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Ensemble pitch and rhythm error discrimination : the identification and selection of predictors Vincent, Dennis Richard 1990

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ENSEMBLE PITCH AND RHYTHM ERROR DISCRIMINATION: THE IDENTIFICATION AND SELECTION OF PREDICTORS Dennis Richard Vincent B. Mus. Ed., Evangel C o l l e g e , 1981 M. A., U n i v e r s i t y of V i c t o r i a , 1987 A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF EDUCATION i n the F a c u l t y of Education We accept t h i s d i s s e r t a t i o n as conforming to the r e q u i r e d standard Dr. A. E. Clingman C. R. Hultberg Dr. J . D. Willms 0 Dennis Richard V i n c e n t , 1990 UNIVERSITY OF BRITISH COLUMBIA December 1990 1 r i g h t s i n whole r e s e r v e d . T h i s t h e s i s may or i n p a r t , by mimeograph without permission of the not be reproduc or other means, author. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of VISUAL A/1/0 PERFORMS A£TV W £QUCAT/ON The University of British Columbia Vancouver, Canada Date xPlA/Wy 22, /??/  DE-6 (2/88) Ensemble Pitch and Rhythm Error Discrimination.' The Identification and Selection of Predictors. Vincent, Dennis Richard. Doctor of Education (Music Education), December, 1990. Supervisor: Allen E . Clingman ABSTRACT This study investigated relationships between 36 predictor variables and ensemble pitch and rhythm error discrimination a b i l i t y . Precollege musical background and other demographic data were collected by means of the Musical Background Questionnaire. Musical achievement was measured by the Al i fer i s -Steckle in Music Achievement Test, College Midpoint Level. Undergraduate musical coursework data were obtained from transcripts. The cr i ter ion variables were measured by the Ramsey-Vincent Test of Instrumental Error Detection; a test of aural-visual pitch and rhythm error discrimination for ful l-score band music of medium d i f f i c u l t y . A l l three instruments were administered to 82 undergraduate music students. Subjects represented three Canadian universities and two community colleges. Pearson product-moment correlation tests were used to identify variables s ignif icantly related to musical ensemble error discrimination at the .10 level of significance. Eighteen variables were found to be s ignif icantly related to ensemble pitch error discrimination. Fourteen variables were found to be s ignif icantly related to ensemble rhythm error discrimination. Regression procedures were performed for each of the significant variables. These variables were then organized into blocks representing precollege musical background, other demographic variables, musical achievement, and undergraduate coursework. Regressions were performed for each of the blocks. Musical achievement, precollege musical background, demographic, and undergraduate coursework blocks of variables accounted for 5, 15, 35, and 21 percent of the variance in ensemble pitch error discrimination scores respectively. Musical achievement, precollege musical background, demographic, and undergraduate coursework blocks of variables accounted for 21, 16, 19, and 12 percent of the variance in ensemble rhythm error discrimination scores respectively. Combinations of variables from these blocks produced a l inear model comprised of five demographic variables plus precollege choral experience that accounted for 42 percent of the variance in ensemble pitch error discrimination scores. Combinations of variables from the four blocks produced a l inear model of ensemble rhythm error discrimination comprised of rhythmic discrimination, choice of a band instrument as one's major performance medium, composition as one's program major, and precollege band or orchestral experience. These four variables accounted for 32 percent of the variance in ensemble rhythm error discrimination scores. The variables selected for use in this study accounted for a substantial portion of the variance in error discrimination scores. To improve the predictive power of future studies, other variables need to be identif ied and included in the model. Ten conclusions were made regarding the prediction of ensemble error prediction a b i l i t y . Three recommendations were made for improving error discrimination training and seven recommendations were made for future research in ensemble error discrimination. CONTENTS Abstract i i Contents i y Figures * i Tables * i i CHAPTER 1 THE PROBLEM 1 Introduction 1 Statement of the Problem 5 Purpose of the Study 6 Research Questions 1 Variables 10 Research Methodology • 10 Design and Procedure 13 Assumptions 15 Limitations 15 Scope and Delimitations 16 Significance 17 Overview 17 iv CHAPTER 2 REVIEW OF THE LITERATURE 19 Musical Listening S k i l l s 19 General Cognitive A b i l i t y • 22 Auditory Competence . . . . 25 Musical Competence . 26 Types of Aural S k i l l s 27 Music Listening and Music Cognition 28 Factors Affecting Music Listening A b i l i t y 32 Characteristics of Music 33 Physical Properties 33 Musical Complexity 33 Environmental Influences • 35 Acculturation . . . . . 35 Characteristics of the Listener 38 Socioeconomic Status 38 Level of Mental Maturity 38 Musical Information Processing Capacities 41 Aural Imagery 41 Memory 41 Attention 46 Selection 46 Control of the Selection/Attention Processes . . . 47 v Perception 51 Rehearsal 52 Eff ic ient Organization of Long-term Memory 53 Hierarchical Organization of Memory 54 Listening Strategies . . . 56 Cognitive Styles 57 Musical Style and Expectation 59 Intercorrelations of Aural Sk i l l s 62 Music Reading 63 Notation 63 Audiation 65 Music Reading S k i l l s . . . . . 66 Musical Discrimination S k i l l s 68 Factors Affecting Musical Discrimination S k i l l s 73 Musical Error Detection Tasks 78 Musical Error Detection S k i l l s 79 Studies in Musical Error Detection 83 Programmed Ensemble Error Detection Training 83 Computer-assisted Ensemble Error Detection Training . 91 Factors Related to Musical Ensemble Error Detection S k i l l 94 Summary 100 v i CHAPTER 3 RESEARCH DESIGN AND METHODOLOGY 101 Overview 101 Research Design 103 Preliminary Selection of Blocks of Variables 103 Musical Achievement Scores 104 Precollege Musical Experiences 104 Tertiary Musical Training 105 Other Demographic Variables 105 Selection of Specific Variables 107 Selection of Subjects 112 Preparation of Instruments 112 The Al i fer i s -Steckle in Music Achievement Test . . . . 112 The Musical Background Questionnaire 113 The Test in Error Detection 114 Procedures 116 Data Collection 116 Data Entry 118 Data Processing and Analysis • 121 Recoding of Data 122 Centering and Standardization of Variables 124 Preliminary Analysis 124 v t i Selection of Regression Variables . . • • 126 Regression Procedures 127 Multiple Regression 128 R* Adjusted 128 Multiple Regression Procedures 131 CHAPTER 4 RESULTS AND DISCUSSION 136 Results 137 Research Question l . a 137 Research Question l . b 144 Research Question 2.a 153 Research Question 2.b 155 Research Question 3.a 157 Research Question 3.b 159 Research Question 4.a 160 Research Question 4.b 163 Research Question 5.a 165 Research Question 5.b 167 Research Questions 6.a and 6.b 169 Research Questions 7.a and 7.b 192 Research Question 8.a 204 Research Question 8.b 206 v i i i Summary of Results and Discussion 212 Music Achievement Test Variables 212 Precollege Musical Background Variables 215 Other Demographic Variables 216 Undergraduate Coursework in Music 217 The Music Achievement Block of Variables . . 219 The Precollege Musical Background Block of Variables . . 219 The Demographic Block of Variables 220 The Undergraduate Coursework Block of Variables 220 Ensemble Pitch Error Discrimination 220 Ensemble Rhythm Error Discrimination 224 CHAPTER 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS 227 Summary 227 Selection and Identification of Predictor Variables . . . 227 Prediction Models of S k i l l in Ensemble Rhythm Error Prediction 231 Prediction Models of S k i l l in Ensemble Pitch Error Prediction 233 Selection of Levels of S ta t i s t i ca l Significance 235 Conclusions and Recommendations 236 Ensemble Rhythm Error Discrimination 237 ix Ensemble Pitch Error Discrimination 238 Early Musical Training 240 Tertiary Musical Training 241 Further Research 248 BIBLIOGRAPHY 254 Appendix A 271 Appendix B 274 x FIGURES 1. Prediction Model of Ensemble Error Discrimination A b i l i t y . 12 2. Ashley's Diagram of Aural S k i l l s as Related to Other A b i l i t i e s 21 3. LeBlanc's Model of Sources of Variation in Music Preference 34 4. Ensemble Error Discrimination Predictors and their Scales of Measurement 114 xi TABLES 1. S k i l l s Necessary for Performance Error Detection 81 2. Variables of Interest with Scales of Measurement, Means, Standard Deviations and Ranges 108 3. Correlations Between Independent Variables and Pitch Discrimination 139 4. Summary Data from Regression of Pitch Discrimination on Individual Selected Variables 142 5. Intercorrelations Between Selected Predictors of Pitch Discrimination 143 6. Correlations Between Independent Variables and Rhythm Discrimination 146 7. Summary Data from Regression of Rhythm Discrimination on Individual Selected Variables 150 8. Intercorrelations Between Selected Predictors of Rhythm Discrimination 152 9. Regression of Pitch Discrimination on Musical Achievement Test Subscores 154 10. Regression of Rhythm Discrimination on Musical Achievement Test Subscores 156 11. Regression of Pitch Discrimination on Precollege Background Variables 158 12. Regression of Rhythm Discrimination on Precollege Background Variables . . . . . 160 13. Regression of Pitch Discrimination on Other Demographic Variables 162 14. Regression of Rhythm Discrimination on Other Demographic Variables 164 15. Regression of Pitch Discrimination on Undergraduate Coursework Variables 166 16. Regression of Rhythm Discrimination on Undergraduate Coursework Variables 168 x i i 17. Regression of Pitch Discrimination on Musical Achievement Test Scores and Precollege Background Variables . . . . . 171 18. Regression of Rhythm Discrimination on Musical Achievement Test Scores and Precollege Background Variables 173 19. Regression of Pitch Discrimination on Musical Achievement Test Scores and Other Demographic Variables 175 20. Regression of Rhythm Discrimination on Musical Achievement Test Scores and Other Demographic Variables 177 21. Regression of Pitch Discrimination on Demographic and Undergraduate Coursework Variables 179 22. Regression of Rhythm Discrimination on Demographic and Undergraduate Coursework Variables 181 23. Regression of Pitch Discrimination on Precollege Background and Other Demographic Variables 183 24. Regression of Rhythm Discrimination on Precollege Background and Other Demographic Variables 186 25. Regression of Rhythm Discrimination on Precollege Background and Undergraduate Coursework Variables . . . . 189 26. Regression of Pitch Discrimination on Demographic and Undergraduate Coursework Variables 191 27. Regression of Rhythm Discrimination on Demographic and Undergraduate Coursework Variables 193 28. Regression of Rhythm Discrimination on Musical Achievement Test Scores and Other Demographic Variables 197 29. Regression of Rhythm Discrimination on Precollege Musical Background, Other Demographic Variables, and Undergraduate Coursework 205 30. Regression of Pitch Discrimination on A l l Selected Variables 209 31. Regression of Pitch Discrimination on A l l Selected Variables Except School Two and School Three 210 x i i i 32. Regression of Rhythm Discrimination on A l l Selected Variables 211 33. Variation in Pitch Discrimination Scores Explained by Blocks of Selected Variables 213 34. Variation in Rhythm Discrimination Scores Explained by Blocks of Selected Variables 214 xiv CHAPTER ONE THE PROBLEM Introduction As greater demands have been placed upon institutions of higher learning, administrators and instructional staff have found that they are having to make d i f f i c u l t decisions regarding which students to admit to their programs, which courses to offer, and what content to emphasize within those courses. Admission to "academic" institutions has usually been based upon secondary school records and scores on tests of academic potential. Institutions providing training in the fine arts, however, have had a greater problem because of the limitations of these tools as predictors of a r t i s t i c achievement (Ernest, 1970). If career success is contingent upon the development of a b i l i t i e s preceding post-secondary training, then schools of music need to develop more precise methods of selecting those students who appear to be most likely to succeed in musical careers. Similarly, coursework should be provided that w i l l best prepare students for these careers. Such instruction should attempt to maximize learning and s k i l l development while also requiring students to achieve the c r i t i c a l competency levels they w i l l need in their professional careers. 1 Many u n i v e r s i t y music students eventually choose careers i n teaching. As with schools of music, maximizing the l i k e l i h o o d of success of t h e i r graduates should be important to f a c u l t i e s of education. Nevertheless, the l i t e r a t u r e indicates that c e r t a i n areas of t r a i n i n g have been neglected. A synthesis r a r e l y occurs between courses within the general area of musicianship or between musicianship courses and professional studies... As a high school instrumental teacher, f o r example, his primary function w i l l be that of a conductor, yet his main college t r a i n i n g i s not i n conducting and other necessary s k i l l s . The courses he completes i n ea r - t r a i n i n g and sight singing r a r e l y advance beyond the simplest vocal textures; indeed, his aural t r a i n i n g i s considered adequate i f he can duplicate i n w r i t i n g a Bach chorale played on the piano, two measures at a time, repeated at least twice. (Contemporary Music Project, 1965, p. 5) Thackray (1969) concluded that choral or instrumental preparation alone were not enough; the successful music teacher needed t r a i n i n g i n both. Wortman (1965) concluded that many students were weak i n t h e i r conducting s k i l l s and recommended that new approaches to the teaching of conducting be investigated. Costanza (1971) and Prausnitz (1983) concluded that t r a d i t i o n a l undergraduate coursework i n musicianship f a i l e d to s u f f i c i e n t l y 3 prepare students for careers r e q u i r i n g substantial conducting in the classroom. A considerable portion of the conductor's undergraduate t r a i n i n g , intended to develop a u r a l - v i s u a l d i s c r i m i n a t i o n , centers around such basic musicianship courses as ear t r a i n i n g and si g h t - s i n g i n g . Although these t r a d i t i o n a l courses are considered fundamental to the development of score-reading a b i l i t i e s and a u r a l - v i s u a l d i s c r i m i n a t i o n , the content and effectiveness of such courses have been challenged regarding t h e i r adequacy i n developing such s k i l l s . (Costanza, 1971, p. 453) S i d n e l l (1971) reported that: Experience i n aural music theory classes i s often unrelated to the aural d i s c r i m i n a t i o n s k i l l s needed by instrumental teachers. Rarely, i f ever, are future teachers asked to detect and i d e n t i f y errors produced i n a musical texture involving various instruments. Aural s k i l l s are developed i n ear t r a i n i n g classes but there i s l i t t l e evidence of trans f e r to the problems that confront the conductor. Students are unable to synthesize existent s k i l l s and focus them i n solving the rehearsal problems of the conductor-teacher. In order to develop score-reading s k i l l , students must experience r e a l i t y - o r i e n t e d material i n a c a r e f u l l y organized format. ( S i d n e l l , 1971, p. 85) 4 Various a u t h o r i t i e s on conducting have emphasized that conductors must possess highly developed a u r a l - v i s u a l d i s c r i m i n a t i o n and score reading s k i l l s (Gattiker, 1977; Green, 1987; Hunsberger & Ernst, 1983; Morris & Ferguson, 1982; Prausnitz, 1983). However, Skapski (1971) found that many college and u n i v e r s i t y music students were weak at " r e l a t i n g sounds to the v i s u a l symbols representing them" (p. 408). Si d n e l l (1971) suggested that highly developed score-reading a b i l i t y "can have a p o s i t i v e e f f e c t on the judicious use of av a i l a b l e teaching time. E f f i c i e n t rehearsal procedures f a c i l i t a t e student learning through accurate music performance experience" (p. 85). In 1972 the Music Educators National Conference (MENC) addressed t h i s problem as follows: The development of music teacher competencies should r e s u l t from the t o t a l program of the teacher t r a i n i n g i n s t i t u t i o n . The demonstration of competence, rather than the passing of a course, should be the deciding factor i n c e r t i f i c a t i o n " (Commission on Teacher Education, 1972, p. 4). In that same year the National Association of Schools of Music (NASM) adopted a basic musicianship statement s t r e s s i n g the need f o r competency-based education u t i l i z i n g an integrated approach to the t r a d i t i o n a l course sequence (NASM, 1972). 5 More recently, Shellahamer (1983) has mentioned that music ensemble teachers need a u r a l - v i s u a l d i s c r i m i n a t i o n s k i l l s to properly detect e r r o r s , both on and o f f the podium. Deal (1985) has noted that the a b i l i t y to detect p i t c h and rhythm errors i n ensemble performance are two e s s e n t i a l s k i l l s f o r teachers d i r e c t i n g ensembles. Parr (1976) has reported that s k i l l i n detecting p i t c h and rhythm errors while viewing printed scores i s e s s e n t i a l to success i n d i r e c t i n g ensembles. Taebel (1980) considered these s k i l l s to be the two most important musical competencies for the instrumental music teacher. Statement of the Problem At present there are no comprehensive models of how such complex variables as i n i t i a l musical capacity, maturation, musical experiences, i n t e r e s t i n music, i n t e l l i g e n c e , motivation, personality type, r e l a t i v e complexity of the music, reading a b i l i t y , and sex are related to a u r a l - v i s u a l d i s c r i m i n a t i o n of ensemble performance e r r o r s . In f a c t , few researchers, to date, have attempted to predict the a b i l i t y of music majors to detect and i d e n t i f y errors i n musical ensemble performance. Further studies are thus needed to provide methods of i d e n t i f y i n g which students are most l i k e l y to need remedial t r a i n i n g i n ensemble p i t c h and rhythm di s c r i m i n a t i o n and which students are most l i k e l y to benefit from such t r a i n i n g . Based upon a review of the literature, the present study was designed to determine whether precollege musical background, other demographic variables, undergraduate training, and measures of musical achievement can be used as predictors of two important prerequisites of success in instrumental teaching: the a b i l i t y to discriminate pitch and rhythm errors in ensemble performance. Hereafter, the term "ensemble error discrimination a b i l i t y " w i l l refer only to pitch and rhythm discrimination a b i l i t y unless otherwise stipulated. Purpose of the Study This study w i l l investigate the relationship between the musical ensemble error discrimination a b i l i t y of undergraduate music majors and other musical and demographic variables. A review of the research literature reveals that previous studies have focussed upon the relationship between measures of music achievement, precollege musical background, and undergraduate coursework to error discrimination. Efforts w i l l be made to verify the existence of these relationships, to identify other useful predictors of ensemble error discrimination, and to extend present knowledge by providing information regarding the magnitude and nature of these relationships. The results of this study should be useful to musical training program designers. 7 Research Questions For undergraduate music students, which v a r i a b l e s , or combinations of v a r i a b l e s , are s i g n i f i c a n t l y r e l a t e d to a u r a l - v i s u a l d i s c r i m i n a t i o n of p i t c h and rhythm errors i n musical ensemble performance? In p a r t i c u l a r : l a . Which variables account for a s i g n i f i c a n t portion of the variance i n p i t c h discrimination scores? l b . Which variables account for a s i g n i f i c a n t portion of the variance i n rhythm discrimination scores? Can blocks comprised of these variables be used to predict the p i t c h or rhythm d i s c r i m i n a t i o n a b i l i t y of undergraduate music students? 2a. Can musical achievement test variables be used to predict p i t c h d i s c r i m i n a t i o n a b i l i t y ? 2b. Can musical achievement test variables be used to predict rhythm di s c r i m i n a t i o n a b i l i t y ? 3a. Can precollege musical background variables be used to predict p i t c h d i s c r i m i n a t i o n a b i l i t y ? 8 3b. Can preco l lege musical background v a r i a b l e s be used to p red ic t rhythm d i s c r i m i n a t i o n a b i l i t y ? 4a. Can other demographic var iab les be used to p r e d i c t p i t c h discrimination a b i l i t y ? 4b. Can other demographic va r iab les be used to p r e d i c t rhythm d i s c r i m i n a t i o n a b i l i t y ? 5a. Can undergraduate coursework v a r i a b l e s be used to p r e d i c t p i t c h d i s c r i m i n a t i o n a b i l i t y ? 5b. Can undergraduate coursework var iab les be used to p red ic t rhythm discrimination a b i l i t y ? When one block of v a r i a b l e s i s a l ready in the model, w i l l the add i t ion of v a r i a b l e s from another block increase the amount of var iance explained by the model? 6a. Is p r e d i c t i o n of p i t c h d i s c r i m i n a t i o n a b i l i t y s i g n i f i c a n t l y increased when v a r i a b l e s from one block are added to a model comprised of v a r i a b l e s from another block? 9 6b. Is prediction of rhythm discrimination a b i l i t y significantly increased when variables from one block are added to a model comprised of variables from another block? Will the addition of variables from a third block significantly increase the variance explained over a model comprised of variables from two blocks? 7a. Is prediction of pitch discrimination a b i l i t y significantly increased when variables from a third block are added to a model comprised of variables from two blocks? 7b. Is prediction of rhythm discrimination a b i l i t y significantly increased when variables from a third block are added to a model comprised of variables from two blocks? Will the addition of variables from a fourth block significantly increase the variance explained over a model comprised of variables from three blocks? 8a. Is prediction of pitch discrimination a b i l i t y significantly increased when variables from a fourth block are added to a model comprised of variables from three blocks? 10 8b. Is prediction of rhythm discrimination a b i l i t y s ignif icantly increased when variables from a fourth block are added to a model comprised of variables from three blocks? Variables Based upon a review of the l i terature , this study selects variables that appear to be of interest in predicting a b i l i t y to discriminate errors in musical ensemble performance. Few studies, to date, have attempted to identify predictor variables of error discrimination a b i l i t y . Thus, relat ively few of the variables salient to error discrimination have been identif ied. However, at least two other types of studies have suggested variables that may be related to error discrimination a b i l i t y : studies of musical achievement; and, studies in musical l istening s k i l l s . Summaries of these studies are reported in Chapter 2. Research Methodology The purpose of this study is twofold: to explore the relationship between the musical error discrimination a b i l i t y of undergraduate music majors with other musical and demographic variables; and, to develop methods of predicting the musical error discrimination a b i l i t y of those students. Multiple linear regression thus appears to provide an appropriate data analysis technique. 11 Mult i p l e regression i s a method of analyzing the c o l l e c t i v e and separate contributions of two or more independent variables to the v a r i a t i o n of a dependent v a r i a b l e . The sin g l e dependent or c r i t e r i o n v a r i a b l e i s predicted from the set of predictor or independent v a r i a b l e s . The c o r r e l a t i o n between the actual c r i t e r i o n v a r i a b l e and the predicted variable i s the multiple c o r r e l a t i o n (R). The square of a multiple c o r r e l a t i o n c o e f f i c i e n t may be interpreted as the proportion of the variance i n the c r i t e r i o n variable that i s predicted or explained by the composite set of p r e d i c t o r s . The separate contribution of one or more of the predictor variables may be examined by omitting that p a r t i c u l a r variable from the model and t e s t i n g the d i f f e r e n c e i n the multiple c o r r e l a t i o n s achieved with and without t h i s v a r i a b l e . Unexplained variance r e s u l t s from omission of relevant v a r i a b l e s , measurement error, and random error (Pedhazur, 1982). Multiple regression analysis can be used to determine which of the independent variables i n question are useful predictors of ensemble p i t c h and rhythm error detection s k i l l . The regression equation takes the form y = bo + bi xi + hz X2 + . . . + b* x* , where xi , X2 , x* are the independent -variables, bo , bi , bz ,..., bi are the regression c o e f f i c i e n t s determined from the data, and y i s the dependent v a r i a b l e . Because no model presently e x i s t s to explain the causes, e f f e c t s , and i n t e r a c t i o n s of these v a r i a b l e s , t h i s study i s l i m i t e d to p r e d i c t i o n . Thus, the hypothesized p r e d i c t i o n model of e r r o r d i s c r i m i n a t i o n a b i l i t y i s given as follows: Musical Achievement Variables Precollege Musical Background Variables Other Demographic Variables Ensemble Error Discrimination ( P i t c h or Rhythm) Undergraduate Coursework Variables Figure 1. P r e d i c t i o n Model of Ensemble Err o r Discrimination A b i l i t y 13 This study should contribute to the research community's understanding of factors related to error detection by determining which of these variables appear to be related to error detection, identifying interrelationships among these predictor variables, and the strength of their predictive ab i l i t i e s for the population represented by the data. Design and Procedure Data w i l l be gathered from four sources: Ramsey's Test in Error Detection (TIED); the researcher's Musical Background Questionnaire (MBQ); the AJiferis-Stecklein Music Achievement Test (ASMAT); and student transcripts. TIED excerpts were chosen for the ensemble error test because, currently, i t is the only widely accepted test of ensemble pitch and rhythm error detection. The TIED consists of tape recordings of full-band l i terature plus one example excerpt. Each excerpt contains one pitch or rhythm error which has been judged by a panel of experts as representing a typical error in the performance of band l i terature of medium d i f f i c u l t y . These items have also been judged to adequately represent the continuum of band l i terature c lass i f ied as medium-difficult. Fifteen pitch items and 15 rhythm items were selected to form a longer and more rel iable version of Ramsey's test. 14 The MBQ includes questions on subjects' precollege musicaL background and other control variables of interest. In designing the questionnaire, university calendars were examined for information regarding entrance and program requirements. The ASMAT was selected as the test of musical achievement because i t is a highly rel iable norm-referenced test of general musical aural-visual discrimination s k i l l s . The College Midpoint Level form of the ASMAT contains three subtests: melodic, harmonic, and rhythmic. Eighty-two undergraduate music student volunteers attending three Canadian universities and two community colleges participated in the study. In brief , data col lection proceeded as follows. The researcher attempted to make sure that suitable testing conditions were provided at each inst i tut ion . Subjects were issued pencils, test booklets, and a MBQ Form. Participants were assured that individual results for a l l aspects of the study would remain confidential and requested to permit access to their transcripts. Subjects f i l l e d out the MBQ form after completing the new TIED. The ASMAT was then administered. Once access to transcript information was granted by each of the inst i tut ions , the researcher calculated the quantity and quality of coursework in music completed by each of the subjects. The combined data were then analyzed using multiple regression techniques. 15 Assumptions Error discrimination s k i l l s are specialized forms of musical discrimination a b i l i t y . Musical discrimination s k i l l s f a l l within the domain of musical l istening s k i l l s and constitute a form of musical achievement. The following four s ta t i s t i ca l assumptions w i l l be made as outlined by Glass and Hopkins (1984, p. 141): 1. Y scores are normally distributed at a l l points along the regression l ine . 2. There is a l inear relationship between the Y values and the expected values of Y. 3. The residuals for Y along this l ine have a mean of zero. 4. Homoscedasticity. Limitations Many related and worthwhile research questions are beyond the scope of the study. Because Ramsey's test items are short musical excerpts, this study does not investigate subject a b i l i t y to identify errors from long-term memory requiring large formal contextual clues. These excerpts were tape-recorded, so subjects w i l l not be able to derive cues from seeing an ensemble and i t s 16 conductor in actual performance. Similarly, subjects w i l l not have the opportunity to practice error detection while conducting. No attempt w i l l be made to measure student a b i l i t y to identify typographical errors in musical scores. Similarly, this study w i l l not investigate any direct relationship that may exist between musical talent and score-reading a b i l i t y or the relationship between sight-reading a b i l i t y and error discrimination a b i l i t y . Furthermore, this study w i l l not investigate s k i l l in identifying other types of ensemble errors such as errors in dynamics, interpretation, precision, tempo, tonal balance, or tone control. No comprehensive theory of how musical training variables contribute to error detection s k i l l s exists at present. As a result, this study w i l l not be able to explain why various correlations exist between these variables. Scope and Delimitations This study examines how the musical backgrounds of undergraduate music students and their current levels of general musical discrimination are related to their a b i l i t y to detect and identify pitch and rhythm errors in band performances. Previous and current musical experiences were chosen as predictors of musical discrimination a b i l i t y since they are, presumably, more closely related to s k i l l in musical discrimination than are other academic ac t i v i t i e s . Current levels of relatively simple musical 17 discrimination s k i l l s were measured by the ASMAT. Other readily available demographic variables were included in order to reduce unexplained variance in the system. However, variables unacceptable for use in formulating admission pol icies (such as race, re l ig ion , and socioeconomic status) were not included in the model. Significance of the Study This study contributes to the research l i terature by determining which combinations of variables can be used most effectively to predict s k i l l in identifying pitch and rhythm errors in band music. This information w i l l be of interest to those concerned with precollege and undergraduate development of musical a b i l i t i e s : administrators, course counsellors, music instructors, course planners, psychologists, music education researchers, school d i s t r i c t s , and especially those involved with teacher education. Overview Chapter 1 introduced the problem and the purpose of this study. I then posed accompanying research questions and presented an outline for data collection and analysis procedures. The assumptions, scope, and limitations of this study were also included in this chapter. Chapter 2 reviews previous musical error detection studies. Few studies to date have investigated the prediction of error detection 18 s k i l l s . Thus, the review of the l i t e r a t u r e also draws from research i n music l i s t e n i n g and music achievement i n order to i d e n t i f y musical and demographic variables r e l a t e d to success at ensemble er r o r detection. Terms are defined during t h i s review of the l i t e r a t u r e . Chapter 3 i d e n t i f i e s the predictor variables selected and provides reasons f o r the s e l e c t i o n of the p a r t i c u l a r t e s t instruments used i n t h i s study. In t h i s chapter, I provide further explanation of multiple regression procedures pertaining to the research methodology used i n t h i s study. Chapter 4 reports the data analysis phase of the study. The chapter also includes a discussion of whether ensemble p i t c h and rhythm errors can be predicted by various combinations of the independent v a r i a b l e s . The r e s u l t s of the study are interpreted i n Chapter 5. Conclusions are then made regarding the p r e d i c t a b i l i t y of these error detection s k i l l s . The chapter includes comments on the implications of t h i s study for the f i e l d of music education and makes recommendations f o r future studies i n musical error detection. CHAPTER TWO REVIEW OF THE LITERATURE Since few studies of error detection have attempted to i d e n t i f y e f f e c t i v e means of p r e d i c t i n g undergraduate musical error detection a b i l i t y , t h i s chapter w i l l also report findings from two r e l a t e d areas: the l i t e r a t u r e i d e n t i f y i n g factors r e l a t e d to musical achievement; and the l i t e r a t u r e on l i s t e n i n g to music. A b i l i t y to detect musical errors i s a s p e c i a l i z e d form of musical d i s c r i m i n a t i o n s k i l l . However, i t appears to be c l o s e l y r e l a t e d to, and possibly f a c i l i t a t e d by, other music reading and l i s t e n i n g s k i l l s . Since many music achievement tests are designed to measure a u r a l - v i s u a l d i s c r i m i n a t i o n a b i l i t i e s , factors that have previously been found to be r e l a t e d to musical achievement may also be useful predictors of error d i s c r i m i n a t i o n a b i l i t y . Musical Li s t e n i n g S k i l l s Music i s a ubiquitous and universal phenomenon (Serafine, 1988, p. 1). However, though music plays an important part i n the l i v e s of people of many cultures (Howell, Cross, & West, 1985, p. x i i i ) , great d i s p a r i t y i s evident between i n d i v i d u a l l e v e l s of musical achievement. Even f o r i n d i v i d u a l s who seem to possess superior 19 20 musical a b i l i t y , the process of becoming a musician i s generally a very time-consuming one, and one which many persons f i n d d i f f i c u l t (Ashley, 1982, p.11). Differences are also evident between i n d i v i d u a l s i n terms of l i s t e n i n g s k i l l s (Fiske, 1985, p. 63). Ashley (1982) has stated that such " s k i l l s are, f i r s t and foremost, about equipping a person to know music" (p. 26). Without such s k i l l s , one's a b i l i t y to experience music i s severely l i m i t e d . A person l i s t e n i n g to music i s best understood as a complex cognitive e n t i t y dealing with a complex changing environment. The l i s t e n e r i s seen thereby as a l i m i t e d cognitive system, i n that he must act i n r e a l time i n understanding the music, and he i s not omniscient. The process of music l i s t e n i n g can, i n t h i s framework, be seen as a control structure f o r the a l l o c a t i o n of scarce cognitive resources. Given a system with only so much memory, and so much attention, the question i s one of a sort of cognitive economy — with marshalling the forces to meet the demand of the task. (Ashley, 1982, p. 36) Ashley r e l a t e s aural s k i l l s to other a b i l i t i e s as follows (See Figure Two). Auditory and musical competencies f a l l within the domain of general cognitive a b i l i t y . Some of the auditory competencies used i n everyday l i v i n g cannot properly be termed musical competencies and others are useful i n musical a c t i v i t i e s . 