as clustering variables. It uses them to compute the required similarity and distance matrices internally. No similarity matrix is input by the user.) Passages that are close to each other on a number of adjective scales will tend to be strongly clustered. The clustering diagrams derived from adjective scale means collected after single or repeated listening are shown in Fig. 1. They are remarkably similar. For both solutions, each cluster contains passages from both the A and B themes. Thus, the control of passage characteristics across theme categories appears to have been successful so far as these characteristics are concerned. If thematic categories are observed in the similarity data, we cannot attribute them to any one of these scales or their combination. The theme categories are not to be found in secondary parameters, but only in the primary parameters, their distinctive melody and rhythm. In addition, we find that repeated listening has very little effect on how loud or soft, fast or slow, and so on, the passages sound. These perceptual

2 3 4 5 6 7 8‘?lKl Al

61

SINGLE

82

A2

B4

LISTENING

A4

A3

83

CONDITION

2 3 4 5 6 7 6‘m Al

81

REPEATED

82

A2

64

LISTENING

A4

A3

B3

CONDITION

FIG. 1. A cluster analysis of Liszt passages belonging to Theme A (Al-A4) and Theme B (B 1- B4) was performed to ensure that characteristics measured by the adjective scales were distributed between theme categories. Mean ratings on the 15 adjective scales obtained in single and repeated listening were used as clustering variables (see text). Notice that each cluster contains both A and B exemplars.

THEMATIC

CONCEPTS

IN

MUSIC

77

dimensions are fairly stable and accessible to the listener. The similarity data show that repeated listening affects the listener’s appreciation of more subtle conceptual relations among musical passages. Similarity Data Explanation of SZNDSCAL program. Similarity data collected from subjects in each session were analyzed with the aid of SINDSCAL, a version of INDSCAL, the individual scaling technique developed by Carroll and Chang (1970). The inputs to this program are lower-half similarity matrices excluding the diagonal (one for each subject) for the target items, in this case eight musical passages. For a given dimensionality, both a stimulus space and a weights space are computed. The stimulus space locates each of the nine passages in a multidimensional space by treating similarity as proximity and using a weighted metric algorithm to compute the scaled values. The correlation of the observed values with the predicted values produced in the scaling solution is computed after each iteration. When the program’s criterion for a solution is reached, this correlation squared or R2 value can be interpreted as the proportion of variance in the similarity data that is accounted for by the scaling solution. The larger this R2 value, the better the fit. (This is a goodness-of-fit measure, rather than a stress measure, which is computed in some other programs.) Ideally, one seeks the solution of lowest dimensionality that accounts for a substantial proportion of the variance. Another feature of SINDSCAL is that a unique solution is generated with fixed axes. The least-squares algorithm used in calculation arrives at a solution which maximizes the proportion of variance accounted for in both the stimulus and weights spaces. The weights space embeds subjects in a space of the same dimensionality as the corresponding stimulus space. The position of a subject in the weights space indicates the contribution of that subject’s data to the overall solution. The coordinates can be interpreted as the subjective importance of each dimension to that subject or the weight attached to it. The underlying model assumes a common stimulus space with individual differences arising only in relative perceived importance of the dimensions. For a given individual, the stimulus space may be an expanded or contracted version of the overall stimulus space, depending on the weighting of each of the dimensions. The farther a subject’s point is from the origin of the weights space, the more variance in that subject’s data is accounted for and the better the fit of the overall scaling solution to that subject’s data. The stimulus space is an average over all these subject weights. Emergence of theme dimension in group solutions. Although other musical dimensions are important at first, a dimension representing theme category steadily gains in prominence with repeated exposures. This

78

LUCY

POLLARD-GOT7

theme dimension was not present after one listening session, but gradually emerged and developed after a second and third opportunity to listen. Finally, the theme dimension achieved preeminence for expert listeners who had had extensive experience with the composition. Separate multidimensional scaling solutions (INDSCAL) were computed for the similarity data collected in Sessions 1, 2, and 3 of the main repeated listening condition. In addition, solutions were also obtained for the single listening condition and for the two experts. The dimensionality of each solution was arrived at using two accepted criteria (Shepard, 1972; Ryan & Hurtig, 1980). First, the number of dimensions in each possible solution was plotted against total variance accounted for (R*) by that solution. When the curve begins to level off, additional dimensions are not adding much to the goodness of fit of the solution. Second, the interpretability of the dimensions was considered. The first few dimensions are usually quite straightforward, but higher dimensions often seem obscure. For the single listening condition and the first session of repeated listening, three-dimensional solutions were arrived at. Each of these accounted for about 60 to 65% of the variance. For Sessions 2 and 3, fourdimensional solutions were most appropriate, accounting for 67% of the variance. The new fourth dimension represents the theme category of the passages, with all the A passages on one side and all the B passages on the other. In Session 2, the theme dimension first emerges, and by Session 3, the themes are clearly differentiated into two distinct groups. The positions of the passages on each dimension of the INDSCAL solutions are shown in Fig. 2. The proportion of variance accounted for by each dimension is given to the right. Each dimension was interpreted with the aid of ratings of each passage on a variety of adjective scales. Fits were obtained by correlating the INDSCAL coordinates for a given dimension with the mean ratings of passages on an adjective scale that was a potential match to the INDSCAL dimension. In Table 2, Pearson product-moment correlations with all relevant rating scales are presented for each of the four solutions. The first dimension was either smoothness or pitch. For these particular passages, these dimensions have much in common. Passages A3 and B3 are both high pitched and smooth. The more rhythmic and varied passages, Al and Bl, are also low in pitch. Loudness describes the second dimension very well in each case except Session 2 (111(2)) where Happy-Sad gives a better fit. The third dimension in each of the solutions is best described as Simple- Complex. The Simple-Complex dimension is marked by the closeness of Theme Al to its variation, A3. They share the same unadorned melodic line, although played in different keys, and are rated

