Predicting memorization efficiency through compositional characteristics

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Mishra

Predicting Memorization Efficiency

Predicting Memorization Efficiency through Compositional Characteristics

Pr

Pr

Jennifer Mishra University of Houston Houston, Texas

o

o

Abstract

o

o

f

f

co

co

I N TRO D U CT I O N Memorizing music for performance can be a long and tedious process encompassing many hours of practice. Musical compositions contain a large amount of information, which must be recalled through the physical motions of performance. It is not uncommon for one piece of music to contain thousands of pitches; each bound to rhythmic, expressive, stylistic, and other implied musical and lyrical information. Not only must the pitches be performed correctly and with the correct musical information attached, but also must be performed in a specified sequence. Further, the individual pitches must be connected to form a communicative shape. Memorizing music then is a multilayered, serial-position task in which the final product must coalesce into a new and understandable entity. Musicians, formally or informally, develop an image of their own memorization skills by comparison with others (real or idealized). The distinction of success may be based on how quickly music can be consigned to memory (efficiency) or on the number of memory lapses during performance (stability). However, musicians often decide whether they are “good” or “poor” memorizers based on a handful of salient experiences

pY

pY

44

The purpose of this study was to explore the effects of compositional characteristics on memorization efficiency. Thirteen research studies investigating musical memorization provided efficiency data and sufficient information to collect the notation for memorized excerpts (N = 55). Compositional characteristics chosen for inclusion in the regression model were number of bars, number of beats, number of notes, density, tonality, number of sharps/flats in key signature, number of chromatic tones, meter, tempo, number of repeating bars, and rhythmic complexity. Number of notes (representing amount of memorized material) was found to be the single best predictor of memorization efficiency (Adjusted R2 = .701) with additional factors, number of beats (representing length) and rhythmic complexity, accounting for 80.5% of the variance. A curve estimation was computed to project memorization efficiency of concert pieces. Compositional characteristics, isolated from memorization strategies, predict the amount of time required to memorize a piece.

45

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Method

Materials

pY

pY

46

co

co

minutes to memorize the same 36-bar exercise.

f

f

1 For instance, Mishra (1999) found that university instrumentalists required between 9 and 100

The musical material has been shown to have an effect on memorization. Halpern & Bower (1982) found that musicians remembered “good” melodies better than “bad.” Though non-musicians were not influenced by the quality of the music, both groups remembered melodies (regardless of quality) better than random pitches. Zielinska and Miklaszewski (1992) found that tonal melodies were easier to memorize than modal. A finding supported by Nuki (1984), Sloboda, Hermelin, & O’Connor (1985), and Oura & Hatano (1988). Research directly concerned with the effects of musical characteristics on memorization efficiency is scarce; however, indirect confirmation is embedded in many of the experimental studies cited in the previous section. In most research studies investigating the efficiency of memorization strategies, various musical compositions were used. In some research, the compositions were especially composed and features of the music were controlled; other times music was chosen without discussion as to the method of selection. In most cases, the compositions were treated as incidental to the treatment, but in a few cases, composition was included as a treatment variable. When composition was included as a variable in statistical computations, indications of a significant composition-effect were apparent (e.g., Nellons, 1974; Rubin-Rabson, 1937, 1939, 1940b, 1941a, 1941c, 1941d; Schlabach, 1975). However, the importance and implications of the significant effects of composition on efficiency were not explored, nor were conclusions as to why some compositions were memorized significantly faster presented. In a regression study, significant correlations were reported (Lehmann and Ericsson, 1998) between memorization time and difficulty of the piece (r = .82) and the number of key-strokes (r = .79) also linking music complexity and memorization efficiency. The purpose of this study was to further explore the effects of compositional characteristics, especially characteristics that relate to the difficulty of the piece, on memorization efficiency using the regression procedure of Lehmann and Ericsson. While each composition of music is unique and carries unique challenges and musical ideas, similar elements reoccur allowing for some level of comparison across disparate pieces.

o

o

For nearly a century, researchers have been interested in discovering how quickly music can be memorized and whether the process can be expedited. Early research into the process of memorization primarily revolved around the experimental investigation of memorization strategies designed to speed the memorization process including: whole and part strategies (Brown, 1928; Clapp, 1924; Eberly, 1921; O’Brien, 1943; Rubin-Rabson, 1940a); practicing hands separately/together (Brown, 1933; Rubin-Rabson, 1939); use of aural, visual, and/or kinesthetic memory (Nuki, 1984; O’Brien, 1943); analysis (Jones, 1990; Reynolds, 1975; Rubin-Rabson, 1937, 1941a; Ross, 1964; Schlabach, 1975); blocking chords (Nellons, 1974), memorization instruction (Bryant, 1985, Ross, 1964, Williamson, 1964), listening (Buckner, 1970; Rubin-Rabson, 1937; Schlabach, 1975), and incentives (Rubin-Rabson, 1941b). Results from experimental studies have been mixed and a panacea for quick musical memorization has not emerged. For instance, Rubin-Rabson, (1937 & 1941a) and Ross (1964) found a pre-performance analysis of the piece facilitated memorization, but Reynolds (1975), Schlabach (1975), and Jones (1990) found no effects from analysis. The whole strategy (playing from beginning to end during each repetition) was found by early researchers (Brown, 1928; Clapp, 1924; Eberly, 1921) to speed memorization, but more recent qualitative research indicates the need for a part strategy (e.g., Chaffin, Imreh, & Crawford, 2002; Miklaszewski, 1989; Nielsen, 1999). Though the effects of many memorization strategies have been investigated, others remain unexplored (e.g., slow practice, visualization, practicing piece from the end, and age-related effects).