21 Similarly, some musical competencies are music-specific. Thus, aural s k i l l s f a l l within the bounds of general cognitive a b i l i t y and depend on auditory competence as well as musical competence. general cognitive a b i l i t y auditory competence musical competence aural s k i l l s i Figure 2. Ashley's Diagram of Aural Sk i l l s as Related to Other A b i l i t i e s (from Ashley, 1982, p. 34). 22 General Cognitive A b i l i t y Individuals do, of course, possess dif fering capacities for knowledge, intell igence, and music (Hornstein, 1986). However, since both intelligence and musical a b i l i t y are functions of the brain, many researchers have hypothesized that the mental processes which create both intelligence and musical a b i l i t y are similar (Gardner, 1983; Restak, 1984). Mursell (1932) found that the superiority of high school students on the Seashore Measures was not suff ic iently marked to warrant any educational advice. Highsmith (1929) and More (1933) found scores on intelligence tests to have a sl ight superiority over the Seashore Measures as means of predicting success in musical performance. Beinstock (1942) used the Kwalwasser-Dykema music tests, intelligence measures, previous training, and performance to predict grades in music courses for 122 students enrolled in the High School of Music and Art in New York City . By themselves, the Kwalwasser-Dykema music tests were not found to be rel iable in predicting individual success. This is hardly surprising. Tests of discrimination a b i l i t y in a musical context generally have low r e l i a b i l i t y (Whellams, 1970). In Beinstock's study, intelligence measures were the best predictors of later success. The least effective cr i ter ion was the extent of previous training. 23 Neely (1959) studied the relationship between mental f a c i l i t y and response to ear-training involving rhythm. He reported that there was a positive correlation between the two variables. Young (1971) studied the scores of 91 fifth-grade instrumental students on Gordon's Musical Aptitude Profi le (MAP), the Lorge-Thorndike Intelligence Test, and the Iowa Tests of Basic Skills (ITBS) with three musical achievement tests under development at the University of Iowa. He concluded that: Those achievement cr i t er ia that did not demand the a b i l i t y to read music showed a greater relationship with tests from the MAP battery than those that required music reading a b i l i t y . On the other hand, those achievement c r i t e r i a that involved reading a b i l i t y appeared to be more related to intelligence and academic achievement than those that did not require this a b i l i t y , (p. 338) In the f ina l phase of his study, Young compared the IQ scores (as measured by the Henson-Nelson Intelligence Test) and ITBS achievement scores of 261 instrumental music students with their scores on the Watkins-Farnum Performance Scale (a scale heavily-weighted towards sight-reading). This time, he found that IQ scores did not seem to affect reading a b i l i t y . IQ scores had very l i t t l e importance to either musical aural discrimination a b i l i t i e s or to musical achievement. 24 After reviewing previous studies of the relationship between intel l igence, musical aptitude, and musical a b i l i t y , Sergeant and Thatcher (1974) concluded that "it is a common observation of music teachers that children with high intelligence generally tend to reach higher levels of musical achievement than do children with more modest inte l lectual ab i l i t i e s" (p. 32). Furthermore, Intelligence must therefore be regarded as an integral component of musical a b i l i t i e s . A favorable musical environment cannot redeem the absence of the level of intelligence necessary for musical cognition, nor can intelligence alone suffice for the development of musicality. (p. 56) Robinson (1983) suggested that subjects who score highly on musical tests tend to possess "a high level of intell igence, although a high level of intelligence cannot necessarily predict high musical abi l i ty" (p. 21). Hornstein (1986) also reviewed the l i terature on the relationship between intelligence and musical a b i l i t y . He concluded that "viewed as a whole, previous study of the intelligence/musical a b i l i t y relationship has suggested that the nature and magnitude of this relationship fluctuates when the particular musical factor under study changes. Though this is not a surprising conclusion, i t does further suggest that perhaps different components of musical 25 a b i l i t y may be related to intel lectual ab i l i t i e s in different ways" (P- 15). Hornstein claimed that the positive relationship noted between IQ test scores and music achievement test scores results in large part from their emphases on reading a b i l i t y . "Ski l l in reading, no matter whether i t be notes or words, w i l l increase scores on IQ tests. Therefore, the more ski l led music readers w i l l also be more sk i l l ed in verbal manipulation and score higher on IQ tests" (p. 54). Auditory Competence Seashore believed that the sensi t iv i ty of the ear to pitch could not be improved appreciably by practice. However, he did agree that pitch training could develop s k i l l s needed in hearing the intricacies of music (Seashore, 1919). Mursell (1937) reported that musical achievement due to training was associated with certain a b i l i t i e s : aural perception, technical a b i l i t i e s , and s k i l l in reading musical notation. Neely (1959) studied the relationship between intel l igence, aural threshold, and musical achievement. His results indicated that there was a definite and positive relationship between aural acuity and response to the phase of ear-training having to do with pitch and harmonic structure. 26 Musical Competence There has been considerable controversy over the nature of musical a b i l i t y among music researchers (Vincent, 1989). Early studies by Drake (1939), McLeish (1953), and Wing (1941) sought to support the existence of a single general musical factor. Other researchers and musicians, however, f e l t that musical a b i l i t y was comprised of a number of different factors or elements. Seashore, for example, believed that musical a b i l i t y is "not one, but a hierarchy of talents" (1938, p. 21). Farnsworth (1969) believed in "the existence of several rather independent musical a b i l i t i e s rather than a single all-embracing one" (p. 152). Drake (1954) eventually supported the notion that there were two musical factors. Franklin (1983) suggested the existence of two musical factors: a "mechanical-acoustic" factor involving pitch, timbre, time, and intensity discrimination; and, a "judicious-musical" factor, an aesthetic factor which indicates creative musical talent. Bower (1945) concluded that there were three group factors. Burroughs and Morris (1962) found four factors and Karl in (1941, 1942) identif ied eight. Henkin argued that there are four musical aural discrimination components: rhythmic discrimination, melodic discrimination, sensi t iv i ty to instrumental tone color (1955), and an additional polyphonic melodic factor (1957). From his analysis of the major musical aptitude and achievement tests Gordon (1971, p. 27) identif ied five types of tasks: 27 audio-acoustic perception, tonal concepts, rhythm concepts, expressive-interpretive concepts, and achievement s k i l l s . Gordon suggested that "audio-acoustic perception" is not real ly a factor of musical ab i l i t y but one of sensory acuity. "Tonal concepts" and "rhythmic concepts" seem to be dist inct factors. The "expressive-interpretive" factor seems to relate to areas often deemed as aesthetic. By "achievement sk i l l s" , Gordon seemed to mean the a b i l i t y to function in a musical context. Types of Aural Sk i l l s Ashley (1982) has identif ied three types of aural s k i l l s used in musical ac t iv i t i e s : component s k i l l s , independent s k i l l s , and diagnostic s k i l l s . By component s k i l l s , he seems to mean extramusical aural s k i l l s such as identifying the sound of a t ra in . Independent s k i l l s represent speci f ical ly musical act iv i t ies such as sight-singing. The third form of s k i l l is of particular interest to this dissertation. Diagnostic s k i l l s are useful as means of ascertaining a student's level of a b i l i t y or accomplishment (p. 107). Throughout the music l i terature , diagnostic s k i l l s are customarily called discrimination s k i l l s . Musical discrimination tasks seldom occur in i so lat ion. Many musical discrimination tasks require the a b i l i t y to read musical notation and recognize the 28 timbre of musical instruments. Thus, musical discrimination frequently requires competence in a l l three areas of aural s k i l l s . Music Listening and Music Cognition Various language and music researchers have commented that l istening is an active mental process (Ashley, 1982; Brink, 1980; Chomsky, 1965; Laske, 1977; Longuet-Higgins, 1985; West, Howell, & Cross, 1985). Listening to music thus requires both time and effort . As demonstrated in previous response time studies, music decision-making requires measurable amounts of processing time that vary in respect to both task and stimulus manipulations (Fiske, 1987). Listening to music i s a complex process. Effective l istening requires the l istener to both "act upon and respond to a complex changing environment" (Ashley, 1982, p. 36). Fiske (1987) has argued that music l istening is a constructive process and not simply a copy-comparison process. That i s , musical patterns are a product of auditory processing mechanisms rather than an aural "photo-copy" of tonal-rhythmic structures. Since about 1960, there has been renewed interest and growth in cognitive theories (Laske, 1977). The application of cognitive theory to musical experience has resulted in a form of research called music cognition. Cognition refers to the processes of knowing in the broadest sense, including such constituents of mental 29 l i f e as attention, perception, imagery, memory, thought, and problem-solving. According to the cognitive approach, man, not the environment, produces the world of experience. Whatever man knows of the world is mediated by his sense organs and operated on by complex interacting systems that result in behavior. Cognition refers to a l l the processes by which sensory input is transformed, reduced, elaborated, stored, recovered, and used. (Neisser, 1967, p. 4) Currently, there are many gaps in our knowledge of the mental processes that occur during musical experiencing (Horning, 1982). Since composition and performance require additional s k i l l s , music cognition research has focussed primarily on explicating music l istening (Sloboda, 1988). There is already considerable consensus that l istening to music, as well as remembering music, involves active mental reconstruction of musical processes (Brink, 1980; Serafine, 1988). One approach to music cognition research has explored the capacities of the brain as a music processor. The other main approach has dwelt on the a b i l i t y of the brain to internally construct musical structures. The f i r s t approach tends to examine the brain as i f i t were a form of computer (Laske, 1977). In his book Music, Memory and Thought, Laske (1977) notes that perception is also determined "by 30 the parameters (musical and otherwise) of the memory system, that processes sound" (p. 136). Bregman and Campbell (1971) have also indicated that the sensory-memory systems place constraints on the way auditory stimuli are perceived and processed. Many stages are involved in l i s tening. Brink mentions that there at least seven stages in l istening: sensation, perception, imagery, retention, r e c a l l , problem-solving, and thinking (Brink, 1980, p. 20). The second approach to music cognition focusses on the a b i l i t y of the l istener to deal with music in terms of musical structures. Many researchers have chosen this approach. Fiske (1987) suggested that music l istening can be described as a hierarchy of l istening tasks. Deutsch and Feroe (1981) suggested that a small number of highly overlearned structures act on each other in a hierarchical fashion (p. 511). Gardner (1981) and Zenatti (1969) wrote that children immersed in a musical culture internalize the structures that are implic i t in the bulk of music they hear. Cross, Howell, and West (1985) fe l t that most adults conceive of music in terms of enculturated structures. Bregman (1978) claimed that, in the mind, a variety of competing organizational strategies were u t i l i zed for auditory information. Thus, the extent to which listeners share a common experience depends on the piece i t s e l f , the way i t is performed, and the particular audience. 31 Several authorities in music cognition believe that there are two types of structures: rhythmic and tonal (Gordon, 1971; Longuet-Higgins, 1985). In commenting on Schenker's theories, Salzer (1952) wrote that "understanding of tonal organisms is a problem of hearing; the ear has to be systematically trained to hear not only the succession of tones, melodic l ines , and chord progressions, but also their structural significance and coherence" (p. 52). Similarly , l istening to musical rhythms is a process that is the reverse of a performer — extracting beat intervals from a sequence (Longuet-Higgins, 1982; Steedman, 1977) and organizing individual tones around markers. The development of rhythmic s k i l l s in both listeners and performers is understood... as being largely a question of acquiring a wide variety of procedural representations to cope with the rhythmic structures commonly — and less commonly — found in music. (Clarke, 1985, p. 224) Pflederer (1964) suggested the existence of two additional types of musical structures: harmonic and formal. Superior musical intel l igence, in her opinion, resulted in a superior organization and equilibrium of cognitive structurings of musical elements in the mind (p. 255). To these structures, LeBlanc (1982) added texture. Such structures provide a framework for an individual to reason about music (Harding, 1986, p. 24). 32 Explication of music l istening is a very complex problem. Much s t i l l remains to be discovered regarding the structure and operation of the brain and how i t approaches music l i s tening. The development of new compositional techniques and philosophies, along with new methods of analyzing music, indicates that the mind does not automatically interpret music in terms of Western musical structures. Furthermore, no single theory of music, system of analysis, or method of aural training, seems to deal adequately with a l l music (West, Howell, and Cross, 1985, p. 21). In Western cultures, however, the mind eventually learns to deal with music in terms of Western musical structures (Brink, 1980; Laske, 1977). Fiske (1987) has emphasized that "music l istening is a decision-making process contingent upon questions or tasks pertaining to the function, style , or quality of perceived musical patterns" (p. 32). Operation of these structures is essential to effective music l i s tening. Fiske suggested that music cognition is a self-terminating, pattern comparison hierarchy, that is time-dependent and restricted to a f in i t e set of decision levels . Factors Affecting Music Listening A b i l i t y Although l istening s k i l l s are fundamental for a l l professional musical ac t iv i ty (Brink, 1980), the actual strategy followed by the brain in processing musical information is yet to be determined (LeBlanc, 1982). Conley (1981) suggested that l istening to music is 33 very similar to problem-solving. Pembrook and Taylor (1986) stated that the perceptual and cognitive processes of tonal and rhythmic discrimination are not well understood (p. 19) and that " l i t t l e information exists on the relevance of background experiences to individual musical sk i l l s" (p. 3). LeBlanc and S h e r r i l l (1986), on the other hand, have already constructed a model of factors influencing preferences in musical selection (See Figure Three). They suggest that three major sources of information influence the music l is tener's decisions! the physical characteristics of the. music i t s e l f , the influence of the cultural environment in which the l istener l ives , and the personal characteristics of the l i s tener . Characteristics of Music Physical Properties. Most music, at least in the West, consists of multiple and simultaneous sequences of events, as in polyphonic music, melody-plus accompaniment pieces, and the more common complexities of contemporary music. In such cases, the l istener needs to track two or more simultaneously sequences of events as they move in paral le l through time (Serafine, 1988, p. 134). Musical Complexity. Relative musical complexity can be considered as related to the effort which a person needs to expend to create and maintain one's internal model of the music being heard. 34 [ A«|*CUOn I I A c c t O l i n C I I , | Wapttiliun I _ I H«iyl I J L _J Lf^ s!imu,i'J " Li'^ J _ J yMened I itlUM I AuQiloiy I MuliCtl S«n*ili*ily Ability Fuilhn EiplorAlion of Sltmulut •nd/or Envno'imffll t Htmc G >oup L>» 1 I A«pt«l»d I _ I H«ighlan«d I _ I | Sampling | ~*l Atltnlion | " Ptnon jltty Cu*(«nl AlUcitv* S u i t Socio-economic S u i u i Mltuf«lton I •» ~^y" Amotion 1 1 1 PtoptHi** tt Stimulus zuzi CoiTipHiily ot Slimuiui I R«l*f«nft«l lfp«/form Mf jnmg ol Ouftlily Sdmuluft fPhy uoiyyical I Enabling ConU«lio<>» J ^ - • » ~ - • . • - • . - - • 1 THE MUSIG 1 / Gioup F*miy f UuC4lO«S «nd AulhOMly f tgurtft THE lr>od*m«l f. orvl«riuniiig [ENVIRONMENT Figure 3. LeBlanc's Model Preference (LeBlanc of Sources of Variation in Music and Sherr i l l , 1986, p. 222). 35 Conley (1981) found that density of musical events is the prime determinant of perceived musical complexity. Ashley (1982), however, suggested that both top-down and bottom-up processing takes place in a l l cognition, so both the l i s tener's thoughts and the music's aspects should have a place in a theory of musical experience (p. 59). Environmental Influences Numerous environmental influences shape the musical preferences of l isteners. Peer group, family, and various authority figures can have an important effect on the quantity and type of music to which the l istener is exposed. In addition, these individuals may affect the l istener's future preference for different types of music. The l istener's world, however, is probably not limited to the musical influences of these individuals. The increased ava i lab i l i t y of aural-visual media now provides the l istener with many opportunities to experience a great diversity of musical styles and performance media. Acculturation. Western music theory seems to indicate that common features extend over the entire h i s tor ica l range of Western music. To some extent, Western musical history may be viewed as evolutionary and well-defined principles may be applied to, or drawn from, music of the last 400 years more or less equally. However, 36 the form that Western music takes changes gradually over time. Music of one period i s differentiable from music of other periods by sets of features which constitute different styles (La Rue, 1970). Nevertheless, certain factors or principles do seem to remain constant as styles change, part icularly in music c irca 1600-1900 (Cross, 1985; Serafine, 1988). The music of other cultures clearly does not conform to these principles and individuals from those cultures appear to apply different principles when they l i s ten to music. Horning (1982) states that: Many musical styles exist not as unchanging physical processes in the world of nature, but as psychological processes ingrained as habits in the perceptions, dispositions, and responses of those who have learned through practice and experience to understand a particular style . But what remains constant from style to style? While scales, modes, harmonies, and manners of performance a l l vary, what remains constant throughout every style , in every culture, i s the psychology of the mental processes -the ways in which the mind selects and organizes the stimuli that are presented to i t (p. 127). In l istening to music we are dealing with a sound phenomenon so complex that extensive cultural experience i s required to appreciate i t (Swain, 1986). One area of interest in music research is that of 37 the effect of acculturation on musical perception a b i l i t y . When musicians f i r s t encounter music in a different cultural idiom they are l ike ly to perceive i t according to the convention of their own cultures and hence to misperceive and misinterpret i t . Thus, i t i s important to find ways of distinguishing between persons "whose ears are not part icular ly keen", and those who have not become "well acculturized to their own music" (Meyer, 1956). The role of cultural preparation in music perception has recently received experimental support. Castellano, Bharucha, and Krumhansl (1984) compared the a b i l i t y of North Indians with the a b i l i t y of Western listeners to perceive North Indian melodies. Indians were able to use their knowledge of Indian scale structures in achieving effective hierarchical perception of melody, whereas Western listeners were not. In a similar study, Kessler, Hansen, and Shepard (1984) compared the a b i l i t y of Western and Balinese listeners in perceiving Balinese melodies. Like the aforementioned researchers, they concluded that "in general, the use of the tonal hierarchy and scale membership response strategies were used to a greater extent when a group of l isteners was familiar with the scales underlying the context" (p. 163). Thus, i t appears that hierarchical perceptions are not innate but derived from the culture of the l i s tener . 38 Characteristics of the Listener LeBlanc and S h e r r i l l (1986) acknowledge that to l i s ten to music one must possess the physiologically enabling conditions necessary for hearing and attending to s t imul i . However, an individual's current affective state is also involved in the l istening process and this factor may be largely responsible for the low test-retest r e l i a b i l i t y of music l istening tests (Whellams, 1970). Socioeconomic status. Sergeant and Thatcher (1974) studied the relationship of social status and intelligence to aural s k i l l s in music. They concluded that music, as a form of behavior, appeared to be more characteristic of higher socioeconomic groups than of lower groups and suggested that children from the favored background would be more l ike ly to develop high levels of musical a b i l i t y . Level of mental maturity. Researchers from discipl ines other than music have found that the majority of subjects within the range of 14 to 50 years of age are operating at either the concrete level of operations or at a transit ional level between concrete and formal operations (Higgins-Trenk and Gaite, 1971). Subjects who are operating at levels lower than formal operations have d i f f i c u l t y in understanding concepts which require log ica l , c r i t i c a l , and analytical thinking s k i l l s (Lawson and Renner, 1975; Purser and 39 Renner, 1983). Since undergraduate music majors are required to take cognitively-oriented music classes demanding the use of log ica l , c r i t i c a l , and analytical thinking s k i l l s , undergraduate music majors functioning at levels lower than Piaget's formal operations stage are less l ike ly to succeed (Harding 1986, p. 3). Harding attempted to determine whether Piagetian levels of cognitive functioning exhibited by undergraduate music majors at three Colorado universit ies were s ignif icantly related to achievement in cognitively-oriented undergraduate music classes, music special ization, gender and chronological age. Of the 195 undergraduate music majors tested with the Classroom Test of Formal Reasoning (CTFR), 40 percent were found to be operating at the formal stage, 55 percent at the transit ional stage between formal and concrete, and 5 percent at the concrete stage. Subjects operating at the formal stage had a s ignif icant ly higher mean grade point average than subjects in the lower stages. Music program specialization was also found to be s ignif icantly related to CTFR scores at the .05 level of significance. No significant relationships were found between CTFR scores and age or gender. Hiranpradist (1986) studied the effect of level of cognitive development on the l istening behavior of 72 music and non-music majors (Michigan State University). The Music Listener Learning Style Inventory was used to assess subjects' cognitive level of operations. She found that the problem-solving strategies of 72 40 percent of the music students were congruent with Piaget's formal operational l eve l . This group correctly answered approximately 61 percent of Hiranpradist's Melodic Strategram test items and 44 percent of these music majors employed a decentrational l i s tening strategy. The remaining music majors were judged to be functioning at the concrete-formal operational l eve l . For this group, only eight percent of their answers were correct and only six percent employed a decentrational l istening strategy. The problem-solving strategies of the nonmusic major students reflected deficiencies in formal operational approaches with a propensity toward more primitive types of strategies. The preferred music l istener learning styles of music and nonmusic majors differed with regard to their verbalization, declared decision making, and task d i f f i c u l t y . Hiranpradist made several important recommendations. Since differences were found in the problem-solving strategies and l istening preferences of the music and non-music majors, music teachers should provide instruction geared to the cognitive level of their students. Many music majors did not possess adequate perceptive and verbal a b i l i t i e s so, in future studies, researchers should use demographic information as a preliminary means of identifying students requiring special assistance. In addition, training in decentrational l istening should be incorporated into aural musical tasks. 41 Musical information processing capacities. The human sensory-processing system is capable of handling a tremendous amount of information within an extremely short period of time (Bower and Hilgard, 1981). This is accomplished by rapidly coding, p r i o r i t i z i n g , and selecting s t imul i . The manner in which the human sensory processing system copes with aural stimuli is of great importance to the investigation of how the musician deals with music (Kepner, 1986, p. 2). Aural imagery. Echoic codes are the aural counterpart of visual images. Aural stimuli entering the ear are translated from physical energy to neural e l ec tr ica l energy and sent to sensory memory. Some of the encoded impulses are then taken into short-term memory where they may be strengthened through rehearsal. They may then be compared to other images from long-term and sensory memory. Once associations are formed, the new image may be transformed into a permanent form for long-term storage (Block, 1981). Memory. Horning (1982) defines music as specific sound in specific time (p. 13). Since music l istening occurs in real time, one cannot behold a musical work in an instant. The a b i l i t y to understand music depends upon the l istener's memory of musical events which have taken place both within the piece and during the l istener's entire lifetime of musical experience. Memory, therefore plays a more v i t a l role in music than in any other art form. 42 As noted above, at least three memory systems and their different capacities for storing information need to be considered. These systems are sensory or trace memory, short-term memory, and long-term memory (Sperling, 1967). Sensory memory is subconscious and holds information that has entered the senses for a few fractions of a second. The image fades during the next few seconds i f i t is not brought into short-term memory (Laske, 1977; Klatzky, 1980). In l istening to a complex piece of music, a l istener is usually not aware of every aspect of the music. However, sensory memory is able to store v iv id and complex information temporarily. Horning (1982) claims that this a b i l i t y may allow humans to experience and respond to music even when they are not completely aware of every aspect of i t . Sensory memory stores information as i t is received from the mental act iv i t ies of sensation. The selection process subconsciously analyzes and selects images from sensory memory. When we become conscious of a particular sense experience, that experience i s , at the moment i t becomes conscious, brought into short-term memory. Sensory memory is already quickly fading by the time short-term memory decides to process part of sensory information. The conscious act iv i t ies of short-term memory themselves cause interference with the images in sensory memory; causing other sensory information to be lost . 43 Short-term memory holds on to that which i t salvages from sensory memory; focussing and sharpening the image which remains. Only four to ten images can be called into short-term memory from sensory memory at one time, especially i f the images are isolated and not meaningful (Mi l l er , 1956). Many images in sensory memory are not brought into short-term memory. Thus, mental processing capacity imposes constraints on the ways that people can operate musical structures during l istening (Radocy and Boyle, 1979, p. 53). Klatzky (1980) identif ied the contact between the sensory register and short-term memory as pattern recognition or coding. Fi t t s and Posner (1967) reported results similar to those of M i l l e r . "Short-term memory involves about the f i r s t sixty seconds after presentation of a new stimulus. After that time, either the items are lost or they are transferred to a long-term memory system" (pp. 65-66). The number of "chunks" formed depends on the individual's a b i l i t y to formulate and translate information into chunks (pp. 66-67). Short-term memory, then, operates between two other memory systems: sensoral memory and long-term memory. Sensoral memory can handle large amounts of information temporarily but operates unconsciously. Long-term memory can store huge amounts of information permanently. Between them stands short-term memory; "a memory buffer of limited storage capacity that can be hindered from overflowing only by recoding" (Laske, 1977, p. 303). 