THEMATIC

CONCEPTS

IN

79

MUSIC

A. -6-5-4 . .

-I 0 . . . SESSION A3

-3-2 .

.

DIM I BY

HIGH DIM2

I .

2 .

3 .

4 .

6VAF .

I I 2891 8”:

*& *54s,

84Al

5 .

81 LOW il94)

9;3pi3

SPFT t 174)

LOUD DIM 3 A3

93

Al

SIMPLE

SESSIOtL? A4 “,4(

HAPPY DIM 3

A2

*,

SIMPLE DIM4

I2921 92*2

81

A3pll

83

84

83

81

COMPLEX (068)

93 y2

THEME A

SESSION DIM I

LOUD DlM3

A2 A4

Al

BI 93

A3

SIMPLY’ DIM4

A4

82 94

AI *2 A3

A4 A

9

Al B,

02

“B”, A2

03 84

THEME

3 ( 2221

A4

HIGH DIM2

THEME

( 1511

*2*4 82

A2 81

A3

JUMPY ( 159) s*D

81 82

*3 :a

84AI

LOW I2111

93*3

*2g,

SOFT II471

62

COMPLEX (0911

~819483

THEME

9

0. -.6 -.5 -.4 -.3 -.2 -,I . . . . . .

0 .

_I .2 .3 . . .

.4 .

.5 .

.6 VAF . (283)

DIM I A393 SMOOTH DIM2 94141 LOUD DIM 3

A2

A4 A4

A2

8411 El

92

81 JUMPY I 2281

02 *3 83 *4

*39

AI

83

I

,“,’

SOFT 1134)

A2 COMPLEX

SIMPLE

C. DIM

A3

I

h2

*I THEME

A

A4

BI 828843

I.9361 THEME

8

FIG. 2. The main multidimensional scaling results are presented here. The positions of the Liszt passages are plotted on each SINDSCAL dimension for (A) three repeated listening sessions, (B) single listening, and (C) the expert condition. An interpretation of each dimension is given, as well as the variance accounted for by each dimension (VAF) in its particular solution.

very simple. Although the fits are not outstanding (nonsignificant in Session 3), the major features of the third dimension coincide with the Simple-Complex scale in each case. It would be unparsimonious to seek a different interpretation just for Session 3, since it is well correlated with the third dimension in Sessions 1 (r = .86, y < .006) and 2 (r = .90, p < .002). Better fits might have been obtained by combining some of the adjective scales, but this level of precision was adequate for our purposes. In single listening and each session of repeated listening, the first three dimensions represent a sampling of the variety of extrathematic dimensions which characterize the selected passages.

80

LUCY POLLARD-GOTT TABLE 2 Correlations of Adjective Scales with SINDSCAL Dimensions Condition I

Dimension 1 I:Firm-Flowing

Rhythm

III:Firm-Flowing

Rhythm

I:Melodious-unmelodious III:Melodious-unmelodious I:Smooth-Jumpy

Melody

III:Smooth-Jumpy

Melody

I:Strong- Weak III:Strong- Weak

III:High-Low

III:Loud-Soft

.82 t.011 .85 C.01)

.98 (.ooll .98 (.ool)

.93 (.ool) .94 (.OOl)

.89 (.tJo3) .89 (.flb31 .83 t.011 .84 t.011

III:Happy-Sad

III: Simple-Complex

III (3)

.99 (.OOl) .99 (.OOl)

I:Happy-Sad

Dimension 3 I:Simple-Complex

III (2) .96 (.OOl) .99 (.OOl) .94 (.OOl) .94 (.c@l) .97 (.Wl) .97 (.OOl) .98 (.OOl) .99 (.OOl)

.94 (.ool) .89 (.003) .95 (.OOl) .94 (.OOl) .86 ( ,005) .88 (.tJo4) .82 (.Oll .82 (-011

I:High-Low

Dimension 2 I:Loud-Soft

III (1)

