Questioning a Melodic Archetype: Do Listeners Use Gap- Fill to Classify Melodies?

Transcription

1 Music Perception Winter 2000, Vol. 18, No. 2, BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA ALL RIGHTS RESERVED. Questioning a Melodic Archetype: Do Listeners Use Gap- Fill to Classify Melodies? PAUL VON HIPPEL Ohio State University and Stanford University Leonard B. Meyer (1973) argued that listeners experience of melodies is shaped by certain melodic archetypes. Among these archetypes is gapfill, a name for melodies in which an early skip is followed by some of the pitches that have been skipped over. In experiments conducted with Rosner, Meyer tested gap-fill s effect on the ways in which listeners compare and classify melodies (B. S. Rosner & L. B. Meyer, 1982, 1986). The present reanalyses of Rosner and Meyer s experimental results, however, suggest that gap-fill played little or no role. Together with an earlier study suggesting that gap-fill has no influence on melodic shape (P. von Hippel & D. Huron, 2000), these reanalyses tend to weaken the claim that gap-fill is an important concept for classifying melodies. Received June 14, 1999; accepted July 8, C LASSIFICATION is one of the oldest tasks in music analysis. Throughout history, scholars have classified music according to mode, meter, character, and social function, as well as other qualities. Ordinary listeners, too, are remarkably adept at classifying music, as demonstrated by their split-second ability to recognize the format of a radio station (Perrott & Gjerdingen, 1999). Psychologists studying musical classification have often invoked the concepts of prototype or schema. A schema is a mental representation for the way that features fit together in a familiar setting for example, the objects and events to expect in a restaurant (Graessner & Nakamura, 1982; Schank & Abelson, 1977). In music, schematic knowledge enables listeners to predict the pitches and chord progressions that are most likely to occur in a given key (Krumhansl & Castellano, 1983). Schemas are often related to prototypes, which are exemplary or idealized representatives of a class; a robin, for example, is a highly prototypical bird. Prototypes are used as Address correspondence to Paul von Hippel, School of Music, Ohio State University, 1866 College Ave., Columbus, OH ( von-hippel.1@ohio-state.edu). ISSN: Send requests for permission to reprint to Rights and Permissions, University of California Press, 2000 Center St., Ste. 303, Berkeley, CA

2 140 Paul von Hippel mental references to which other members of a class are compared (Posner & Keele, 1970; Rosch, 1978). In music, for example, listeners tend to hear chromatically inflected melodies as departures from diatonic prototypes (Bartlett & Dowling, 1988; Cohen, Thorpe, & Trehub, 1987). Among psychological theories of melodic classification, the ideas of Leonard Meyer (1973) are strikingly ambitious. Instead of classifying melodies by such basic qualities as chromatic or diatonic content, Meyer has proposed a more refined classification based on a handful of melodic archetypes. Archetypes, according to Meyer s colleague Robert Gjerdingen, are [Meyer s] term for innate or universally valid schemata (Gjerdingen, 1988, p. 7). Meyer sometimes refer to archetypes as archetypal schemata a usage that corroborates Gjerdingen s definition (Meyer, 1973). Meyer s archetypes have also been discussed under the heading of prototypes (Gjerdingen, 1991, p. 131). The connection between archetypes and prototypes is not hard to see: when Meyer (1973) discusses archetypes in terms of exemplary cases, or when he rates musical examples according to how well they exemplify a given archetype (Rosner & Meyer, 1986, Tables 1 5), one could certainly imagine that it is prototypes that are under discussion. Despite these correspondences, it is not clear that Meyer would claim for archetypes all of the measurable effects that are associated with prototypes and schemas. For example, schemas often induce memory errors: features that violate the prevailing schema tend to be forgotten, and features that fit the prevailing schema tend to be remembered even if they did not occur (Brewer & Treyens, 1981). A distinctive feature of prototypes, on the other hand, is asymmetries in perceived similarity: when a prototype is at work, the perceived similarity of two items depends on the order or the grammatical relationship in which they are presented (Tversky, 1977; Bartlett & Dowling, 1988). These characteristic effects of prototypes and schemas have never been claimed for Meyer s archetypes. Instead, with the exception of two experiments to be discussed in this article (Rosner & Meyer, 1982, 1986), Meyer s archetypes remain a theoretical concept rather than an operational one. The archetypes identified by Meyer include linear, triadic, complementary, changing-note, and Adeste Fideles melodies (Meyer, 1973; Rosner & Meyer, 1986). Perhaps the most important of Meyer s archetypes, however, is gap-fill. A gap-fill melody typically begins with a large skip (or gap), then continues by filling in scale tones that have been skipped over. Figure 1 displays Meyer s most straightforward examples of gap-fill: the chorus from the show tune Over the Rainbow and the fugue subject from Geminiani s Concerto Grosso in E Minor, op. 3, no. 3 (Rosner & Meyer, 1982).

