The interaction of repetition and difficulty for working memory in melodic dictation tasks

Abstract

This research examines the effect of repetition on melodic dictation tasks in an undergraduate ear-training class. A pilot group of freshman music majors (n = 17) were asked to notate four melodies, of which two were slightly more difficult since they contained more melodic leaps. Participants heard two melodies repeated three times and two other melodies six times. An analysis of variance (ANOVA) suggests that the number of repetitions had a significant effect on participants’ dictation accuracy, both for scores on pitch and on rhythm. In addition, dictation accuracy was significantly lower when the melodies contained more leaps (controlling for other factors). Overall, we found a statistical interaction between the number of repetitions and the number of leaps in the melody, both of which factors affect the working memory load in these dictation tasks. Given the similarity of the notated melodies, these findings suggest that ear-training pedagogues must carefully select melodic dictations appropriate for student ability and control the number of melodic leaps. Furthermore, we found evidence that the variance in working memory for music among this population is wider than Karpinski (2000) hypothesizes. These findings provide pedagogues with melodic characteristics well-suited for the average incoming freshman music major. Finally, this first empirical evidence of the dictation ability of incoming undergraduate music majors invites a long-term study on the extent to which working memory and/or chunking ability may increase during the multi-semester ear-training curriculum.

Keywords

aural skills ear-training melodic dictation theory pedagogy working memory

Introduction

Foundational studies on musical memory have examined general factors affecting retention, and accuracy. Based on Miller’s (1956) seminal “magical number seven” concept,¹ these studies have examined the limit of how much information can be comprehended in a single hearing and suggested strategies for “chunking” multiple notes into a single conceptual unit to reduce the memory load (Wheatley, 1991). A more recent survey of the research (Cowan, 2001) suggests that the “magic number” limiting working memory may actually be 3–5 chunks rather than 5–9. Factors found to affect retention of a melody include time (Williams, 1975), intervening distractor tones (Deutsch, 1972; Madsen & Staum, 1983), tonality (Pembrook, 1986), timbre (Schellenberg & Habashi, 2015; Weiss, Vanzella, Schellenberg, & Trehub, 2015), interaction of rhythmic and melodic patterns (Schellenberg & Moore, 1985), and voicing with a contrapuntal texture (Killam, Baczewski, & Hayslip, 2003). The present research investigates the practical implications of these concepts for classroom procedures in ear-training classes, particularly for melodic dictation tasks.

The general influence of factors such as these on working memory can be explained by concepts such as Owens and Sweller’s (2008) cognitive load theory, which posits that the load which a task imposes on working memory is a function of the complexity of the information involved, the format in which the information is presented, and the subject’s ability to use appropriate schemata to chunk and filter the information (Owens & Sweller, 2008, p. 31). A melodic dictation task, involving multiple layers of information which must be processed in multiple domains, has a high intrinsic cognitive load. However, instructors can reduce the extraneous cognitive load in three key ways. First, they may carefully control the number of challenging notes, rhythms, and intervals within the melodic stimuli they present to students. Second, stimuli should be presented to students in a graded progression which they can learn to grasp intuitively. Finally, instructors can also reduce the germane cognitive load by helping students develop a store of melodic and tonal schemata to help them process the information they are hearing.

For working memory in the context of melodic dictation tasks, Lawson (1970) posits a “memory retention limit” based on the number of bits of information, duration of the stimulus, number and spacing of repetitions of the stimulus, redundancy of the stimulus, and the similarity of the stimulus to information previously stored in long-term memory. In Owens and Sweller’s (2008) terms, the first two of these categories pertain to intrinsic cognitive load, the next two to extrinsic cognitive load, and the last one to germane cognitive load (i.e., the more familiar a listener is with melodies similar to the stimulus presented, the less taxing the memory load it will present).

Williamson, Baddeley, and Hitch (2010) describe working memory as composed of multiple components (p. 163): the “phonological loop,” which temporarily stores the most recently received aural information for processing; the “visuospatial sketchpad,” which does the same for visual information; and the “episodic buffer,” which holds information called up from long-term memory. The “central executive,” which oversees the other components, directs conscious attention to each component as needed to enable information processing. Berz (1995) postulates a separate “music memory loop” which processes specifically musical aural information (pp. 361–362), as evidenced by the relative lack of interference between musical and verbal aural recall (pp. 359–360). Of course, melodic dictation tasks place the heaviest demands on the phonological loop (or music memory loop) component, but the influence of the central executive (as manifested in listeners’ ability to direct their attention moment-by-moment during the task) should not be ignored either.