.86 C.01) .97 (.OOl)

.77

C.02) 64

C.08)

.73 (J-w .73 (.041

.60

c.121 .55

C.16)

Nore. Parenthetical number is level of confidence. A new fourth dimension is added in Sessions 2 and 3. It marks the emergence of theme structure in listener perceptions of the relationship holding among the passages. In the second session, the passages belonging to Theme A are on one side and those belonging to Theme B are on the other, although they are not tightly grouped. Passage A2, which is the most difficult variation of Theme A, is least clustered with the other A

THEMATIC

CONCEPTS

IN

MUSIC

81

passages at this point. It shares key and some harmonic elements with neighboring Passage B 1. By the third session, the fourth dimension is more well differentiated into two distinct theme clusters. Passage A2 has been brought into the center of the A cluster, and the stimulus values are more bimodal. Therefore, the dimension is more indicative of a theme concept where any given passage falls into one of two distinct categories, A or B. After three listening sessions, the theme dimension is still only fourth in importance, accounting for only 9% of the variance of the similarity data. Theme is just beginning to play a role in subject’s perception of the composition. It would be desirable to extrapolate these results to listeners who have had many more exposures. The two experts on the Liszt sonata fell into this category, since they had extensive experience to bring to the task. They provided similarity data for the target passages in a single session as in Condition I. In the experr solution, the theme dimension emerged as the preponderant source of variation accounting for 83.6% of the variance in a onedimensional solution (see Fig. 2 for passage positions). For these experts, theme was the most important basis for similarity judgments, the dominant relationship holding among sonata passages. One expert commented that after the similarity task was over, he realized that there might have been other criteria for judging similarity such as relative loudness. Yet when he heard the passages, their thematic relations were compelling and seemed to be the only natural basis for comparing them. What about other musicians in the repeated listening group? Perhaps the theme dimension was more salient for them too, even after two or three sessions. This question can be answered by referring to the subject weights for the theme dimension computed by INDSCAL. From the background questionnaire, 15 sophisticated musicians were identified, and the remaining 9 had had little or no formal training. Musicians gave higher weight on average to the theme dimension in Session 2 (MannWhitney U = 36, p < .OS,one tailed) and session 3 (U = 36.5, p < .05) than did nonmusicians. Even though the theme dimension was fourth in importance in the group solution, there were four musicians in Session 2 and three in Session 3 for whom theme was the most important dimension. Individual

Conceptual

Attainment

We have seen evidence for an emerging theme dimension in the group multidimensional scaling solutions of the similarity data. We would also like to examine more detailed information about individual behavior on the similarity task. Conceptual structure ratios can be constructed for individuals on the basis of their similarity matrices (Hartley & Homa,

82

LUCY

POLLARD-GOTT

1981). A conceptual structure ratio compares average within-category similarity to average between-category similarity. A ratio greater than 1 indicates high conceptual clustering since category members are rated as highly similar to one another and items from different categories are rated as dissimilar. Ratios less than 1 indicate low conceptual clustering. In one sence, the task was designed to be very difficult. The balancing of extrathematic characteristics of the passages tended to produce between-category similarity. Many subjects did not produce conceptual structure ratios greater than 1 even after three listening sessions. The distributions are skewed toward the lower end, as we would expect if extrathematic dimensions were dominating the similarity structure. The mean ratios in Session 1 were .87 and .93 for A and B, respectively. (In Condition I, they were .94 and 1.00.) By Session 3, the mean A and B ratios rose very slightly above 1, at 1.02 and 1.14. The distributions deviated so greatly from normality that the usual parametric tests were inappropriate. The Wilcoxon signed-ranks test for related samples was performed to test for an increase in individual conceptual structure ratios from Session 1 to Session 3. There was a significant increase in the clustering index for Theme B (p < .05). The effect approached significance for Theme A (p < .lO). For those listeners with ratios above 1, it is also meaningful to look at levels of differentiation. A and B ratios greater than 1.2 or 1.4 are more suggestive of category discrimination than ratios barely greater than 1. The number of people at each level of concept attainment were tabulated across sessions. That more people achieved conceptual differentiation in Session 3 than in Session 1 is shown in Table 3. This was true for each level of concept attainment, indicated by the cutoff points. As the criteria are moved to higher and higher degrees of differentiation, they are only reached in the later sessions. There were no ratios greater than 1.6 in Session 1, only one in Session 2, and a total of five in Session 3. The largest conceptual ratio of all occurs in Session 3 for Theme B. With repeated listening, more people base their similarities on thematic catew-y. These data do not include the two experts. As expected, their conceptual structure ratios are large. Their A ratios were 2.5 and 1.7 and their B ratios were 3.0 and 2.2. Classification

Data

Overall performance. The similarity data measure concept acquisition indirectly, because listeners are not advised to use any particular criterion to rate passage similarity, and no mention is made of the theme structure. Even so, thematic structure appeared to play a greater and greater role in listener judgments with repeated listening.