Musical Characteristics

o

o

Memorization Strategy

Predicting Memorization Efficiency

Pr

Pr

or informal conversations rather than systematic observation and comparison. There is no doubt that some musicians memorize faster than others1; however even the most advanced musician requires time to memorize. A good memorizer may be a musician who can memorize relatively quickly, but in reference to what standard? A poor memorizer may perceive the memorization process as time-consuming and difficult, but without a constant for comparison, this self-perceived “poor” memorizer may simply be experiencing the normal level of frustrations encountered when mastering the difficult task of memorizing music. Recent qualitative studies have confirmed that memorization requires a great deal of time, even for the professional musician (e.g., Chaffin, Imreh, and Crawford, 2002). It is not yet known whether memorization efficiency is influenced consistently by identifiable factors and whether influential factors are within or beyond the control of the musician to alter for a more efficient memory. A large number of factors may potentially influence the amount of time required to memorize which appear to fall broadly into two categories: memorization strategy and characteristics of the composition.

Mishra

Published and unpublished research reports were carefully examined for memorization efficiency data, regardless of whether memorization efficiency was a central feature of the research design. Memorization efficiency has generally been reported either in terms of total memorization time or number of learning trials required to memorize a composition. In studies reporting learning trials, musicians were required to memorize using a whole-method and the number of complete performances, rather than the amount of time, required to memorize the piece was reported. Even when sufficient information was provided, including length of composition and tempo, converting trial data into 47

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Instrument/ No. ParticiVoice pants

Brown, 1928

Piano

No data 16-32

1.13-16.46

130-508

4-82

0-11

24-96

Brown, 1933

Piano

No data 24-26

4.21-8.46

134-437

9-41

0-6

72-105

Bryant, 1985

Brass

42

16

1.12

65

4

1

32

Buckner, 1970

Strings & winds

28

16

1.29-1.59

36-68

4-15

0-1

48-64

Eaton, 1978

Keyboard

73

4-8

0.30-0.32

46-53

0-3

0-2

8-24

Mishra, 1999

Strings & winds

60

36

1.14

90

8

0

144

Nellons, 1974

Piano

22

22-30

2.20-7.48

212-217

21-78

0-5

50-90

Nuki, 1984

Piano

30

41

1.05-1.41

522

27

0

164

O’Brien, 1943

Piano/Vocal 4

16-32

0.12-0.26

64-336

1-11

0-18

48-128

Reynolds, 1975

Vocal

29

16-31

1.15-2.01

53-80

6-21

0-1

64-94

Rubin-Rabson, 1937

Piano

24

16-26

2.07-3.89

136-227

2-8

0-4

48-78

Schlabach, 1975

Piano

24

16-17

1.01–2.80

130-231

0-3

0-3

56-68

Williamon & Valentine, 2000

Piano

22

16-70

11.48-25.56

148-1492 9-271

0-1

48-237

Williamson, 1964 Vocal

86

18-26

1.67-2.31

55-73

0-5

54-84

No. Bars

Length of Composition.

M MemorizaNo. No. tion Time per No. Notes Chromatic Repeated No. Beats Bar (minutes) Tones bars

co

co

Researcher/ Date

f

f

4-9

In research studies of musical memorization, the most commonly reported descriptor of the compositions was the total number of bars. Implied in the inclusion of these data was a relationship between the length of the piece and the time required to memorize. However in music this assumption has not been experimentally tested. Generally, music used for research was short, averaging 22.12 bars (SD = 9.19). Computing the mean time required to memorize per bar allowed a comparison between compositions of varying length (see Table 1). The average amount of time required to memorize per bar was 4.68 minutes, however the large standard deviation (4.93 minutes per bar), indicated a great deal of variability. An alternative measure of length was also included in the regression, number of beats. This measure reflects the variable lengths of pieces in different meters. A piece with four beats per bar will be longer than a piece with an equal number of bars in a meter of

pY

pY

48

Research studies providing sufficient memorization efficiency data and compositional information for inclusion in regression computations. Characteristics of compositions memorized and sample are reported.

o

o

Notation was examined for musical characteristics that reflected the difficulty of the composition or potentially influenced the time required for memorization. The choice of compositional characteristics was closely constrained due to the availability of the data (including only information contained within the design of the study and/or in the notation itself ) and the limitations of quantifying musical descriptors. In many cases, the variables represent a level of musical complexity and/or difficulty, but may not be a complete manifestation of the musical concept. The compositional characteristics chosen for inclusion in the regression model were number of bars, number of beats, number of notes, density, tonality, number of sharps/flats in key signature, number of chromatic tones, meter, tempo, number of repeating bars, and rhythmic complexity. Rationales for inclusion of these characteristics as well as descriptive statistics follow.