Several earlier studies have examined the effect of repetition on memory in an applied setting. Sloboda and Parker (1985) had participants hear a folk-song melody six times and sing it back after each hearing. Although the number of notes participants attempted tended to increase after each hearing, the percentage of notes sung correctly remained steady. In a similar study, Long (1977) assessed participants’ memory of a melody by asking them whether a given test tone occurred in the melody. Although they were able to complete the task fairly accurately, accuracy decreased slightly on longer melodies. One critique of this method is that if participants were aware a melody was diatonic (as most of Long’s melodies were), they could achieve well above 50% accuracy simply based on whether or not the test tone was diatonic.

Two studies in the past 40 years have specifically examined the effect of repetition in a melodic dictation task, but results are contradictory. Hofstetter (1981) studied participants notating rhythms on a self-paced computerized learning program and found no significant correlation between the number of times participants heard the exercise and the accuracy of their responses. However, since participants could choose to hear the exercise as many times as desired, the number of repetitions was correlated with the difficulty of the exercise and thus became an additional variable affecting the results. Langsford’s (1959) earlier research (reviewed in Carlsen, 1965) also found no significant relationship between amount of outside practice time and melodic dictation results.

On the other hand, Pembrook (1986) found that participants hearing a 6-, 10-, or 16-note melody twice, notated it with significantly higher accuracy than those hearing it only once. However, accuracy rates were still relatively low, and the experiment did not test whether additional hearings would continue to raise accuracy levels. Many ear-training curricula include melodic dictations much longer than this, and it remains to be seen to what extent this effect would hold for longer melodies. Pembrook also found that having subjects sing back their answer before writing it down actually lowered their accuracy when notating the melody, and a follow-up experiment (Pembrook, 1987) confirmed this result. The present study aims to build on Pembrook’s (1986) findings by extending his method to longer melodies and increased numbers of repetitions to more closely simulate the types of dictation experiences often offered in ear-training classes.

More recently, attention has turned to the application of these cognitive findings to inform methods that can aid in melodic dictation exercises in the ear-training classroom. This recent research has compiled useful qualitative studies examining the strategies of successful students in taking dictation (Buonviri, 2014) and of instructors in teaching dictation (Klonoski, 2006; Paney & Buonviri, 2014). Some commonly used pedagogical techniques have been found to be counterproductive: for example, Paney (2007, 2016) found that instructing participants on what to listen for in between hearings of a melody actually reduced accuracy rates in taking dictation. Buonviri (2015) found that singing a solfège pattern to establish the tonality prior to hearing a melody also lowered dictation accuracy rates, as did singing the melody between hearing it and notating it (Buonviri, 2018). Baker and Green (2013) found evidence that regular practice in informal improvisation or “ear playing” (as laid out in detail in Varvarigou, 2017) improved students’ ability to play back melodies by ear, a more musically integrated activity which requires many of the same skills as written dictation.

Little empirical research has been done towards determining recommendations for optimal presentation of melodic dictations in the ear-training classroom. Thus, many opportunities remain for research to help ear-training classes better facilitate the learning process by applying cognitive principles to melodic dictations. In particular, instructors vary widely in their approach to repeating the stimulus melody for dictation. Some instructors only present the stimulus once or twice and expect students to hold it in their memory while notating it, while others give students almost unlimited hearings so that memorization is essentially not a factor in the task. The research cited above has only tested dictation accuracy on a relatively low number of hearings, and thus it remains unclear whether instructors may be cutting the learning process short by giving too few hearings of melodic dictations or wasting valuable class time by giving too many. Our pilot study aimed to gather preliminary data on what might be an optimal number of hearings in the context of a melodic dictation exercise in the classroom. Our primary research question was whether the number of hearings and the difficulty of the melody would have an effect on listeners’ ability to notate it.