THEMATIC

Levels of Conceptual

CONCEPTS

83

IN MUSIC

TABLE 3 Differentiation with Repeated Listening Number

Session Conceptual

Conceptual

Conceptual

Conceptual

Conceptual

Conceptual

ratios 1 2 3 ratios 1 2 3 ratios 1 2 3 ratios 1 2 3 ratios 1 2 3 ratios 1 2 3

Theme A

Theme B

5 8 10

6 15 12

2 4 6

3 4 5

1 2 3

0 3 3

0 0 2

0 1 3

0 0 1

0 1 2

0 0 0

0 0 1

> 1.0

> 1.2

> 1.4

> 1.6

> 1.8

1 2.0

Note. N = 24.

A classification test measures people’s explicit knowledge of theme categories. Such a test was administered at the conclusion of the final listening session, where subjects were apprised of the theme structure for the first time. Confusion data from that test will be presented and then its relation to the more implicit similarity measures of categorization will be explored. The dependent measure used in scoring the classification test was number of confusions between Theme A and Theme B passages. A confusion occurred when an A passage was called a B passage or vice versa. “Neither” passages were included to foil an A-or-not-A strategy of responding. Many of the Neither passages, although based on subsidiary motifs other than the main themes, were harmonically related to the themes and so they posed problems for some subjects. Some listeners adopted a very strict criterion, calling too many passagesNeither, whereas others were very liberal and categorized nearly all passages under one or

84

LUCY

POLLARD-GOTT

the other theme. The index of confusion between A and B counts only errors of commission. It is the discrimination measure most analogous to the conceptual structure ratios and theme dimension weights. Few confusions indicate that the listener has both theme categories differentiated. The most important confusion error is between the themes themselves, PassagesAl and B 1. Subjects who did not categorize the themes correctly at the end of testing were not included in further analyses. In each of the single and repeated listening conditions, there were two listeners out of 24 who were mixed up about one or both themes by the end of the test. These four subjects were all nonmusicians. None of the musicians confused the standard themes. For the remaining test items, the mean number of confusions was 3.14 after single listening and 2.77 after repeated listening. The reduction in errors from the single listening group to the repeated listening group was not significant, t < 1. Confusions made by musicians and nonmusicians were also totaled separately. They made equivalent numbers of errors in the single listening condition (M = 3.2, N = 15 musicians; M = 3.0, N = 7 nonmusicians). In the repeated listening condition, however, musicians made significantly fewer confusion errors (M = 2.33) than nonmusicians (M = 3.71, t(20) = 2.17, p < .04). Musicians profited more, it seems, from the repeated listening experience. Finally, the experts, who were most experienced with the piece, made no confusion errors. Relation of confusions to theme dimension weights. We would predict that people for whom the theme dimension was highly salient in the INDSCAL spatial representation would tend to make very few confusions. (The reverse may not be true. People who gave low weight to the theme dimension in the similarity task may “discover” the themes categories when the classification test is explained and the two themes are revealed.) In Fig. 3, confusions are plotted against INDSCAL weights on the theme dimension for subjects in multiple listening sessions to assess the possible relationship. Although errors are plotted as equal intervals, there may be much more psychological difference between 0 and 1 confusion than between 5 and 6 confusions. The two experts had the highest theme dimension weights and made 0 confusions. A regression analysis was performed to fit a line through the data as shown. The model accounts for 32% of the variance, a significant proportion, F( 1, 22) = 10.33, p < .004. We can see that listeners who gave very high weight to the theme dimension tended to make very few confusion errors in classification. Although there is a small, significant linear trend, the data are fairly noisy. In Experiment 2, we return to the relationship of theme dimension weight to classification accuracy. The question of transfer. There was no effect of old versus new exemplars of the themes in the classification test. If anything, the new

THEMATIC

CONCEPTS IN MUSIC

85

IO-

i k ” g

z7-

:,

6-

z

.5-

$

4-

0

3-

2

2-

F

I-

.

.

. . : i

*

\______

O-

l

l

l

. :

. .

. .

l

-.I -

11

I I 01234567

II

fi

1

I

TOTAL THEME CONFUSIONS

FIG. 3. For each subject, the number of confusions between Themes A and B in the classification test are plotted against individual weights on the theme dimension. Data are from the final session. The best-fitting line is drawn through the points. 0, Repeated listening subjects (Condition III); X, expert subjects.

exemplars were easier to classify than the old. The percentage of confusion errors in Condition I were .25 for the old passages and .20 for the new. In Condition III, the percentage of errors were .21 and .19, respectively . Experiment 2 presents a new transfer task that asks listeners to supply similarity judgments between all pairs of the transfer passages. A multidimensional configuration of transfer passages can then be computed just as it was for the original passages. By comparing the similarity structure of new, transfer passages after single or repeated exposures to the old target passages, the effect of repeated exposure on transfer can be investigated . EXPERIMENT