Table 1

o

o

Compositional Characteristics

Predicting Memorization Efficiency

Pr

Pr

time data for comparison with other research findings required an unacceptable level of estimation. Thus, studies reporting memorization efficiency in terms of learning trials were omitted from further analyses. Inclusion in the analyses performed in this study was limited to research studies where precise information concerning the total amount of time required for memorization of each composition was reported and where the exact notation for the memorized composition, or enough information to obtain the notation, was provided. Fourteen research studies were initially identified that provided both efficiency data and compositional information (see Table 1). The studies were assessed for internal validity and data from one study (Nuki, 1984) was subsequently removed from analysis as Participants were stopped after one hour regardless of memorization progress, thus potentially limiting memorization time and resulting in uncertainty as to the level of memorization achieved. Table 1 provides an overview of the 14 research studies. For comparison purposes only, memorization time is expressed in terms of minutes per bar; however, in the regression analysis, total memorization time (in minutes) was used as the dependent variable. Notation for 55 out of 59 different compositions and compositional excerpts used in the 13 research studies was obtained. When multiple compositions were used within one study, the range of mean memorization times is expressed in Table 1; however, each individual composition was treated separately in the regression analysis. Additionally, for experimental research studies, the mean memorization time for treatment and control groups were included separately for a total of 67 data points.

Mishra

49

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

three. While potentially highly related to number of measures, the variable was included partially to determine if these two measures differentially affected memorization time.

Meter.

o

o

Tempo.

co

co

Meter is the grouping of beats within a bar generally associated with patterns of emphasis. The most common meters in western tonal music are duple (two or four beats per bar, emphasizing beats one and, to a lesser extent, three) and triple (three beats per bar, emphasizing beat one). Meters may also be asymmetrical, generally in bars with an odd number of beats (other than one and three), in which emphases are unevenly applied (e.g., 5/4, 7/8). Compound meters describe compositions in which the beat is subdivided into three rather than the more standard two (e.g., 6/8). Just over half (52%) of the compositions used in studies of musical memorization were in duple meter and 44% were in triple meter. None of the compositions chosen for inclusion in memorization studies were written in asymmetrical or compound meters; again, limiting the variability of the sample.

f

f

Tempo is the pace at which the music is performed. Often, a tempo indication is notated in the piece using either broad category (e.g., andante, allegro) or as a metronome marking (mm) reflecting the number of beats per minute. If tempo varies, two pieces with an equal number of beats will require a different amount of time to complete one performance. It is possible that total performance time may influence total memorization time. Tempo was entered as continuous data as many composers noted the beats per minute on the notation or the information was provided. In cases where tempo was expressed in the form of a descriptive word (e.g., allegro), the data were transformed to the average beats per minute for music in the relevant tempo category. The average tempo was mm = 94.45 (SD = 31.16). Notated tempo is an inexact measure as few researchers reported whether the musicians practiced and performed at the notated tempo. It is possible for a discrepancy to

pY

pY

2 In a survey of Beethoven’s instrumental works, 94% were written in keys with three or fewer

The number of chromatic tones (pitches outside of the key as identified by the addition of a sharp, natural, or flat in the notation) was included as one measure of harmonic complexity. Harmony is the simultaneous or successive sounding of pitches to form chords. Harmony relates to key in that notes are, to some extent, predictably combined and ordered into progressions to reflect the key’s center. Simple harmonies are produced using only the pitches designated in the key (diatonic). An increase in chromatic pitches or pitches outside of the key generally reflects a greater level of harmonic complexity. The average number of chromatic tones included in the compositions used in memorization studies was 19.21, but this number fluctuated greatly with a standard deviation of 36.22.

o

o

Tonality, broadly speaking, defines the relationship between pitches. Western tonal music predominately utilizes major and minor tonalities, but other pitch organizations are possible including the use of modal scales and atonal compositional techniques. The majority of the compositions used in studies of memory were either in major (63%) or minor (21%) tonality. Sharps or flats that will consistently be used throughout the piece are notated at the beginning in the key signature. Key signatures do not denote tonality as the same grouping of sharps or flats may refer to a major, minor, or modal tonality. Western tonal music is generally written with three or fewer sharps or flats in the key signature2. Familiarity with these keys may facilitate memory performance. Key signatures are also important, as they must be considered as part of the memory-load. Musicians must remember which sharps or flats were notated in the key signature and perform the appropriate alteration to the pitches throughout the piece. It is possible that as the number of sharps or flats increases, the available storage space decreases; however, the effect of accidentals may be more relevant for research with novice performers rather than expert musicians.

50

As with tonality, there was limited variability in the sample with 87% of pieces used in studies of memorization in keys with fewer than two sharps or flats.