44 Mi l l er (1956) suggests there are two techniques that the brain uses to improve i t s processing capabi l i t ies . Since only about seven bits of information can be transferred at a time to long-term memory, i t would seem that this imposes a severe l imitat ion on the rate at which information can be stored in long-term memory. However, before transfer to long-term memory, bits of information can be organized, categorized, and combined into a compound image. Short-term memory can process about seven items regardless of their content. This allows the mind to retrieve up to seven images and reprocess them into a complex compound image. These newly formed images can be stored in long-term memory. Thereafter, they can be recalled and combined to form potentially more powerful images. In short-term memory, images received from sensory memory can be compared and interpreted with reference to images stored in long-term memory. This permits information to be organized into larger and larger chunks (Laske, 1977, p. 46). The disadvantage of this time-intensive form of processing is that the effort of organizing images in short-term memory before storing them in long-term memory reduces the amount of information that can be brought in from sensory memory. The other processing technique i s that of setting up expectations in short-term memory in order to speed up the process of categorization and f i l i n g . Expectation causes short-term memory 45 to select reduced sets of images for association from long-term memory. Thus, the mind does not have to conduct such an intensive and time-consuming search for appropriate images. When new information coming from the senses relates easi ly to the compound images already stored in long-term memory, i t is more easi ly and quickly assimilated into previously memorized compound images (Horning, 1982). One disadvantage of this technique is that, when related images from long-term memory are not found, the brain either works harder to discover or create associations, or, as frequently occurs, to terminate this effort . When an inappropriate or incomplete set of images is selected, information that does not conform to this set is l ike ly to be forgotten. Alternatively , new images not related to any previously stored images may be rehearsed, organized, categorized, and f i l e d in an appropriate place in long-term memory (Broadbent, 1971). Expected musical events can be processed more ef f ic ient ly but unexpected events require considerable processing. Practice helps bring about the "automatic, unconscious performance of sk i l l s" (Norman, 1976, p. 201). Since music occurs in time, l isteners must respond rapidly to a changing stimulus. Practice in l istening to music can dramatically improve the accuracy and rate of a repertoire of musical perceptual/cognitive s k i l l s . Effective music l istening requires a sort of cognitive economy. That i s , the l istener must select processes that are both 46 appropriate and eff icient to the task of understanding the music (Ashley, 1982, p. 36). Attention. Horning (1982) defined attention as "the focussing of consciousness on one bi t of information to the exclusion of others" (p. 49). In attending, short-term memory selects information from sensory memory to rehearse and process. Madsen (1985) studied the effects of background music on a studying task. He concluded that listeners can only attend to one stimulus at time but that they are able to shift their attention between tasks very rapidly. Horning (1982) also contended that an individual can only attend to one thing at a time. Selection is the process which controls attention. Before sensory information can be attended to, i t must be selected. But how can selection take place before attention? The selection signal contains some information regarding what sensory information to search for in the sensory memory. These expectations are based upon information in short-term memory as well as information stored in long-term memory (programs). The selection signal always searches for pertinent information. Other information is not selected for attention. The selection/attention signal scans a l l available channels of sensory information continuously and stops on the channel which is most pertinent. (Horning, 1982, p. 55) 47 Control of the selection/attention processes. Controll ing the selection /attention process is an important s k i l l . Selection and attention cannot operate simultaneously. Great musicians and athletes develop the a b i l i t y to concentrate on one incoming set of information to the exclusion of a l l other incoming images. However, there are times when we wish to not only attend to certain incoming information but also to keep track of other available sensory information. In this case, the individual attends to a specif ic incoming channel, but interrupts this attention at various intervals to scan the other available incoming information. Although this individual may in the process lose some of the message attended to, i f the information contained in the message was f a i r l y homogeneous, i t may be possible to make an intel l igent guess at what was missed. Scanning permits the l istener to reassess one's expectations and whether or not they need to be replaced by another set of expectations. If a new set of expectations is called into play, the sensory information that was being attended to may lose i t s pertinence and the selection process w i l l take over and scan for sensory information which is more pertinent to current expectations. Horning (1982) believes that when two incoming sensory bits are of roughly equal pertinence the selection scanner w i l l either switch back and forth between them, picking up as much as possible from both, or w i l l distinguish between details of the incoming messages to select the more pertinent message for attention. If attention is 48 alternated between several sensations, then the one which receives the most attention w i l l be clearer. When we l i s ten for a certain note in a chord or a certain voice in a choir, the one we attend to sounds louder. We can distinguish i t s parts more clearly and we can perceive more easi ly . And yet, in spite of the fact that attention makes the sensation attended to stronger, we make allowances for the different amounts of attention and are aware to some extent of the true perspective. (Horning, p. 57) Bartholomew (1986) considered the implications of Cherry's (1953) research in speech perception for musical perception. He believed that, in l istening to music, one can distinguish a central , or focal aspect of the auditory f i e l d and a corresponding fringe area surrounding this focus. In l istening there is always a focus — a figure — set inside a fringe — or against a background. Within this polyphony one can focus on a single strand, in which case the other strands recede and become fr inge- l ike . As one refocuses and attends to a different strand the previously focal strand now becomes part of the background. The proportion between the focus and the strand, however, i s not stable. One can widen the focus (which correlat ively reduces the fringe) and vice versa. As the focus is 49 widened, though one is s t i l l aware that there are parts to the f i e l d , i t becomes more d i f f i c u l t to distinguish them, (p. 62) M i l l e r ' s findings would seem to support Bartholomew's comments. As more variables are added, total processing capacity increases but the accuracy for any particular variable decreases. In other words, an individual can make re lat ive ly crude judgments of several things simultaneously (1956, p. 88). Several models have been developed which describe the selection /attention process. Although they agree with each other in some respects, they d i f fer primarily in specifying the stage in the process at which relevant information is selected and irrelevant information is ignored (Horning, 1982, p. 61). Two of the most promising models for further study are those of Broadbent (1958) and Deutsch-Deutsch (1963). In Broadbent's model, selection is made on the basis of physical features such as intensity, pi tch, and spacial local izat ion of sound. Swets (1963), for example, noted that people tend to be more sensitive to midrange frequencies than high and low frequencies. In addition, there is considerable variation between individuals in sensi t iv i ty to different frequency ranges. Gray and Hedderburn (1960) found that this selection is also often made on the basis of analysis of meaning. 50 Treisman (1964) explored Broadbent's theory of selective f i l t e r i n g . She found that a l l sensory information is analyzed by a sequence of operations. The f i r s t level of analysis is based upon physical characterist ics , the second upon sound patterns, and the third on structure and meaning. If certain sensory events are expected to occur, then selection is biased and the analysis is simple. When sensory events have clear physical dist inct ions , then i t is possible for selection to take place at an early level of analysis. However, i f i t is d i f f i c u l t to distinguish between sensory events, the analysis must be more thorough before selection can occur. Deutsch and Deutsch (1963) proposed a model in which every sensory signal finds i t s stored image in long-term memory and is selected or not selected for attention based upon i t s relevance to previously analyzed information. If the incoming sensory information and the information previously judged to be pertinent both excite the same image in long-term memory, then that information i s selected for attention and further processing. For example, a student l istening to a piece believed to be in sonata-allegro form w i l l select musical events judged to be pertinent to sonata-allegro form and reject those believed to be irrelevant to the form. In addition, a student familiar with the performance practices of a given period in music history, w i l l expect to hear certain sound patterns in certain musical situations. 51 Perception. Carlsen (1981a) defines perception as follows: Perception is the extraction of information contained in the structure of a stimulus in the perceptual f i e l d . These stimuli may consist of the time and space boundaries of the perceptual f i e l d , the objects that appear in that space, or the events that occur over time. The perceptual f i e ld includes objects and events that exist outside of a person, but may also involve things and events within the person, (p. 2) Thus, perception involves interpretation of sensory information. This interpretation is influenced by which sensory information is selected from attention and by which sensory information is not selected (Horning, 1982). Perception takes place in short-term memory because i t is the only conscious part of the memory systems and because this is where images are analyzed to a degree which w i l l allow perception. An image must be associated, compared, and distinguished before i t can be perceived. Before conception can take place, the mind must perceive and categorize enough information about a thing so that the relationship of i t s many parts are also perceived and the mind forms a sense of the whole. At times, sensory information may be perceived but there may not be enough previously stored information in that category to form an idea of the whole. For example, we must attend to harmonies before we can perceive them. After we have attended to harmonies, 52 we associate them with harmonies which we have heard before both in the piece we are experiencing and in other pieces of the same sty le . We compare these harmonies with those we have heard before, and we distinguish them from those we have heard before. F ina l ly , we perceive the harmonies. Rehearsal. The only way short-term memory can hold on to an item long enough for processing to occur is through rehearsal. Since rehearsal in short-term memory takes a re lat ive ly long period of time, i t imposes a major load on short-term memory (Landauer, 1962). During rehearsal new images are transferred from sensory memory to long-term memory. As the image fades from sensory memory, the subject rehearses the sound in short-term memory, and the image becomes clearer. This occurs because during rehearsal more related information is pulled from sensory memory and long-term memory. This information is associated with the image in short-term memory, causing the image to be sharpened and focused. Because certain details of the stimulus tend to be focused upon at the expense of other detai l s , the f ina l version of the image in short-term memory is different from the original stimulus. Where the image i s blurred, we tend to f i l l in the gaps with educated guesses. Thus, the image f ina l ly stored in long-term memory may have gaps and, sometimes, distortions. However, i f rehearsal is interrupted before 53 the transfer is accomplished, the image is lost (Horning, 1982, p. 23). Eff ic ient organization of long-term memory. Images seem to be stored in long-term memory in specific ways. It would appear that the way information i s i n i t i a l l y categorized determines how quickly and how accurately the information can be retrieved (Funkhouser, 1968). Morin, DeRosa, and Stultz (1967), for example, asked subjects to report whether a given dig i t belonged to a set of d i g i t s . They found that subjects responded more quickly i f the d ig i t was far removed from the set rather than close. That i s , i f given the set of digi ts from 7 through 11, subjects would respond more quickly that 1 was not in the set than that 6 was not in the set. They hypothesized that the subject took longer to determine whether 6 f e l l within the range of 7 through 11 because 6 was f i l ed much closer to 7 in long-term memory. When an individual is presented with a problem which asks for material in precisely the way that i t was f i l e d , the answer comes quickly. However, when presented with a problem which requires information in organizational structures not available in long-term memory, copies of a l l relevant material must retrieved, transferred from long-term memory to short-term memory, and reorganized into a usable form. As a result , problem solution takes longer (Horning, 1982). 54 When information is pulled from long-term memory other information may, at times, be retrieved that interferes with the item which is the solution. Anisfeld and Knapp (1968) found that, when a l i s t of unrelated items were presented to subjects and they were asked to remember the l i s t , subjects often reported words which were not on the l i s t but were close associates to words on the l i s t . Horning (1982) asserts that this indicates that when any image is selected from long-term memory, other images in the compound image come with i t . In l istening to music, l isteners may, at times, experience what they expect to hear and not notice the discrepancy between what they expect and the sensory information they receive. Hierarchical organization of memory. In recent years, music theorists and cognitive psychologists have agreed that hierarchical organizations are an effective means of describing structural and perceptual aspects of music (Swain, 1986). Swain has recommended that hierarchical theories of music cognition should be l imited because the amount of information humans are able to take in and process is l imited. When music i s perceived according to Gestalt pr inciples , the l imit of organization w i l l be three or four events on a l eve l . When musical perception is aided by cultural experience, this number of events may be exceeded by grouping the events into processing units called musical constituents. In this way, the hierarchical theory 55 accounts for both the abstract and cultural aspects of musical experience. (Swain, 1986, p. 121) Serafine agrees that hierarchical structuring imposes a more simplified structure on the vast array of sounds in the piece (1988, p. 85). Individuals appear to vary with respect to the quality and number of transformations of musical events they are able to perform while l i s tening. They also vary in how such transformations effect their discriminative judgments. Thus, different levels of musical complexity w i l l match the musical processing capabil i t ies of various l isteners. Music which is more or less complex w i l l be preferred more or less in proportion to i t s extent of departure from the l istener's complexity ideal (LeBlanc, 1982, p. 31-32). Musical constituents seem to be marked by the l is tener's appreciation of musical context and function. They could be defined, then, as formal perceptions aris ing from sens i t iv i ty to the musical language (Swain, 1986, p. 129). Musical constituents are context sensitive (Swain, 1986, p. 127). Bharucha and Krumhansl (1983) maintained that the hierarchy of tones is entirely context-dependent, since the twelve chromatic tones are perceived as equally stable i n t r i n s i c a l l y . Only when a certain set is selected and highlighted is a hierarchy established. The hierarchy of chords is both context-independent and context-dependent. "Chords bui l t upon the seven steps of the diatonic scale are perceived as being i n t r i n s i c a l l y differentiated in terms of 56 s tab i l i ty : additional differentiation also occurs when they are perceived in the context of other chords" (p. 93). Constituent processing requires cultural experience or learning (Swain, 1986). Listeners must learn to internalize the hierarchical relations of a culture's musical language in order to appreciate i t s music in depth. Constituents seem to be an important part of the hierarchical process. They are the f i r s t structures formed by an interaction of the music and the l istener's musical competence. Musical constituents may constitute a c r i t i c a l level between the lower levels of raw material and the higher ones of abstracted experience. Listening Strategies. In his book, Making Sense in Music, Jos Kunst (1978) claimed that experienced music listeners select mental programs for l i s tening. Karma (1986) suggested the existence of two broad l istening strategies: passive recognition and active prediction. Ashley (1982) suggested that l isteners use different strategies depending on the situation at hand. For example, the musical selection chosen, fatigue, the form of the piece, and possible plans for future performance of the work effect the way an individual l istens to a musical work. In effect, the l istener selects which features are to be attended to, and which others are to be ignored. 57 Other researchers have investigated theories of multimodalities of musical experience. Musicians may, for example, choose between analytic and synthetic modes in l istening to music. Although some listeners may habitually use the same mode, other l isteners may choose to l i s ten analyt ical ly or h o l i s t i c a l l y on different occasions, for different purposes, and depending on the fami l iar i ty of the music (Fiske, 1985). LeBlanc (1982) suggested that mental processing includes "the formulation and testing of expectations, development of fantasy or imagery, and the signaling and experiencing of physiological and motor responses, including body movements (p. 39). It is l ike ly that an unknown cluster of sate l l i te variables influence the processing options chosen by the brain. Cognitive Styles. Schmidt (1984) investigated the relationships of cognitive styles and language-bound/language optional perception with performance of aural discrimination tasks. The cognitive styles studied were f i e ld dependence/independence, ref lect ion/ impulsivity, and performance on aural discrimination tasks. Field dependence was defined as the tendency to perceive a perceptual f i e l d either analyt ical ly or global ly . F ie ld independence was described as the a b i l i t y to experience items as discrete from their background and a b i l i t y to overcome embeddedness. Reflection/impulsivity was described as the tendency, when faced with simultaneous response alternatives, to select either careful 58 deliberation and relative certainty of response correctness or speed of response and high r isk of incorrect response. The language-bound/language-optional variable was described as perceiving and remembering aural events primarily in language terms or using language rules, or setting rules aside depending on the nature of the task at hand. In Schmidt's study, reflection/impulsivity did not account for a significant portion of the variance in scores on the aural discrimination tasks. However, f i e l d dependent/field independent styles and language-bound/language-optional constructs were found to be significant at the .05 level ; each accounted for about eight percent of the variance. Morgan (1984) investigated the problem solving a b i l i t y of high school instrumental students. He concluded that one can be taught to change l istening strategies i f the situation merits. However, because cognitive styles are part of one's personal makeup, they are much less adaptable. Although cognitive strategies can have the effect of counteracting the influence of one's style in a particular s ituation, one cannot truly adopt a new style . The l ink of cognitive style with the personality gives i t strong longitudinal consistency. Although the maturation process tends to make a l l people more analyt ical , the person who, at an early age, shows himself to be analytical relative to his peers 59 w i l l tend to remain so throughout l i f e . . . Like creat iv i ty , certain cognitive styles have obvious advantages in the educational arena; others show their value only when one looks outside the domain of tradit ional academic d isc ip l ines , (p. 45) Brink (1980) stated that, in fact, a l l individuals hear music relative to their own particular l istening processes. In planning music theory and aural s k i l l s instruction i t is necessary to consider both the nature of the mind and differences between individuals. Musical Style and Expectation. Although a l l cultures possess music there are many vastly different types of music, even within a single culture. "Musical styles may be thought of as categories. . . Style categories are organized around more prototypical members which reflect the redundant features of members in that category" (Unyk, 1985, p.13). Meyer claims that musical meaning results from the creation of tension as a result of s t y l i s t i c expectations. Once a musical style has become part of the habit responses of composers, performers, and practiced l isteners, i t may be regarded as a complex system of p r o b a b i l i t i e s . . . Out of such internalized probability systems arise the expectations — the tendencies — upon which musical meaning is b u i l t . (1967, p. 8) 60 Meyer distinguishes the role of memory processes in expectancy from the role of memory processes in music recognition. Even when listeners have heard a composition many times, some musical events in the work are s t i l l experienced as surprising (1956, p. 90). If l isteners have not internalized the probabil it ies appropriate to a musical style , their l istening experiences involve considerable expectational uncertainty. Serafine (1988) seems to believe that two kinds of cognitive strategies are used in l istening to music. An individual familiar with a particular style of music selects style-specif ic processes when l istening to that music. When l istening to unfamiliar music, generic processes are applied. Listeners gradually but continuously make minor adjustments in what they are wi l l ing to accept, so that even new, unfamiliar works can eventually be understood. Thus, the principles on which new pieces are based are incorporated into what listeners know and accept about the style at hand. Krumhansl, Bharucha, and Castellano (1982) propose that musical patterns conform to patterns that are characteristic of a musical culture. Through experience with this music, l isteners abstract and internalize the underlying regularit ies in these patterns. These internalizations are cognitive representations of music and give r i se to expectations about what is l ike ly to follow in unfolding musical patterns. Such expectancies are hypothesized to influence musical perception. 61 Carlsen (1981b) studied cultural differences in musical expectancy with musicians from Germany, Hungary, and the United States. Subjects from different countries were found to consistently hold different expectations for melodic beginnings and sung continuations. In relation to music transcription, Unyk (1985) noted that musical patterns must be accurately discriminated, identi f ied, and stored in short-term memory before they can be recal led. For Western l isteners, tone sequences that obey the constraints imposed by the system of Western scales and keys are more easi ly recognized, learned, and discriminated than other sequences of comparable complexity (West, Howell, and Cross, 1985, p. 73). Thus, expectation systems appear to influence musical memory and reca l l processes (Meyer, 1956; Jones, 1982). Postman, Bruner, and Walk (1951) suggest that when an individual has strong expectations for a particular event, less information is necessary to identify an event when i t does occur. Conversely, more information is necessary to perceive and identify an event that does not f u l f i l l this expectancy. Unyk (1985) hypothesized that events that violate strong expectancies require more information to identify than events that violate weak expectancies. Bruner and Postman (1949) observed three reactions when individuals were i n i t i a l l y unable to identify unexpected events. 62 Subjects either made the correct educated guess, identif ied the event as something in between what was expected and what actually took place, or were unable to even label the event. Krumhansl studied an aspect of cognitive representation of pitches in tonal contexts through s imi lar i ty judgments. She concluded that the organization of cognitive representations of pitches in scale contexts does indeed revolve around the central focal point of the tonic note and the tonic tr iad (Krumhansl, 1979; Krumhansl & Kessler, 1979; Krumhansl and Kessler, 1982; Krumhansl and Shepard, 1979). Shatzkin (1984) found further evidence of this tonic effect in tonal contexts. Intercorrelation of variables associated with aural s k i l l s . Various aspects of musical a b i l i t y appear to be so intimately connected that a reasonable minimum of all-round efficiency is needed. The effect of the maturation variable on aural s k i l l s , for example, is d i f f i c u l t to separate from the influence of cultural environment variables, musical training, auditory sens i t iv i ty , socioeconomic status, and memory (LeBlanc, 1980). Aural comprehension includes a whole set of interrelated competencies. Inabi l i ty to account for structural relationships may be due to lack of aural , verbal, notational, reading, or analyt ical s k i l l s . It i s sometimes d i f f i c u l t to distinguish the various 63 competencies required in a given musical task because they interrelate so closely (Brink, 1980, p. 70). Music Reading Musical scores provide reduced visual representations of music from i ts aural form (Brink, 1980). Since music lacks the speci f ica l ly assigned connotations found in language, a given musical symbol can take on an abundance of interpretations depending on the h i s tor ica l setting and the intentions of the composer (Langer, 1973). Notation. Musical notation i s , essential ly, functional for cultural participants. It embodies particular aspects of music, and an accurate usage of musical notation w i l l only occur i f the user is aware of the context of the notation. That i s , notation is selective. At least as much information other than that which is exp l i c i t l y derivable from the notation may be required to produce an accurate interpretation of the music that the notation is intended to represent (Ferguson, 1975; Tyler , 1980). Sloboda (1982) wrote that musical notation i t s e l f reflects the strategies and structures that are important in musical cognition at the level of perception. Traditional Western notation reflects the emphases of i t s tonal styles . 64 In the West, style has been defined primarily in terms of pitch and rhythm. These are the two parameters most accurately captured by notation and most thoroughly subjected to analysis. Pitch, which provides both harmony and melody, has been given the most attention, rhythm considerably l e s s . . . The other parameters — timbre, dynamics, etc. — have not been given rigorous analysis and are not precisely notated. (Serafine, 1988, p. 51) Bartholomew (1986) noted that in Western European musical tradit ion i t is common to associate music with i t s written notation and there is much to know about score reading. For example, in reading band and orchestral scores i t is important to know that many of the brass and woodwind instruments are transposing instruments. Score readers need to take note of the various transpositions made by different instruments before they begin mental construction of the work. However, there i s a tendency to assume that one who reads music "knows" more about music or is musically more educated than one who cannot. If "reading music" only means that one is able to recite the names of the notes and the rhythms, and not to hear the relationships of the sounds represented by these notations, then i t can be argued that such knowledge may be about music but is not by i t s e l f knowledge of music. Thus, both knowledge about music reading and audiation s k i l l s are needed for music reading. 65 Audiation. Gordon defined audiation as follows: Audiation is the basis of both developmental and stabi l ized music aptitudes. Audiation takes place when one hears music s i l ent ly ; that i s , when the sound is not physically present. One may audiate in recal l ing music or in improvising or composing music. In contrast, aural perception takes place when one hears music when the sound is physically present. Although the term "aural imagery" rather than aural perception is sometimes used to describe the audiation process, i t is not recommended because the word "image" is associated with the v isual , not the aural , sense... Notational audiation takes place when one hears music seen in notation when the sound is not physically present. One may notationally audiate by reading music, by writing music, or by composing music. (1984, p. 2) Bartholomew (1986) believed that audiation or "inner hearing" is not actual hearing but one aspect of musical thinking. He suggested that "music experienced in inner-hearing bears the same temporal and structural aspects that the music would have in external perception" (p. 330). Thus, inner hearing is "thinking in sounds" (p. 119). Inner hearing can also be incomplete. 