2

In this experiment, new groups of subjects were exposed to the Liszt sonata. This furnished the opportunity to replicate the finding of an emergent theme dimension for the target passages. In addition, listeners provided similarity judgments for the transfer passages, i.e., the exemplars of Themes A and B from the latter part of the sonata that is never played for them. The prediction is that after multiple exposures to the old target passages, listeners will impose a greater degree of conceptual structure on the new transfer passages. Method

Subjects Twenty-four Princeton students participated in the third study. Twelve of them came for three sessions (Condition IIIb) and 12 for a single session (Condition Ib). One of the single-

86

LUCY POLLARD-GOTT

session participants was found to be an expert. She was a 4th-year graduate student in music and was well acquainted with the Liszt sonata, although she had not played it herself.

Materials The transfer passages for this experiment are the same ones that served as new exemplars of A and B in the classification test in Experiment 1. They were taken from the part of the sonata that was not played for subjects. Passage AS (measures 354-357) is an ornamented variation of a fragment of Theme Al. Passage A6 (measures 507-516) pits two variations of the theme against each other. In the upper voice, each note is doubled and the rhythm is syncopated. At the same time, the inversion of Al is played in the lower voice. Passage A7 (measures 639-646) is very much like Passage A4, only faster, with harmonized runs played over top of the theme. Passage A8 (measures 735-741) incorporates a change of key and some harmonic variation in the accompaniment. Passage B5 (measures 347-353) plays Theme Bl in octaves in the upper voice, with ornament at the end. Passage B6 (measures 431-440) transposes the theme to the 3rd and 6th scale degrees. Passage B7 (measures 593-597) recapitulates part of Theme B in the original key of B-minor. This time, however, it is played fortissimo in both hands without the staccato treatment and is transposed within the scale. Passage B8 (measures 727-734) repeats the thematic figure as an ostinato bass and harmonizes in chords above it. The transfer passages are in a wider variety of keys than the original targets. The progression of keys is as follows: B5 and A5 in A-major; B6 in F-sharp major; A6 in A-minor; B7 in the main key of B-minor; A7 in its parallel major, B-major; and finally, B8 and A8 in G-sharp minor. The total number of passages in major and minor keys are again balanced between theme A and theme B.

Procedure Listeners became acquainted with the sonata and provided similarity judgments for the old passages in one or three sessions as in Experiment 1. Then the transfer similarity task was administered. It was explained that the purpose of this task was to see how well they could apply their current understanding (gained in one or three sessions) to new passages from the same composition. The new passages were played for them once and then pairs of the passages were played. Subjects were told to rate the similarity of each pair just as they had been doing for the old passages. They did not write any observations about the new passages, nor did they hear the second part of the sonata in which they occurred. They were advised to use the same criteria in judging the new passages as they had just used for the old. When all the similarity data had been collected, the classification test was administered as before. Finally, subjects rated each of the transfer passages on the 15 bipolar adjective scales.

Design The paired comparison lists for the transfer passages were prepared in the same manner as the old passages. Six lists (1, 2, 3, la, 2a, 3a) were generated from three randomized list orders crossed with two (mirror-image) pair orders. Subjects received the transfer list with the same number as the old passage list for single listening or the last list for repeated listening. Transfer passages were recorded in order of their occurrence (B5, A5, B6, A6, B7, A7, B8, A8) and also in four random orders for use in the last phase of the study where the transfer passages were rated on 15 adjective scales. There were six versions of the rating questionnaire. Single listening subjects each received a unique combination of passage order and

THEMATIC

CONCEPTS

IN

MUSIC

87

questionnaire version. An assignment error in Condition IIIb caused two duplications of order-by-version combinations. However, this should not pose a serious design problem. since the ratings obtained in the two conditions serve as replications of each other.

Results

and Discussion

In the results, we first checked to see that theme emergence with repeated listening was replicated with the old passages. Then we focused on the results with the new passages used to assess transfer of thematic knowledge. Musical Background As in Experiment 1, there were no significant differences (t < 1) between Conditions Ib and IIIb on relevant indices of musical experience, and neither group was superior on all indices. Single listening subjects (Condition Ib) had had an average of 1.45 music courses, 6.64 years of performing experience, 3.18 years of piano instruction, and 4.73 years maximum of instruction on any instrument. The corresponding means for repeated listening subjects (Condition IIIb) were 2.17, 5.92, 2.58, and 5.42, respectively. The expert subject had had over 12 music courses and played both the violin (12 years) and piano (5 years). Similarity Data: Replication with Original Passages Experiment 2 replicates the emergence of the theme dimension with repeated exposures. Similarity data collected in the single listening condition and in each of three repeated listening sessions were submitted to INDSCAL for multidimensional scaling analyses. The principal dimensions in early sessons were based on extrathematic characteristics such as were found in Experiment 1: pitch, smoothness, complexity, dynamics, happiness, and one new dimension, activity. A thematic dimension consistent with the categories of A and B passages emerged in Session 3 of repeated listening. The expert subject produced similarity data dominated by a single theme dimension. Only two dimensions were needed to describe the results after one or two listening sessions, whereas three dimensions were adopted for the third session. Passageratings obtained in the previous study were used to interpret these dimensions. The dimensions for the single listening condition (Ib) were well described by pitch (v = .98- .99,p < .OOOl)and activity level (v = .99). For repeated listening subjects, the first dimension in Sessions 1 and 2 corresponded to smoothness. Pearson correlations with the relevant adjective scales were all above .90 and highly signiticant. The first dimension in the third session was interpreted as either dynamics or strength (r = .93-.94, p < .OOl). The second dimension in each of the three sessions was consistent with either Happy-Sad or Simple-Complex. Correlations ranged from .76 to .96 and were significant (p < .03).