We hypothesized that a graph of students’ dictation skill against the number of hearings needed to accurately notate a melody would follow a logistic curve (Figure 1). If a melody was far beyond the students’ skill level (in the zone of difficulty), the number of hearings would not affect the accuracy of their answer, as they would get little of it correct. Similarly, if a melody was too simple for listeners (the zone of mastery), the number of hearings would also not make a difference, as they could notate it in a single hearing. However, if the melody was precisely at the students’ skill level, that is, if it was just complex enough that they could correctly perceive and notate it, but only with some perceived difficulty and labor, the number of hearings would matter. Thus, pedagogues are tasked with selecting exercises for ear-training students that fall into this optimal zone of learning, similar to that identified by Vygotskiĭ (1978, p. 86) as the “zone of proximal development.” At this difficulty level, students might make mistakes in notating a melody on their first attempt but be able to correct their work on a subsequent hearing. In addition, the difficulty of comprehension might still interfere with their ability to remember and actually lower the limit of their working memory, making it more difficult to use chunking to facilitate recall of the material.

The number of repetitions required to fit the optimal zone of learning may depend on the difficulty of the melody. Therefore, we tested participants’ accuracy in notating similar melodies, with two of the melodies made more difficult due to the increased number of leaps. In our experiment, we designed two pairs of melodies (further described below): one pair that we hypothesized would fall slightly to the left of (i.e., easier than) the optimal zone of learning for our participant population, and the other, slightly to the right (i.e., more difficult; see Figure 1). Theoretically, participants should be able to notate a melody easier than their optimal zone of learning correctly on a small number of hearings, but they should not be able to notate a melody harder than their optimal zone of learning correctly, even on a large number of hearings.

Thus, knowing the right number of hearings to target the optimal zone of learning for incoming freshman music majors would be pedagogically powerful. Whether the number of hearings affects dictation accuracy on otherwise comparable melodies could help pedagogues determine how many times to play dictation exercises in class or on quizzes. Whether adding more leaps to a melody has an effect (keeping all other characteristics of the melody the same) could help determine more precisely the optimal zone of learning. The following pilot study asked incoming freshman music majors to notate four melodies, of which two were slightly more difficult since they contained more melodic leaps. Participants heard two melodies three times and two other melodies six times.

In our data analysis, we first tested scores on the rhythm component of the melodies, hypothesizing that scores would be affected by the number of hearings but not the number of leaps in the melody. We then tested scores for pitch, hypothesizing that more hearings would increase scores, but more leaps in the melody would decrease them. Finally, we tested scores on leaps alone to determine what part of the effect on pitch (if present) was due specifically to the leaps, and whether more hearings would still increase scores. Since all of these melodies are similar to those notated by incoming freshman students at the start of their first semester, findings can then be used to more carefully determine the optimal zone of learning for this cohort.

Experiment

Research was conducted with the approval of the Institutional Review Board at the authors’ institution. Participants consented to participate and were informed that taking part in the experiment was voluntary and would not affect course grades.

Participants

Participants were volunteers solicited by class announcements in freshman ear-training classes. Participants were screened for having absolute pitch, and therefore no one with absolute pitch was included in the following study. Data are reported here for 17 freshman music majors (11 male, 6 female). Participants had a mean age of 18.88 years (SD = 1.37). They reported to have studied their primary instrument for a mean of 9.31 years (SD = 5.06), studied piano as a secondary instrument (among those who were not piano majors) for a mean of 2.66 years (SD = 4.68), and studied music theory for a mean of 1.53 years (SD = 1.91). Due to the small sample size, we present these results as a pilot study inviting future replication with larger student populations.

Apparatus

The experiment took place in a classroom at the authors’ institution in two sessions, held on each of two consecutive days at the beginning of the 2016–17 academic year. On each day, participants were divided into two groups, and the groups were tested separately from each other. Each group received different numbers of hearings of the melodies, in a counterbalanced design to control for potential order effects (see Table 1). Melodic stimuli were recorded on a grand piano, and the melodies and spoken instructions were compiled into an .mp3 audio track played for participants through classroom speakers. Throughout the experiment, participants wrote their responses on paper questionnaires at their desks while listening to the audio track. Prior to hearing each melody, participants were provided with a musical staff on their questionnaire, as well as the clef, key signature, time signature, and starting notehead for each melody they were asked to notate.

Table 1.

Number of hearings for each of the four melodies.