66 It may lack the determination of some of the necessary patterns of sound: pitch, loudness, timbre, or duration. One can inner-hear the rhythm of a piece of music quite precisely without attending to the pitches presented. In this case, the pitches might be only vaguely present as pitches. Or the pitches of a melody can be inner-heard, but the rhythmic presentation is indeterminate. These two cases have parallels in actual performance situations: some undeveloped performers are able to account for the pitches but not the rhythms, and with others i t is the reverse. (Bartholomew, 1986, p. 117) Gordon (1985) has identif ied seven types of audiation as represented by the following tasks: l istening to familiar or unfamiliar music; reading familiar or unfamiliar music; writing familiar or unfamiliar music; recal l ing familiar music s i l ent ly or performing i t vocally or on an instrument; writing familiar music from r e c a l l ; creating or improvising music s i l ent ly or performing i t vocally or on an instrument; and writing music that is being improvised or created (p. 34). Music Reading S k i l l s . Though dist inct from l istening s k i l l s , music reading s k i l l s are essential for musical act iv i t ies associated with musical scores. "Any educated musician must function to some degree on both levels; f i r s t of a l l l i s tening, but then also reading, in 67 order to carry out tasks in composition, performance, or scholarship" (Brink, 1980, p. 64). Music educators have agreed that music reading s k i l l s are important to the musical development of the individual (Petzold, 1960). Practice in music reading can help develop aural imagery, stimulate and reinforce aural perception, enhance musical understanding, reduce the time needed to learn new works, contribute to musical self-dependency, and lead to s k i l l in sight-reading (Kliewer, 1973, p. v i ) . Many music majors, unfortunately, find reading music to be a d i f f i c u l t task: Students who choose to become music majors in college are usually experienced performers but are largely ignorant of theoretical matters, and, except for a fortunate few, usually have had no prior instruction in a systematic study of the aural forces which interrelate to produce the music they perform so well . In part icular, they experience d i f f i cu l ty in correlating sound with symbol and in translating the sounds they hear into musical notation, and are often discouraged by their i n i t i a l attempts to improve their aural awareness, recognizing the gap that exists between their performance s k i l l s and their capacity to identify the organic relationships within the music they are studying. (Kreter, 1976, p. ix) 68 Many attempts have attempted to identify the characteristics of good music readers (Bartholomew, 1986, p. 61). Kwalwasser (1955) reported on a number of studies by his students relating the a b i l i t y to read music accurately and rapidly with other variables. Many of these studies found music reading to be posit ively correlated with intelligence as measured by standardized tests. Music reading s k i l l was also generally related to musical a b i l i t y . Kwalwasser hypothesized that good reading s k i l l s relate posit ively to the performer's a b i l i t y to anticipate the notes as intended by the composer. Musical Discrimination S k i l l s Musical discrimination s k i l l s permit an individual to evaluate a musical performance. Fiske (1982a, 1982b, 1984) suggested that pattern discrepancy detection and identif icat ion in music l istening involve the mental testing of hypotheses. Such "tests" probably occur sequentially, with each successive test dependent on the processing requirements of preceding tests. Fiske (1985) tested two popular notions about discrepancy detection with regard to music. He hypothesized that music l istening either involves the comparison of an active auditory-like image against an incoming pattern or a set of "instructions" used to test the agreement of the structure of an incoming pattern with that of a recalled pattern. The f i r s t model implies that discrepancies in an incoming pattern are identif ied by 69 their fa i lure to match a mental replay of the pattern. The second model implies the use of a checklist set of characteristics which one expects to find between the individual tonal relationships i f the patterns are identical rather than the comparison of a series of mental images. For an image-comparison strategy, the structural characteristics of a pattern would primarily affect the quality and accuracy of the formed image. Successful discrepancy detection would depend upon an isomorphic relationship between this image and an incoming comparison pattern. This strategy depends, therefore, on an eff icient image-formation process. It is this processing stage which would rely upon the characteristics of a pattern rather than would the pattern-comparison stage i t s e l f . Therefore, the degree of success in such a comparison would be reflected primarily by the error rates, (p. 57) If a checklist strategy describes the pattern-comparison process, the characteristics of a pattern would determine the descriptors the l istener stores in memory. Discrepancy detection would depend upon expl ic i t processing instructions based upon these descriptors. The length and complexity of this l i s t w i l l vary with the characteristics of the original pattern. Both error rate 70 and response time would be affected by different pattern manipulations since a long l i s t of instructions would be more prone to error and require more processing time than would a shorter l i s t . (p. 58) Fiske concluded that both image comparison and checklist comparison act iv i t i es are used during discrepancy detection. Kepner (1986) proposed a musical discrimination cycle as related to instrumental performance. F ir s t of a l l , an instrumentalist would use his sense of vis ion to read the musical score. If performing from memory, this phase of the cycle would not include the act of physically looking at the notated music. Instead, the performer would "look" at mental pictures of the music or perform some other cognitive task to recal l the music which has been memorized. The next phase contains two independent, but closely related, processes; audiation and kinesthetic anticipation. Audiation is the process by which the instrumental musician forms mental images of the notated music. Kinesthetic anticipation causes the instrumentalist to mentally "play" the audiated notation. Both audiation and kinesthetic anticipation include the use of short-term and long-term memory in order to transform the visualized symbols into identif ied or learned concepts. Both are limited by the level of expectation of the instrumental performer. These performance expectations are based upon the instrumentalist's prior musical experience and musical a b i l i t y . This two-part phase is followed by 71 the actual performance on the instrument. Following the performance on the instrument, a comparison is made between the perceived musical performance, both auditory and kinesthetic, and the original audiation and kinesthetic anticipation completed prior to the performance. The comparison phase is also dependent upon the instrumentalist's level of expectation. A decision by the instrumental performer regarding the correctness of the musical performance follows the comparison phase (p. 12). The cycle is completed in a fraction of a second by the sensory processing system of the instrumental musician. A problem arises i f there is a break at some point in the cycle. Since so much information enters the instrumentalist's sensory processing system in a short amount of time, i t seems l ike ly that the system must find some unique way to deal with a l l of the s t imul i . This is the point where sensory blocking becomes involved. Kepner suggests that incoming stimuli are pr ior i t i zed . When the sensory system receives more stimuli than can be processed, high pr ior i ty stimuli receive attention and low pr ior i ty stimuli are blocked (p. 13). Kepner hypothesized that during performance high school instrumentalists are so concerned with correct fingerings and other "mechanics" of performing that they end up giving low pr ior i ty to much of the hearing aspects of performing. Thus, when a sensory overload occurs they w i l l block the perception phase. 72 Musical perception involves the most complex of mental operations; problem solving (West, Howell, and Cross, 1985, p. 48). In musical problem solving i t is essential to know the premises and the inference rules used in discovering what relationships between tones have perceptual relevance (Hochberg, 1981; Null and Young, 1981; Risset and Wessel, 1982; Watkins and Dyson, 1985). Musical discrimination is a specialized form of musical perception. The discrimination of complex tone sequences is affected by physical discrepancies between them and by subtle interactions with factors concerned with perceptual organization (Howell, Cross, and West, 1985). Krumhansl and K e i l (1982) have found that children are able to distinguish between diatonic notes at a very early age. However, even though people seem to be able to differentiate between frequency ratios to a very fine level of accuracy when tones are presented in single pairs , that level of accuracy diminishes rapidly when tones occur in a more extended context (Burns and Ward, 1982). Discrete pitch perception i t s e l f is not a simple, or universal s k i l l (Serafine, 1988). Yet, when tones are presented simultaneously sensi t iv i ty to frequency ratios becomes even more c r i t i c a l (Balzano, 1982). When this occurs, although the music becomes more complex, i t now also provides more information regarding how individual tones or patterns relate to the overall structure. 73 Factors Affecting Musical Discrimination Sk i l l s In 1950, A l i f e r i s and Stecklein conducted a nationwide study of the A l i f e r i s Music Achievement Test, College Entrance Level in the United States (Stecklein and A l i f e r i s , 1957). This test should, perhaps, be called a test of musical discrimination rather than a general music achievement test. Major instruments were grouped into six categories: strings, woodwinds, brass, percussion, piano, and voice. Significant differences were found at the .01 level of significance between each of the groups in each of the three subsections of the test. String players scored s ignif icantly higher on the melodic portion of the test than other groups. A l i f e r i s and Stecklein claimed that, because these instruments do not have frets , string players have to develop greater sensi t iv i ty to intonation. Pianists scored highest on the harmonic portion of the test and also had the second highest mean on the total test. Woodwind, brass, and percussion players scored almost equally high on the rhythmic portion of the test. Percussionists and vocalists had the lowest total mean scores. Rainbow (1963) investigated correlations between the musical aural discrimination a b i l i t i e s of school children as measured by the Seashore Measures of Musical Talents and the Drake Musical Memory Test. Rainbow included factors such as home enrichment, interest in music, and participation in music by relatives as well as more 74 tradit ional considerations of intel l igence, school achievement, and musical achievement and training. He concluded that intelligence (as measured by the Lorge-Thorndike Intelligence Test and the Otis Intermediate, Self-Administering Test of Mental A b i l i t y ) , along with tonal memory, musical achievement, interest in music, and socioeconomic background were significant contributors to musical aural discrimination s k i l l s . Douglas (1965) attempted to determine the effect of music theory instruction on the musical discrimination s k i l l s of entering college music majors. After analysis of scores obtained using the A l i f e r i s Music Achievement Test, College Entrance Level, the population was divided into three groups: high, medium, and low. After one and two quarters of music theory significant differences s t i l l existed in the aural discrimination s k i l l s of the three groups. Douglas found no significant relationship between a student's choice of degree program and his present level of aural discrimination. Neither did he find any significant relationship between a student's major instrument and his present level of aural discrimination. However, Thostenson (1967) concluded, in a later study, that the major instrument area and the extent of training were both important factors in aural discrimination but that the relationship seemed to weaken as the extent of college training increased. 75 In his study of the relationship of musical a b i l i t i e s and sex differences to aural-musical capacities Whellams (1973) rejected the hypothesis that standardized test scores could be used to discriminate between individuals or groups solely on the basis of inherited aural-musical capacity. Test performance d id , however, appear to be affected by both instrumental performance and gender. Long (1975), for example, developed the Long Indiana-Oregon Musical Discrimination Test. The test consists of 43 musical selections. In each case, the subject was presented with two renditions of a selection and asked to t e l l which rendition was musically better. Subjects were awarded an extra point for correctly indicating whether the difference between the two renditions was harmonic, melodic, or rhythmic. In validating his test , Long found the following correlations between student musical background and scores for college students on the test: extent of piano lessons .58, band and orchestra experience .34, total number of instruments in home .39, self-estimate of performance .50, and expressed preference for concert music .56. For his doctoral dissertation, Paul (cited in Verrastro, 1975) developed two collegiate level music tests, one of music theory achievement, the other of aural-visual achievement. In establishing the claim of construct va l id i ty for his tests, Paul found significant relationships between the number of years of private 76 study, classroom music instruction, and scores on his aural-visual test . Larson (1976) studied the relationships between the academic achievement, musical achievement, and the error detection s k i l l s of college music education majors. Significant relationships were found between dictation scores, sight-singing scores, grades in music theory, and error detection s k i l l s . He also noted that the highest a t t r i t i on rate for f i r s t and second year music students occurred among those students having the least amount of precollegiate private study on their major performance medium. Hornstein (1986) attempted to explore the strength and nature of relationships between the specific intel lectual information-processing s k i l l s included in Guilford's Structure of the Intellect (SOI) model and specific aural discrimination s k i l l s . Meeker's Structure of Intellect - Learning A b i l i t i e s Test and Gordon's Musical Aptitude Prof i le were used as the test instruments. Both tests were administered to 387 fourth, f i f t h , and sixth grade students from schools in the Dallas area. Only six specific SOI inte l lectual dimensions were found to be s ignif icantly related to melodic, rhythmic, and aesthetic discrimination a b i l i t i e s . A l l six involved the s k i l l s of "cognition" arid "evaluation". The study indicated that "semantic" mental information-processing s k i l l s , involving the a b i l i t y to reca l l an abstract meaning or procedure given an external stimulus, play an extremely 77 important part within this relationship. S k i l l s of a "figural" nature, which involve comprehending either a physical object or a non-physical idea and separating i t from other impinging stimuli also enter into the relationship. Dimensions involving an understanding of "systems", those mental s k i l l s which deal with groupings of figures, symbols, or semantic relationships, were also found to be important to the relationship. Regression analysis determined that inte l lectual information-processing s k i l l s accounted for between 10 and 15 percent of the variance in individual musical aural discrimination a b i l i t i e s . Pembrook and Taylor (1986) examined relationships between selected background variables of prospective college students and their scores on a Melodic Discrimination Test. Extent of musical experience and class level were both found to be posit ively correlated to melodic discrimination a b i l i t y . However, major instrument and years of music theory study were not found to be s ignif icantly related to the cr i ter ion variable. Heritage (1986) attempted to predict the aural-visual discrimination s k i l l s of 97 undergraduate music students on the College Midpoint Level version of the Al i fer i s -Steckle in Music Achievement Test. Eight predictor variables were used: attendance at a public or private college, the size of that college's music major enrollment, access to computer-assisted music instruction, socioeconomic background, religious background, precollege music 78 theory instruction, precollege musical experience, and parental involvement in music. No significant relationships were found between the cr i ter ion variables and the predictor variables either individually or col lect ively at the .05 l eve l . However, post hoc analysis identif ied a significant relationship between school choir experience and the ASMAT interval subscore. Comparison of the f u l l regression model to the model without school choir experience revealed that 6.7 percent of the var iab i l i ty was accounted for by the school choir variable. Similarly , post hoc analysis identif ied a significant relationship between school band experience and ASMAT rhythm subscores at the .05 level . In this case, the school band experience increased the variance explained by four percent. Musical Error Detection Tasks Musical error detection is a specialized form of musical discrimination. So far , l i t t l e research has been done to identify how individuals detect errors in musical performances. However, one theory is that when one's internalized system of rules are violated, one quickly identif ies the discrepancy ( s t i l l ) in sensory memory. The degree of discrepancy from the expected rendition of the work and the resolving powers of the l istener's auditory system thus determine whether or not the deviation f a l l s within the l imits of acceptable performance practice (Harvey, 1985). Morgan (1984) has 79 suggested that, in error detection, convergent thinking s k i l l s are directed toward identif icat ion of the error (p. 47). Musical Error Detection S k i l l s . Kepner (1986) has identif ied the s k i l l s necessary for error detection while performing on an instrument (See Table One). Some of the performance s k i l l s , such as embouchure formation and breath support, are not necessary for detecting pitch and rhythm errors while l istening to music and reading the musical score. However, others, such as experience with different instruments, can be useful in detecting errors made playing those instruments. For example, famil iar i ty with the performance errors frequently made on an instrument seems to improve the accuracy and efficiency of error detection. Error detection may be fac i l i ta ted by a set of expectations (Grunow, 1980) and subsequent use of a specialized set of error detection s k i l l s . Kepner (1986) and Grunow (1980) consider a b i l i t y to read music to be an important part of detecting errors in personal musical performance. In directing a large musical ensemble this a b i l i t y is also essential. As noted previously in this chapter, the conductor needs to possess strong music reading s k i l l s . In a musical ensemble, the player may partly rely on the conductor to interpret the musical score and detect errors but the conductor needs to thoroughly understand the entire score and be able to detect errors 80 fo r the ent i r e ensemble. Rapid score reading s k i l l s help f a c i l i t a t e e f f i c i e n t attention to a l l aspects of the performance. S i m i l a r l y , the performer needs to be able to recognize and perform musical elements. Again, the conductor needs highly e f f i c i e n t l i s t e n i n g s k i l l s f o r assessing the o v e r a l l q u a l i t y of the performance and i d e n t i f y i n g i n d i v i d u a l performance problems. F a m i l i a r i t y with the tone color or timbre of the d i f f e r e n t instruments i n the ensemble f a c i l i t a t e s tracking of i n d i v i d u a l musical parts. Several forms of audiation s k i l l may be related to error detection s k i l l . Before d i r e c t i n g an ensemble, the conductor usually studies the score. Notational audiation i s used to convert musical symbols into a mental construction of the work. List e n i n g to a recording or l i v e performance of the work provides another means of mentally constructing the musical piece. R e c a l l i n g the music from memory provides s t i l l another means. In a l l cases, the conductor mentally constructs an i d e a l i z e d performance of the work. Even i n l i s t e n i n g to an imperfect performance there i s evidence that the mind attempts to construct an i d e a l i z e d performance (Morgan, 1984). Error detection involves comparison of a performance with one's expectations. I t i s possible f o r an i n d i v i d u a l to detect errors i n a musical performance without score study or previous exposure to that p a r t i c u l a r work. Errors detected are v i o l a t i o n s of acceptable 81 Table 1 S k i l l s Necessary for Performance Error Detection A b i l i t y to Perform on a Given Instrument Tone Production 1. Embouchure formation 2. Breath support 3. Hand or st ick position Knowledge of Instrument 1. Notes and correct fingerings or positions 2. Finger and hand coordination A b i l i t y to Read Music Pitch and key notation Rhythm notation Dynamic markings Time and tempo markings Articulat ion symbols Style markings A b i l i t y to Recognize and Perform the Elements of Music Pitch and Melody 1. Intonation 2. Scales Rhythm and Tempo Harmony 1. Intervals 2. Chords Tone Color Form Dynamics A b i l i t y to Concentrate A b i l i t y to Use Intellectual Processes Tonal and Rhythmic Memory Translate written symbols into fingered and performed notes, rhythms, and dynamics Hear pitches and rhythms within the mind (audiation) Remember performance and compare i t with audiated model (from Kepner, 1986, p. 20). 82 compositional and performance practice for that l i s tener. Score study, however, has several advantages over simply relying on general expectation. The score reader does not have to deal with a l l the complexities of the music at performance tempo. On f i r s t reading, the score reader can attend to selected aspects of the work. Subsequently, the score reader may review them or begin to concentrate on other characteristics of the work. Eventually, the score reader may develop a rather thorough conception of how the musical work should sound. In western tonal music, musical notation is generally intended to express the essential structural details of works. However, musical notation also tends to neglect many of the finer details related to performance practice. These are left to the experience and creative imagination of the score reader or performer (Brink, 1980). Score study and l istening to recordings of the work before l ive rehearsal permit the conductor to develop a more complete mental conception, and, thus, a more detailed set of expectations for the ensemble's performance. Error discrimination appears to have two phases: the discovery that performance expectations have been violated; and, the exercise of explaining just what has occurred. Experienced listeners may anticipate common errors and use mental error detection programs to quickly pinpoint and identify those errors. 83 In summary, several factors appear to be essential to eff icient error discrimination: fami l iar i ty with that performance medium, possession of a complete conception of the work, a highly developed sense of musical discrimination, and possession of the appropriate repertoire of error detection s k i l l s . Studies in Musical Error Detection Studies of musical ensemble error detection a b i l i t y f a l l neatly into two classes. By far the largest group of error detection studies have investigated the efficacy of using programmed materials in error detection to improve the a b i l i t y of students to identify performance errors. The other group of studies has attempted to relate musical training factors to error detection a b i l i t y (Blocher, 1986, p. 13). Programmed Ensemble Error Detection Training Since complete "live" ensembles are often unavailable for rehearsal practice, numerous studies have investigated the use of programmed materials to teach aural-visual discrimination s k i l l s . Carlsen (1962) used a teaching machine to teach melodic dictat ion. Daniels (1964) studied teaching harmonic dictation through programmed instruction. Like Carlsen and Daniels, Spohn and Poland concluded that training in melodic and harmonic intervals could be improved by the use of programmed instructional materials (Spohn, 84 1963; Spohn and Poland, 1963). Later, Ihrke (1971) concluded that automated music programs could provide both val id and effective training in rhythmic performance, pattern ident i f icat ion, and error detection. Dolbeer (1969) developed an individualized program of instruction in identifying pitch and rhythm errors in recordings of band music. Students who had completed a formal conducting course, had high grades in music theory, and had extensive applied instrumental study or band experience showed the greatest improvement. Michels (1970) developed a series of sel f - instructional d r i l l materials designed to help students improve their a b i l i t y to detect pitch errors in choral singing. Fifty-four choral conducting students participated in the study. After a six-week training program, Michels compared the posttest scores of subjects to their pretest scores. He concluded that pitch error detection a b i l i t y is a competency that can be taught through self- instructional materials. Costanza (1971) used programmed instruction to teach melodic and harmonic score reading s k i l l s at Pennsylvania State University. Sixteen undergraduate music education and music majors who had completed a l l required theory and ear training courses used his Self-Instructional Program in Score Reading (SIPSR) to practice detecting errors in brass or clarinet quartet performances. After 85 participating in two 30-45 minute programmed instruction sessions per week for eight weeks, subjects were tested using Costanza's Score Reading Test. Costanza concluded that melodic and harmonic score-reading s k i l l s can be taught effectively by programmed instruction using aural-visual materials. Shaw (1971) designed and evaluated a se l f - instruct ional rhythm error program for choral conducting students. He also investigated the relationship between selected variables and rhythm error detection a b i l i t y . Number of years of private instrumental study, number of years played in band or orchestra, and mathematics scores on the Scholastic Achievement Test (SAT) were found to be s ignif icantly related to rhythm error detection a b i l i t y . However, piano and vocal instruction, theory grades, age, and gender were not found to be s ignif icantly related to rhythm error detection s k i l l s . Shaw also concluded that students could improve their rhythm error detection s k i l l s through the use of programmed materials. Sidnell (1971) had university music education students practice conducting while using self - instructional d r i l l materials consisting of tape recordings of band music. Subsequent testing with the Drake Musical Memory Test, the Visual Score Reading Test, the Score Reading A b i l i t y Test, and the Aural Harmony Achievement Test indicated that student conductors could effectively use se l f -instructional d r i l l materials to develop their score-reading s k i l l s . 86 Borer (1974) studied whether undergraduate music majors could use programmed instruction to improve their error detection s k i l l s . During the eight-week training period, subjects in the experimental group started with band and orchestral excerpts written on one stave and progressed to excerpts using eight staves. After analyzing pretest and posttest scores for both the experimental and control groups, Boyer concluded that the experimental group had improved s ignif icantly more than the control group. Boyer, suggested that se l f - instruct ional error detection programs be made available to undergraduate students as a supplement to courses in ear training and that students should be required to demonstrate competence in this area prior to professional f i e l d experience. Li les (1978) investigated the effect of a supplementary rhythmic d r i l l program on third and fourth year conducting students. Nineteen students registered in an advanced conducting class at Ohio State University were involved in the study. L i l e s prepared the forty-one examples used in the eight-week training program. Bach example was presented in f u l l score, as a piano reduction, and as a rhythmic analysis. The programmed materials included typical rhythmic problems and suggested strategies for correcting those problems during rehearsal. Bach example was played by a l ive ensemble and conducted from a f u l l score. Judges' ratings of pre-test and post-test videotapes were gathered to measure the effectiveness of the training program. Li l e s claimed that a 87; significant improvement in the identif ication and correction of rhythmic problems occurred as a result of the training program. Ramsey (1978) designed a teaching program to improve students' pitch and rhythm error detection ab i l i t i e s and to determine whether there was an optimum length of training program. Practicing instrumental music teachers suggested typical pitch and rhythm errors and these were inserted into full-score band music and recorded by a college band. Short, medium, and long versions of the training program were prepared. The 77 participants who completed the tests and assigned materials were prospective music teachers attending The University of Iowa, The Ohio State University, and The University of Texas at El Paso. Each subject was enrolled in a conducting or an instrumental methods course and had completed two years of aural training and music theory at the post-secondary leve l . Subjects were divided into four groups. Three groups practiced the different versions of Ramsey's materials and the fourth group served as a control group. Ramsey reported that music education students were successful at developing error detection s k i l l s when they used self- instructional tapes of the band l i terature . Though s ta t i s t i ca l l y significant at the .05 l eve l , the gains, however, were relat ively small. The 114- and 76-item forms of the test were found to be more effective than the 38-item form. Stuart (1979) investigated the effect of two training techniques on the development of error detection s k i l l s . 88 Undergraduate students in an orchestra methods class were divided into two groups. Both groups received tradit ional training in the methods class; including participation as the teacher-conductor of ensembles. In addition, members of the experimental group used videotapes, s l ides , textual materials, and classroom discussion to practice four types of error detection training: aural perception, bowing, positional aspects, and intonation. Stuart suggested that the use of program materials, discussion, and "live" conducting experience a l l contributed to the development of error detection s k i l l s . He concluded that error detection s k i l l s are most effectively taught when trainees are exposed to a variety of aural-visual stimuli in conjunction with participation as a teacher-conductor of ensembles. Grunow (1980) studied the relative effectiveness of four modes of score preparation on the development of visual-aural discrimination s k i l l s : study of the score only, study of the score with recorded examples, study with recorded examples only, and no preparation. Thirty-four undergraduate junior and senior music majors enrolled in two conducting classes at the University of Michigan participated in the study. Grunow's Visual-Aural Discrimination Test (VADS) was used as the measurement instrument. VADS is a test of a b i l i t y to identify: general discrepancies in tempo, balance, style of art iculat ion, tone quality, intonation, and phrasing; and specific discrepancies in rhythmic accuracy, note 89 accuracy, pitch accuracy, art iculat ion, and dynamics in instrumental performances. Following the pretest, subjects participated in six one-hour score study sessions. VADS was then re-administered as the posttest. Analyses of both adjusted and unadjusted covariance produced non-significant F ratios at the .05 level for the rhythmic, melodic, and expressive components of the test. Of a l l the variables l i s ted above, only note accuracy was s ignif icantly related to score preparation. No significant differences in achievement levels were found for the four modes. Nevertheless, Grunow concluded that a l l four modes of score preparation were effective means of developing aural-visual discrimination s k i l l s . Grunow commented that "It is generally assumed that v i sua l -aural discrimination is an achievement-based s k i l l and not an aptitude" (p. 37). However, "while there appears to be considerable agreement as t o . . . the necessity of visual-aural discrimination s k i l l s , there is less consensus concerning the method to develop these s k i l l s . . . Undoubtedly, the modern conductor, faced with a variety of instrumental textures, contemporary idioms, and recording technology, w i l l have a choice of several possible methods to prepare a score" (p. 5). DeCarbo (1982) compared the effects of programmed error detection instruction to podium-based error detection training. For 16 weeks, one instrumental conducting group practiced error detection using tape-recorded program materials. During that time, 90 the podium-based group conducted a l ive instrumental ensemble. Both approaches included practice in identifying errors in dynamics, rhythmic precision, intonation, note accuracy, rhythmic accuracy, and style as performed by a brass ensemble. No significant difference was found between the podium-based group and the programmed instruction group on a written error detection test but the podium-based group scored s ignif icantly higher on the conducting version of the test. DeCarbo concluded that podium-based error detection training was feasible with both conducting and methods classes. Training in error detection s k i l l s using a podium-based approach may transfer as well as training using a programmed format to nonconducting situations such as score reading and score study. Malone (1986) developed and evaluated an approach to increasing pitch error detection s k i l l s . The error detection program consisted of six instructional modules of choral examples contained in booklets and accompanying tapes. These materials were used for supplementary error detection practice by students in choral conducting classes. Results indicated that the materials were effective in improving the pitch error detection s k i l l s of choral music education students. Programmed learning has been shown to be one of the most effective methods for developing error detection s k i l l s (Boyer, 1974; Costanza, 1971; DeCarbo, 1982; Dolbeer, 1969; Grunow, 1980; S idnel l , 1971; Stuart, 1979). Several weaknesses or limitations 91 have, however, been apparent in such studies', the absence of sequencing strategies for excerpts; the use of homogeneous timbres; the occurrence of unplanned errors and inaccuracies due to using human subjects to record excerpts; expensive duplication of materials; minimal feedback, reinforcement, and interaction; and, the inab i l i ty to control students' progress through the materials (Deal, 1985). Such studies have also fa i led to identify those students who are most l ike ly to need such training and are most l ike ly to benefit from such training. Computer-assisted ensemble error detection training. Studies by Hofstetter (1975), Vaughn (1978), and Canelos, Murphy, Blombach, and Heck (1980) have suggested that a microcomputerized approach to aural s k i l l development may be superior to the more tradit ional approach of using taped examples with printed materials. To overcome some of the problems mentioned above, Deal (1985) used computer-assisted music instruction (CAMl) techniques to present materials from Ramsey's Program in Error Detection (PED). The resulting microcomputer version of PED was the Computer-Assisted Program in Error Detection (CA-PED). The subjects participating in this study were 65 volunteer instrumental music major students from three major midwestern universit ies . A l l subjects had completed the music theory and aural s k i l l s requirements at their respective universities and were enrolled in instrumental conducting or 92 instrumental methods courses. Using random assignment techniques, 33 were assigned to a group using CA-PED and 32 were assigned to a group using PED. Subjects in the PED group practiced pitch and error detection s k i l l s with taped materials. PED seemed to have several advantages over previously used taped programmed materials: excerpts had been selected from medium-difficult full-band l i terature; heterogeneous timbres had been used; the errors were ones which had been identif ied as "typical" by