3 Do Listeners Use Gap-Fill to Classify Melodies? 141 Fig. 1. Two gap-fill melodies. Top: the chorus from Over the Rainbow, by Harold Arlen and E. Y. Harburg. Bottom: the first-movement fugue subject from Geminiani s Concerto Grosso in E Minor, op. 3, no. 3. Both melodies begin with large skips or gaps that are gradually filled in. Meyer has written more about gap-fill than about any other archetype (Meyer, 1956, 1973; Rosner & Meyer, 1982, 1986). Perhaps this is because the gap-fill concept fits so well with Meyer s ideas about melodic shape and expectation. Meyer (1956) has claimed that listeners, after hearing a gap, expect it to be filled in a claim that fits the results of several cognitive experiments (e.g., Schellenberg, 1997; Schmuckler, 1989). Meyer (1956) further claims that many melodies are constructed to satisfy an expectation for gap-fill. Indeed, he argues, this may be the reason why centuries of pedagogues have taught that a skip should be followed by a contrary step (e.g., Nanino & Nanino, ca. 1600; Fux, 1725/1943; Prout, 1890; Kostka & Payne, 1995). The prevalence of gap-fill melodies, in turn, might explain why listeners would develop an archetypal schema for representing them. This web of ideas related to gap-fill has recently frayed. Statistical analyses have shown that, contrary to centuries of teaching, melodies are not generally constructed to fill gaps. Instead, the melodic shape that Meyer calls gap-fill seems to be an artifact of constraints on range or tessitura (von Hippel & Huron, 2000). Skips tend to land near the extremes of a melody s tessitura, and from those extremes, a melody has little choice but to retreat by changing direction little choice, that is, but to regress toward the mean. If melodies are not constructed to fill gaps, it seems reasonable to reopen the question of whether gap-fill is really a psychological archetype. To address this question, I reanalyzed two sets of experiments designed to test the archetypal status of the gap-fill pattern (Rosner & Meyer, 1982, 1986). To the degree that the experimental results can be interpreted, the reanalyses suggest that gap-fill had little if any effect on listeners. These findings encourage further skepticism regarding the psychological importance of gap-fill.