Pr

Pr

The number of notes contained in each composition reflected the amount of material memorized. Inclusion of this measure was based on a preliminary exploration of the data which revealed that pianists memorized significantly slower (M = 131.34 minutes) than single-line instrumentalists (M = 22.00 minutes) or vocalists (M = 32.18 minutes). Single-line instrumentalists and vocalists were four to five times faster at memorizing than pianists. This finding was logical in that piano music often includes multiple voices and thus more musical material. This finding was confirmed, with piano compositions containing an average of 287 notes versus 66.57 for vocal and 63.64 for single-line instrumental compositions. Number of notes represents only one aspect of memory-load as musicians must encode information in addition to just pitch including duration, expressive elements (e.g., dynamics and articulations), phrasing, and non-notated information implied in the music (e.g., pedaling and fingerings). No attempt was made to quantify the total amount of material that must be encoded with each note, but was included as a representative of the amount of memorized material. In addition, density, a measure of the number of notes per beat, was added which reflected vertical (chords) as well as horizontal groupings (sub-divisions) of notes.

sharps or flats.

Predicting Memorization Efficiency

Number of Chromatic Tones.

Number of Notes & Density.

Tonality and Key.

Mishra

51

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

MEMX BARS NOTES REPEAT INST METER KEY TONALITY CHROM MM BEATS DENSITY

Multiple Regression The purpose of this study was to explore the effects of compositional characteristics on memorization efficiency. A multiple regression was conducted to determine whether

.551 1.000 .739 .137 .160 -.016 -.104 .226 .690 .040 .914 .139 .014

NOTES

.840 .739 1.000 .029 .407 .085 -.203 .018 .820 -.054 .746 .629 .243

REPEAT

Correlations

-.094 .137 .029 1.000 .185 -.135 -.063 -.082 -.006 .119 .081 .034 -.059

INST

.324 .160 .407 .185 1.000 -.219 -.204 -.077 .195 .190 .082 .649 .070

METER

-.041 -.016 .085 -.135 -.219 1.000 -.175 .178 -.076 .217 .343 -.291 .052

KEY

-.135 -.104 -.203 -.063 -.204 -.175 1.000 .057 -.126 -.160 -.199 -.098 -.110

TONAL

.055 .226 .018 -.082 -.077 .178 .057 1.000 .068 .487 .313 -.143 .011

CHROM

.727 .690 .820 -.006 .195 -.076 -.126 .068 1.000 -.158 .638 .401 .167

MM

-.154 .040 -.054 .119 .190 .217 -.160 .487 -.158 1.000 .167 -.077 -.151

BEATS

.527 .914 .746 .081 .082 .343 -.199 .313 .638 .167 1.000 .060 .044

DENSITY RHYTHM

.618 .139 .629 .034 .649 -.291 -.098 -.143 .401 -.077 .060 1.000 .341

.513 .014 .243 -.059 .070 .052 -.110 .011 .167 -.151 .044 .341 1.000

Table 3. Model Summary of linear regression indicating the number of notes, number of beats, and rhythmic complexity significantly predicted memorization time. Model Summary

R Adjusted Std. Error of R Square Square R Square the Estimate Change Model R 1 .902a .814 .805 61.28366 .814 a. Predictors: (Constant), NOTES, RHYTHM, BEATS

pY

pY

R e s u lt s

RHYTHM

1.000 .551 .840 -.094 .324 -.041 -.135 .055 .727 -.154 .527 .618 .513

BARS

co

co

Rhythm describes the duration of pitches. Though constrained to a certain extent by meter, pitches may be performed with varying lengths. These lengths are combined to form patterns with varying levels of difficulty. Rhythms aligned with beats with few subdivisions are generally easier than syncopated rhythms that are off-set from the beat and include many subdivisions. Rhythmic complexity was defined as the maximum number of subdivisions of the beats. Over half of the pieces used in studies of memorization (52.23%) were relatively simple with a maximum of only two divisions of the beat (eighth notes), though a large number included four divisions of the beat (34.32%). Measured ornamentations were included resulting in a maximum rhythmic complexity score of 32. This measure is limited as it does not account for syncopations or inter-play between parts.

52

Pearson Cor relation

MEMX

f

f

Rhythmic complexity.

Table 2. Correlation matrix of linear regression.

o

o

Form is the pattern of repetitions and contrasts within a piece. A formal analysis of the pieces used in studies of memorization was limited primarily due to the briefness of the musical examples. Thus, form was reflected in the number of repeated bars within the piece. A repeated bar may result in a savings of learning and reaction time. The number of repeating bars however did not reflect sequences (repeating material at a different pitch level) or bars that were similar, but not identical. This measure also did not reflect repetitions within bars or vocal music that repeated melodically, but not textually. On average, only 2.24 bars were repeated within the compositions used in studies of memorization.

independent variables (number of bars, number of beats, number of notes, density, tonality, number of sharps/flats in key signature, number of chromatic tones, instrument, meter, tempo, number of repeating bars, and rhythmic complexity) were predictors of total memorization time. In all but two cases, independent variables consisted of continuous data; tonality and instrument were entered as dummy variables using the categories: major, minor, atonal/modal for tonality and single-line instrument, vocal, and piano for instrument. When all variables were entered into the regression, the adjusted R2 was .816. Three variables, number of bars, density, and number of chromatic tones, were found to be highly correlated with others and were removed from the analysis (see Table 2). The number of sharps/flats in key signature, meter, instrument, number of repeated bars, tempo, and tonality were also removed, as these variables did not significantly contribute to the variance.

o

o

Repetitions.