experts; and materials were incorporated into a continuum of lesser to greater d i f f i c u l t y . Subjects in the CA-PED group used Deal's program on an Apple 11+ microcomputer to practice pitch and rhythm error detection s k i l l s . After they selected a program section, the computer would display a musical excerpt on the screen. Pressing the "Return" key caused the computer to play the excerpt with an embedded error. The subject could then choose whether to l i s ten to the excerpt again or to indicate in which measure the error occurred, whether the error was one of pitch or rhythm, in which voice the error occurred, and what was played. After two attempts or a correct identif icat ion of the error, subjects could choose to view the incorrect version on the monitor before proceeding to the next question. CA-PED had several advantages over taped materials. It provided immediate feedback, reinforcement, and summarization of 93 student performance. In addition, the program could be duplicated quickly and cheaply. CA-PED also had some disadvantages. Excerpts played by CA-PED consisted of four-voice reductions of the full-band PED excerpts played by an electronic device. Also, 16 of the 114 excerpts in Form A of Ramsey's PED were omitted because the researcher's equipment was not capable of adequately simulating various percussion instruments. Pretest and posttest scores were obtained for the two groups by using Ramsey's Test in Error Detection. Both groups scored s ignif icantly higher on the posttest than on the pretest. However, neither program was found to be more effective than the other. Recent developments in music technology have made i t possible to further improve computer-assisted instruction (CAI) in ensemble error detection s k i l l s . In 1982, MIDI (Musical Instrument Digi ta l Interface), was accepted by the electronic musical instrument industry as the standard communications protocol for electronic musical instruments, computers, and related peripheral equipment. With MIDI, a computer or dedicated sequencer can now make electronic musical instruments simultaneously play up to 128 notes with different timbres. One advantage of using computer-controlled synthesis or sampling equipment is that i t becomes possible to vary the type, severity, and location of errors in a musical excerpt. The advent of affordable large memory devices, such as compact disk 94 and optical disk players, now makes i t possible for computers to rapidly select and play musical excerpts; f a c i l i t a t i n g computer-assisted learning (CAL) of error detection s k i l l s . Factors Related to Musical Error Detection S k i l l Hansen (1955) conducted one of the f i r s t studies of error detection a b i l i t y . In designing his test, melodic and harmonic errors were embedded in recorded performances of choral music. Musicians inspected the scores while l istening to these performances and attempted to identify any errors. In addition, Hansen compared test scores to factors such as theory training and performance medium. He concluded that theory training was not related to any increase in a b i l i t y as measured by the test. However, keyboard training was found to be highly related to error detection s k i l l s . Hansen recommended that reading and l istening to a l l parts of the score simultaneously should be the predominant method used in score study. Kreter (1976) has mentioned that harmonic, rhythmic, and motivic or melodic audiation s k i l l s are important to error detection. Pagan (1970), for example, measured the a b i l i t i e s of musicians to form accurate aural images of chords in a musical score. Single chords of four notes were used in the f i r s t portion of the test while three-chord sequences were used on the latter part of the test. Participants were asked to indicate whether the chords 95 viewed were the same as or different from the chords performed on an organ. Significant positive correlations were found between keyboard study, formal music study, private vocal or instrumental study, and scores on the chordal error detection test. Flom (1971) studied the growth of musical facts and concepts, musical discrimination, and vocal performance proficiency of Grade 10-12 students in selected mixed choirs from 10 Minnesota high schools with enrollments over 1,000. Measurement instruments administered included the Indiana-Oregon Music Discrimination Test (MDT), the Choral Music Test (CMT), and the Vocal Performance Test (VPT). A three-way analysis of variance found significant differences between schools. Tests by grade, sex, and musical experience did not find any significant differences. Flom attributed significant general differences between schools to instruction provided by the vocal classroom teacher and concluded that significant score increases between pretest and posttest probably resulted from maturation. Gonzo (1971) used tapes of choir music to compare the error detection s k i l l s of experienced secondary choral teachers attending the state music convention with those of University of Wisconsin music students who had completed two years of music theory. In general, no significant difference was found between the a b i l i t y of experienced secondary school choral directors and the a b i l i t y of undergraduate music students to detect pitch errors. Juniors, 96 seniors, choral teachers with 1-5 years teaching experience, and choral teachers with over 10 years of teaching experienced performed s imilarly on the test. However, teachers with 6-10 years of teaching experience scored s ignif icantly higher than the students. Also, a significant "relationship" was observed between subjects' educational levels and their performance on the pitch error detection test. The highest percentage of teachers possessing masters degrees had taught for 6-10 years and students with a composite "A" average in two years of music theory scored s ignif icantly higher than subjects with "B" or "C" averages. Of the college courses considered, only choral arranging appeared to contribute s ignif icantly to subjects' performance on the pitch error detection test. Brand and Burnsed (1981) attempted to measure the correlation between undergraduate instrumental music education majors' previous musical experiences and a b i l i t i e s , and their s k i l l in detecting errors in band performance. Five variables identif ied by the Commission on Teacher Education (1972) as highly valued components of precollege experiences and college training were selected: a b i l i t y in music theory, ab i l i t y in sight singing and ear training, ensemble experience, number of instruments played, and years of private instruction prior to university. Twenty-one second semester juniors or f i r s t semester seniors participated in the Music Error Detection Inventory, a test of ab i l i t y to identify errors in 97 dynamics, interpretation, precision, tempo, tonal balance, and tone control . No s t a t i s t i c a l l y significant correlations were found between s k i l l in detecting music errors in instrumental performance and each of the independent variables. Brand and Burnsed acknowledged that these findings may have resulted from using a test instrument with a r e l i a b i l i t y of only .59. Like previous researchers (Fiske, 1979), they questioned whether the a b i l i t y to detect errors in instrumental performance is related to other musical a b i l i t i e s and whether i t is acquired along with the development of other s k i l l s . They suggested that the teaching-learning strategies used in music classes may be quite different from those that develop evaluation a b i l i t y . Mount (1982) investigated the effect of l istening conditions on the a b i l i t y of graduate choral students to identify pitch and rhythm errors. The l istening test consisted of a recorded Bach chorale prepared with 25 pitch and rhythm errors. Subjects identif ied errors under five separate l istening conditions: parts alone, three sets of paired voices, and a l l parts together. Subjects were better at identifying pitch and rhythm errors when parts were played alone or in paired voices. Forsythe and Woods (1983) investigated the effect of conducting on the error detection a b i l i t y of undergraduate and graduate conductors. Grunow's VADS was adapted for the study. Subjects only conducted half of the test items. Mean test scores did not di f fer 98 s ignif icantly between undergraduate and graduate conductors. However, the act of conducting was found to inhibi t l istening s k i l l s . Shellahamer (1983) tr ied to determine whether experienced instrumental conductors detected common performance errors in a different manner than inexperienced instrumental conductors. Error types included errors in rhythm, pitch name, intonation, phrasing, dynamic contrast, and art iculat ion. Subjects conducted tape recorded brass t r io examples and c irc led errors detected on the score. Results indicated that error types were attended to in the following pr ior i ty order: rhythm, art iculat ion, dynamic contrast, intonation, pitch name, and phrasing. The order in which experienced conductor/teachers attended to the error types appeared to di f fer somewhat from the order in which inexperienced subjects attended to the error types. DeCarbo (1984) studied the effects of years of teaching experience and major performance instrument on the error detection scores of instrumental music teachers. His Error Detection Test consisted of two- to four- l ine scores of four-measure excerpts performed by brass instrumentalists. The EDT contained dynamic, intonation, note accuracy, and rhythmic errors. Teachers with 11 or more years of teaching experience scored s ignif icantly higher on the EDT than instrumental teachers with less teaching experience. No 99 significant relationships were found between major performance instrument and error detection a b i l i t y . Blocher (1986) studied the a b i l i t y of 141 college instrumentalists enrolled in the band program at Florida State University to detect common types of performance errors. Blocher's Error Detection Test (EDT) served as the data gathering instrument. EDT consisted of 11 recorded brass t r i o excerpts containing randomly assigned errors in art iculat ion , dynamics, intonation, note accuracy, phrasing, and rhythmic accuracy. Results indicated that there were no significant differences in overall error detection performance across the error types selected. Conducting experience also did not s ignif icantly affect overall error detection s k i l l s . However, post hoc comparisons did find that music majors detected errors with s ignif icantly greater accuracy than non-music majors. Brass players identif ied performance errors more accurately than non-brass instrumentalists. Also, while no significant differences were detected for the scores of upper classmen and graduate students, both groups detected errors with s ignif icantly greater accuracy than the lower level groups. The above studies have dealt with the a b i l i t y of the music educator to detect errors while following the score. This task involves perceiving what is on the score, what the music should sound l ike (notational audiation), l istening to a musical performance, and identifying errors (Kepner, 1986). 100 Summary In this chapter i t was shown that musical a b i l i t y is a complex, multidimensional attribute. Musical cognition requires the l istener to be able to determine which musical stimuli are the most sal ient , select and apply an appropriate repertoire of musical processing s k i l l s , and c a l l into operation other s k i l l s as needed. Musical discrimination appears to be essential to the eff icient operation of musical structures. Error detection s k i l l s appear to be highly specialized forms of musical discrimination. Evidence suggests that error detection s k i l l s are called into action when performance expectations are violated. Many aspects of innate capacity for music as well as musical background appear to be related to general aural-visual musical discrimination. Ensemble error detection s k i l l s may be related to these factors as well as to factors previously found to be related to ensemble error detection. Based upon this review of the l i terature , variables w i l l be selected for this study. CHAPTER THREE RESEARCH DESIGN AND METHODOLOGY Overview Although ensemble error discrimination s k i l l s have frequently been cited as essential for success in directing musical ensembles, l i t t l e research has been conducted to help identify which music students are l ike ly to be able to identify errors in musical ensemble performance and which music students are l ike ly to need remedial practice to develop this a b i l i t y . Thus, methods of predicting the a b i l i t y of undergraduate students to discriminate errors in ensemble performance need to be developed. Many variables were identif ied in Chapter 2 as potentially useful predictors of student s k i l l at ensemble error discrimination. These variables f a l l neatly into two classes: measures of capacity for performing the processes involved in musical problem-solving and variables affecting the efficiency of these processes; and measures of musical background, musical achievement, and other demographic variables. 101 102 The f i r s t class of variables hold promise in terms of improving understanding of the processes involved in musical error discrimination. However, no unified model of the mental processes involved in error discrimination currently exists and i t would be d i f f i c u l t to construct re lat ive ly pure measures of these processes. In addition, the time required for the administration of highly rel iable versions of these measures would l ike ly be prohibit ive. A good ensemble error discrimination test would probably take less time to administer and provide a more accurate measure of ensemble error discrimination a b i l i t y . While the second class of variables do not explain the processes involved in error discrimination, they are l ike ly to provide useful predictors of error discrimination. Data for these variables are certainly more readily obtainable. Precollege musical background, extracurricular musical experience, and other demographic data can be obtained accurately and rapidly from a questionnaire. Musical coursework data, reflecting a combination of musical background and musical achievement, can be obtained by examination of student transcripts. Musical achievement data, part icularly those from measures related to musical error discrimination, can be obtained by using tests of musical achievement. Thus, I decided to investigate whether ensemble error discrimination a b i l i t y can be predicted by the following types of variables: precollege musical background, quantity and quality of 103 various kinds of undergraduate coursework, scores on an aural-visual test of musical achievement, and other demographic variables. Research Design This chapter presents the research methodology used in this study. Multiple l inear regression methods were used to select various combinations of predictors. Preliminary Selection of Blocks of Variables No comprehensive models were available to explain how such complex variables as i n i t i a l musical capacity, maturation, musical experiences, interest in music, intell igence, motivation, reading a b i l i t y , and gender are related speci f ical ly to aural-visual discrimination of ensemble performance errors. Nevertheless, as mentioned in the previous chapter, considerable attention has been given over the years to relationships between independent variables and melodic, rhythmic, and harmonic discrimination. I expected that many of these variables would also be related to ensemble error discrimination a b i l i t y . 104 Musical achievement scores Previous studies have found significant relationships between musical aural-visual error discrimination and music achievement test scores (Flom, 1971; S idne l l , 1971). Other researchers have also asserted that musical achievement is related to musical error discrimination (Kreter, 1976; Pagan, 1970). Precollege musical experiences Petzold (1960) concluded that auditory perception s k i l l s appear to be f a i r l y well developed by Grade Three and to progress slowly thereafter. Students identif ied early as having high auditory ab i l i t i e s relative to their peers tended to retain this advantage. Thackray's (1972) findings also seemed to support the notion that early musical experiences are important. Thackray found that most musical development occurred by the age of twelve and that musical a b i l i t y levelled off around the age of fifteen or sixteen. These findings suggest that, at least with respect to single components of musical aptitude, precollege musical experiences should provide good predictors of future success in music. Pembrook and Taylor (1986) reported that the extent of precollege musical experience was related to melodic discrimination a b i l i t y . Kepner (1986) found that experience with different instruments was related to ensemble error discrimination. Shaw (1971) found that the number of years of private instrumental study 105 and the number of years of band or orchestra experience were related to error detection s k i l l . Tertiary musical training Effective audiation of instrumental scores requires the ab i l i t y to hear internally what those instruments w i l l sound l ike both individually and col lect ive ly . Post-secondary training in music, presumably, helps students to develop the s k i l l s they w i l l need in their professional careers. Thostenson (1967) found that the extent of precollege musical training was an important factor in aural training but that this effect diminished as the amount of college training increased. Paul (cited in Verrastro, 1975) found significant relationships between classroom music instruction and scores on his aural-visual music test. Larson (1976) found significant relationships between aural training, music theory, and error detection s k i l l s . Forsythe and Woods (1983) found significant relationships between conducting and error detection s k i l l s . Others, however, have not found similar relationships between undergraduate training and error detection s k i l l s (Pembrook and Taylor, 1986). Other demographic variables Other factors may be related to success in aural-visual ensemble error discrimination. For example, DeCarbo (1984), Gonzo 106 (1971), and Shellaharaer (1983) found music teaching experience to be posit ively related to musical error discrimination. Familarity with a culture's music, and especially with particular genres, appears to be related to success in error discrimination tasks. Sloboda (1988) suggested that people immersed in a musical culture acquire implicit awareness of i t s musical structures without expl ic i t instruction. Brink (1980) stated that the amount of musical detai l that an individual is able to process stands in direct proportion to that individual's familarity with the syntax of a given musical system. Thus, the more familiar one is with a musical genre the better one is able, after l i s tening, to demonstrate comprehension of i ts structure in de ta i l . Repeated practice enables the l istener to develop strategies to handle a variety of different situations. As these mental processes are exercised they become more eff ic ient . Thus, both authors suggest that l isteners can exercise more efficient l istening strategies when relying on perception of familiar musical structures than when l istening to unfamiliar forms of music. Students possessing appropriate repertoires of eff icient l istening s k i l l s should require fewer repetitions to detect, locate, and identify errors in complex musical performances. 107 Selection of Specific Variables Because complex music reading and l istening s k i l l s are needed for successful aural-visual error discrimination, variables representing many aspects of musical experience were considered. Based upon the review of the l i terature , 36 predictor variables were selected (See Table Two). Music achievement variables included the harmonic (chords), melodic (melody), and rhythmic (rhythm) aural-visual discrimination measures of the Al i fer i s -Steckle in Music Achievement Test, College Midpoint Level. A l l three subtests provided data on the interval scale of measurement. Precollege background variables included: the number of band instruments played before college (band instruments played), the amount of band or orchestral experience (band or orchestra), the number of years of choral experience (choral experience), the number of courses in music theory or ear training completed before university (music courses), and the number of years of private music performance lessons (music lessons). A l l precollege musical background variables were variables on the ratio scale. Other demographic variables included age (age), tert iary inst i tut ion attended {college or university), extracurricular performance experience (extracurricular performance), sex (gender), major performance medium (major performance medium), music teaching Table 2 Variables of I i t e r t i t litk Sealei of leasirement, leans, Standard D e v i a t i o n , aid tanget Tariables Ensemble Error Discrimination titth discrimination - Scores on the pitcb subtest of the net Test in Error Detection Jh/thmic discrimination - Scores on the rhythm subtest of the new Test in Irror Detection Music Achievement Test Scores Coords - Scores 01 the chord snbtest of the A l i f e r i s - Stecklein Rusk Achievement Test tkloij - Scores on the lelodic snbtest of the Al i fer i s -Steckle in Basic k h i e m e n t Test I n / t i l - Scores on the rhythmic subtest of the Al i fer i s -Steckle in Music Achievement Test Precollege Musical Background land ins t rnes t s played - lumber of band instruments played before college Jaod or orchestra - Ruber of years of band or orchestral eiperience Chora/ eiperience - Ruber of years of choral eiperience Music courses - Ruber of courses in ins ic theory or ear training completed before university Music lessons - luiber of years of ins ic performance lessons before college Other Demographic variables Aft - Age by years College or University - School of music attended School One - (0 = other, 1 : School One) - (o = " School Two other, I : School Tio) School Three - (0 : other, 1 : School Three) School Four - (0 : other, 1 r School Pour) Extracurricular perfonaoce - Current ei tracorricular performance eiperience ( in hours per month) Cender - Sei (0 - male, 1 - female) Scale M SD d in . Hai Interval 18.582 7.281 1 38 Interval 12.241 5.(4( 0 23 Interval ' 8.325 4.948 3 25 Interval 12.974 7.427 3 34 Interval 14.(40 3.574 3 19 Eatio 1.(80 1.544 0 8 l a t i o 5.093 3.990 0 20 Eatio 2.(93 3.13( 0 14 Eatio 1.(27 2.039 0 9 Eatio 7.507 4.944 0 20 Eatio 21.5(0 4.889 18 45 lominal 0.089 0.284 0 1 0.430 0.498 0 1 0.203 0.404 0 1 0.278 0.451 0 1 Eatio 9.773 13.7(4 0 (0 Rominal 0.494 0.503 0 1 Continued Tabic 2 (Cont'd) Variable* of I i t c r e i t with S u l c i of l e a i a r a e i t , leans, Standard foliation, aid langes Tariablet Scale la jo r Perforaanee ffadiu l o i i n a l l a i d instruments * (0 : other, I : band instrument) Itjboirds - (0 = other. 1 ; keyboard) Strings • (0 : other. 1 : keyboard) Foice - (0 : other, i : voice) Untie teaching - Int ie teaching eiperience bj years i t increments of .1 ta t io Preferred lose iMe - l is tening preference bv type of enseible l o i i n a l Instrumentalist - (0 : other, 1 : unaccompanied i tstraaentalist) Accompanied solois t - (0 : other, 1 - soloist with choral and/or instrumental accoapaniHnt) Sull chortl ensemble • (0 : other, 1 = choral enseible with no tore than s is leibers) S a i l l iasrrmestaf easemile - (0 = other, 1 : instrumental ensemble with no lore than six leabers) Urge ebonl ensemble - ID : other, 1 : choral enseibles with seven or tore enseibles) large instrumental ensemble - (0 : other, 1 : instrniental enseible with seven or tore members) Preferred T/ype of At t ic - Listening preference by style l o i i n a l Clmittl - (0 = not c lass ica l , 1 : c lass ical) hsj l i s tening - (0 = not easy l is tening, 1 : easy listening) J a : i - (0 : not j a i l , 1 : jazz) Popular - (0 : not popular, 1 - popular) foci - (0 : not rock, 1 : rock) Other - (0 : not other, 1 : other) Program - Program Major l o i i n a l Composition major (0 = other, 1 : coiposition) Conducting major (6 - other, 1 - conducting) General or utitthrti aajor (0 '- other, 1 1 general or undeclared) ftsie edaeation aajor (0 : other. 1 - music education) Ifasie history aajor (0 - other. 1 : ins ic history) Performance ai jor (0 : other, 1 : performance) fear - Tear in undergraduate prograa Ordinal • Si Hin. l a i . 0.304 0.463 0 1 0.241 0.430 0 1 0.190 0.395 0 1 0.165 0.373 0 1 0.619 1.450 0.0 10.0 0.101 1.304 0 1 0.278 0.451 0 1 0.013 0.113 0 1 0.2S3 0.438 0 1 0.013 0.113 0 1 0.246 0.445 0 I 0.291 0.457 0 1 0.051 0.221 0 1 0.228 0.422 0 1 0.051 0.221 0 1 0.266 0.445 0 1 0.025 0.158 0 1 0.405 0.494 0 1 0.241 0.430 0 1 0.013 0.113 0 1 0.063 0.245 0 1 0.203 0.404 0 1 0.013 0.113 0 1 1.651 0.949 1 5 Continued Table 2 (Coit 'd) Yariablea of Iitereat f i t h Scales of leasirement, leans, Standard Deviations, amd langes Tariables Scale If St l i n . S i i . Undergraduate Coorsewri ippliti lessons - lionnt of coorsework in applied ins ic lessons (in university credits) CPA it lessons * CPA in applied ins ic lessons (on a nine-point scale) Eatio Interval 5.526 6.0)3 4.050 1.635 0.0 2.90 20.0 9.00 Aural training -Amount of coursework in aural training ( in university credits) G?A in aural tniaiet * (on a nine-point scale) Eatio Interval 1.092 5.507 1.148 2.726 0.0 0.00 5.0 9.00 land instrument techniques - Aiount of coursework in band instrument techniques ( in universi CPA in band iostroient techniques - (on a nine-point scale) ty credits) Eatio Interval 0.421 6.516 1.068 1.398 0.0 4.00 6.0 8.25 Composition - Amount of coursework in composition ( in university credits) CPA in composition - (on a nine-point scale) Eatio Interval 0.086 6.667 0.419 1.155 0.0 6.00 3.0 8.00 Conducting - Amount of coursework in conducting (in university credits) CM ii conducting • (on a nine-point scale) Eatio Interval 0.257 6.197 0.866 1.886 0.0 3.00 5.0 8.00 Ensembles - Amount of coursework io ensembles ( in university credits) Cm in ensembles - CPA in ensemble coursework (on a nine-point scale) Eatio Interval 2.658 5.989 1.960 1.939 0.0 0.50 9.0 9.00 ffusie history - Amount of coursework in music history ( in university credits) CPA in music history (on a nine-point scale) Eatio Interval 3.520 4.167 1.797 2.244 0.0 0.00 9.0 8.25 ffosie theory * Amount of coursework in music theory (io university credits) CPA in music theory - (on a nine-point scale) Eatio Interval 4.868 4.931 3.011 2.246 0.0 0.92 16.0 9.00 Orchestration and arranging - Amount of coursework in orchestration or arranging ( in university credits) Eatio CPA in orchestration or arranging - (on a nine-point scale) Interval 0.309 5.929 0.770 1.900 0.0 3.00 3.0 9.00 I l l experience (music teaching), l istening preference by type of ensemble (preferred ensemble), l istening preference by style (preferred type of music), program major (program), and year in the undergraduate program (year). With the exceptions of the ratio variable age and the ordinal variable year, the demographic variables provided data on the nominal scale. Undergraduate music variables included: the number of credits of applied music lessons completed (applied lessons) and the GPA for those lessons (GPA in lessons); the amount of coursework in sight-singing and ear training (aural training) and the GPA for that aural training (GPA in aural training); the amount of coursework in brass, percussion, and woodwinds completed (band instrument techniques) and the GPA for those courses (GPA in band instrument techniques); the amount of coursework in composition (composition) and GPA for coursework in composition (GPA in composition); the amount of coursework in conducting (conducting) and GPA in conducting (GPA in conducting); the amount of ensemble experience (ensembles) and the GPA for that experience (GPA in ensembles); the amount of coursework completed in music history (music history) and the GPA for that coursework (GPA in music history); the amount of coursework in music theory (music theory) and the GPA for that coursework (GPA in music theory); and, the amount of coursework in orchestration and arranging (orchestration and arranging) and the GPA for orchestration and arranging (GPA in orchestration and arranging). 112 A l l coursework variables provided data on the ratio scale. A l l grade point average variables provided data on the interval scale. Selection of Subjects The population studied was comprised of undergraduate music students attending Canadian colleges and universit ies . Eighty-two volunteers from two community colleges, one private university, and two public universities participated in the study. Preparation of Instruments The Al i fer i s -Steckle in Music Achievement Test The College Midpoint Level version of the Al i fer i s -Steckle in Music Achievement Test (ASMAT) was used to assess subjects' ab i l i t i e s in specific areas of musical discrimination; melodic, harmonic, 'and rhythmic. The ASMAT was chosen because i t is one of the most widely accepted tests of general aural-visual music discrimination s k i l l s . Whybrew (1971) reported that i t s development seems to have been careful and thorough. Wing (1968) found the test to be quite satisfactory as a measure of auditory-visual discrimination. Two versions of the ASMAT were available: the College Entry Level and the College Midpoint Level. The College Midpoint Level 113 was selected to avoid ce i l ing effects for upperclassmen resulting from an easy test. This version of the ASMAT contained three auditory-visual discrimination subtests: melodic, harmonic, and rhythmic. A l l tape recorded items were or ig inal ly played on a piano. The authors claimed a r e l i a b i l i t y of .92 for the 79 item test and r e l i a b i l i t y coefficients of .90, .84, and .69 for each of the respective subtests. The Musical Background Questionnaire The Musical Background Questionnaire (MBQ) was designed and used to collect survey data about the following areas: precollege musical involvement; and related information including age, amount of extracurricular musical performance experience, selected program major, major performance medium, school of music attended, gender, year in undergraduate program, the type of music most enjoyed, the type of ensemble listened to most, and the amount of full-t ime music teaching experience. The MBQ was developed to fac i l i ta te collection of data on the 15 demographic and precollege musical experience variables (See Appendix A) . During construction of the questionnaire, college and university calendars were examined for information regarding entrance and program requirements. Music department chairpersons were also consulted at that time to gain further c lar i f i ca t ion about programs offered by their inst i tut ions . 114 The Test in Error Detection A new version of the Test in Error Detection (TIED) was designed and used to improve upon the r e l i a b i l i t y of Ramsey's test of pitch and rhythm error discrimination for band performance. As part of his doctoral study Ramsey (1978) prepared 135 recorded excerpts of errors in full-band performance. Each excerpt contained a single pitch or rhythm error. This pool of excerpts was judged by a panel of experts to adequately represent the continuum of band l i terature c lass i f ied as medium d i f f i c u l t . Previous sp l i t -ha l f analysis of this test produced an internal r e l i a b i l i t y coefficient of .63. This somewhat low value part ia l ly resulted from Ramsey's decision to select excerpts representing the continuum of d i f f i cu l ty for pitch and rhythm errors in medium-difficult band music. Test-retest analysis resulted in a Pearson's correlation coefficient of .71. This value was reasonably high in comparison with other tests measuring musical discrimination s k i l l s in a musical context. Ramsey selected ten of the excerpts containing pitch errors, ten rhythm error excerpts, and one example excerpt for his test . The fact that some of these items were very easy and others were very d i f f i c u l t undermined the discrimination a b i l i t y of the test. As noted by Gulliksen (1945), items should be approximately equal in d i f f i cu l ty and they should also be of medium d i f f i c u l t y . From Ramsey's pool of items the present researcher constructed a new version of the TIED in an effort to improve the r e l i a b i l i t y of 115 the test (See Appendix B). Items were selected which represented typical errors made by band students playing different instruments. Two strategies were employed in an effort to improve the r e l i a b i l i t y of the test. Whenever possible, items were selected from Ramsey's table of test item d i f f i cu l ty which had d i f f i cu l ty indices close to 0.5. The new test contained thirty items plus an example. Fifteen items contained pitch errors and the other fifteen items contained rhythm errors. To offset the additional length of the test, the study and answer time per item was reduced from one minute and f i f ty - f ive seconds to seventy seconds. Subsequent tests of internal consistency using Hoyt's alpha calculated a r e l i a b i l i t y index of .74 for the ensemble pitch error discrimination subtest and .63 for the ensemble rhythm error discrimination subtest. The overall estimate of internal r e l i a b i l i t y for the test was calculated to be .76. These values are estimates of systematic variance in test item responses. Therefore, no more than . 742 or 54.76 percent of the variance in pitch discrimination scores and .632 or 39.69 percent of the variance in rhythm discrimination scores could legitimately be explained by regression procedures in this study. 