4 142 Paul von Hippel An Experiment on Learning The earliest experiment on the gap-fill archetype was carried out by Rosner and Meyer in This experiment was designed to test the authors claim that archetypes are easily learned (p. 319) a claim that could also apply to prototypes or schemas. Specifically, Rosner and Meyer sought to test whether listeners could learn by example that is, without explicit instruction to recognize the presence or absence of the gap-fill pattern. At the beginning of the experiment, listeners heard two gap-fill melodies. Listeners were not told that these melodies were called gap-fill, nor were they told the melodies defining attributes. Instead, listeners were simply told that the melodies were Type A. After hearing these two examples, listeners began a training session in which they learned to categorize 16 melodies by using the Type A label. Eight of these melodies were meant to illustrate gap-fill (though none was as clear a specimen as the examples in Figure 1); the remaining 8 melodies were intended to be foils. After hearing each melody, listeners guessed whether the melody was Type A, and the experimenter told them whether their answer was correct. This training session could go on until the entire set of 16 melodies had been played 12 times. For the introductory stage of a cognitive experiment, this is quite a lot of training. Because each playing of the training set took about 8 minutes (Rosner & Meyer, 1982, p. 329), the training stage could last up to 96 (12 8) minutes more than an hour and a half. To put the point another way, listeners could receive feedback on up to 192 (12 16) practice classifications. Not all of the listeners received so much feedback, however. If a listener classified 14 of the 16 melodies correctly, and did so two times in a row, the training session ended, and the listener was considered to have passed. Of the 17 listeners who completed the study, 14 passed this training stage. The chances are extremely remote that 14 of 17 listeners could have passed the training stage by indiscriminate guessing (p < ). 1 It does not 1. It is not clear from Rosner and Meyer s (1982) article whether listeners were told how many Type A and non-type A melodies they would hear. If listeners were privy to this information, then the independence of the data would be reduced, because the likelihood of a Type A answer would depend partly on the number of Type A answers that were given earlier. If the independence of the data is compromised in this way, then statistical tests in the first half of this article and in Rosner and Meyer s (1982) original analyses exaggerate the significance of the results. Assuming that the data are independent, however, the probability given in the text (p < ) was calculated in five steps: 1. Suppose that a listener is guessing. With two classes available to her, her chance of correctly classifying any one melody is.5.

5 Do Listeners Use Gap-Fill to Classify Melodies? 143 necessarily follow, however, that listeners were attending to the gap-fill archetype. Instead, they could have passed the training stage simply by memorizing which melodies were given the Type A label. To test this possibility, Rosner and Meyer administered a test of generalization, in which listeners classified 12 melodies that they had not heard in the training stage. Six of these melodies were meant to be instances of gap-fill; the remaining 6 melodies were meant to be foils. Without benefit of feedback, listeners tried to determine which melodies should take the Type A label. Of the 12 melodies in the generalization test, listeners classified a mean of 7.5 correctly. This level of accuracy, Rosner and Meyer found, was only marginally inconsistent with the idea that listeners were guessing. When a two-tailed Kolmogorov-Smirnov test (Conover, 1980) was applied to the 14 listeners who had passed training, the results only verged on statistical significance (D max (14) =.3271, two-tailed p <.10). The conventional threshold for significance was crossed only when the analysis included the 3 listeners who had failed the training stage (D max (17) =.3356, two-tailed p <.05). The statistical tests used by Rosner and Meyer, however, were two-tailed. Because this experiment was concerned only with the claim that listeners accuracy was better than chance (not worse), Rosner and Meyer could have improved the apparent significance of their results by conducting onetailed tests in which case the p values would be half as large. Regardless of the level of significance, these results do not necessarily support the authors claim that listeners could learn to classify gap-fill melodies easily. The mean score of 7.5 correct answers is lower than it may seem. Listeners had only two class names available, so that, given 12 melodies, on average they could provide 6 correct answers simply by guessing. A mean of 7.5 correct answers, therefore, is just one quarter of the way from a chance score to a perfect one. To put the point another way, the results suggest that listeners recognized the class of just one quarter of the melodies (3 of 12), because, by guessing the class of half the remainder ( In a single playing of the training set, a listener s binomial probability of correctly identifying at least 14 of the 16 melodies is.002. (See Howell, 1997, pp , for the pertinent formula.) 3. Given two consecutive playings of the training set, the listener s probability of both times reaching the specified level of accuracy is Because a listener could hear the training set up to 12 times, she had 11 opportunities to reach the specified level of accuracy in two consecutive playings. Given 11 opportunities, therefore, her chance of two consecutive successes is close to 11 x.002 2, or 4.4 x (The situation is analogous to a Bonferroni correction for 11 nonindependent tests see Darlington, 1990, p The exact probability, which is closer to 4.39 x 10 5, can be obtained by a recursive procedure [Mario Peruggia, personal communication, February 24, 2000]). 5. If each listener s chance of two consecutive successes is 4.4 x 10 5, the binomial probability of 14 out of 17 listeners having two consecutive successes is less than 10 58, as claimed above.