Predicting Memorization Efficiency

Pr

Pr

exist between the notated and performed tempi. Some researchers attempted to control for tempo fluctuations by requiring practice to conform to the notated tempo. In these studies, musicians were required to practice with a metronome to standardize the tempo while in other studies performers were allowed to freely practice without tempo restrictions. As tempo variability could influence overall memorization time, the use of metronome was initially treated as an independent variable; however a preliminary findings, based on a t-test for Independent Means indicated no significant difference (p < .05) in mean memorization time required for performers required to conform to a metronome (M = 105.23 total minutes) and those with no tempo restrictions (M = 103.30 total minutes).

Mishra

Change Statistics F Change df1 df2 91.938 3 63

Sig. F Change .000

Regression results indicated number of notes, number of beats, number and rhythmic complexity significantly predicted total memorization time and were found to account for 80.5 % of the variance (see Tables 3 & 4). As density was a measure reflecting the number of notes per beat, this variable was substituted for the variables number of notes and number of beats, but with rhythmic complexity only explained 46.9% of the variance. 53

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Mishra

Standardized Coefficients Beta .311 -.127 .859

t -.601 5.420 -1.522 10.002

Sig. .550 .000 .133 .000

9 00 Zero-order

Correlations Partial

Part

.513 .527 .840

.564 -.188 .783

.294 -.083 .543

8 40 7 80

Collinearity Statistics Tolerance VIF .899 .424 .400

7 20

1.112 2.358 2.500

6 00 5 40 4 80 4 20 3 60 3 00 2 40

O b s erved L inea r 16

15

13

14

12

11

00

00

00 00

00

00

00

0

0

0

0

0

0

0

0

NOTES

10

90

80

70

60

50

40

30

0



20

0

o

o

N O TofEStotal memorization time based on observed memorizaFigure 1. Linear curve estimation

tion times.

f

co

co

pY

pY

An exponential curve estimation was also computed (see Figure 2) as discussion in the psychological literature is divided on whether learning time as a function of serial list length is linear or exponential (see Slamecka, 1985 for discussion). If memorization time increases exponentially, a piece containing 1000 notes would require 12.77 (766 minutes) to memorize and a piece containing 1500 notes would require 70.90 hours (4254 minutes) to memorize. The linear curve estimation appeared to match the observe data better than the exponential curve estimation. To verify the validity of the curve estimations, the predictions were compared with actual data collected by Williamon and Vallentine (2000). In this research, pianists of various levels were asked to practice a composition by J.S. Bach, matched to their level and then perform the composition in a recital setting. This study was more naturalistic than most experimental research as performers prepared technically-appropriate composition and were expected to perform in a recital-setting, rather than to a criteria of one or two correct performances. Table 4 allows for a comparison between actual memorization times as reported by Williamon and Valentine (2000) and the projected memorization time based on the curve estimation. Predicted memorization times were generally less than actual memorization time. Times predicted by the linear model were closer to actual memorization times than those predicted by the exponential curve estimation.

f

Compositions used in studies of musical memorization were generally short with an average of 22 bars and 213 notes. Musical compositions prepared for performance however are often much longer with bars containing many more notes. It is not uncommon for pianists to prepare pieces with hundreds of bars and thousands of notes. A curve estimation was computed to predict memorization time for longer compositions (see Figure 1). Time was predicted as a function of the number of notes in the composition as this was the factor most predictive of memorization time in the regression analysis. As number of notes was not a perfect predictor of memorization time, the curve estimation is, of course, approximate. The curve estimation is also limited to 1500 notes as the maximum number of notes in the data set was 1492. Assuming that memorization time progresses in a linear fashion, a composition containing 1000 notes would require 9.22 hours (553 minutes) to memorize and one containing 1500 notes would require 13.95 hours (837 minutes) to memorize.

o

1 80 1 20 60 0

10

o

Curve Estimation

6 60

Pr

Pr

The number of notes was the single most predictive variable; accounting for 70.1 % of the variance. Thus, the amount of musical material as reflected in the number of notes was the most influential variable in determining the amount of time required for memorization.

54

Estimated Memorization Time

Minutes M in utes



Coefficientsa Unstandardized Coefficients Model B Std. Error (Constant) 1 -13.305 22.128 RHYTHM 11.444 2.111 BEATS -.553 .363 NOTES .580 .058 a. Dependent Variable: MEMX

Es ti mated Mem or ization T ime



Table 4. Coefficients table for variables included in regression model.

Predicting Memorization Efficiency

55

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Es ti mated Mem or iz aton Ti me - Ex ponential

Estimated Memorization Time Minutes M in utes



16

15

14

13

12

10

11

90

00

00

00

00

00

00

00

0

0

NOTES

0

0

0

0

0

0

0

Composition

Number of Notes

Number of Beats

Rhythmic Complexity

Actual M Memorization Time*

Linearly predicted Memorization Time*

Exponentially predicted Memorization time

Polonaise in G minor from Anna Magdalena Notebook BWV 119 by J.S. Bach

148

48

4

3.68

1.17

0.69

Two Part Invention in C Major BWV 772 by J.S. Bach

472

88

32

9.37

4.23

2.09

Three Part Invention in B Minor BWV 801 by J.S. Bach

672

114

6

7.27

6.12

4.15

Prelude and Fugue in D Minor from The Well-Tempered Clavier I BWV 851 by J.S. Bach