116 Procedures Data Collection The test administrator made sure that suitable testing conditions were provided with good l ight ing, reasonably comfortable chairs, adequate room, and an absence of external noise or other distracting conditions. Participants were issued pencils, ASMAT and TIED test booklets, and a MBQ Form. After assuring participants that individual results for a l l aspects of the study would remain confidential, participants were asked to grant permission to access their transcripts. The forty-f ive minute TIED was administered. Prerecorded instructions were played while subjects read the instructions from test booklets. The test administrator then stopped the tape and answered subjects' questions before continuing with the test. The following sequence was used for the example and for each of the test items: the item number was announced; subjects had 40 seconds to study the musical score excerpt; subjects then heard the excerpt for the f i r s t time; subjects had 20 seconds to answer the questions or to continue to studying the score; subjects then heard the excerpt for the second time; and subjects had 10 more seconds time to answer the questions. For each item, subjects were expected to answer the three questions l i s ted on the answer sheet: "in what measure does 117 the error occur?" "in what instrument does the error occur?" and "What is the exact nature of the error?" After completing the TIED, participants took approximately ten minutes to f i l l out the MBQ form. This also provided a change of act iv i ty between the two aural-visual discrimination tests. Subjects then participated in the th ir ty minute ASMAT. Once again, the test administrator read the instructions for the melodic subtest from A l i f e r i s and Stecklein's examiner's booklet before playing the f i r s t example recorded on the tape. The melodic example consisted of four chromatic notes played in sequence. The f i r s t three notes were notated. Four alternatives were provided for the f ina l note. After hearing the f inal note, subjects wrote down a letter associated with that note; either "A", "B", "C", or "D". The second example and the 34 items followed the same format. The researcher answered any further questions before playing the second example. Barring any further questions, the melodic test proceeded. Instructions were read from the examiner's booklet for the harmonic subtest. Two examples and 26 items were played. Major, minor, augmented, diminished, and various seventh and ninth chords were used in this test. In each case, a chord was incorrectly notated on the answer sheet and, after hearing the chord, the subject was requested to identify which part contained the wrong note: soprano ("S"), alto ("A"), tenor ("T"), or bass ("B"). 118 The rhythmic subtest proceeded after instructions were read from the examiner's booklet. For each of the 19 items plus two examples, subjects read a six-beat pattern notated in the test booklet. Beats Two through Five were identif ied as "A", "B", "C", and "D" respectively. Subjects were requested to identify the beat on which the rhythmic pattern heard did not match the notated rhythmic pattern. Transcript data were accessed once formal permission was obtained from subjects and from the particular institutions participating in the study. I examined the transcripts of participants and collected data regarding the quality and amount of tert iary coursework completed in selected areas of musical study: subjects' major performance media, ensemble experience, instrumental techniques, music history, music theory, aural training, orchestration and arranging, composition, and conducting. Data entry Age, band instruments played, band or orchestra, choral experience, music lessons, and year were recorded in years. Extracurricular performance was recorded in terms of extracurricular performance experience in hours per month. Music teaching was recorded in estimated equivalents of full-t ime music teaching experience to a resolution of tenths of a year. 119 College or university, gender, major performance medium, preferred ensemble, preferred type of music, and program were i n i t i a l l y coded as categorical data. College or university data were a r b i t r a r i l y coded as '1' for School One, '2' for School Two, '3' for School Three, '4' for School Four, and '5' for School Five. Only two students from School Five participated in the study. They could hardly be considered to comprise a representative sample of that inst i tut ion's music students so School Five and the results for individuals attending School Five were eliminated at this stage. The dichotomous variable, gender, was coded as follows. Female subjects received a score of '1' and male subjects received a score of '0' . Major performance medium data were coded as '1' for band instruments, '2' for keyboards, '3' for strings, and '4' for voice. A l l participants f i t ted one of these categories. Preferred ensemble data were coded as '1' for unaccompanied singer, '2' for unaccompanied instrumentalist, '3' for accompanied soloist, '4' for small choral ensemble, '5' for small instrumental ensemble, '6' for large choral ensemble, '7' for large instrumental ensemble, and '8' for other. No subjects selected the categories unaccompanied singer or other so these categories were eliminated from further consideration. Preferred type of music was coded as '1' for classical, '2' for i country, '3' for easy l istening, '4' for jazz, '5' for popular, '6' 120 for rock, and '7' for other. None of the participants selected country as their preferred type of music so this category was eliminated. Program data were divided into six categories. These were coded as '1' for composition major, '2' for conducting major, '3' for general or undeclared major, '4' for music education major, '5' for music history major, and '6' for performance major. Separate scores were entered for each of the Al i fer i s -Steckle in subtests. Each item answered correctly increased a subject's score by one mark. Thus, the maximum scores for chords, melody, and rhythm were '26', '34', and '19' respectively. For the TIED, subjects received a score of '0' , ' 1 ' , '2' , or '3' for each of the items. For example, a subject correctly answering two of the questions for a given item would receive a score of '2' . Since each of the two subtests was comprised of 15 items, the highest score possible for pitch discrimination or rhythm discrimination was '45'. Coursework completed at college was converted to equivalent university credit . That i s , coursework completed under the semester system was divided by a factor of two. Each of the institutions used different grading systems so i t was necessary to convert such data to a common grading system. Two institutions used a four point grade scale in s l ight ly different ways, another inst i tut ion used a 4.33 grade scale, one inst i tut ion 121 used a nine point scale, and another inst i tut ion awarded marks out of f i f t y for each credit completed. From a preliminary examination of transcript data i t was clear that numerical grades awarded had alphabetic counterparts such as "B" and their finer distinctions such as "B+" and "B-". Thus, grade point averages were calculated on a nine-point scale with an "A+" receiving a mark of 9.00, "A" receiving a mark of 8.00, "A-" receiving a mark of 7.00 and so on. On the nine-point system "C" is a mark of 2.00 and "D" is a mark of 1.00. Occasionally, some institutions awarded a " C - " . When this happened, subjects were given, for the purposes of this study, a mark of 1.50. Fai l ing grades were given a mark of 0.00. The grade of "pass" was not entered into the GPA. Some institutions simply awarded "pass" or "fai l" marks for certain courses while others awarded pass marks for barely acceptable performance. A pass may or may not have indicated much regarding the quality of a student's coursework at one inst i tut ion in comparison to the mark of a student at another inst i tut ion. Data Processing and Analysis The data set was stored on the University of Br i t i sh Columbia's Michigan Terminal System (MTS) which runs on a 48 megabyte Amdahl 5860 mainframe computer. The data were then analyzed using the 122 Extended Version of the Stat i s t i ca l Package for the Social Sciences (SPSS-X) Release 3.0. Recoding of data SPSS-X was used to create variables as needed to indicate the presence or absence of characteristics of interest. This resulted in a total of 57 independent variables. For college or university, a score of '1' was assigned to the school of music attended and a score of '0' was assigned to other schools. For example, i f an individual attended School Two, a score of '1' was assigned to School Two and a score of '0' was assigned to School One, School Three, and School Four for that individual . Major performance medium was divided into categorical four variables; band instruments, keyboards, strings, and voice. Band instrument players received a score of '1' for band instruments and '0' for the other three major performance medium categories. Similarly, keyboard majors, string majors, and voice majors received a score of '1' for keyboards, strings, and voice respectively, and a score of '0' for the other three major performance medium categories. Six variables were created for preferred ensemble. A score of '1' was assigned to instrumentalist for each individual that selected "instrumentalist (unaccompanied)" and a score of '0' was assigned to instrumentalist for each individual that did not select 123 this category. Similarly , participants selecting "soloist with accompaniment", "small choral ensemble (six members or less)", "small instrumental ensemble (six members or less)", "large choral ensembles", or "large instrumental ensembles" were assigned a value of '1' for accompanied soloist , small choral ensemble, small instrumental ensemble, large choral ensemble, or large instrumental ensemble respectively. A l l participants were assigned scores of '0' for the categories not selected. The six variables created for preferred type of music included classical, easy listening, jazz, popular, rock, and other. Individuals were assigned a score of '1' for the category they selected and '0' for the other preferred type of music categories. The six variables created for program were composition major, conducting major, general or undeclared major, music education major, music history major, and performance major. Subjects were assigned the value of '1' for the category describing their major and '0' for the other program categories. As much of the data set as possible was retained for analysis. I suspected that deleting the records of subjects not providing complete responses would remove many of the lower scores from the data (Kim and Curry, 1977). Therefore, missing data were special ly coded '999' so that any incomplete records would not have to be deleted. This made i t possible to use pairwise deletion of missing responses rather than deletion of substantially complete records 124 occasionally missing data items. This approach helped to avoid restricted range problems and to preserve the maximum number of degrees of freedom. Centering and standardization of variables Because differences in marks on a test have l i t t l e practical significance, test scores results were standardized. F irs t test score variables were centered by subtracting their means. The centered scores were then standardized by dividing them by the standard deviations of the variables. As a result , the effect sizes for these variables (Beta values) could be compared later in the analysis. Units of measurement for other variables d id , however, possess practical significance so they were retained. Values for these variables were centered. Thus, values for these variables were now expressed relative to their means. This operation did not change the value of any the coefficients. However, i t did change the intercepts for these variables to zero. Preliminary data analysis Distributions of subject scores in pitch discrimination and rhythm discrimination were examined. These distributions appeared to be linear with an approximately normal dis tr ibut ion. However, scores for one participant were more than three standard deviations 125 above the mean. Chatterjee and Price (1977) have noted that "the estimated values of regression coefficients and supporting summary s tat i s t ics are very sensitive to outliers" (p. 25). So that one individual's scores would not distort the results of this study, Case #30 was deleted from the data set; reducing the sample size to 79. Linear regression employs ordinary least squares analysis. Chatterjee and Price (1977) state that "least squares analysis is quite robust in that small or minor violations of the underlying assumptions do not invalidate the inferences or conclusions drawn from the analysis in a major way. Gross violations of the model assumptions can, however, seriously distort conclusions" (p. 9). Therefore, data were examined and tested for violations of the following four assumptions as outlined by Glass and Hopkins (1984, p. 141): 1. Y scores are normally distributed at a l l points along the regression l ine; 2. There is a l inear relationship between the Y values and the expected values of Y. 3. The residuals for Y along this l ine have a mean of zero. 4. Homoscedasticity. 126 Histograms of the standardized residuals were plotted for each variable and approximated the normal curve. No additional outl iers needed to be deleted from the data set. The bivariate distributions of a l l predictor and cr i ter ion variables were visual ly examined to determine whether the relationship between predictor and cr i ter ion variables were l inear . A l l predictor variables met this c r i t e r i a . Normal probability plots of residuals were also made for each of the independent variables. Scatterplots of the standardized residuals versus f i t ted values were made and examined for the presence of out l iers , correlated errors, and for violations of the assumptions of l inear i ty , normality, and homogeneity of variance. A minor flooring effect was occasionally observed but not deemed serious enough to warrant transformation of data. Otherwise, the distribution of residuals was found to be largely random. Selection of Regression Variables To reduce the risk of committing type-I error, I chose the . 1 0 level of significance. While reducing the risk of rejecting variables which are related to pitch or rhythm error discrimination, this decision increased the l ikelihood of committing type-II error; fai lure to reject variables which are not related to pitch or rhythm discrimination. 127 After J:-tests were performed for each of the variables, a Pearson product-moment correlation matrix was constructed and inspected to determine which of the various correlations between the independent and dependent variables were s t a t i s t i c a l l y significant at the jo <. .10 l eve l . Variables found to be s ignif icantly related to pitch discrimination or rhythm discrimination were retained and a l l other variables were eliminated from further consideration. A variance-covariance matrix was also constructed at this time and saved to fac i l i ta te subsequent regression procedures. Regression procedures In simple regression analysis, the value of the dependent variable "y" is predicted as a function of the value of an independent variable "x" and a constant. yi = Bo + Bix/ + £ i where "Bo" is the y-intercept, "Bi" is the slope of the equation, and "6" is the error of prediction. Each of the selected variables was regressed on the independent variables. T-tests were used to determine whether the proportion of var iab i l i ty in y explained by the independent variable was significant at the p_ <. .10 leve l . If none of the individual variables had been found to increase R 2 , the correlation index, an 128 omnibus F_ - test would have been performed to test whether any combination of the variables was related to the dependent variables at the .10 level of significance. Multiple regression Multiple regression analysis is an extension of the procedure of simple regression analysis. Multiple regression measures the relationship between a group of variables and a cr i ter ion variable. Multiple linear regression differs from simple linear regression in that i t attempts to predict the value of the dependent variable from the values of several independent variables and their respective Beta weights. Thus, the model can include higher order terms such as x2 and x3 or more than one independent variable: y = Bo + Bl xi + B2 X2 + ... + Bk x* where the dependent variable y is written as a function of k independent variables. R2 adjusted. R2 is the portion of variance in scores for a dependent variable explained by the independent variables. Although one may generalize from a sample to a population that the population R2 is not l ike ly to be zero, i t may not be true that the sample R2 i s a good estimate of the population R 2 . The smaller the sample and 129 the more independent variables used, the greater the difference between sample R2 and population R2 (Cohen and Cohen, 1975). SPSS-X calculates correlation indexes for both the sample and the population. R 2 adjusted is an estimate of the true value of R2 for the population. R2 adjusted is calculated by the following formula: n - 1 R 2adj. = 1 - (1 - R 2) . n-k-1 where k is the number of predictors and n is the sample size. Suppose, for example, that for the sample used in this study a l l 57 of the independent variables were found to be significant and col lect ively explained 90 percent of the variance in pitch discrimination scores. Thus, R2 = .90, n = 79, and k = 57. Substituting these values into the equation, 130 7 9 - 1 R 2adj. = 1 - (1 - .90) 79-57-1 78 = 1 - (1 - .90) 21 = 1 - (1 - .90) 3.714 = 1 - (.10) 3.714 = 1 - .3714 = .6286 As demonstrated, the shrinkage from R2 to R2 adjusted can be quite considerable when the ratio of sample size to the number of independent variables is small. However, suppose that a subset comprised of five predictor variables could be used to explain 80 percent of the variance in pitch discrimination scores. In this case R 2 = .80, n = 79, and k = 5. 131 Substituting these values into the equation, 7 9 - 1 R 2 - d j . = 1 - (1 - .80) 79-5-1 78 = 1 - (1 - .80) 73 = 1 - (1 - .80) 1.068 = 1 - (.20) 1.068 = 1 - .2136 = .7864 Notice that, although the subset of predictor variables yields a smaller value for R 2 , shrinkage is greatly reduced and the new value for R2 adjusted accounts for considerably more of the variance in the population. Multiple regression procedures I was more interested in accounting for variance in error discrimination a b i l i t y generalizable to the population than in accounting for variance in error discrimination scores for this particular sample. As demonstrated in the above section, including 132 too many variables in a model developed from a re lat ive ly small sample could reduce the portion of variance generalizable to the population. Therefore, I needed to construct parsimonious models producing comparatively large R 2 values. Only variables that s ignif icantly increased R 2 would be permitted to enter the equation. Variables no longer making significant unique contributions to R 2 would be eliminated from the equation. As a result , stepwise regressions were chosen over forward entry and backward elimination procedures. The c r i t i c a l values selected were £ <_ .10 to enter and j> > .10 to reject . This method f i r s t entered the variable producing the largest significant R 2 value. Thereafter, the variable accounting for the largest portion of the remaining variance was selected and entered i f i t s ignif icantly increased R 2 . F-tests were used to determine whether variables retained in the equation s ignif icantly increased R 2 . The F-test for determining whether the increment of R 2 was s t a t i s t i c a l l y significant used the formula (R„ 2 - R , 2 ) / ( P - q) p = 1 (1 - Rp 2 ) / (n - p - 1) where n is the sample s ize, p represents the larger number of variables (the f u l l model), and q represents the smaller set of variables (the restricted model) selected from the f u l l model. 133 If, one or more of the entered variables were found to no longer account for a significant portion of R2, the variable making the smallest unique contribution to R2 would be eliminated from the equation during the next stage of the procedure. If , at a later point, the rejected variable was now able to s ignif icant ly increase R 2 , i t was possible for the variable to reenter the equation. The procedure was terminated whenever none of the remaining variables were able to s ignif icantly increase R 2 . Multiple regression procedures were used to construct prediction models for each of the four blocks of variables: musical achievement, precollege musical background, other demographic variables, and undergraduate coursework. Variables which did not enter the regression equation for their block were eliminated from further consideration. Retained variables comprised the blocks used in subsequent procedures. The next group of multiple regression procedures was used to determine whether adding variables from a second block to a model comprised of one block of variables would s ignif icantly increase R 2 . The following combinations of two blocks of variables were considered: musical achievement and precollege musical background; musical achievement and demographic variables; musical achievement and undergraduate coursework; precollege musical background and demographic variables; precollege musical background and 134 undergraduate coursework; and demographic variables and undergraduate coursework. The number of possible regression procedures for k predictor variables is 2k for each cri ter ion variable. It was not feasible to perform a l l possible regressions of the two cr i ter ion variables on the independent variables. However, many regression strategies are available. Given the relat ively small size of the sample in proportion to the number of variables, I selected an analysis strategy in which a reduced number of variables were considered. In each case, the block producing the largest numerical (rather than s tat i s t i ca l ) R2 value was entered f i r s t into the equation. Individual variables from the other block were then entered in stepwise fashion. The third group of multiple regression procedures was used to determine whether adding variables from a third block to a model comprised of variables from two blocks would s ignif icantly increase R 2 . The following combinations of blocks of variables were considered: music achievement, precollege background, and demographic variables; musical achievement, precollege musical background, and undergraduate coursework; music achievement, demographic background, and undergraduate coursework; precollege musical background, demographic variables, and undergraduate coursework. In each case, the two blocks col lect ively producing the largest R2 value were entered f i r s t into the equation. Individual 135 variables from the third block were then entered in stepwise fashion. The f i n a l group of regression procedures tested involved a l l four blocks of variables. One procedure was used to determine whether adding variables from a fourth block to a model comprised of variables from three blocks would significantly increase R2. The three blocks collectively producing the largest R2 value were entered f i r s t into the equation. Individual variables from the fourth block were then entered in stepwise fashion. Three post hoc regressions were performed to determine the predictive a b i l i t y of these variables when their order of entry was not constrained by block as well as when a reduced set of variables was entered into the equation. Chapter 4 w i l l discuss the extent to which the models constructed in the above-mentioned procedures can be used to predict ensemble pitch and rhythm error discrimination a b i l i t y . At that time, summary statistics w i l l be presented in tabular form and examples w i l l be provided of how to predict scores for individual students. CHAPTER FOUR RESULTS AND DISCUSSION The purpose of t h i s study was twofold: to i d e n t i f y p r e d i c t o r variables of ensemble error d i s c r i m i n a t i o n a b i l i t y ; and, to explore t h e i r usefulness i n p r e d i c t i n g ensemble error d i s c r i m i n a t i o n . Chapter 2 reviewed the l i t e r a t u r e on music l i s t e n i n g , general musical achievement, and musical d i s c r i m i n a t i o n . From t h i s review, variables were i d e n t i f i e d as p o t e n t i a l predictors of ensemble error d i s c r i m i n a t i o n . Chapter 3 outlined the methodological procedures to be followed. In t h i s chapter, hypotheses w i l l be stated for the research questions posed i n Chapter 1. T-tests w i l l be used to s e l e c t ensemble error d i s c r i m i n a t i o n v a r i a b l e s . Once predictor variables have been selected, regression procedures w i l l be used to construct models of ensemble p i t c h error d i s c r i m i n a t i o n and ensemble rhythm error d i s c r i m i n a t i o n . F_-tests w i l l be used to determine which of these variables should be included i n the model. Hereafter ensemble p i t c h and rhythm error d i s c r i m i n a t i o n a b i l i t y w i l l be r e f e r r e d to as p i t c h d i s c r i m i n a t i o n and rhythm di s c r i m i n a t i o n . 136 137 Results Research Question l . a (Pitch) "Which variables account f o r a s i g n i f i c a n t portion of the variance i n p i t c h discrimination?" The n u l l hypothesis f o r t h i s question was Hoip: None of the co r r e l a t i o n s between the independent variables and p i t c h d i s c r i m i n a t i o n w i l l be s t a t i s t i c a l l y s i g n i f i c a n t at the p_ 1 .10 l e v e l . HOIP: 8 = 0 f o r a l l Bk Each independent variable was tested to determine whether i t was s i g n i f i c a n t l y r e l a t e d to scores on the p i t c h error d i s c r i m i n a t i o n portion of the Test i n Error Detection. Two-tailed t.-tests were used as part of t h i s screening process (See Table Three). The following variables were not found to be s i g n i f i c a n t l y r e l a t e d to p i t c h discrimination at the .10 l e v e l : 138 Music Achievement Test Chords Precollege Musical Background Music courses Music lessons Other Demographic Variables College or University: School One and School Four Gender Major Performance Medium: Strings and Voice Music teaching Preferred Ensemble: Instrumentalist, Accompanied soloist, Small choral ensemble, Small instrumental ensemble, and Large choral ensemble Preferred Type of Music: A l l Program: A l l Vear Undergraduate Coursework in Music Applied lessons and GPA in lessons GPA in band instrumental techniques Composition and GPA in composition Conducting and GPA in conducting Ensembles Music history Music theory and GPA in music theory Orchestration and arranging 139 Table 3 Correlations Between the Independent Variables and Pitch Discrimination Variable r JL E. Aliferis-Stecklein Music Achievement Test Subscores Chords Melody Rhythm .1138 .2101 .2526 77 77 75 .324 .067 .029 Precollege Musical Background Band instruments played Band or orchestra Choral experience Music courses Music lessons .2628 .2390 .3498 .0406 .0590 75 75 75 75 75 .023 .039 .002 .730 .615 Other Demographic Variables Age -.2405 75 .038 College or University School One School Two School Three School Four .0857 .3929 -.4367 -.0968 79 79 79 79 .453 .000 .000 .396 Extracurricular performance .2219 75 .056 Gender .1725 79 .128 Major Performance Medium Band instruments Keyboards Strings Voice .3006 -.2295 -.0256 -.0876 79 79 79 79 .007 .042 .823 .443 Music teaching .0600 75 .609 Preferred Ensemble Instrumentalist (Unacompanied) Soloist (Accompanied) Small choral ensemble Small instrumental ensemble Large choral ensemble Large instrumental ensemble -.0792 -.0890 .1161 -.1072 -.0561 .3120 79 79 79 79 79 79 .488 .435 .308 .347 .624 .005 Preferred Type of Music Classical Easy Listening Jazz Popular Rock Other .0293 .0852 .1148 .0612 -.1118 -.0130 79 79 79 79 79 79 .798 .456 .314 .592 .327 .910 Program Composition major Conducting major General or undeclared major Music education major Music history major Performance major Year Applied lessons GPA in lessons Aural training GPA in aural training. Band instrument techniques GPA in band instrument techniques Composition GPA in composition Conducting GPA in conducting Ensembles GPA in ensembles Music history GPA in music history Music theory GPA in music theory Orchestration and arranging GPA in orchestration and arranging -.0209 79 .855 -.1030 79 .366 -.0797 79 .485 .1226 79 .282 -.1187 79 .298 -.0842 79 .461 -.0023 73 .984 rk in Music -.1497 76 .197 -.0294 73 .805 -.2643 76 .021 .2932 46 .048 .2038 76 .077 .0130 16 .962 .0283 76 .808 -.8030 3 .407 -.0214 76 .855 .4691 7 .288 .0885 76 .447 .1961 74 .094 .1859 76 .108 -.2379 70 .047 .1077 76 .354 .0652 73 .584 -.1110 76 .340 .5914 14 .026 140 As a r e s u l t , these variables were excluded from further consideration. Many of the va r i a b l e s , however, were found to be s i g n i f i c a n t l y r e l a t e d to p i t c h d iscrimination at the .10 l e v e l . These included*. Music Achievement Test Melody Rhythm Precollege Musical Background Band instruments played Band or orchestra Choral experience Other Demographic Variables Age College Two College Three E x t r a c u r r i c u l a r performance Major Performance Medium: Band instruments and Keyboards Preferred Ensemble: Large instrumental ensemble 141 Undergraduate Coursework Aural training and GPA in aural training Band instrument techniques GPA in ensembles GPA in music history GPA in orchestration and arranging Because each of these variables would significantly increase R2, it was not necessary to test whether they would collectively account for a significant portion of R2. Therefore, the null hypothesis for pitch discrimination was rejected in favor of the alternative hypothesis that selected variables were significantly related to pitch discrimination. Pitch discrimination was regressed on these variables to determine the proportion of adjusted variance accounted for by individual regressor variables (See Table Four). With the exception of age, GPA in music history, aural training, keyboards, and School Three,, the variables were positively correlated to ensemble pitch discrimination. It should also be noted that the effects of GPA in aural training (N_ = 46) and GPA in orchestration and arranging (N_ = 14) applied only to participants with coursework in those areas. The retained variables were examined for simple intercorrelation (See Table Five). None of the predictor variables were found to be highly intercorrelated. However, some of the variables were 142 T a b l e 4 Summary D a t a From R e g r e s s i o n o f P i t c h P i s c r j ' a n ' n a t i o a on I n d i v i d u a l S e l e c t e d V a r i a b l e s V a r i a b l e M u l t . 1 R£_ A d j u s t e d P h SE b, B e l o d y .21007 .03138 3.4625 0.210 0.113 ihftha .25262 .05099 4.9763' 0.253 0.113 Sa n d i n s t r u m e n t s phjed .26279 .05631 5.4152* 0.170 0.073 Band o r o r c h e s t r a .23897 .04419 4.4213' 0.060 0.028 C h o r a l e x p e r i e n c e .34985 .11037 1 0 . 1 8 0 8 " 0.112 0.035 Age .24048 .04492 4.4807' -0.049 0.023 School JVo .39295 .14343 14 . 0 6 0 3 ' " 0.789 0.210 School Three .43672 .18022 18 . 14 7 2 ' " -1.080 0.253 B i t r a c u r r i c u l a r p e r f o r m a n c e .22193 .03623 3.7818 0.016 0.008 L a r g e i n s t r u m e n t a l e n s e m b l e .31197 .08560 8.3021 0.702 0.244 Band i n s t r u m e n t s .30064 .07857 7 . 6 5 1 0 " 0.650 0.235 K e y b o a r d s .22950 .04037 4.2813' -0.534 0.258 A u r a l t r a i n i n g .26427 .05727 5.5563' -0.230 0.098 CPA i n a u r a l t r a i n i n g .29320 .06520 4.1384' 0.108 0.053 Sa n d i n s t r u m e n t techniques .20383 .02860 3.2078 0.191 0.107 CPA i n e n s e m b l e s .19607 .02509 2.8785 0.101 0.060 CPA i n m u s i c h i s t o r y .23787 .04271 4 .0783' -0.106 0.052 CPA i n o r c h e s t r a t i o n a n d a r r a n g i n g .59140 .29557 6 .4547' 0.311 0.123 •p_<.05. " p j . 