6 144 Paul von Hippel of 9), listeners could reach a total score of 7.5. A skeptic might argue that, after up to an hour and a half of training, one-quarter recognition does not suggest that a system of classification can be learned easily. To assess ease of learning more formally, we would need to know the results of a control condition one in which listeners learned a melodic category that was not based on a nominal archetype. Unfortunately it would be hard to design a suitable control, because Meyer offers no theoretical criteria for deciding whether a melodic pattern is or is not archetypal. Without a control condition, however, we cannot compare the gap-fill results with a non-archetypal standard. In sum, Rosner and Meyer s classification experiment provided no evidence that gap-fill could be learned easily and only weak evidence that it could be learned at all. On the basis of these experimental results, it is not clear that gap-fill should be granted the status of an archetype. Two Experiments on Melodic Similarity In two later experiments, Rosner and Meyer (1986, Experiments 3 and 5) tested the effect of gap-fill on listeners judgments of melodic similarity. In these experiments, listeners were given no instruction or training as to how they should classify melodies. Instead, listeners simply rated the similarity of pairs of musical passages. Twelve passages were used in these experiments. Six were meant to be gap-fill melodies; the other 6 represented an archetype that Rosner and Meyer called Adeste Fideles. An Adeste Fideles melody, according to Rosner and Meyer (1986, p. 19), always involves two characteristic skips. The first spans a fourth and the next one a fifth. Both usually occur in the first half of the melody; the second skip leads to upward motion to the third or fourth of the scale, followed by downward resolution often to the tonic. Two of Rosner and Meyer s examples of this archetype are displayed in Figure 2. The first example is the eponymous Christmas carol, Adeste Fideles (O Come, All Ye Faithful). The second example is the opening melody from the minuet of Händel s Flute Sonata in G, op. 1, no. 5. With respect to gap-fill, a basic question that could be asked of these experiments is whether listeners found the gap-fill melodies more similar to one another than to the Adeste Fideles melodies. Unfortunately, Rosner and Meyer did not address this question, and their listeners similarity judgments are no longer available for analysis (B. Rosner, personal communication, 1997). Rosner and Meyer did, however, represent the aggregate

7 Do Listeners Use Gap-Fill to Classify Melodies? 145 Fig. 2. Two Adeste Fideles melodies. Top: the Christmas carol Adeste Fideles (O Come, All Ye Faithful). Bottom: the opening of the minuet from Händel s Flute Sonata in G Major, op. 1, no. 5. Both melodies have early downward skips of a fourth or fifth, followed by movement up to the third of fourth degree of the scale, followed by at least partial resolution. data graphically in the form of multidimensional scaling plots (Kruskal & Wish, 1978) and hierarchical clustering trees (Aldenderfer & Blashfield, 1984). On the multidimensional scaling plots, redrawn here as Figure 3, melodies that listeners rated as similar are plotted close together, whereas melodies that listeners rated as dissimilar are plotted far apart. Gap-fill melodies are represented by filled circles; Adeste Fideles melodies, by open circles. The plot for Experiment 3 represents 90.5% of the variance in listeners similarity judgments, whereas the plot for Experiment 5 represents 88.8% of the variance (Rosner & Meyer, 1986, pp. 21, 31). Similarity judgments were summed across listeners before entering the scaling algorithm; the plotted distances therefore represent an aggregate tendency, rather than the judgments of individual listeners. If listeners generally found gap-fill melodies similar to one another, those melodies would be closer to one another than to Adeste Fideles melodies. On neither plot, however, is such a pattern evident. To the contrary, on both plots the median distance between gap-fill melodies is actually longer than the median distance between gap-fill and Adeste Fideles melodies. On Rosner and Meyer s plot for Experiment 3, the median distance between gap-fill melodies is 31 mm, half a millimeter longer than the 30.5 mm median distance between gap-fill and Adeste Fideles melodies. 2 On the plot for Experiment 5, the median distance between gap-fill melodies is 32 mm, one-third longer than the 24 mm median distance between gap-fill and Adeste Fideles melodies. 2. All distances were measured from Rosner and Meyer s (1986) original plots (Figures 8a and 13a) and are tabulated in the Appendix to this article. Distances measured on the redrawn plots in the present article will have the same proportions but may differ by a scaling factor.