88

LUCY

POLLARD-GOTT

The third dimension in Session 3, however, does not correspond to any of these extrathematic dimensions. It is an emergent theme dimension. One passage, A4, does overlap with the B passages. This second sample of listeners had not reached the same level of theme differentiation after three sessions as subjects in the previous study did. (Only one subject achieved a conceptual structure ratio greater than 1.6 in Session 3.) However, the A values are greater than the B values by Mann- Whitney test (p = .029, one tailed). The expert subject, with the benefit of multiple past exposures, differentiated those passages belonging to Theme A and Theme B much more decisively. Her theme dimension is bimodal as it was for the experts in the previous study. With only one session, her conceptual structure ratios were 1.5 and 1.9 for themes A and B, respectively. Adjective

Scale Data:

Transfer Passages

The ratings of transfer passages provide information on their baseline relatedness on a number of extrathematic dimensions. Examination of the mean ratings on each adjective scale revealed no single criteria1 dimension for discriminating Theme A from Theme B exemplars. Yet there does appear to be a bit more within-category similarity than existed for the old theme exemplars. Passages B5 and B6 are similar in tempo, dynamics, smoothness, sonority, mode, and activity. Passages B7 and B8 share tempo, pitch, smoothness, simplicity, strength, heaviness, and sadness. These two pairs of B passages are, however, on opposite ends of several dimensions, which must be bridged in order to appreciate their underlying thematic unity. Similarly for the new A passages, A6 and A7 are close in tempo, happiness, complexity, and activity. Passages A5 and A8 are on the other end of these same scales. Of course, between-category pairs (for instance, A6-B7, AS-B5, A8-B8) also share many characteristics. This is born out by the clustering diagrams for these passages based on the adjective scale data. That A and B passages are linked together in each major cluster is shown in Fig. 4. Even if the new exemplars of A and B are somewhat “easier” to discriminate, we can still assess transfer effects by comparing the level of discrimination of new passages after one or three sessions of experience with the old passages. Similarity

Data: Transfer Dimensions

Two-dimensional solutions were arrived at for the transfer passages in both Conditions Ib and IIIb. Passage positions on each dimension are given in Fig. 5. The first dimension in each case corresponds to the level of activity of the musical excerpt. For single listening, ratings of Active-passive and Calm-Energetic are highly correlated with the first transfer dimension (r = .90, p < .002; r = .96, p < .OOl). For repeated

THEMATIC

CONCEPTS IN MUSIC

2 3 4 5 6 7 8‘m A5 85 SINGLE

66 A8 68 A7 A6 07 LISTENING CONDITION

A5

05

2 3 4 5 6 7 8‘fi 86

REPEATED

A7

A8

B8

LISTENING

A6

07

CONDITION

FIG. 4. A cluster analysis of Liszt transfer passages, based on mean adjective scale ratings. As with the old passages (Fig. 11,the combination of these extrathematic characteristics yields clusters that cut across the boundary between theme categories.

listening, the correlations are equally high (r = .93,p < .OOl andr = .9&p < .OOl, respectively). The second dimension is consistent with theme category. After single listening, there is some overlap of the A and B exemplars but the A values exceed the B values by Mann-Whitney test (p = .029, one tailed). Is the second transfer dimension in Condition Ib truly a theme dimension? With the old passages, a theme dimension was not present after a single session in either Experiment 1 or 2. Therefore, it would be inappropriate to say 0 I .2 3 4 5 .6 * . . . . . . . . . . . .

-.6-5-4-,3-.2-l

SINGLE DIM I PASSIVE DIM2

86 E3 A3 A3

THEMEAI

DIM I 6 DIM 2

86

LISTENING A0

9.917

A6 96A0

06

REPEATED A3 E6 AE A3 A.9

THEMEA:

07 A0 97 Be

i 357) ACTIVE (.224) THEME

B

LISTENING

A6

(316)

00 *797 83 06

A6 80 07

i.185) THEME 9

EXPERT DIM I T”EME A

A6 A7

A6 A8

97

83 88

06

i 905) THEME 9

FIG. 5. Positions of Liszt transfer passages on SINDSCAL dimensions after single or repeated experience with old theme exemplars. Expert had only a single session.