1492

4

13.83

13.87

68.98

237

*Total memorization times reported in hours.

f

f

co

pY

pY

Discussion The focus of this research was to investigate whether characteristics of a composition affected memorization efficiency. It is clear that compositional characteristics do affect how much time is required to memorize a piece. The amount of time required for memorization depends to a large extent on the composition itself. The number of notes, reflecting the amount of memorized material, was the single most predictive variable (Adjusted R2 = .701). This finding supports that of Lehmann and Ericsson (1998) who found that practice time could be predicted (R2 = .88) by number of key-strokes and a rating of complexity. Additionally, number of beats, reflecting length, and rhythmic complexity also contributed to memorization efficiency (Adjusted R2 = .805). As to the length of the pieces, it should be noted that the number of bars was not as influential as the number of beats. The influence of length and the amount of material on memorization efficiency was not especially surprising as Ebbinghaus (1885/1964) had noted the list length as a factor in influencing number of trials required for memorization. However, the large effect of composition on memorization efficiency is surprising when considering previous research and pedagogical discussions concerning the musical memorization process.

co

While the number of notes contained in a piece is highly predictive of the amount of time to memorize the piece, other factors such as rhythmic complexity and number of beats also influenced the memorization process. Rhythmic complexity appears especially important specifically when considering the large discrepancy between the actual and predicted values for the musicians memorizing the Two Part Invention in C Major. The actual memorization time was more than double that predicted by the curve estimations. However, the rhythmic complexity of this piece is much higher than that of the other pieces. The discrepancy between predicted and actual times may reflect the influence of complex rhythms on the overall memorization times.

o

o

based on reported memorization times for shorter compositions.

o

E x ponentia l

O TExponential ES Figure N2. curve estimation of total memorization time for longer compositions

56

Table 4

Pr O bs er ved

80

70

60

50

40

30

20

o 10

0



Predicting Memorization Efficiency

Actual memorization time for four pieces memorized for concert performance as reported by Williamon & Valentine (2000) compared with projected memorization times based on a linear and exponential curve estimations.

Pr

4 200 4 000 3 800 3 600 3 400 3 200 3 000 2 800 2 600 2 400 2 200 2 000 1 800 1 600 1 400 1 200 1 000 8 00 6 00 4 00 2 00 0

Mishra

57

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

The role of training and expertise

cians of varying abilities memorizing a standard piece will highlight the importance of task-difficulty relative to compositional characteristics of the music.

Additional Compositional Factors

o

o

f

f

co

co

pY

pY

Compositional factors included in this study were limited by the ability to quantify the variable and other compositional factors were not included due to scarcity or limited variability in the data. Whether vocal lyrics are in the native or foreign language may be important, however with only 10% of the compositions as vocal, there was insufficient data to consider language an important variable. Key and meter were included, but the data did not adequately represent a wide spectrum of variability. It was theorized earlier in this paper that as the number of sharps or flats in the key signature increases, so does the memory load. This theory remains untested as the vast majority of pieces used in memorization studies included key signatures of two or fewer sharps or flats with very few compositions with key signatures of four or five sharps or flats. Consideration of two further issues concerning the effects of key on memory load is warranted. The number of accidentals in the key signature may have differential effects based on level of expertise. The memory of novice musicians may be affected by accidentals in the key signature as experience may be limited to pieces in only a handful of keys. Accidentals rarely encountered by novice musicians may require conscious effort to be remembered and placed appropriately within the piece; while expert musicians may automatically adjust appropriate pitches based on any accidental indicated by the key. Further, the influence of the key signature may differ based on previous training; wind instrumentalists, who generally begin instruction in the keys of F and B-flat (respectively, one and two flats in key signature) may find playing in the key of D (two sharps) problematic. While the results of this study confirm Lehmann and Ericsson (1998) in that the number of pitches (or keystrokes), as a representation of the amount of material contained in the piece, was the single best predictor of memorization time, the results are at odds with research that expert musicians group (or chunk) information. It is highly improbable that these advanced musicians were reading or processing individual notes during memorization. Musicians, especially advanced musicians, chunk individual notes, both vertically and horizontally, based on familiar musical patterns. It is possible that a variable representing the number of meaningful groups would result in a more important predictor of memorization efficiency.