8 146 Paul von Hippel Experiment 3 Experiment 5 Gap-fill melodies Adeste Fideles melodies Fig. 3. These multidimensional scaling plots summarize the results for two of Rosner and Meyer s (1986) experiments on melodic similarity. The filled circles represent gap-fill melodies, and the open circles represent Adeste Fideles melodies. Melodies close together on the plot were judged similar by listeners; melodies far apart were judged dissimilar. This figure is redrawn from Rosner and Meyer s (1986) Figures 8a and 13a. Neither plot, then, suggests that gap-fill melodies sound exceptionally similar to one another. The plots do, however, suggest some kinship among the Adeste Fideles melodies. To begin with the plot for Experiment 3, although the gap-fill melodies are widely scattered, the Adeste Fideles passages [occupy] a remarkably compact region near the left edge of the plot (Rosner & Meyer, 1986, p. 22). To describe this difference quantitatively, the median distance between Adeste Fideles melodies is just 12 mm, less than half the 30.5-mm median distance separating Adeste Fideles from gap-fill melodies; a Wilcoxon rank-sum test (Howell, 1997) indicates that the Adeste Fideles melodies are significantly closer to one another than they are to the gap-fill melodies (W s (15,36) = 208.5, one-tailed p =.0001). A similar, though weaker, pattern is evident in the plot for Experiment 5; here the gap-fill points are scattered peripherally (Rosner & Meyer, 1986, p. 31), but five of the six Adeste Fideles melodies clump together in the lower right. More formally, the Adeste Fideles melodies are significantly

9 Do Listeners Use Gap-Fill to Classify Melodies? 147 closer to one another than to the gap-fill melodies, though the level of significance is mild (W s (15,36) = 307, one-tailed p =.04). The median distance between Adeste Fideles melodies is 15 mm, about one-third shorter than the 24-mm median distance between gap-fill and Adeste Fideles melodies. Analysis of the hierarchical clustering trees, redrawn here as Figure 4, tells a similar story. Here the perceived similarity of two melodies is represented by the vertical length of the branches that connect them. Again, gapfill melodies are represented by filled circles, and Adeste Fideles melodies are represented by open circles. Like the multidimensional scaling plots, these trees represent judgments that have been summed across listeners; they do not necessarily reflect the judgment of individuals. The tree for Experiment 3 represents 79% of the aggregate variance in listeners simi- Experiment 3 10 Vertical branch length 5 0 Experiment Gap-fill melodies Adeste Fideles melodies Fig. 4. These hierarchical clustering trees offer another representation for Rosner and Meyer s (1986) experimental results. Again, the filled circles represent gap-fill melodies, while the open circles represent Adeste Fideles melodies. Melodies connected by short branches were judged similar by listeners; melodies connected by long branches were judged dissimilar. This figure is redrawn from Rosner and Meyer s (1986) Figures 8b and 13b.