90

LUCY

POLLARD-GOTT

that thematic knowledge gained from the old passages had “transferred” to the new passages. Learning must be demonstrated before it can be transferred. Then why is a dimension generated which most naturally conforms to theme category? In the previous section on passage ratings, it was found that the new passages had a pattern of within-category similarity which made them somewhat easier to separate into A and B categories. There may be some redundant cues that were not present for the original target passages. This may account for the early appearance of a themelike dimension. But after repeated listening, the similarities are not dominated by these extrathematic similarities, and transfer passages belonging to Themes A and B are clearly separated on the second dimension. This is true as well for the single theme dimension generated by the expert. We see a marked improvement in the closeness of the B passages as compared with the repeated listening solution. In addition, theme category was not second in importance for the expert, but the primary dimension, accounting for 90% of the variance in her transfer similarity data. Classification Data Overall performance. The classification test has a somewhat different meaning here than it did in Experiment 1, because none of the theme exemplars is completely novel this time. Of the 11 listeners in Condition Ib, only seven provided usable classification data. The others had confused the standards Al and Bl by the end of the test. The mean confusions of A and B for the other seven subjects was 3.28. In the repeated listening group, only one out of 12 listeners confused the test standards. The mean confusion for these 11 listeners was 2.73. Although listeners made fewer confusions on average after three sessions, this difference was not statistically significant. The level of classification performance was somewhat poorer in this study than in the previous one, since all subjects made at least one confusion. In Experiment 1, there were three subjects who made zero confusions. Even the expert listener made one confusion this time. Her weight on the original theme dimension was only .74 as opposed to .90 and .92 for the experts in the previous study. Relation of confusions to similarity data. This time, there are two different theme dimensions that might be related to confusions, one for the old passages and another for the new. Single listening subjects had no theme dimension for old passages, but they did produce a themelike dimension for transfer items. Subject weights on this themelike dimension did not bear much relationship to the number of confusions on the classification test. A linear regression model did not approach significance. Of course, this is a very small sample, only

THEMATIC

CONCEPTS IN MUSIC

91

7 pairs of points. Even so, there is reason to doubt that we are dealing with an authentic theme dimension after only one session. In Fig. 6, confusions are plotted against old theme weights (top graph) and new theme weights (bottom graph) for the multiple exposure listeners. In both diagrams, all the points lie in the lower left triangle. (This was also true in Fig. 3, Experiment 1.) Most points lie on the diagonal, such that low confusions are associated with high weight on the theme dimensions, and high confusions are predicted by low theme weights. There are a few outlying points in the lower left corner. These points represent listeners who did not give particular prominence to theme category during the similarity task. When the themes were revealed and the classification procedure was explained, however, these subjects were able to perform well. They made few confusions (one or two) even though they had not given high weight to theme before. It should not be too surprising that some people could benefit from the additional information provided in the classification instructions. It appears, then, that some

. Repeated Listening x Expert

0’1

”

”

0123456

”

TOTAL THEME CONFUSIONS IO9-

x

B.7-

.

ii

:\

2. I 0 ' ' ' 0123456

. '

'

'

'

TOTAL THEME CONFUSIONS

FIG. 6. Theme confusions in classitication test are plotted against weight on theme dimension for original passages (top) and transfer passages (bottom).

92

LUCY

POLLARD-GOTT

people distinguished theme categories during the similarity phase, whereas others only made the distinction at the time of test. There are no outliers in the upper right corner. That would mean that someone who had given high weight to theme in the similarity task could not discriminate theme members at test. This sort of inconsistency did not occur. The degree of relationship between confusions and theme weights was determined with simple regression. For the old theme weights, the model accounts for 18% of the variance, F( 1, 17) = 2.26,~ = .16, and 22% for the new theme weights, F( 1, 17) = 2.81, p = .12. The fits are poor as a result of the outliers which have just been described, representing subjects with few confusions, but low theme weights. Otherwise, the points do seem to be linear. For example, in the bottom graph, removing the single outlier in the lower left corner would bring the lit of the solution up to 50% variance accounted for, F(1, 16) = 9.14, p < .Ol. Let us summarize the transfer results. Listeners are asked to deal with new passages from a composition after hearing an earlier part of it and considering a set of its passages in lengthy paired comparisons. If they meet the new passages after only one session of this, their similarity judgments for the new passages do not follow theme category membership. At best, we find only an illusory theme dimension that is quite unsuccessful at predicting accuracy in a final classification test. If, however, listeners meet the new passages after they are thoroughly acquainted with the old section of the piece (through repeated listening sessions), their treatment of the new passages gives evidence of theme structure right away. They produce an authentic theme dimension which bears a significant relationship to classification accuracy. The fact that this relationship was rather weak showed us that classification performance depended not only on the notions of similarity among passages built up during the listening sessions, but also on the listener’s ability to take advantage of the special explicit instructions to classify at the time of test. CONCLUDING