o

o

58

Predicting Memorization Efficiency

Pr

Pr

Previous research on the memorization of music has focused on increasing efficiency through the use of memorization strategies. After a content analysis of 121 pedagogical articles concerned with musical memorization, published since 1900, not one mentions compositional characteristics as a consideration and only three acknowledge that difficult passages may be subject to memory failure. The results of this study illuminate the importance of the musical material on how quickly a piece may be memorized. However, the role of training and expertise should not in any way be marginalized in light of the results of this study. It is likely that when the musical material is held constant, individual factors such as expertise, training, and memorization strategy may become very important. Data for this study were average memorization times as reported in previously conducted research. While the average memorization time is an important measure to provide a standard, individual musicians will vary for time needed to memorize a piece of music. Mishra (1999) found that university instrumentalists required between 9 and 100 minutes to memorize the same 36-bar exercise. Upon further qualitative investigation of the fastest and slowest memorizers (Mishra, 2002), different memorization strategies emerged as the most influential difference. Expertise and compositional characteristics may also interact. Halpern & Bower (1982) found that the quality of the musical material influenced memorization, but for musicians only. Non-musicians’ memory was not influenced by the nature of the material. These interactions coupled with well-documented research into expertise development where experts demonstrate a superior memory for meaningful patterns, though not random patterns indicate skill and material interact to influence memorization efficiency. The overall difficulty of a composition was not considered in this study, as it is a relative distinction; a composition that is simple for one musician may be technically beyond another. Presumably, advanced performers would require less time to memorize an easy composition and less advanced performers would find it difficult, if not impossible, to memorize a composition that was beyond their level of expertise. The compositions used throughout the research were diverse in many ways, but a careful reading of the research indicated that most subjects would have found the music technically undemanding. Thus, the results of this research are limited to advanced performers memorizing short, easy pieces. It is conceivable that task-difficulty differentially affects the importance of compositional factors on memorization efficiency. For musicians memorizing technically simple pieces (as determined by individual technical proficiency), compositional factors such as number of notes, beats and rhythmic complexity may reliably predict memorization efficiency. However, when musicians memorize technically demanding music, expertise and memorization strategy may become dominant. Future researchers should consider task-difficulty carefully when choosing music for memorization. Memorization efficiency for music that is relatively easy for the performers should be compared with music of a higher relative difficulty. Further, musi-

Mishra

Conclusion The identification of efficient memorization strategies has been difficult throughout the history of musical memorization research due to inconsistent findings and methodologies. One implication of this study is that compositional characteristics may negate or obscure strategic differences. The musical material has a great deal of effect on the amount of time required for memorization. In general, researchers should be more sensi59

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Predicting Memorization Efficiency

Mishra, J. (1999). The effects of altering environmental context on the Performance of memorized music. Unpublished doctoral dissertation, Kent State University—Kent, OH. Mishra, J. (2002). A qualitative analysis of strategies employed in efficient and inefficient memorization. Bulletin of the Council for Research in Music Education, 152, 74-86. Nellons, C. E. (1974). An experimental investigation of the effects of blocking on the memorization of selected piano music. Unpublished doctoral dissertation—University of Oklahoma, Norman. Nielsen, S. (1999). Regulation of learning strategies: A case study of a single church organ student preparing a particular work for a concert performance. Psychology of Music, 27(2), 218-229.

Pr

Pr

Nuki, M. (1984). Memorization of piano music. Psychologia: An International Journal of Psychology in the Orient, 27(3), 157-163.

O’Brien, C. C. (1943). Part and whole methods in the memorization of music. Journal of Education Psychology, 34, 552-560.

o

Oura, Y., & Hatano, G. (1988). Memory for melodies among subjects differing in age and experience in music. Psychology of Music, 16, 91-109.

o

tive to the effects of the material chosen for memorization. Compositional characteristics have a great deal of influence on the amount of time required to memorize a piece of music. Great care should be taken when choosing music and controls should be in place to minimize effects of composition if this is not the primary focus of the research study. Further, researchers should take care to report relevant compositional features and efficiency data to add to future regression analyses for greater refinement in the model. Memorization is time-consuming, but the purpose of this research was to demonstrate that variables which predict memorization efficiency can be identified and, rather than a myriad of variables, there are a manageable number of variables that systematically affect memorization efficiency (amount of material, length of piece, and rhythmic complexity). The standard provided in through curve estimations allows an estimation of the amount of time required for memorization and goes some way to identifying the optimal amount of time for memorizing music. Longer pieces containing more notes and which are rhythmic complex will require more time for memorization.

Mishra

Reynolds, M. H. (1975). A comparative study of the effects of two experimental methods of guidance on vocal solo memorization. Unpublished doctoral dissertation, North Texas State University— Denton.

Brown, R. W. (1928). A comparison of the “whole,” “part” and “combination” methods of learning piano music. Journal of Experimental Psychology, 11, 235-247.

Rubin-Rabson, G. (1937). Previous research in the psychology of music. In Archives of Psychology the Influence of Analytical Pre-Study in Memorizing Piano Music No. 220, 31, 7-53.

Brown, R. W. (1933). The relation between two methods of learning piano music. Journal of Experimental Psychology, 16, 435-441.

Rubin-Rabson, G. (1939). Studies in the psychology of memorizing piano music: I. A comparison of the unilateral and the coordinated approaches. The Journal of Educational Psychology, 30(5), 321-345.

f

f

Bryant, D. E. (1985). The effect of special memory instruction and guided analysis on the memorization efficiency of college brass players. Unpublished doctoral dissertation, University of Oklahoma— Norman.

o

Ross, E. (1964). Improving facility in music memorization. Journal of Research in Music Education, 12(4), 269-278.

o

References

Rubin-Rabson, G. (1940a). Studies in the psychology of memorizing piano music: II. A comparison of massed and distributed practice. The Journal of Educational Psychology, 31(4), 270-284.