10 148 Paul von Hippel larity judgments; the tree for Experiment 5 represents 81% of the variance (Rosner & Meyer, 1986, pp. 21, 31). 3 If listeners found gap-fill melodies notably similar to one another, then the branches connecting gap-fill melodies would be shorter and at a lower level of the hierarchy than the branches connecting gap-fill to Adeste Fideles melodies. In neither tree is such a pattern evident. To the contrary, in both trees the branches connecting gap-fill melodies are actually longer than the branches connecting gap-fill to Adeste Fideles melodies. Specifically, in Experiment 3 the branches connecting gap-fill melodies have a median vertical length of 12.6, 4 slightly longer than the median length of for branches joining gap-fill and Adeste Fideles melodies. Likewise, in Experiment 5, the branches connecting gap-fill melodies have a median length of 13.1, slightly longer than the median length of 12.4 for branches connecting gap-fill to Adeste Fideles melodies. The hierarchical clustering trees, then, corroborate the multidimensional scaling plots in suggesting that gap-fill melodies did not sound notably similar to one another. However, the trees also corroborate the plots in suggesting that there was notable similarity among the Adeste Fideles melodies. To begin with Experiment 3, the Adeste Fideles melodies are significantly closer to one another than they are to the gap-fill melodies (W s (15,36) = 172, one-tailed p <.0001); the branches connecting Adeste Fideles melodies have a median length of 9.8, nearly one-fifth shorter than the median length for branches joining Adeste Fideles to gap-fill melodies. In Experiment 5, the differences are more modest; branches connecting Adeste Fideles melodies have a median length of 10.9, just over one-tenth shorter than the 12.4 median length for branches connecting Adeste Fideles to gapfill melodies. The difference between branch lengths only borders on significance (W s (15,36) = 321, one-tailed p =.07), but it does reinforce the pattern observed in the corresponding multidimensional scaling plot. Taken at face value, both the trees and the plots suggest that, although similarity judgments were not affected by the gap-fill archetype, they may have been affected by the Adeste Fideles archetype. This convergence of results is not surprising, because both the trees and the plots were derived from the same similarity data. Interpretation of these results, however, is complicated by a number of factors. The musical excerpts used in these experiments were not isolated 3. For the hierarchical clustering trees, Rosner and Meyer did not directly report explained variance directly. Instead, they reported the cophenetic correlations (Aldenderfer & Blashfield, 1984) between ratings of perceived similarity, summed across listeners, and the lengths of branches in the hierarchical clustering trees. These correlations r =.89 for Experiment 3, r =.90 for Experiment 5 (Rosner & Meyer, 1986, pp. 22, 32) must be squared to compute explained variance (r 2 ). 4. The units of measurement are taken from the unlabeled vertical axes of Rosner and Meyer s (1986) Figure 8b and Figure 13b. All branch lengths are tabulated in the Appendix.

11 Do Listeners Use Gap-Fill to Classify Melodies? 149 melodies played with a uniform timbre; instead, they were commercial recordings of solo, chamber, and orchestral works written over a period of one hundred and fifty years. Although Rosner and Meyer ensured that every excerpt had a similar AA B form, they did not control other variables such as mode, rhythm, tempo, harmony, or instrumentation. It is possible that some of these uncontrolled variables confounded the experimental results. Figure 5 suggests a plausible alternative interpretation for the data from Experiment 3. Here the points from that experiment s multidimensional scaling plot have been labeled with the name of each melody s composer. These labels show that the nine melodies on the left were written before 1800 by composers from the late baroque period (Händel) to the late classical (early Beethoven). In contrast, the three melodies on the right were written in or after 1830 by the romantic composers Chopin, Brahms, and Verdi. Although melodic archetype might explain why the six Adeste Fideles melodies are all near the left side of the plot, it cannot explain why three of the gap-fill points are there as well. Stylistic period, however, can explain the horizontal positions of all 12 melodies. In Figure 6, the hierarchical clustering tree for this data has been similarly labeled with the names of the melodies composers. The visual effect here is not quite as striking, but after a little inspection one can see that the tree separates into two major limbs. Consistent with a stylistic interpretation of the results, the left limb branches out to connect the three romantic melodies, whereas the right limb branches out to join the nine baroque and classical melodies. It seems at least plausible, then, that similarity judgments in this experiment were not influenced by archetypes at all, but instead were shaped by Haydn Chopin Experiment 3 Händel early Beethoven Mozart Mozart early Beethoven Mozart Sammartini early Beethoven Verdi Brahms Gap-fill melodies Adeste Fideles melodies Fig. 5. The points plotted here are the same as in the top half of Figure 3. In this version, however, each melody is labeled with its composer, as given in Rosner and Meyer s (1986) Table 3. Relabeling the points in this way shows that the nine melodies on the left were written before 1800 by baroque and classical composers, whereas the three melodies on the right were written in or after 1830 by romantic composers. This distribution of melodies suggests that stylistic features, rather than melodic archetypes, may explain the pattern of listeners similarity judgments.