Melody	Simple		Complex
Melody	1	2	3	4
Group A	3 hearings	6 hearings	6 hearings	3 hearings
Group B	6 hearings	3 hearings	3 hearings	6 hearings

Stimuli

Over the course of the experiment, participants notated four melodies, all composed by the authors (see Figure 2). These melodies are typical in difficulty of those played for first-semester undergraduate ear-training classes at the authors’ institution, as they share similar characteristics to melodies found in Chapter 6 of Rogers and Ottman (2013), which contains melodies in the major mode with single division of the beat and leaps between notes of the tonic and dominant triads. Specifically, all four melodies shared the following characteristics: in terms of pitch, they were diatonic in a major key, containing a total of 18 pitches, beginning on do, mi, or sol and ending on do. Rhythmically, they included only single division of the beat, with no dotted rhythms or anacrusis. All melodies lasted four measures in 4/4 meter, with the last note being a whole note. Since the rhythmic characteristics of all melodies were similar, we hypothesized that participants would be able to notate the rhythmic components of all melodies equally well.

Since melodic leaps present one of the main factors of difficulty in a melodic dictation task, the number and kind of leaps present in the stimuli were carefully regulated. Both melodies moved mostly stepwise, with no more than one immediately repeated note and leaps only occurring between notes with the tonic or dominant chord. All melodies were played in a bass-clef register, and participants were asked to notate them in bass clef.² Melodies 1 and 2 were in keys with two sharps or flats, while melodies 3 and 4 were in keys with three sharps or flats.

Instead of making melodies 3 and 4 harder by making them longer (and thus increasing the demands on working memory), we instead increased difficulty primarily by adding more leaps: while melodies 1 and 2 contained only five leaps (two ascending and three descending), melodies 3 and 4 contained eight leaps (four ascending and four descending). While melodies 1 and 2 did not contain consecutive leaps, melodies 3 and 4 each contained two instances of two consecutive leaps and one instance of three consecutive leaps. The pitch content of the leaps in each pair of melodies was carefully matched: melodies 1 and 2 had leaps of three 3rds (between the scale degrees do-mi, mi-sol, and re-ti), one 4th (re-sol), and one 5th (do-sol), while melodies 3 and 4 had leaps of five 3rds (do-mi, mi-sol [twice], sol-re, and re-ti), one 5th (sol-re), and two 6ths (sol-mi and ti-sol). Put another way, melodies 1 and 2 contained three leaps from the tonic triad and two from the dominant triad, whereas melodies 3 and 4 contained 4 leaps from the tonic triad and 4 from the dominant triad. Additionally, while melodies 1 and 2 had a range of a 6th, from ti up to sol in their respective keys, melodies 3 and 4 had a range of an 11th, from sol up to do in the next octave. Thus, melodies 1 and 2, presented on Day 1, were hypothesized to be slightly simpler than melodies 3 and 4, presented on Day 2 (therefore, in Table 1 and hereafter, melodies 1 and 2 are referred to as the “simple” melodies, and melodies 3 and 4 are referred to as the “complex” melodies).

Procedure

The experiment consisted of three phases:

Pre-test: All participants were asked to notate a warm-up melody that was repeated a total of three times. (This melody was roughly equal in difficulty to the stimuli for Day 2.) Scores were tabulated with one point per correct pitch and one point per correct rhythm, with no partial credit possible. Participants were then ranked by score and divided into two groups (Group A and Group B) for the remaining phases of the experiment, so that each participant was matched with a counterpart with a similar pre-test score in the other group. Two of the 18 participants were not assigned a partner from the opposite group, as the distribution of scores was such that no partners with similar scores were available. Therefore, these participants’ scores were not included in the first phase of paired tests described below, but their data were included in the remaining tests.

Day 1: All participants notated melody 1 and melody 2. As shown in Table 1, Group A heard melody 1 three times, then melody 2 six times, whereas Group B heard melody 1 six times, then melody 2 three times. The number of hearings participants received was reversed between the two groups to control for order. Participants were given 30 seconds to prepare themselves before the first hearing and 60 seconds of silence after each hearing. They were not allowed to hum or make noise during the experiment. Both melodic dictations were scored according to the same method as in the pre-test. After both melodic dictation tasks were completed, participants answered a background questionnaire, including a short test for absolute pitch.

Day 2: All participants notated melody 3 and melody 4. Group A heard melody 3 three times, then melody 4 six times, whereas Group B heard melody 3 six times, then melody 4 three times. After both dictations were completed, participants answered a free-response questionnaire on their strategies used during the experiment.