Chaffin, R., Imreh, G., & Crawford, M. (2002). Practicing perfection: Memory and piano performance.Mahwah, NJ: Lawrence Erlbaum

Rubin-Rabson, G. (1941a). Studies in the Psychology of Memorizing Piano Music. IV. The effect of incentive. The Journal of Educational Psychology, 32, 45-54.

Clapp, P. G. (1924). A university test of better method to memorize piano music. The Musician, 14.

Rubin-Rabson, G. (1941b). Studies in the psychology of memorizing piano music: V. A comparison of pre-study periods of varied length. The Journal of Educational Psychology, 32, 593-602.

Eaton, J. L. (1978). A correlation study of keyboard sight-reading facility with previous training, notereading, psychomotor, and memorization skills. Unpublished doctoral dissertation, Indiana University—Bloomington.

co

Rubin-Rabson, G. (1940b). Studies in the Psychology of Memorizing Piano Music: III. A comparison of the whole and the part approach. The Journal of Educational Psychology, 31(9), 460-476.

co

Buckner, J. F. (1970). The effect of aural models on efficiency of single-line instrumental music memorization. Unpublished doctoral dissertation, University of Kansas—Lawrence.

Rubin-Rabson, G. (1941d). Studies in the psychology of memorizing piano music: VII. A comparison of three degrees of overlearning. The Journal of Educational Psychology, 32, 688-696.

Halpern, A. R., & Bower, G. H. (1982). Musical expertise and melodic structure in memory for musical notation. American Journal of Psychology, 95(1), 31-50.

Schlabach, E. L. (1975). The role of auditory memory in memorization at the piano. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.

Jones, A. R. (1990). The role of analytical prestudy in the memorization and retention of piano music with subjects of varied aural/kinesthetic ability. Unpublished doctoral dissertation, University of Illinois at Urbana-Champaign.

Slamecka, N. (1985). Ebbinghaus: Some associations. Journal of Experimental Research: Learning, Memory, and Cognition, 11(3), 414-435.

Lehmann, A. C., & Ericsson, K. A. (1998). Preparation of a public piano performance: The relation between practice and performance. Musicae Scientiae, 2(1), 67-94. Miklaszewski, K. (1989). A case study of a pianist preparing a musical performance. Psychology of Music, 17, 95-109. 60

pY

Eberly, L. E. (1921). Part v. Whole Method in Memorizing Piano Music. Unpublished masters thesis, Colombia University, New York.

pY

Ebbinghaus, H. (1885/1964). Memory: A Contribution to Experimental Psychology. New York: Dover.

Rubin-Rabson, G. (1941c). Studies in the psychology of memorizing piano music. VI: A comparison of two forms of mental rehearsal and keyboard overlearning. The Journal of Educational Psychology, 32, 593-602.

Sloboda, J. A., Hermelin, B., & O’Connor, N. (1985). An exceptional musical memory. Music Perception, 3(2), 155-170. Williamon, A., & Valentine, E. (2000). Quantity and quality of musical practice as predictors of performance quality. British Journal of Psychology, 91, 353-376.

61

Bulletin of the Council for Research in Music Education

Summer 2008 No. 177

Williamson, S. C. (1964). The effect of special instruction on speed, transfer, and retention in memorizing songs. Unpublished doctoral dissertation, University of Kansas—Lawrence. Zielinska, H., & Miklaszewski, K. (1992). Memorising two melodies of different style. Psychology of Music, 20, 95-111.

The Chelsea House Orchestra

The Chelsea House Orchestra: A Case Study of a Non-Traditional School Instrumental Ensemble

Pr

Pr

Steve Wichita State University Wichita, Kansas

o

o

Abstract

The purpose of this study is to describe the ways in which a high school orchestra program balances the need for a more diverse repertoire of music with the limitations and requirements inherent to traditional instrumental music programs. This research project used a qualitative case study design to analyze the Chelsea House Orchestra (CHO), a nontraditional high school Celtic string ensemble. Data included interviews with CHO’s director, a focus group interview and observations of CHO and traditional orchestra rehearsals. Trustworthiness was further achieved by the use of member checks and peer review. Four themes emerged from the analysis of data. They include: • Social Music Making • The Balance Between Classical and Folk Music Education • Evolving Authenticity • The Creolization Of Musical Transmission Few school instrumental groups exist that perform multicultural music. This study presents a model of an instrumental folk ensemble that lives harmoniously with a fine traditional orchestra program.

o

o

f

f

co

co

keywords: multicultural music education, democratic learning, authenticity

I n t r o du c t i o n Imagine you are attending a Celtic Highland festival. You observe traditional Celtic athletic competitions, traditional foods, pipe and drum competitions, traditional dancing and fiddling. Men wearing kilts and tartan are everywhere and the food and drink are abundant. What you see on the main stage is amazing. Nearly thirty high school musicians are playing fiddles, cellos, guitars, percussion, flute, oboe, and harp. Their music fills the air as you watch fingers flying over the instruments. The musicians are smiling, moving, and obviously having a great time playing a set of traditional Celtic tunes. The next tune they play, though obviously maintaining some aspects of Celtic style, is much more like rock and roll, as the electric guitarist rips off a raucous solo in the middle. The energy subsides as a young girl puts down her fiddle, picks up a microphone, and sings a sweet ballad with the airy,

pY

pY

62

Oare

63