12 150 Paul von Hippel 10 Vertical branch length 5 0 Gap-fill melodies Adeste Fideles melodies Fig. 6. This hierarchical clustering tree offers another view of the pattern shown in Figure 5. Again, each melody is labeled with the name of its composer. The tree is separated into two large limbs; the left limb branches out to join the three romantic melodies, while the right limb branches out to join the nine classical and baroque melodies. Like the multidimensional scaling plot in the previous figure, this tree suggests the influence of stylistic features. differences in stylistic period. These stylistic differences depend on a complex of factors, and the use of the Adeste Fideles archetype could be a part of that complex. There are so many stylistic differences present, however, that pinning an interpretation on any one of them seems rash. Conclusion In summary, a lack of controls made Rosner and Meyer s (1982, 1986) experiments difficult to interpret. Even if these difficulties are ignored, however, the results provide little if any evidence for the gap-fill archetype. When Rosner and Meyer (1982) trained their listeners, those listeners remained near chance levels in their ability to classify melodies in terms of gap-fill. When Rosner and Meyer (1986) did not train their listeners, judgments of melodic similarity showed no effect of gap-fill at all. Together with a recent study suggesting that gap-fill has no influence on melodic shape (von Hippel & Huron, 2000), these results tend to weaken the claim that gap-fill is an important concept for classifying melodies I thank Jonathan Berger, Chris Chafe, David Huron, Eleanor Selfridge-Field, and especially David Temperley for comments on this article before its submission. During the review process, I benefited from the feedback of Burton Rosner and two anonymous reviewers.

13 Do Listeners Use Gap-Fill to Classify Melodies? 151 References Aldenderfer, M. S., & Blashfield, R. K. (1984). Cluster analysis. Beverly Hills, CA: Sage Publications. Bartlett, J. C., & Dowling, W. J. (1988). Scale structure and similarity of melodies. Music Perception, 5, Brewer, W. F., & Treyens, J. C. (1981). Role of schemata in memory for places. Cognitive Psychology, 13, Cohen, A. J., Thorpe, L. A., & Trehub, S. E. (1987). Infants perception of musical relations in short transposed tone sequences. Canadian Journal of Psychology, 41, Conover, W. J. (1980). Practical nonparametric statistics (2nd ed.). New York: John Wiley & Sons. Darlington, R. B. (1990). Regression and linear models. New York: McGraw-Hill. Fux, J. J. (1943). Steps to Parnassus: The study of counterpoint [from Gradus ad Parnassum] (A. Mann, Trans.). New York: Norton. (Original work published 1725) Gjerdingen, R. O. (1988). A classic turn of phrase: Music and the psychology of convention. Philadelphia, PA: University of Pennsylvania Press. Gjerdingen, R. O. (1991). Defining a prototypical utterance. Psychomusicology, 10, Graessner, A. C., & Nakamura, G. V. (1982). The impact of a schema on comprehension and memory. In G. H. Bower (Ed.), The psychology of learning and motivation: Advances in research and theory (Vol. 16, pp ). New York: Academic Press. Howell, D. C. (1997). Statistical methods for psychology. Belmont, CA: Duxbury Press. Kostka, S., & Payne, D. (1995). Tonal harmony with an introduction to twentieth-century music. New York: McGraw-Hill. Krumhansl, C. L., & Castellano, M. A. (1983). Dynamic processes in music perception. Memory and Cognition, 11, Kruskal, J. B., & Wish, M. (1978). Multidimensional scaling. Beverly Hills, CA: Sage Publications. Meyer, L. B. (1956). Emotion and meaning in music. Chicago: University of Chicago Press. Meyer, L. B. (1973). Explaining music: Essays and explorations. Berkeley, CA: University of California Press. Nanino, G. M., & Nanino, G. B. (ca. 1600). Regole di contrappunto [Rules of counterpoint]. Unpublished manuscript, Civico Museo Bibliografico Musicale, Bologna, Italy. Perrott, D., & Gjerdingen, R. O. (1999, August 15). Scanning the dial: An exploration of factors in the identification of musical style. Paper presented at the meeting of the Society for Music Perception and Cognition, Evanston, IL. Posner, M. I., & Keele, S. W. (1970). Retention of abstract ideas. Journal of Experimental Psychology, 83, Prout, E. (1890). Counterpoint: Strict and free. London: Augener. Rosch, E. (1978). Principles of categorization. In E. Rosch & B. B. Lloyd (Eds.), Cognition and categorization (pp ). New York: John Wiley & Sons. Rosner, B. S., & Meyer, L. B. (1982). Melodic processes and the perception of music. In D. Deutsch (Ed.), The psychology of music (pp ). New York: Academic Press. Rosner, B. S., & Meyer, L. B. (1986). The perceptual roles of melodic process, contour, and form. Music Perception, 4, Schank, R. C., & Abelson, R. P. (1977). Scripts, plans, goals and understanding. Hillsdale, NJ: Lawrence Erlbaum Associates. Schellenberg, E. G. (1997). Simplifying the implication-realization model of melodic expectancy. Music Perception, 14, Schmuckler, M. A. (1989). Expectation in music: Investigation of melodic and harmonic processes. Music Perception, 7, Tversky, A. (1977). Features of similarity. Psychological Review, 84, von Hippel, P., & Huron, D. (2000). Why do skips precede reversals? The effect of tessitura on melodic structure. Music Perception, 18,