Results

For both rhythm and pitch, we used a binary scoring system: if a participant notated the correct duration (or pitch) for that note (identified by its sequential position in the melody), they received 1 point; if not, they received no points. No partial points were possible. Series of notes notated correctly but shifted earlier or later than their proper sequence received credit for pitch but not for rhythm. A series of notes transposed higher or lower than their proper pitches did not receive credit for pitch, but could receive credit for rhythm.

Preliminary comparisons of paired melodies to establish similarity

There was no significant difference between mean performance in notating melodies 1 and 2, so the two melodies were determined to be of similar difficulty level: participants hearing melody 1 three times averaged a score of M = 68.97% correct (SD = 19.49%), and participants hearing melody 2 three times averaged a score of M = 72.26% (SE = 27.97%). A paired t-test of matched participants who performed similarly on the pre-test, comparing their scores on whichever melody they heard three times on Day 1, found no difference between their scores, t(6) = .00, p = 1.00. Similarly, participants hearing melody 1 six times averaged a score of M = 91.83% (SD = 6.49%), and participants hearing melody 2 six times averaged a score of M = 84.49% (SD = 10.54%). A paired t-test of matched participants from the pre-test, comparing their scores on whichever melody they heard six times on Day 1, also showed no significant difference between their scores, t(6) = 1.29, p = .25.

When these tests were repeated with the Day 2 results, we hypothesized melody 3 and melody 4 to also be of the same difficulty due to their similar characteristics (see discussion under the Stimuli heading, above). Participants hearing melody 3 three times scored M = 63.66% (SD = 15.14%), and participants hearing melody 4 three times scored M = 77.51% (SD = 10.17%). A paired t-test of matched participants who performed similarly on the pre-test, comparing their scores on whichever melody they heard three times on Day 2, found no significant difference between their scores, t(7) = 2.07, p = .08. Participants hearing melody 3 six times averaged a score of M = 76.09% (SE = 13.91%), and participants hearing melody 4 six times averaged a score of M = 79.66% (SD = 10.85%). A paired t-test of matched participants from the pre-test, comparing their scores on whichever melody they heard six times on Day 2, found no significant difference between their scores, t(7) = 0.77, p = .46.

Overall results

Having established that the two simple melodies were in fact equal in difficulty, as were the two complex melodies, we were able to test for our primary research question, which was whether the number of hearings and the difficulty level of the melody had an effect on participants’ scores, either alone or in interaction (Figure 3). A 2×2 ANOVA with repeated measures on both factors (simple vs. complex, 3 hearings vs. 6 hearings) indicated that there was no main effect for difficulty, F(1, 16) = 3.453, p = .082: that is, participants did score more accurately on the simple melodies, but this difference was not significant. However, there was a main effect for number of hearings: participants scored significantly more accurately when hearing the melodies six times than three times, F(1, 16) = 16.057, p = .001. There was a significant interaction between the two variables, F(1, 16) = 4.335, p = .054: depending on the number of hearings, the difficulty of the melody resulted in different scores.

Results for rhythm

Since the number of hearings had a significant effect on participants’ scores, we investigated whether this effect appeared in their ability to notate the melody’s rhythms, pitches, or both. We broke down each participant’s score on each melody into rhythm and pitch components and ran separate ANOVAs on both. For rhythm (Figure 4), a 2×2 ANOVA with repeated measures on both factors indicated that once again, there was no main effect for difficulty, F(1, 16) = 3.429, p = .083, but there was a main effect for number of hearings, F(1, 16) = 6.459, p = .022. The interaction between these variables was not significant, F(1, 16) = 2.622, p = .125. Thus, participants notated the rhythms significantly more accurately when they heard the melody six times than when they heard it three times. As hypothesized, scores were not significantly different between the simple and complex melodies, since the rhythmic characteristics of all melodies were similar.

Results for pitch

On the pitch component of participants’ scores (Figure 5), a 2×2 ANOVA with repeated measures on both factors indicates that there was a main effect for both the difficulty of the melody, F(1, 16) = 17.035, p < .001, and the number of hearings, F(1, 16) = 12.165, p = .003. However, the interaction was not significant, F(1, 16) = 2.598, p = .127. Thus, participants notated the pitches of the melody more accurately on the simple melodies than the complex ones, and also more accurately when hearing the melody six times than three times.