COMMENTS

Listeners’ changing conceptions of a composition were investigated through repeated presentation and multidimensional scaling of short passages drawn from the composition. The relationships that listeners perceived among passages corresponded with higher order thematic structure after repeated exposure, but not after a single exposure to the music. The themes and variations in the Liszt sonata were deliberately chosen for their subtlety and the challenge they would pose to listeners, even experienced musicians. Discrimination of the two thematic categories de-

THEMATIC

CONCEPTS IN MUSIC

93

pended on the discovery of melodic invariants in the face of a host of other transformations which the composer brought to bear on the themes. As a theme is developed in a composition, it makes a complex journey through a variety of keys, moods, and textures. With thorough acquaintance, the mature listener comes to recognize the theme at the end of its travels, even though the changes have left their mark on its character. Experienced listeners seem to move more quickly from reliance on extrathematic, “perceptual” characteristics of the music to a more conceptual appreciation of a composition’s structure. Yet the underlying cognitive tusk may be the same for all listeners. Most important, this paper has introduced a naturalistic method for studying musical appreciation from a cognitive perspective. Its use has been illustrated with the investigation of the acquisition of themes as conceptual categories in a composition. It should serve for other questions and other pieces of music. The structure of a musical composition can be found in the relations of note to note, phrase to phrase, beat to beat, voice to voice, and chord to chord. This method asks what relations do listeners perceive and when do they perceive them. REFERENCES Berlyne, D. E. Dimensions of perception of exotic and folk music. Scienfific Aesthetics, 1977, 1, 257-270. Bransford, J. D., & Franks, J. J. The abstraction of linguistic ideas. Cognitive Psychology, 1971,2, 331-350. Carroll, J. D., & Chang, J. -J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition. Psychometrika, 1970, 35, 283-319. Copland, A. What to listen for in music. New York: McGraw-Hill, 1957. Duerksen, G. L. Recognition of repeated and altered thematic materials in music. Journal of Research in Music Education, 1968, 16, 3-30. Frances, R. La perception de la musique. Paris: La Librairie J. Vrin, 1958. (Second edition with English summary, 1972.) Gabrielsson, A. Similarity ratings and dimension analyses of auditory rhythm patterns. I and II. Scandinavian Journal of Psychology, 1973, 14, 138- 176. Getz, R. P. The effects of repetition on listening response. Journal of Research in Music Education, 1966, 14, 178- 192. Grove’s dictionary of music and musicians. E. Bloom, Ed. New York: St. Martin’s, 1960. 5th ed. Hare, F. G. Dimensions of music perception. ScientiJic Aesthetics, 1977, 1, 271-290. Hartley, J., & Homa, D. Abstraction of stylistic concepts. Journal of Experimental Psychology: Human Learning and Memory, 1981, 7, 33-46. Homa, D., Rhoads, D., & Chambliss, D. Evolution of conceptual structure, Journal of Experimental Psychology: Human Learning and Memory, 1979, 5, 11-23. Hopkins, A. Talking about sonatas. Exeter, NH: Heinemann Educational Books, 1971. Johnson, S. C. Hierarchical clustering schemes. Psychometrika, 1967, 32, 241-254. Kalmus Piano Series, No. 3639. Melville, NY: Belwin Mills Pub.

94

LUCY POLLARD-GOTT

Meyer, L. B. Explaining music: Essays and explorations. Chicago: Univ. of Chicago Press, 1973. Newman, W. S. The sonata in the classic era. Chapel Hill: Univ. of North Carolina Press, 1963. Newman, W. S. The sonata since Beethoven. Chapel Hill: Univ. of North Carolina Press, 1969. Rosch, E., & Mervis, C. B. Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 1975, 7, 573-605. Rosner, B. S., & Meyer, L. B. Melodic processes and the perception of music. In D. Deutsch (Ed.), The Handbook of Perception: The Psychology of Music. New York: Academic Press, 1982. Ryan, M. P., & Hurtig, R. R. Does the structure of the evidence base “cause” verdicts of guilty and innocent? Discourse Processes, 1980, 3, 231-261. Shepard, R. N. Introduction to Volume 1. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.), Multidimensional scaling. New York: Seminar Press, 1972. Vol. 1. Trabasso, T., & Bower, G. H. Attention in learning: Theory and research. New York: Wiley, 1968.

REFERENCE

NOTES

1. Welker, R. L. Abstractions of themes from melodic variations. Paper presented at the meeting of the Psychonomic Society, St. Louis, November 1980. 2. Shaw, M. Recognition of musical styles. Address delivered at Bell Laboratories, June 1980. (Accepted June 2, 1982)