14 152 Paul von Hippel Appendix TABLE A1 Distances Between Melodies on Rosner and Meyer s (1986) Multidimensional Scaling Plots (in Millimeters) Experiment 3 Gap-Fill Melodies Adeste Fideles Melodies GF GF GF GF GF GF AF AF AF AF AF AF AF AF AF AF AF GF GF GF GF GF Experiment 5 Gap-Fill Melodies Adeste Fideles Melodies GF GF GF GF GF GF AF AF AF AF AF AF AF AF AF AF AF GF GF GF GF GF NOTE The acronyms in the table margins ( 3 GF 1, etc.) were used by Rosner and Meyer to indicate the position of each melody on the multidimensional scaling plots (Rosner & Meyer, 1986, Figures 8a and 13a). Acronyms including the letters GF represent Gap-Fill melodies; acronyms containing AF represent Adeste Fideles melodies. In order to calculate the distances reported here, the multidimensional scaling plots were scanned and viewed using image-processing software. The x and y coordinates of each melodic acronym were measured against an on-screen ruler, then converted from the ruler units (sixty-fourths of an inch) to millimeters. Finally, the distance between acronyms was computed by the Euclidean distance metric, x 2 + y 2. For the purpose of these measurements, the coordinates of each acronym were taken at the upper-left corner of its letter F. As a check for gross errors of measurement or transcription, the ordering of the transcribed x and y coordinates was visually compared with the ordering of horizontal and vertical positions on the plots. This error check revealed no discrepancies.

15 Do Listeners Use Gap-Fill to Classify Melodies? 153 TABLE B1 Vertical Lengths of Branches Joining Melodies in Rosner and Meyer s (1986) Hierarchical Clustering Trees Experiment 3 Gap-Fill Melodies Adeste Fideles Melodies GF GF GF GF GF GF AF AF AF AF AF AF AF AF AF AF AF GF GF GF GF GF Experiment 5 Gap-Fill Melodies Adeste Fideles Melodies GF GF GF GF GF GF AF AF AF AF AF AF AF AF AF AF AF GF GF GF GF GF NOTE The acronyms in the table margins ( 3 GF 1, etc.) were used by Rosner and Meyer to specify the melody that terminated each branch of the hierarchical clustering trees (Rosner & Meyer, 1986, Figures 8b and 13b). The branch lengths were measured by hand against the unlabeled vertical axes of Rosner and Meyer s figures. As a check for errors, the tabulated values were measured and transcribed twice. Four errors were corrected in this way.

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