Results for leaps

Since we designed the complex melodies to be more difficult primarily because of their greater number of leaps, we ran a final 2×2 ANOVA on the percentage of leaps participants notated correctly (Figure 6). (A correctly notated leap had to have both the starting and ending pitches correct.) Since the simple melodies had five leaps each and the complex melodies had eight leaps each, we expressed each participant’s score as a percentage of correctly notated leaps so that the values could be compared. As with the pitch scores as a whole, we found a main effect for both the difficulty of the melody, F(1, 16) = 11.398, p = .004, and the number of hearings, F(1, 16) = 17.426, p < .001. In addition, the interaction between the variables was significant, F(1, 16) = 4.557, p = .049. Thus, not only did participants score less accurately on the melodies that had more leaps in them (as was hypothesized), they actually notated a lower percentage of those leaps correctly when the leaps were more numerous. In addition, they scored more accurately on the leaps when hearing more repetitions of the melody, and the size of this effect depended on how many leaps there were.

Correlations between participant background and dictation ability

Variance in participants’ backgrounds did not affect dictation scores. No significant correlation was found between participants’ combined score for all melodies and their scores on the absolute-pitch test, r(16) = .15, p = .55, their years of experience on their primary instrument, r(16) = .23, p = .36, or their years of piano study, r(15) = .41, p = .09.

Discussion

Conclusions and pedagogical implications

Findings suggest a main effect from the number of hearings of a melody, both on participants’ overall scores, as well as on each component of their scores (rhythm, pitch, and leaps). There was a main effect for difficulty on pitch and leap scores, but not on rhythm scores, as the complex melodies contained more melodic leaps but maintained similar rhythmic characteristics. In addition, there was an interaction between number of hearings and difficulty on the leaps component of the scores. This interaction is a sign of the cumulative effects of intrinsic cognitive loading for a complex task such as melodic dictation, especially since participants, being first-year undergraduates with little to no prior music theory study (see Participants, above), likely had little in the way of schemata to help them. In other words, participants’ working memory was overloaded by the presence of more difficult information which they were unable to chunk.

Indeed, other scholars have attempted to model how dictation scores are affected by a combination of working memory capacity and chunking ability. Karpinski (2000) has proposed the formula $H = \frac{N}{L} + 1$ . In this formula H is the number of hearings needed to produce a correct answer. N is the number of chunks in the melody (which Karpinski theorizes is equivalent to one note for the average college freshman without prior ear-training experience). Finally, L is the limit of working memory (a simplified version of Lawson’s, 1970, formula). In other words, the idealized number of hearings necessary to correctly complete a melodic dictation should be precisely enough to divide up the melody into segments short enough to be retained in working memory and written down one at a time, plus an additional hearing to compensate for any errors that may occur in the process. Based on a modified version of Miller’s “magic number seven,” Karpinski believes the limit of working memory as it relates to musical information is between 4 and 8.³ Based on our results, we can utilize the empirical data to clarify the working memory limit for ear-training tasks for the typical untrained freshman music major, and thus the optimal characteristics for melodies given to this particular cohort.

Since Karpinski’s formula discussed above ( $H = \frac{N}{L} + 1$ ) can be solved for any of its variables, including the limit of working memory (L), our data can be used to clarify the possible range of working memory skill in the freshman class at our institution. For N, Karpinski hypothesizes that beginning ear-training students would possess little to no aural chunking ability, and therefore the number of notes in the dictation would be a reasonable proxy for the number of chunks perceived. Since there were 18 notes in the melody, we set N to 18 in applying Karpinski’s formula. Solving Karpinski’s formula for the limit of working memory (L) with values of H = 3 hearings yields L = 9, and with H = 6 hearings yields L = 3.6.

However, in the participant population of these untrained first-year students, only 22% of the participants (4 of 18) notated the simple melody heard six times with 100% accuracy, and only one participant achieved 100% accuracy on just three hearings. Since most participants could not notate the dictation with complete accuracy even after six hearings, their limit of working memory would theoretically be even lower than 3.6. Karpinski’s (2000) interpretation of Miller’s (1956) theory of working memory predicted a range of 4 to 8 for L. Thus, our findings suggest the variance in working memory could be even wider than what Karpinski predicts. This variance speaks to the difficulties instructors face in selecting melodic dictation exercises at the proper level to challenge an entire freshman class, making the evidence that melodies 1 and 2 are better-suited to the skill level of the incoming freshman population especially useful. Further research could be done to determine the optimal characteristics for other (larger or differently skilled) cohorts of students.

Due to the interaction between the number of times a melody is heard and the difficulty of the melody, it is impossible to recommend the “right number of hearings” to give for a melody, as it simply depends on the melody and the skill level of the student cohort. Instead, data herein can be used to provide characteristics of melodies that lie in the optimal zone of learning for the typical incoming freshman at our institution. Referring back to Figure 1, this suggests that the two simple melodies were closer to the optimal zone of learning for participants, while the two complex melodies seem to have fallen into the zone of difficulty. Thus, five leaps seem to be in the zone of learning, and instructors should mind the number of leaps they present to this student cohort. This first empirical evidence of the dictation ability of incoming freshman music majors can be used to inform placement tests and initial melodic dictation exercises presented in ear-training classes at our institution.

Furthermore, scores for rhythm approached 100%, whereas scores for pitch did not. This suggests that the level of rhythms presented fell into the zone of mastery for this population.

The discrepancy between students’ pitch accuracy versus rhythm accuracy also raises larger questions for the relative pacing of pitch and rhythm elements in ear-training classes. Seminal ear-training texts (e.g., Rogers & Ottman, 2013) introduce single division of the beat first and hold this rhythmic difficulty level constant while increasing the difficulty of pitch content. Second division of the beat is not introduced until much later (Chapter 10). Other texts, such as Jones, Shaftel, and Chattah (2014), ask students to hear and sing second division of the beat even in Chapter 1. It remains to be seen whether the high rhythmic accuracy in the pilot study herein only shows that the rhythmic content of the stimuli was significantly easier to comprehend than its pitch content, or that these easier rhythms were necessary to then correctly determine the pitches.

Limitations of the study

It seems that the following mental factors are involved in melodic dictation: pure working memory capacity, chunking ability, translation or transcription ability, and capacity for selective attention. However, these various parameters are difficult to disentangle from one another: for example, we cannot say for certain whether some students achieve more accurate results on their dictations because they possess superior working memory or simply a better schema for chunking pitches or rhythms into an easily manageable number of pieces of information. It could be useful to develop a battery of stimuli systematically designed with a certain range of intrinsic cognitive load in mind and pilot-tested to determine whether they would be valid for the population of typical freshman music majors.

The small sample size is another limitation of the pilot study described herein. As a result, our analysis may have failed to capture some effects or interactions that would be evident from studying a larger pool of participants. In addition, the pilot study presented melodies in the same order to all participant groups, and a larger participant group would allow for an experimental design that varies the order of melody presentation systematically as well. In this design, the experiment would have eight groups, for all possible combinations of which melody of each pair was heard more times, which melody of each pair was heard first on each day, and whether the simple pair or complex pair of melodies was heard on Day 1.

Future directions

The results and limitations of the study suggest at least four further directions for fruitful research. First, repeating this experiment with a larger sample size is necessary to confirm these findings and possibly offer additional insight into which parameters of the melody significantly affected listener’s scores. Second, a longitudinal study testing students’ memory before and after each semester of ear-training could provide firsthand evidence and quantitative evaluation of the extent to which students’ working memory and/or chunking ability potentially changes over the course of a multi-semester ear-training curriculum. Students could be tested with similar melodies after each semester as a control, as well as with melodies of increasing difficulty to match their advancing optimal zone of learning. Third, while the findings suggested that major-mode melodies with single division of the beat are well-suited for incoming freshman music majors, it remains to be seen whether melodies with other characteristics (e.g., minor mode or second division of the beat) would also be appropriate for this population. Fourth, implementing the experiment with varying numbers of repetitions of the melody (such as 3, 4, 5, 6) could help determine more precisely where the threshold for accuracy (inversely corresponding to the limit of working memory) lies for various students.

Footnotes

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Nathan Cornelius

Notes

Author biographies

Nathan Cornelius pursues a multifaceted career in performance, composition, and teaching. He teaches ear training and music theory at the Peabody Institute of the Johns Hopkins University. His research interests include the application of working memory principles to music classroom pedagogy and the extent to which models of post-tonal theory accurately describe listeners’ perception of unfamiliar music.

Jenine L Brown joined the music theory department at the Peabody Institute of The Johns Hopkins University in 2015. Courses taught include the undergraduate ear training core curriculum and an upper-level post-tonal ear training elective. These courses offer Brown the opportunity to guide students on their journey to hearing musical structure, a pursuit in which she is extremely passionate. Brown’s research explores the perception of post-tonal music and the interaction between empirical research and aural skills pedagogy.

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