0 1 . ' " p U O l . H o t e . The v a l u e s o f t h e c o n s t a n t s and t h e new means f o r a l l v a r i a b l e s a r e z e r o . Table 5 Intercorrelations Between Selected Predictors of fitch Jiscrinipation Variables Rhythm Sand Sand Choral Age School School Ultra- Large Sand lybds Aural CPA in Sand CtA in CPA in CPA in iost. or eip. Two Three eurr. inst. inst. training aural inst. ens, music orch. played orch. perf. ens. training tech. history and arr. Melody .4676 .0368 .1199 Rhythm — .1527 .3602 Sand i . p. — .5819 Sand or orch. — Choral eip. Age School Two School Three Extracurricular performance Large instrumental ensemble Sand instruments Keyboards Aural training CPA in aural training Sand instrument techniques CPA in ensembles CPA in music history CPA in orchestration and arranging .1867 -.2654 -.2256 -.2845 .1029 -.2434 -.0979 -.1305 .1776 .1047 -.0894 .1724 .0477 .1573 -.1769 .0452 .1032 .0896 -.2413 .1381 .3153 .4380 0332 -.0019 -.1380 .1612 -.0384 0558 .1022 .2138 .0850 -.2192 4138 .0139 .2923 -.1584 -.0172 2484 .1202 .5103 -.3308 -.0711 0273 .1567 -.0976 -.1493 -.0471 2433 -.0352 -.0261 .0402 .2752 0546 .1135 .1485 -.0106 -.2003 1562 -.3032 -.0590 .0112 .1422 .1233 .1264 -.2108 .0153 . . . . -.2879 -.1375 .1178 -.3717 -.0658 — .1585 .5972 .0884 .4475 .2046 .4264 .6319 .2246 .5650 .2215 .3310 -.0111 .0758 .1699 -.0620 -.5429 .1617 .3026 .3846 .0014 -.1596 .3511 .1478 .1198 .0316 .4391 -.1474 .1458 -.1240 .2026 .0727 -.1871 .0171 -.1924 -.4174 -.2192 -.1289 -.1718 .0928 -.2733 .0467 -.1195 .1771 -.0537 -.0430 .2726 .4061 .2022 .0377 .3056 -.0389 .3595 .1746 -.2690 -.0617 -.0552 -.2211 -.0739 .0994 .1623 -.1527 -.0321 -.0914 .2028 .1281 .2028 .6468 .4291 .8443 — .2546 -.0034 .4228 — .3986 .3018 — .2337 144 variables were moderately intercorrelated. Although OLS regression procedures could s t i l l be used for different combinations of variables, i t would be necessary to remain aware of the interactive effects and small c e l l sizes of the above-noted variables. Research Question l .b (Rhythm) "Which variables account for a significant portion of the variance in rhythm discrimination?" The null hypothesis for this question was Hom'. None of the correlations between the independent variables and rhythm discrimination w i l l be s ta t i s t i ca l l y significant at the _p_ <. .10 leve l . Hois: fi = 0 for a l l fik The following variables were not found to be s ignif icantly related to ensemble rhythm discrimination at the p_ <_ .10 level (See Table Six): 145 Music Achievement Test Chords Melody Precollege Musical Background Choral experience Music courses Music lessons Demographic Variables Age College or University'. A l l Gender Major Performance Medium: Keyboards, Strings, and Voice Preferred Ensemble: Soloist (Accompanied), Small choral ensemble, Large choral ensemble, and Large instrumental ensemble Preferred Type of Music'. Classical, Easy listening, Popular, Rock, and Other Program: Conducting major, General or undeclared major, Music education major, Music history major, and Performance major Year Undergraduate Coursework Applied lessons and GPA in lessons Aural training Band instrument techniques and GPA in band inst . tech. Composition Conducting Ensembles GPA in music history Music theory and GPA in music theory Orchestration and arranging and GPA in orch. and arr . Table 6 Correlations Between the Independent Variables and Rhythm Discrimination 146 Variable B. £ Aliferis-Stecklein Musical Achievement Test Subscores Chords Melody Rhythm .0174 .1002 .4734 77 77 75 .881 .386 .000 Precollege Musical Background Band instruments played Band or orchestra Choral experience Music courses Music lessons .2426 .4161 -.0483 -.0247 .0061 75 75 75 75 75 .036 .000 .681 .834 .959 Other Demographic Variables Age -.1057 75 .367 College or University School One School Two School Three School Four -.0372 .0356 -.0272 .0086 79 79 79 79 .745 .755 .812 .940 Extracurricular performance .2154 75 .064 Gender -.1732 79 .127 Major Performance Medium Band instruments Keyboards Strings Voice .3200 -.0980 -.0955 -.1712 79 79 79 79 .004 .390 .402 .132 Music teaching .2456 75 .034 Preferred Ensemble Instrumentalist (Unaccompanied) Soloist (Accompanied) Small choral ensemble Small instrumental ensemble Large choral ensemble Large instrumental ensemble -.1864 -.1776 .1162 .2241 .0557 .1785 79 79 79 79 79 79 .100 .117 .308 .047 .626 .116 Preferred Type of Music Classical Easy listening Jazz Popular Rock Other -.0275 -.0408 .2726 -.0099 -.1075 .0936 79 79 79 79 79 79 .810 .721 .015 .931 .346 .412 Program Composition major Conducting major General or undeclared major Music education major Music history major Performance major .1927 -.1058 -.0104 -.1033 -.1058 .0428 79 79 79 79 79 79 .089 .354 .928 .365 .354 .708 Year .0862 73 .469 Undergraduate Coursework in Music Applied lessons CPA in lessons Aural training GPA in aural training Band instrument techniques GPA in band instrumental techniques Composition CPA in composition Conducting GPA in conducting Ensemble experience GPA in ensembles Music history CPA,in music history Music theory GPA in music theory Orchestration and arranging CPA in orchestration and arranging .0855 76 .463 .0905 73 .446 -.1731 76 .135 .3501 46 .017 .1865 76 .107 .0154 16 .955 .0282 76 .809 .1806 J 76 .119 -.8020 7 .030 .1352 76 .244 .3696 74 .001 .2607 76 .023 -.0228 70 .852 .1045 76 .369 .1114 73 .348 .1613 76 .164 .2199 14 .450 147 Consequently, these variables were excluded from further consideration. Many of the independent variables were also found to be s ignif icantly related to rhythm discrimination at the p_ <_ .10 level of confidence. These included: Music Achievement Test Rhythm Precollege Musical Background Band instruments played Band or orchestra Demographic Variables Extracurricular performance Major Performance Medium: Band instruments Music teaching Preferred ensemble: Instrumentalist (Unaccompanied) and Small instrumental ensemble Preferred Type of Music: Jazz Program: Composition major Undergraduate Coursework GPA in aural training GPA for ensembles Music history GPA for conducting 148 Therefore, the nul l hypothesis for rhythm discrimination was rejected in favor of the alternative hypothesis that col lect ively the selected variables were s ignif icantly related to rhythm discrimination. Separate regressions procedures were performed for each of the selected variables (See Table Seven). The regression equation for one variable takes the form y = bo + bi xi + & i , where bo is the regression coefficient for the constant, bi is the regression coefficient for the variable, xi is the value for a subject on that variable, £. i is the sampling error for individual i , and y is the predicted value on the cr i ter ion variable. We could calculate, for example, the expected ensemble rhythm error discrimination value for an individual based upon that individual's extracurricular performance. The mean value for extracurricular performance was 9.773 hours per month. For a subject possessing the mean value for extracurricular performance, or for a subject for whom extracurricular performance was unknown, we would calculate our best estimate of y as follows. The constant 149 was zero, so bo did not need to be included in the equation. Therefore, y = bi xi Because extracurricular performance was centered, the mean value o xi is now zero. The value of bi is 0.016. Substituting in these values the predicted value for y is y = 0.016 * 0.000 = 0.000 For an individual not involved in extracurricular performance the value of xi would be the old value of x minus the old mean of xi = 0.000 - 9.773 = -9.773 The predicted value of y would be y = 0.016 * -9.773 = -0.156 Based upon this single predictor, a subject not involved in extracurricular performance experience would be expected to score 0.156 standard deviations below the mean. 150 T a b l e 7 S m e a r y D a t a f r o a B e g r e s s i o n o f i b y t i a fliscriaination on I n d i v i d u a l S e l e c t e d V a r i a b l e s V a r i a b l e H u l t . 1 V_ A d j u s t e d I h SI bi S i i / t l i i .47342 .21350 21 .0872* *• 0.473 0.103 Sand i n s t r u a e n t s p l a y e d .24263 .04598 4.5663' 0.157 0.074 Sand o r o r c h e s t r a .41611 .16182 1 5 . 2 8 6 4 " ' 0.104 0.027 Extracurricular p e r f o r a a n c e .21536 .03332 3 . 5506 0.016 0.008 Sand i n s t r u a e n t s .32002 .09075 8 . 7 8 5 3 " 0.691 0.233 M u s i c teaching .24559 .04744 4.6856' 0.169 0.078 I n s t r u n e u t a l i s t ( U n a c c o a p a n i e d ) .18641 .02221 2.7720 -0.613 0.369 S a a l l i n s t r u m e n t a l e n s e i b l e .22411 .03789 4.0720' 0.512 0.254 J a z z .27257 .06227 6.1799' 0.646 0.260 Composition M a j o r .19272 .02464 2.9703 0.786 0.456 GPA i n a u r a l t r a i n i n g .35013 .10265 6.1476' 0.128 0.052 CPA i n c o n d u c t i n g .80203 .57190 9.0154' -0.425 0.142 CPA i n e n s e m b l e s .36963 .12464 11 . 3 9 4 1 " 0.191 0.056 M u s i c b i s t o r y .26074 .05539 5.3979' 0.145 0.062 •p_<.05. "p_<.01. "V<.ooi. N o t e . The v a l u e o f t h e c o n s t a n t s and t h e new a e a n s f o r a l l v a r i a b l e s a r e z e r o . 151 Similar regression equations could be calculated for all predictor variables on the criterion variables pitch discrimination and rhythm discrimination. Individually these predictor variables accounted for relatively little of the variance in pitch or rhythm discrimination. To account for more of the variance in ensemble error discrimination, more variables needed to be included in the equation. The retained variables were examined for simple intercorrelation (See Table Eight). Although some of the variables were moderately intercorrelated, none of the predictor variables were found to be highly intercorrelated. As a result, it would not be necessary to use other types of regression procedures. Of the above variables, only GPA in conducting and instrumentalist (unaccompanied) were negatively correlated with rhythm discrimination. Note also that the effects of GPA in aural training (N = 46) and GPA in conducting (N = 7) applied only to subjects with coursework in those areas. Variables retained at this stage comprised the blocks of variables used to answer the following fifteen pairs of research questions and accompanying hypotheses. Table 8 I n t e r c o r r e l a t i o n s Between Se lec ted P r e d i c t o r s of M y t h s D i s c r i m i n a t i o n V a r i a b l e s Hand land U l t r a - I n s t . S n a i l Music Sand Jazz Coop. CPA i n CPA i n CPA i n Music i n s t . or c u r r . (unacc . ) i n s t . teaching i n s t . major a u r a l cond. ens. h i s t o r y played o rch . p e r / . ens. training SkyChi .152? .3607 .0558 - .0708 .0159 .1828 .2138 .1087 .0873 .6319 .2230 . 5650 .2947 Band i n s t . p layed .5819 .4138 -.1532 .1848 .4983 .2923 .1580 .0209 - .0111 -.6601 .1699 .4062 Sand or o r c h . .2484 - .1825 .0238 . 5055 .5103 - .0211 - .1546 .1617 -.3108 .3846 .2379 S z t r a c u r r . p e r f . - .1301 .0453 .4350 .1256 - .0158 .0044 .0467 - .8814 .1771 .2305 I n s t . (Unaccompanied) -.1954 -.0405 -.1305 - .0823 - .0873 - .1129 - .1107 .0442 Small i o s t . ensemble .1764 .1853 .3778 .3269 .0183 - .7287 .0159 - .0401 Husic teaching .1340 -.0463 - .0035 .0871 - .7393 .1606 .1976 Band ins t ruments .1661 - .171? - .0389 .0675 .1746 .1451 Jazz .2306 - .0582 - .4248 .1260 - .0495 Composit ion major .0809 -.3647 .0509 .0417 CPA i n au ra l t r a i n i n g .4823 .6468 .2294 CPA i n conduct ing .1731 -.4667 CPA i n ensembles .3334 Music h i s t o r y 153 Research Question 2.a (Pitch) "Can musical achievement test variables be used to predict pitch error discrimination ability?" For Yp predicted by Aliferis-Stecklein Music Achievement Test subscores the null hypothesis was Ho2f' Musical achievement variables will not account for a significant portion of the variance in pitch discrimination scores at the D_ <_ .10 level. Ho2f>: R2mo\stij f rhytha = 0 As noted below in Table Nine, rhythm did significantly increase R2 at the .10 level of significance. The null hypothesis was therefore rejected in favor of the alternative hypothesis that music achievement scores can be used to predict pitch discrimination ability. 154 Table 9 Regression of Pitch Discrimination on Musical Achievement Test  Subscores (N = 75) Source DF. Regression SS P_ R Mult. JR. R£ Adj. (Increment) (Total) (Total) Rhythm 1 4.723 4.976 .0288 .25262 .05099 Parameter b b T for Ho'. R Parameter = 0 Rhythm 0.252 0.113 2.231 .0288 Constant 0.000 0.111 0.000 .9997 The regression procedure selected rhythm first because it was the variable that accounted for larger portion of the variance in pitch discrimination. Melody was not added to the equation because it did not significantly increase R2 at the .10 level. The resulting regression equation, therefore, was y = bchrthm * Xrortha 155 Because rhythm was standardized, the mean value of Xrhrthm was now zero. The value of brbrtha was 0.2526. The predicted value of y was obtained by substituting standardized xr&rtha scores into the following equation: y = 0.252 * x rhrt n. Research Question 2.b (Rhythm) "Can musical achievement test variables be used to predict rhythm error discrimination ability?" For Y R predicted by Aliferis-Stecklein Music Achievement Test subscores the null hypothesis was HO2R'. Musical achievement variables will not account for a significant portion of the variance in rhythm discrimination scores at the j?_ <. .10 level. H02R: R2rhyth» = 0 Rhythm was the only variable included in this block since neither melody nor chords were found to be significantly related to 156 rhythm discrimination at the j>_ < .10 level. As in Horn, rhythm accounted for a significant portion of R2 at the g_ < .10 level so the null hypothesis was rejected in favor of the alternative hypothesis that music achievement test scores are significantly related to rhythm discrimination. Rhythm accounted for 21.350 percent of the variance in rhythm discrimination scores (See Table Ten). Table 10 Regression of Rhythm Discrimination on Musical Achievement Test  Subscores (N_ = 75) Source D £ Regression SS F. £_ Mult. R. R£ Adj. (Increment) (Total) (Total) Rhythm 1 16.585 21.087 .0000 .47342 .21350 Parameter b SE b T for Ho.* £ . Parameter = 0 Rhythm 0.473 0.103 4.592 .0000 Constant 0.000 0.100 -0.001 .9993 157 Research Question 3.a (Pitch). The next research question addressed the relationship between precollege background variables and ensemble pitch error discrimination. "Can precollege background variables be used to predict pitch error discrimination ability?" For Yp predicted by precollege background variables the null hypothesis was Hojpt Precollege background variables will not account for a significant portion of the variance in pitch discrimination scores at the p_ <_ .10 level. Hoap: R2band or orch. + band i. p. * choral exp. ~ U When first entered into the equation, choral experience accounted for 11.037 percent of the variance in pitch discrimination scores and was significant at the p_ < .10 level (See Table Eleven). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that precollege background variables are related to ensemble pitch error discrimination skill. Addition of band or orchestra increased the variance explained to 14.892 158 percent. The addition of band instruments played, however, did not significantly increase R 2. Table 11 Regression of Pitch Discrimination on Precollege Background  Variables (N = 75) Source DP. Regression SS F. p_ Mult. R R2. Adj. (Increment) (Total) (Total) Choral exp. 1 9.058 10.181 .0021 .34985 .11037 Band or orchestra 1 3.665 7.474 .0011 .41463 .14892 Parameter SE b T for Ho: Parameter = 0 Choral exp. 0.108 0.034 3.160 .0023 Band or orchestra 0.056 0.027 2.075 .0415 Constant 0.000 0.107 0.000 .9999 159 Research Question 3.b (Rhythm). The parallel research question addressed the relationship between precollege background variables and ensemble rhythm error discrimination. "Can precollege background variables be used to predict rhythm error discrimination ability?" For Y K predicted by precollege background variables the null hypothesis was HO3R: Precollege background variables will not account for a significant portion of the variance in rhythm discrimination scores at the j> <_ .10 level. H03R* R2band or oroh. »• band i. p. = 0 Band or orchestra accounted for 16.182 percent of R 2 and was significant at the p_ < .10 level (See Table Twelve). Thus, the null hypothesis was rejected in favor of the alternative hypothesis that precollege background variables are related to rhythm error detection skills. The addition of band instruments played to the system did not significantly increase R 2. 160 Research Question 4.a (Pitch). The research question regarding the next block of variables was "Can demographic variables be used to predict pitch discrimination ability?" Table 12 Regression of Rhythm Discrimination on Precollege Background  Variables (N = 75) Source DP. Regression SS F_ p. Mult. R. R£ Adj. (Increment) (Total) (Total) Band or orchestra 1 12.813 15.286 .0002 .41611 .16182 Parameter b SE b T for Ho* R. Parameter = 0 Band or orchestra 0.104 0.027 3.910 .0002 Constant 0.000 0.103 -0.001 .9991 161 For Yp predicted by demographic variables the null hypothesis was Ho4p" Demographic variables will not account for a significant portion of the variance in pitch discrimination scores at the j>_ <. .10 level. HO4P : R 2 a g . • School Two * School Throe • extracurr. perf. • large lost. ens. + band inst. • keyboards ~ 0 School Three accounted for 17.964 percent of the variance in pitch discrimination scores and was significant p_ < .10 level (See Table Thirteen). Thus, the nuE hypothesis was rejected in favor of the alternative hypothesis that demographic variables are related to pitch discrimination. The addition of extracurricular performance increased the amounted of variance accounted for to 25.695. The further addition of band instruments increased the amount of variance accounted for by 4.819 percent to 30.514 percent. School Two increased the variance accounted for by another 2.689 percent. The addition of age to the equation increased the amount of variance accounted for to 35.119 percent. At this point, keyboards and large instrumental ensembles did not produce any further significant increase in R2. 162 Table 13 Regression of Pitch discrimination on Other Demographic Variables (W = 75) Source 0P Regression SS f_ p_ Mult. R_ EL Adj. (Increment) (Total) (Total) School Three 1 14.115 17.204 .0001 .43672 .17964 Sxtracurr. perf. 1 6.386 13.794 .0000 .52633 .25695 Band instruments 1 4.165 11.832 .0000 .57733 .30514 School Two 1 2.578 10.196 .0000 .60674 .33203 Age 1 1.990 9.011 .0000 .62852 .35119 Parameter b SB b T for Hot £ Parameter - 0 School Three -0.800 0.270 -2.965 .0042 gitracurricular perf. 0.022 0.007 3.052 .0032 Band instruments 0.450 0.207 2.176 .0330 School Two 0.420 0.211 1.992 .0503 Age -0.036 0.021 -1.751 .0843 Constant 0.000 0.091 -0.005 .9964 1 6 3 Research Question 4 .b (Rhythm). For Y R predicted by demographic variables the question was "Can demographic variables be used to predict rhythm discrimination?" The null hypothesis was HO4R' Demographic variables will not account for a significant portion of the variance in rhythm discrimination scores at the _p_ <_ . 1 0 level. Hois' R^ extraeurr. pert. • comp. major * instrumentalist + sa. inst. ens. • band insts. • teaching exp. + Jazz = 0 Band instruments accounted for 9 . 0 1 1 percent of the variance in rhythm discrimination scores and was significant at the p_ < . 1 0 level (See Table Fourteen). Therefore, the null hypothesis was rejected in favor of the null hypothesis that demographic variables are related to rhythm discrimination. Addition of composition major to the equation increased the amount of variance accounted for to 1 4 . 2 4 4 percent. Addition of teaching experience increased the amount of variance accounted for to 1 7 . 1 8 7 percent. Finally, addition of jazz increased the amount of variance accounted for to 1 9 . 3 3 3 percent. The addition of extracurricular performance, 164 Table 14 Regress ion of Rhrthm Discrimination on Other Demographic V a r i a b l e s (H = 75) Source DP_ Regression SS £ p_ Mult. R RL*dj. (Increment) (Total) (Total) Keyboards 1 7.578 8.329 .0051 .32002 .09011 Composition major 1 4.677 7.146 .0015 .40696 .14244 Teaching experience 1 2.947 6.119 .0009 .45236 .17187 Jazz 1 2.330 5.434 .0007 .48676 .19333 Parameter b SE b T for Ho: Parameter - 0 £ . Keyboards 0.636 0.237 2.684 .0091 Composition major 0.820 0.449 1.825 .0723 Teaching experience 0.149 0.073 2.039 .0453 Jazz 0.444 0.261 1.700 .0936 Constant 0.000 0.101 -0.001 .9994 165 instrumentalist, and small instrumental ensemble did not significantly increase the amount of variance for by the equation. Research Question 5.a (Pitch). "Can undergraduate coursework variables be used to predict pitch error discrimination ability?" For Yp predicted by undergraduate coursework completed the null hypothesis was HO5P" Undergraduate coursework variables will not account for a significant portion of the variance in pitch discrimination scores at the £_ <_ .10 level. H 0 5 P : R2aural training V GPA la aural training + band teoh. + GPA in ensembles + GPA in Music history = 0 GPA in aural training accounted for 6.312 percent of the variance in pitch discrimination scores and was significant at the p_ < .10 level (See Table Fifteen). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that undergraduate coursework is related to pitch discrimination ability. Addition of GPA in music history improved the amount of variance accounted for 166 Table 15 Regression of Pitch Discrimination on Undergraduate Coursework Variables (H = 42) Source 0F Regression SS P p_ HuJt. R R*_Adj. (Increment) (Total) (Total) GPA in aural t r . 1 3.525 3.762 .0505 .29320 .06312 GPA in music hist. 1 6.647 6.434 .0038 .49808 .20953 Parameter b SE b T for H»: p_ Parameter - 0 GPA in aural tr. 0.178 0.056 3.152 .0031 GPA in music hist. -0.199 0.069 -2.900 .0061 Constant 0.000 0.102 0.000 .9999 167 to 20.953 percent. Addition of the variables GPA in ensembles, band instrument techniques, and aural training did not produce any further significant increase in R 2. Research Question 5.b (Rhythm). For Y R predicted by undergraduate coursework completed the research question was "Can undergraduate coursework variables be used to predict rhythm error discrimination ability?" Ho5R* Undergraduate coursework variables will-not account for a significant portion of the variance in rhythm discrimination scores at the p_ <_ .10 leveL Ho«: R 2 C P A In aural training I- GPA in ensembles + ausic history ~ 0 GPA in ensembles accounted for 11.655 percent of the variance in rhythm discrimination scores and was significant at the p_ < .10 level (See Table Sixteen). Thus, the null hypothesis was rejected in favor of the alternative hypothesis that undergraduate coursework is related to rhythm discrimination ability. Neither music history nor GPA in aural training significantly increased the variance accounted for by GPA in ensembles. 168 Table 16 Regression of Rhythm Discrimination on Undergraduate Coursework Variables (N = 45) Source DP_ Regression SS P_ p_ Mult. R_ R?_Adj. (Increment) (Total) (Total) GPA in ensembles 1 6.012 6.805 .0125 .36963 .11655 Parameter b SE b T for Ht! p_ Parameter = 0 GPA in ensembles 0.191 0.073 2.609 .0125 Constant 0.000 0.108 0.000 .9998 169 Research Questions 6.a (Pitch) and 6.b (Rhythm). "Is prediction of pitch discrimination significantly increased when variables from one block are added to a model comprised of variables from another block?" The parallel question for rhythm discrimination was as follows: "is prediction of pitch discrimination significantly increased when variables from one block are added to a model comprised of variables from another block?" The research question was restated for each two blocks of variables. As discussed in Chapter 3, the reduced block explaining the largest amount of variance for that criterion variables was entered into the equation before individual variables from the other block were considered. "Is prediction of pitch discrimination significantly increased when musical achievement variables are added individually to the model comprised of precollege background variables?" For Yp predicted by musical achievement and precollege background variables the null hypothesis was 170 Ho$p* Using musical achievement and precollege background blocks of variables in the equation will not significantly increase the amount of variance in pitch discrimination scores accounted for at the £_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. H06P' R2*ch. rars. • background »ars. If R2kackground rara. As in Ho3P, the precollege variables band or orchestra and choral experience accounted for a little less than 15 percent of the variance in pitch discrimination scores (See Table Seventeen). Addition of rhythm did not significantly increase R 2 at the p_ < .10 level so the null hypothesis was retained. Therefore, the addition of music achievement variables to precollege background variables did not increase the amount of variability accounted for in ensemble pitch error discrimination. "is prediction of rhythm discrimination significantly increased when precollege background variables are added individually to the model comprised of musical achievement variables?" 171 Table 17 Regression of Pitch Discrimination on Musical Achievement Test and Precollege  Background Variables (ff - 71) Source DF. Regression SS F_ p_ Mult. R_ R*_Adj. (Increment) (Total) (Total) Background Vars. 2 12.035 7.059 .0016 .41463 .14757 Parameter b SB b T for Ho: p_ Parameter = 0 Choral experience 0.108 0.035 3.071 .0031 Band or orchestra 0.056 0.028 2.017 .0477 Constant 0.000 0.107 0.000 .9999 172 Por Y R predicted by musical achievement and precollege background variables the null hypothesis was HO6R*. Using musical achievement and precollege background variables in the equation will not significantly increase the amount of variance in rhythm discrimination scores explained at the £_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. Ho«B: R2«c„. vara. * background vara, vara. Rhythm accounted for 21.288 percent of the variance in rhythm discrimination scores. Addition of band or orchestra increased R 2 by an additional 5.966 percent; significant at the p_ < .10 level (See Table Eighteen). Thus, the null hypothesis was rejected in favor of the alternative hypothesis that musical achievement and control variables do collectively account for significantly more of the variance in ensemble rhythm error discrimination than when these blocks are used individually. "is prediction of pitch discrimination significantly increased when musical achievement variables are added individually to the model comprised of other demographic variables?" 173 Table 18 Regression of Rhythm Discrimination on Musical Achievement Test and Precollege  Background Variables (tf = 71) Source DF. Regression SS £ £ Mult. £ Ri_Adj. (Increment) (Total) (Total) Achievement Vars. 1 15.689 19.932 .0000 .47342 .21288 Band or orchestra 1 4.844 14.113 .0000 .54160 .27254 Parameter b SE b T for Htt p_ Parameter - 0 Rhythm 0.372 0.109 3.401 .0011 Band or orchestra 0.071 0.027 2.581 .0120 Constant 0.000 0.098 -0.001 .9991 174 For Yp predicted by musical achievement and demographic variables the null hypothesis was Hojel Using musical achievement and demographic variables in the equation will not significantly increase the amount of variance in pitch discrimination scores explained at the p_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. Tars. * demo. rars. f R^demo. rars. demo, vars. As in Ho4p, the demographic variables School Three, Band instruments, extracurricular performance, age, and School Two accounted for over 34 percent of the variance in pitch discrimination scores (See Table Nineteen). The addition of rhythm did not significantly increase R 2 at the p_ < .10 level of significance. Therefore, the null hypothesis was retained that use of both achievement and demographic blocks of variables did not account for significantly more of the variance than use of the demographic block of variables. "is prediction of rhythm discrimination significantly increased when demographic variables are added individually to the model comprised of musical achievement variables?" 175 Table 19 Regression of Pitch Discrimination on Musical Achievement Test Scores and Other Demographic Variables (#= 71) Source DP Regress ion SS I £_ Mult. R EL A d j . (Increment) (Total) (Total) Demographic Vars. 5 27.654 8.489 .0000 .62852 .34850 Parameter b SE b T for Ha: 2. Parameter - 0 School Three -0.800 0.270 -2.965 .0042 Extracurr. perf. 0.022 0.007 3.052 .0032 Keyboards 0.450 0.207 2.176 .0330 School Txo 0.420 0.211 1.992 .0503 Age -0.036 0.021 -1.751 .0843 Constant 0.000 0.091 -0.005 .9964 176 Por YR predicted by achievement and demographic variables the hypothesis was HOTS'' Using musical achievement and demographic variables in the equation will not significantly increase the amount of variance in rhythm discrimination scores explained at the £ . < .10 level over when the block accounting for the largest portion of R 2 is used alone. Hon'. R2ac«. Tars. * demo. rars. rars. Rhythm accounted for 21.288 percent of the variance in rhythm discrimination scores. Addition of band instruments significantly increased the variance accounted for by 4.007 percent (See Table Twenty). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that achievement and demographic variables do account for significantly more of the variance in ensemble rhythm error discrimination. The addition of composition major significantly increased the variance accounted for to a total of 28.344 percent. The subsequent addition of teaching experience and jazz to the equation did not produce a significant increase in R2. 177 Table 20 Regression of Rhythm Discrimination on Musical Achievement Test Scores and Other  Demographic Variables (W = 71) Source DP. Regression SS P p_ M u l t . R R*_ A d j . (Increment) (Total) (Total) Achievement Vars. 1 15.689 Keyboards 1 3.512 Composition major 1 2.790 19.932 .0000 .47342 .21288 12.851 .0000 .52373 .25295 10.229 .0000 .56049 .28344 Parameter b SE b T for Ho: p_ Parameter - 0 Rhythm 0.397 0.104 3.809 .0003 Keyboards 0.583 0.228 2.557 .0128 Composition major 0.834 0.422 1.973 .0526 Constant 0.000 0.095 -0.002 .9982 178 "Is prediction of pitch discrimination significantly increased when musical achievement variables are added individually to the model comprised of undergraduate coursework variables?" For Yp predicted by musical achievement and undergraduate coursework variables the null hypothesis was Hoae'. Using musical achievement and undergraduate coursework variables are in the equation will not significantly increase the amount of variance in pitch discrimination scores explained at the D_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. Hoep'' R2»ch. rare. * coursework rare, rare. Collectively, GPA in aural training and GPA in music history accounted for 20.952 percent of the variance in pitch discrimination scores (See Table Twenty-One). The addition of rhythm did not significantly increase R 2 so the null hypothesis was retained that the use of musical achievement variables and undergraduate coursework variables did not account for significantly more of 179 Table 21 Regression of Pitch Discrimination on Demographic and Undergraduate Coursework  Variables (W = 42) Source DP. Regression SS P p_ Mult. R Ri_Adj. (Increment) (Total) (Total) Undergraduate Vars. 2 10.172 6 .434 .0038 .49808 .20953 Parameter b SE b T for Ht>: £_ Parameter = 0 GPA in aural training 0 .178 0.056 3 .152 .0031 GPA in music history - 0 . 1 9 9 0 .069 - 2 . 9 0 0 .0061 Constant 0 .000 0 .103 0 .000 .9999 180 ensemble pitch error discrimination skill than undergraduate coursework alone. "Is prediction of rhythm pitch discrimination significantly increased when undergraduate coursework variables are added individually to the model comprised of musical achievement variables?" For Y R predicted by musical achievement and undergraduate coursework variables the hypothesis was Hoax' Using musical achievement and undergraduate coursework variables in the equation will not significantly increase the amount of variance in rhythm discrimination scores explained at the p_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. ran. *• course work ran. rars. Rhythm accounted for 21.288 percent of the variation in rhythm discrimination scores (See Table Twenty-Two). Addition of GPA in ensembles did not significantly increase R 2 so the null hypothesis was retained that the addition of undergraduate coursework variables 181 Table 22 Regression of Rhythm Discrimination on Musical Achievement Test and Undergraduate Coursework Variables (£= 71) Source DP Regression SS (Increment) P £ Mult. R (Total) EL Adj. (Total) Achievement Pars. 1 15.689 19.932 .0000 .47342 .21288 Parameter b SE b r for Ha: Parameter - 0 R. Rhythm Constant 0.473 0.000 0.106 0.102 4.464 -0.001 .0000 .9993 182 did not account for significantly more of ensemble rhythm error discrimination skill than musical achievement scores alone. "Is prediction of pitch discrimination significantly increased when precollege background variables are added to the model comprised of other demographic variables?" For Yp predicted by precollege background and demographic variables the null hypothesis was Hoop: Using both precollege background and demographic variables in the equation will not significantly increase the amount of variance explained in pitch discrimination scores at the jp_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. Ho9P» R2tacJtgrt>tind rars. • demo. rars. f R2rfeao. rars. The demographic variables School Three, band instruments, extracurricular performance, age, and School Two collectively accounted for 35.119 percent of the variance in pitch discrimination scores. The addition of choral experience increased R 2 by 7.177 percent (See Table Twenty-Three). Therefore, the null hypothesis 183 Table 23 Regression of Pitch Discrimination on Precollege Background and Other Demographic  Variables (£ = 75) Source DP. Regression SS F p_ Mult. R R*_Adj. (Increment) (Total) (Total) Demographic Vars. 5 29.234 9.011 .0000 .62852 .35119 Choral experience 1 5.529 10.040 .0000 .68538 .42296 Parameter b SE b T for Hi! p_ Parameter - 0 School Three -0.630 0.260 -2.419 .0183 Extracurricular performance 0.021 0.007 3.128 .0026 Keyboards - 0.521 0.196 2.656 .0098 School Two 0.422 . 0.199 2.122 .0375 Age -0.034 0.019 -1.741 .0862 Choral experience 0.091 0.029 3.095 .0029 Constant 0.000 0.085 -0.004 .9968 184 was rejected in favor of the alternative hypothesis that the use of both precollege background variables and demographics variables accounts for significantly more of ensemble pitch error discrimination skill than demographic variables alone. The subsequent addition of band or orchestra provided no significant increase in R 2. "Is prediction of rhythm pitch discrimination significantly increased when precollege background variables are added to the model comprised of other demographic variables?" For Y R predicted by precollege background and demographic variables the null hypothesis was Ho»: Using both precollege background and demographic variables in the equation will not significantly increase the amount of variance explained in rhythm discrimination scores at the p_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. H09X* R^ tMckground raro. • demo. Tars, mo. Tars. 185 The demographic variables jazz, teaching experience, band instruments, and composition major collectively accounted for 19.333 percent of the variance in rhythm discrimination scores. Addition of band or orchestra to the equation significantly increased R 2 to 25.536 percent (See Table Twenty-Four). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that background variables and demographic variables collectively account for significantly more of ensemble rhythm error discrimination skill than demographic variables alone. "is prediction of pitch discrimination significantly increased when undergraduate coursework variables are added to the model comprised of precollege background variables?" For Y P predicted by background and undergraduate coursework variables the null hypothesis was Howe'. Precollege background variables and undergraduate coursework variables will not significantly increase R 2 at the _p_ < .10 level over when the block accounting for the largest portion of R 2 is used alone. vara. *• coarsairork ran. f R2coursework vara. 186 Table 24 Regression of Rhythm Discrimination on Precollege Musical Background and Other  Demographic Variables (H_ - 75) Source DP. Regression SS P_ p_ Malt. R_ R±_Adj. (Increment) (Total) (Total) Demographic Vars. 4 17.533 5.434 .0007 .48676 .19333 Band or orchestra 1 5.086 6.075 .0001 .55287 .25536 Parameter b SE b T for Ho: p_ Parameter - 0 Keyboards . 0.287 0.264 1.089 .2798 Composition major 0.910 0.433 2.101 .0393 Teaching experience 0.039 0.082 0.482 .6304 Jazz 0.496 0.252 1.970 .0528 Band or orchestra 0.090 0.034 2.614 .0110 Constant 0.000 0.097 -0.002 .9981 187 As in Hose, GPA in aural training and GPA in music history accounted for 20.953 percent of the variance of pitch discrimination scores. Neither the addition of band or orchestra nor the addition of choral experience significantly increased R 2. Therefore, the null hypothesis was retained. The addition of precollege background variables did not account for significantly more variance in ensemble pitch error discrimination than undergraduate coursework variables alone. "is prediction of rhythm discrimination significantly increased when undergraduate coursework variables are added to the model comprised of precollege background variables?" For Y R predicted by background and undergraduate coursework variables the null hypothesis was HOIOR'. Precollege background variables and undergraduate coursework variables will not significantly increase R 2 at the £ . < .10 level over when the block accounting for the largest portion of R 2 is used alone. vara. #• course work vara. r R2background vara. 188 Band or orchestra accounted for 16.099 percent of the variance in rhythm discrimination scores. The addition of GPA in ensembles significantly increased R 2 by another 4.056 percent (See Table Twenty-Five). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that precollege undergraduate musical background and undergraduate coursework variables account for significantly more of the variance in ensemble rhythm error discrimination than precollege background variables alone. "Is prediction of pitch discrimination significantly increased when undergraduate coursework variables are added to the model comprised of other demographic variables?" For Yp predicted by demographic and undergraduate coursework variables the null hypothesis was Hour: When demographic variables and undergraduate coursework variables are used in the equation the amount of variance accounted for in pitch discrimination scores will not increase significantly at the j> < .10 level over when the block accounting for the largest portion of R 2 is used alone. Ho up* R2<fea0. rars. *• coursework rars. rars. 189 Table 25 Regression of Rhythm Discrimination on Precollege Background and Undergraduate  Coursework Variables (H - 70) Source DF. Regression SS P_ p_ Mult. R R£_Adj. (Increment) •. (Total) (Total) Background Var. 1 11.947 14.239 .0003 .41611 .16099 GPA in ensembles 1 3.557 9.709 .0002 .47402 .20155 Parameter b SB b T for fl».* £ Parameter - 0 Band or orchestra 0.081 0.029 2.759 .0075 GPA in ensembles 0.127 0.060 2.111 .0385 Constant 0.000 0.103 -0.001 .9995 190 Collectively, the demographic variables School Three, band instruments, extracurricular performance, age, and School Two accounted for 31.101 percent of the variance in pitch discrimination scores. The addition of GPA in aural training significantly increased the variance accounted by 5.439 percent (See Table Twenty-Six). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that demographic and undergraduate coursework variables collectively account for significantly more of the variance in ensemble pitch error detection skill than demographic variables alone. The addition of GPA in music history did not significantly increase R 2. "is prediction of rhythm discrimination significantly increased when undergraduate coursework variables are added to the model comprised of other demographic variables?" For YR predicted by demographic and undergraduate variables the null hypothesis was 191 Table 26 Regression of fitch Discrimination on Demographic and Undergraduate Coursework  Variables (ff = 42) Source DF_ Regression SS _P p_ ffult. R_ R* Adj. (Increment) (Total) (Total) Demographic Vars. 5 16.197 4.701 .0021 .62852 .31101 GPA in aural tr. 1 2.593 4.935 .0009 .67696 .36540 Parameter b School Three -0.557 Bztracurr. perf. 0.019 Keyboards 0.465 School Two 0.614 Age -0.030 GPA in aural tr. 0.101 Constant 0.000 SE b T for H»: p_ Parameter - 0 0.378 -1.473 .1496 0.010 2.034 .0496 0.275 1.693 .0994 0.296 2.072 .0457 0.028 -1.080 .2874 0.050 2.021 .0509 0.090 -0.004 .9966 192 HOUR'. Using demographic variables and undergraduate coursework variables in the model will not significantly increase R 2 for rhythm discrimination scores at the £. < .10 level over when the block accounting for the largest portion of R 2 is used alone. H O U R ! R2de«o. Tars. * course iror 4 rars. / R2deao. rars. The demographic variables jazz, teaching experience, band instruments, and composition major accounted for a total of 18.998 percent of the variance in rhythm discrimination scores. The addition of GPA in ensembles significantly increased the variance explained to 24.834 percent (See Table Twenty-Seven). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that demographic and undergraduate coursework variables collectively accounted for significantly more of the variance in rhythm discrimination than demographic variables alone. Research Questions 7.a (Pitch) and 7.b (Rhythm). "Will the addition of variables from a third block significantly increase the variance in pitch discrimination scores explained by a model comprised of variables from two blocks?" 193 Table 27 Regression of Rhythm Discrimination on Demographic and Dndergraduate Coursework Variables (S - 70) Source DP Regression SS I p_ Mult. R RL Adj. (Increment) (Total) (Total) Demographic Vars. 4 16.348 5.046 .0013 .48676 .18998 GPA io ensembles 1 4.545 5.559 .0003 .55028 .24834 Parameter b SE b T for Ht: JL Parameter - 0 Keyboards 0.550 0.240 2.295 .0250 Composition major 0.750 0.450 1.668 .1002 Teaching experience 0.122 0.074 1.657 .1024 Jazz 0.385 0.262 1.470 .1464 GPA in ensembles 0.137 0.056 2.459 .0166 Constant 0.000 0.098 0.001 .9996 194 The parallel question for rhythm discrimination was as follows: "Will the addition of variables from a third block significantly increase the variance in rhythm discrimination scores explained by a model comprised of variables from two blocks?" The research question was restated for each model comprised of three blocks of variables. "Is prediction of pitch discrimination significantly increased when musical achievement variables are included in the model comprised by demographic and precollege background variables?" For Yp predicted by musical achievement, precollege background, and demographic variables the null hypothesis was Hoi2p: Adding individual musical achievement variables to the model comprised of demographic and precollege background variables will not significantly increase R2 for pitch discrimination at the p_ < .10 level. 195 Hoi2fl R2acfc. rars. *• background vara. • demo. ran. f R2t>«efc«ro«a<4 ran. * demo, vara. Tests of Hon found that the demographic variables School Three, band instruments, extracurricular performance, age, and School Two plus choral experience collectively accounted for 42.296 percent of the variance in pitch discrimination scores. Once again, band or orchestra failed to significantly increase R2. As in Horp, the addition of rhythm did not significantly increase R2. Therefore, the null hypothesis was retained. The addition of musical achievement variables did not account for significantly more variance in pitch discrimination scores than demographic and precollege background variables combined. "Is prediction of rhythm discrimination significantly improved when precollege background variables are included in the model comprised by musical achievement and other demographic variables?" For Ys predicted by musical achievement, precollege background, and demographic variables the null hypothesis was 196 HOI2K'. Adding individual precollege background variables to the model comprised of musical achievement and demographic variables will not significantly increase R 2 for rhythm discrimination at the p_ < .10 level. H012S'. R2aek. ran. *• background ran. * demo. ran. r ran. * demo, ran. Tests of Hon found that the musical achievement variable rhythm plus the demographic variables band instruments and composition major accounted for a total of 28.344 percent of the variance in rhythm discrimination scores. The inclusion of band or orchestra in the equation significantly increased R2 to 31.629 percent (See Table Twenty-Eight). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that the addition of precollege background variables significantly increased the variance in rhythm discrimination scores accounted for by achievement and demographic variables. "Is prediction of pitch discrimination significantly improved when musical achievement and precollege background variables are included in the model comprised by undergraduate coursework variables?" 197 Table 28 Regression of Rhythm Discrimination on Musical Achievement Test Scores and Other Demographic Variables (N = 70) Source 21 Regression SS (increment) I p_ Mult. R (Total) EL Adj. (Total) Achievement and Demographic Vars. 3 21.676 10.077 .0000 .56049 .28297 Band or orchestra 1 2.883 8.980 .0000 .59660 .31629 Parameter b SE b T for Ht! Parameter = 0 £ Rhythm 0.328 0.108 3.034 .0035 Keyboards 0.349 0.252 1.383 .1713 Composition major 0.941 0.419 2.245 .0282 Band or orchestra 0.063 0.031 2.053 .0441 Constant 0.000 0.093 -0.003 .9973 198 For Yp predicted by musical achievement, precollege background, and undergraduate coursework variables the null hypothesis was Ho UP'. Adding individual musical achievement and precollege background variables to the model comprised of undergraduate coursework variables will not significantly increase R 2 for pitch discrimination at the p_ < .10 level. Hour". R2aeb. vara. * background vara. * course work vara. f vara. Tests of Hoap and HOIOP both found that GPA in aural training and GPA in music history accounted for 20.953 percent of the variance of pitch discrimination scores. Attempts to include band or orchestra, choral experience, and rhythm in the equation did not significantly increase R 2. Therefore, the null hypothesis was retained. The addition of precollege background and musical achievement variables did not account for significantly more variance in pitch discrimination scores than undergraduate coursework variables alone. 199 "Is prediction of rhythm discrimination significantly improved when undergraduate coursework variables are included in the model comprised by musical achievement and precollege background variables?" For Yp predicted by musical achievement, precollege background, and undergraduate coursework variables the null hypothesis was Hon*: Adding individual undergraduate coursework variables to the model comprised of musical achievement and precollege background variables will not significantly increase R 2 for rhythm discrimination at the £_ < .10 level. rars. • bad ground rars. * coursework rars. f rars. * background rars. Tests of H06R found rhythm plus band or orchestra to account for 27.254 percent of the variance in rhythm discrimination scores. Addition of GPA in ensembles to the equation did not significantly increase R2. Thus, the null hypothesis was retained. The addition of undergraduate coursework variables did not account for significantly more of the variance in rhythm discrimination scores than achievement and precollege background variables combined. 200 "Is prediction of pitch discrimination significantly improved when musical achievement variables are included in the model comprised by demographic and undergraduate coursework variables?" For Yp predicted by musical achievement, demographic, and undergraduate coursework variables the null hypothesis was Hoi4i>: Adding individual musical achievement variables to the model comprised of demographic and undergraduate coursework variables will not significantly increase R 2 for pitch discrimination at the p_ ^  -10 level. HOI4P* R2acfc. raro. • demo. vara. * coursework Tara. J R2tfeao» vara. * coursework Tars. As found in tests of Hour, the demographic variables School Three, band instruments, extracurricular performance, age, School Two and the undergraduate coursework variable GPA in aural training accounted for 36.540 percent of the variance in pitch discrimination scores. As in Hozp, the addition of rhythm failed to significantly increase R2. Therefore, the null hypothesis was retained. The addition of achievement variables to the equation did not account 201 for significantly more of the variance in pitch discrimination scores than demographic and undergraduate variables combined. Again, the addition of GPA in music history did not significantly increase R 2. "is prediction of rhythm discrimination significantly improved when undergraduate coursework variables are included in the model comprised by musical achievement and demographic variables?" For Y K predicted by musical achievement, demographic, and undergraduate coursework variables the null hypothesis was Hons'. Adding individual undergraduate coursework variables to the model comprised of musical achievement and demographic variables will not significantly increase R 2 for rhythm discrimination at the p_ < .10 level. HOUR: R2ach. rars. • demo. rars. • coursework rars. f rars. + demo, rars. As per Hone, the achievement variable rhythm plus the demographic variables band instruments and composition major accounted for a total of 28.344 percent of the variance in rhythm 202 discrimination scores. As in Hosn, the subsequent addition of GPA in ensembles to the equation did not produce a significant increase in R 2. Therefore, the null hypothesis was retained. The addition of undergraduate coursework variables to the equation did not account for significantly more of the variance in rhythm discrimination scores than achievement and demographic variables combined. Once again, teaching experience and jazz failed to enter the equation. "is prediction of pitch discrimination significantly improved when undergraduate coursework variables are included in the model comprised by demographic and precollege background variables?" For Yp predicted by precollege background, demographic, and undergraduate coursework variables the null hypothesis was Hoi5p" Adding individual undergraduate coursework variables to the model comprised of demographic and precollege background variables will not significantly increase R 2 for pitch discrimination at the j> < .10 leveL Houp" R2bsckgroand rare. * demo. ran. * coursework ran. / R2 background rara. *• d e s t o . ran. 203 As per Ho9P, the demographic variables School Three, band instruments, extracurricular performance, age, School Two and the precollege background variable choral experience accounted for a total of 42.296 percent of the variance in pitch discrimination scores. The addition of GPA in aural training and GPA in music history did not significantly increase R 2. Therefore, the null hypothesis was retained. The addition of undergraduate coursework variables did not significantly increase the variance in pitch discrimination scores accounted for by demographic and precollege background variables. "is prediction of rhythm discrimination significantly improved when undergraduate coursework variables are included in the model comprised by demographic and precollege background variables?" For Y R predicted by precollege background, demographic, and undergraduate coursework variables the null hypothesis was Hoi5K* Adding individual undergraduate coursework variables to the model comprised of demographic and precollege background variables will not significantly increase R 2 for rhythm discrimination at the p_ < .10 level. 204 vara. *• demo. vara. *• coursework vara. f vara. * demo. vara. As per Ho9x, the demographic variables jazz, teaching experience, band instruments, composition major and the precollege background variable band or orchestra accounted for 25.536 percent of the variance in rhythm discrimination scores. Addition of GPA in, ensembles s ignif icantly increased R2 to 27.364 percent (See Table Twenty-Nine). Therefore, the null hypothesis was rejected in favor of the alternative hypothesis that the addition of undergraduate coursework variables s ignif icantly increased the amount of variance in rhythm discrimination scores accounted for col lect ively by demographic and precollege background variables. Research Question 8.a (Pitch). "Is prediction of pitch discrimination ab i l i t y s ignif icantly increased when variables from a fourth block are added to a model comprised of variables from three blocks?" More speci f ical ly For Yp predicted by musical achievement, precollege background, demographic, and undergraduate coursework variables the nul l hypothesis was HOUR'. R2 background R2 background 205 Table 29 Regression of Rhythm Discrimination on Precollege Musical Background. Other  Demographic Variables. and Undergraduate Coursework (N. - 70) Source Dl Regression SS P_ p_ Mult. R H_Adj (Increment) (Total) (Total] Demographic Vars. 4 16.348 5.046 .0013 .48676 .18998 Band or orchestra 1 4.743 5.635 .0002 .55287 .25143 GPA in ensembles 1 2.148 5.332 .0002 .58035 .27364 Parameter b SB b T for Ht>: £. Parameter - 0 Keyboards 0.311 0.270 1.151 .2539 Composition major 0.836 0.445 1.880 .0647 Teaching experience 0.047 0.084 0.565 .5738 Jazz 0.440 0.259 1.696 .0948 Band or orchestra 0.067 0.037 1.797 .0771 GPA in ensembles 0.100 0.058 1.720 .0904 Constant 0.000 0.096 -0.002 .9986 206 tioiep'- Adding individual musical achievement and undergraduate coursework variables to the model comprised of demographic and precollege background variables will not significantly increase R2 for pitch discrimination at the j> < .10 level. Hoi6r>: R 2 a c n . v a r a . + c o u r s e w o r k In tests of H09P the demographic variables School Three, band instruments, extracurricular performance, age, School Two and the precollege background variable choral experience accounted for 42.296 percent of the variance in pitch discrimination scores. As per Hoi2P and HOUP, achievement variables and undergraduate coursework variables once again failed to significantly increase R2. Thus, the null hypothesis was retained. Neither achievement variables nor undergraduate coursework variables significantly increased the variance in pitch discrimination scores accounted for by demographic and precollege background variables. Research Question 8.b (Rhythm). "Is prediction of rhythm discrimination a b i l i t y significantly increased when variables from a fourth block are added to a model comprised of variables from three blocks?" *• b a c k g r o u n d v a r a . *• demo. vara. vara. ? R 2 b a c k g r o u n d T a r s . + demo. T a r s . 207 For YR predicted by musical achievement, precollege background, demographic, and undergraduate coursework variables the nul l hypothesis was Hoi6R* Adding individual undergraduate coursework variables to the model comprised of musical achievement, precollege background, and demographic variables w i l l not s ignif icantly increase R2 for rhythm discrimination at the p, < .10 leve l . Hoi 6 R '• R2 a e h . vara. * b a c k g r o u n d v a r s . + demo. r a r s . * c o u r s e w o r k r a r s . R2 a c t , v a r s . *• b a c k g r o u n d r a r s . *• Tests of Hoi2R found that the musical achievement variable rhythm, the demographic variables band instruments and composition major, and the precollege background variable band or orchestra col lect ively accounted for a total of 31.629 percent of the variance in rhythm discrimination scores. As in HOSR the inclusion of undergraduate coursework variables fai led to s ignif icantly increase R 2 . Therefore, the nul l hypothesis was retained. Addition of undergraduate coursework variables to the equation containing achievement, demographic, and precollege background variables did demo . v a r s . 208 not s ignif icantly increase the amount of variance accounted for in rhythm discrimination scores. Two additional efforts were made to predict ensemble pitch error discrimination using a l l 18 selected predictors. A stepwise procedure using D_ < .10 to enter or reject variables produced the following results (See Table Thir ty) . The variables School Three, Band instruments played, School Two, GPA in aural training, and GPA in music history were selected by the procedure. In to ta l , they accounted for 41.169 percent of the variation in pitch discrimination scores. When the variables representing post-secondary institutions were removed from the regression, quite a different equation resulted (See Table Thirty-One). The variables choral experience and band instruments were selected by the procedure and accounted for 19.635 percent of the variation in pitch discrimination scores. Two efforts were made to predict rhythm discrimination using a l l 14 selected predictors. A stepwise procedure using .£ < .10 to enter or reject variables produced the following results (See Table Thirty-Two): The variables rhythm, band or orchestra, and jazz were selected by the procedure. These variables accounted for 30.346 percent of the variation in rhythm discrimination scores. i 209 Table 30 Regression of Pitch Discrimination on All Selected Variables (W = 42) Source DP Regression SS (Increment) P Mult. R (Total) RLAdj (Total School Three 1 7.820 9.427 .0038 .43672 .17050 Band inst. played 1 4.830 8.700 .0008 .55544 .27305 School Two 1 2.164 7.165 .0006 .60108 .31087 GPA in aural tr. 1 3.264 7.294 .0002 .66400 .38045 GPA in music hist. 1 1.744 6.738 .0002 .69530 .41169 Parameter 6 School Three "0.642 Band instruments played 0.208 School Two 0.560 GPA in aural training 0.146 GPA in music history -0.111 Constant 0.000 SB b T for Ha: p_ Parameter - 0 0.355 -1.809 .0788 0.079 2.626 .0126 0.299 1.873 .0693 0.052 2.837 .0074 0.064 -1.722 .0937 0.086 -0.006 .9954 210 Table 31 Regression of Pitch Discrimination on A l l Selected Variables Bxcept School Two and  School Three (tf = 42) Source DF. Regression SS F p_ Mult. R R£_ Adj. (Increment) (Total) (Total) Choral experience 1 5.018 5.579 .0231 .34985 .10045 Keyboards 1 4.640 6.009 .0053 .48534 .19635 Parameter b SE b T for Ht: p_ Parameter - 0 Choral experience 0.122 0.045 2.721 .0097 Keyboards 0.730 0.304 2.403 .0211 Constant 0.000 0.101 0.001 .9989 211 Table 32 Regression of Rhythm Discrimination on All Selected Variables (8 = 45) Source DP Regression SS P Mult. R EL Adj. (Increment) (Total) (Total. Rhythm 1 9.861 12.421 .0010 .47342 .20608 Band or orchestra 1 3.045 8.717 .0007 .54160 .25968 Jazz 1 2.535 7.390 .0005 .59241 .30346 Parameter b SE b T for Ha! £. Parameter = 0 Rhythm 0.339 0.136 2.496 .0167 Band or orchestra 0.075 0.034 2.211 .0327 Jazz 0.573 0.300 1.908 .0634 Constant 0.000 0.094 0.000 .9998 212 Summary of Results and Discussion Because volunteers comprised the sample, the mean scores for pitch discrimination and rhythm discrimination may have been biased. The regression coefficients, however, are probably not biased substantially. If they are, they are probably biased downward. Given the r e l i a b i l i t y of the ASMAT and the TIED, and the possible homogeneity of the sample, estimates of R2 are probably underestimated as well . Sixteen pairs of hypotheses were tested regarding the use of predictor variables to account for variance in pitch discrimination and rhythm discrimination scores. Three subsequent regressions were performed using various combinations of variables to provide additional information on the prediction of ensemble pitch or rhythm error discrimination a b i l i t y (See Tables Thirty-Three and Thirty-Four) . Musical achievement test variables. Many of the variables i n i t i a l l y selected as potential predictors of ensemble error discrimination were not found to be s ignif icantly related to either ensemble pitch or ensemble rhythm error discrimination. S k i l l at aural-visual chord discrimination (ASH) was not s ignif icantly related to ensemble pitch or ensemble rhythm error discrimination. Chord discrimination strategies apparently had l i t t l e transfer effect to pitch and rhythm 213 Table 33 Variation in Pitch Discrimination Scores Accounted For by Blocks of Selected  Variables Blocks Order of Bntry Rj Adj. Achievement Vars. Background Vars. Demographic Vars. Undergraduate Vars. Achievement and Background Vars. Achievement and Demographic Vars. Achievement and Undergraduate Vars. Background and Demographic Vars. Background and Undergraduate Vars. Demographic and Undergraduate Vars. Achievement, Background, and Demographic Vars. Achievement, Background, and Undergraduate Vars. Achievement, Demographic, and Undergraduate Vars. Background, Demographic, and Undergraduate Vars. All blocks Rhythm .05099 Choral experience, band or orchestra .14892 School Three, extracurricular performance, Band instruments, School Two, age .35119 CPA in aural training, GPA in music history .20953 Background Vars. .14757 Demographic Vars. .34850 Undergraduate Vars. .20953 Demographic Vars., choral experience .42296 Undergraduate Vars. .20953 Demographic Vars., GPA in aural training .36540 Demographic Vars., choral experience .42296 Undergraduate Vars. .20953 Demographic Vars., GPA in aural training .36540 Demographic Vars., choral experience .42296 Demographic Vars., choral experience .42296 School Three, Band instruments played, School Two, GPA in aural training, GPA in music history .41169 Choral experience, band instruments .19635 214 Table 34 Variation in Rhythm Discrimination Scores Accounted For by Blocks of Selected  Variables Blocks Order of Entry Rj Adj. Achievement Vars. Background Vars. Demographic Vars. Undergraduate Vars. Achievement and Background Vars. Achievement and Demographic Vars. Achievement and Undergraduate Vars. Background and Demographic Vars. Background and Undergraduate Vars. Demographic and Undergraduate Vars. Achievement, Background, and Demographic Vars. Achievement, Background, and Undergraduate Vars. Achievement, Demographic, and Undergraduate Vars. Background, Demographic, and Undergraduate Vars. All blocks Rhythm .21350 Band or orchestra .16182 Band instruments, composition major, teaching experience, jazz .19333 GPA in ensembles .11655 Achievement Vars., band or orchestra .27254 Achievement Vars., Band inst., comp. major .28344 Achievement Variables .21288 Demographic Vars., band or orchestra .25536 Background Vars., GPA in ensembles .20153 Demographic Vars., GPA in ensembles .24834 Achievement Vars., band instruments, composition major, band or orchestra .31629 Achievement Vars., band or orchestra .27254 Achievement Vars., band inst., comp. major .28344 Demographic Vars., band or orchestra, GPA in ensembles .27364 Achievement Vars., band instruments, composition major, band or orchestra .31629 Rhythm, band or orchestra, jazz .30346 215 discrimination. In l istening for pitch and rhythm errors in band music, subjects did not seem to rely on chordal expectations to detect errors. Melody was not found to be related to aural-visual ensemble rhythm error discrimination. This is somewhat surprising. Melody and rhythm were moderately correlated. Rhythm was also moderately correlated to ensemble rhythmic error discrimination. However,skill in aural-visual melodic discrimination appears to be unrelated to the a b i l i t y to discriminate rhythm errors in band performance. Melody was, of course, related to aural-visual ensemble pitch error discrimination. Similarly, rhythm was related to aural-visual ensemble rhythm error discrimination. However, rhythm was also related to aural-visual pitch error discrimination. Precollege background variables. Among college students, the number of precollege music courses and years of music lessons were not found to be related to ensemble error discrimination. Choral experience was not s ignif icantly related to rhythm or rhythm discrimination. Although choral experience was not found to be related to melody, i t was moderately related to pitch discrimination. Precollege famil iar i ty with band instruments, as represented by band instruments played and experience in band or orchestra, was related to both pitch and rhythm discrimination. 216 Other demographic variables. Age was negatively correlated with pitch discrimination. That i s , younger students were generally better than older students at identifying ensemble pitch errors. College or university attended was not related to rhythm discrimination. However, pitch discrimination was posit ively correlated with attendance at School Two and negatively correlated with attendance at School Three. This may have resulted from different student admission cr i t er ia or the nature of programs offered by those inst i tut ions . Extracurricular performance experience was found to be related to both pitch and rhythm discrimination. Generally, the higher the level of participation in extracurricular performance, the better subjects were at ensemble error discrimination. Gender was not s ignif icantly related to either cr i ter ion variable. Sexual stereotyping effects do not seem to apply to ensemble error discrimination. Musical l istening preference by style was not related to pitch discrimination. However, preference for jazz was posit ively correlated with rhythm discrimination. Preference for l istening to large instrumental ensembles was posit ively related to pitch discrimination. Preference for l istening to unaccompanied instrumentalists was negatively correlated with rhythm discrimination. However, preference for l istening to small instrumental ensembles or large instrumental 217 ensembles was posit ively related to rhythm discrimination. Preference for l istening to any choral medium was not s ignif icantly related to pitch or rhythm discrimination for recorded band performances. Among undergraduate music students, music teaching experience was not s ignif icantly related to pitch discrimination. Music teaching experience was, however, posit ively related to rhythm discrimination. Selection of a band instrument as one's performance medium (band instruments) was posit ively related to both cr i ter ion variables. The choice of keyboard instruments (keyboards) as one's major performance medium was negatively related to pitch discrimination. Selection of various program majors was not related to pitch discrimination. Composition majors, however, were s ignif icantly better at rhythm discrimination. Subjects' year in the undergraduate program (year) was not related to either type of ensemble error discrimination. This supports Brand and Burnsed's (1981) contention that undergraduate training in music does not appear to contribute to the development of these s k i l l s . Undergraduate coursework in music. Of a l l the areas of musical training considered only two were found to be s ignif icantly related 218 to both ensemble pitch and rhythm discrimination. These were: GPA in aural training and GPA in ensembles. Several types of undergraduate coursework were not related to either pitch or rhythm discrimination. These included: the amount of coursework in applied lessons and GPA in lessons; the amount of coursework in ensembles; GPA in band instrument techniques; the amount of coursework in music theory and GPA in music theory; and the amount of coursework in orchestration and arranging. In accordance with earl ier studies, many areas of musical training apparently do not predict success in musical ensemble error discrimination. A few other undergraduate coursework variables were not s ignif icantly related to rhythm discrimination. These included: GPA in orchestration and arranging; GPA in music history; and, the amount of coursework in band instrument techniques. Rhythm discrimination in particular seems to be unrelated to many areas of current undergraduate musical training. Two additional areas of training were posit ively related to pitch discrimination: the amount of coursework in band instrument techniques; and GPA in orchestration and arranging. The amount of aural training, however, was negatively related to pitch discrimination. Two unexpected relationships were found. GPA in conducting was negatively related to rhythm discrimination and GPA in music history 219 was negatively related to pitch discrimination. These relationships may have result from emphasis upon l istening tasks other than pitch and rhythm error discrimination. The l i terature on music l istening would suggest that many variables are related to this complex ac t iv i ty . The variables selected in this study may, in fact , serve as proxy variables for as yet unidentified variables. Nevertheless, these variables can serve two purposes. Used in combination they can par t ia l l y account for variation in both pitch and rhythm discrimination scores. They may also suggest further steps in identifying better predictor variables of ensemble error ident i f icat ion. The music achievement block of variables. Of the selected musical discrimination variables rhythm alone comprised the block selected by H 0 2 . Rhythm accounted for over 5 percent of the variation in pitch discrimination scores and for over 21 percent of the variation in rhythm discrimination scores. The precollege musical background block of variables. Choral experience and band or orchestral experience accounted for close to 15 percent of the variation in pitch discrimination scores. Band or orchestra alone accounted for 16 percent of the variation in rhythm discrimination scores. 220 The demographic block of variables. Attendance at School Two or School Three, amount of extracurricular performance experience, the choice of a band instrument as one's major performance medium, and age accounted for over 35 percent of the variation in pitch discrimination scores. Choice of a band instrument as one's major performance medium, the choice of composition as a program major (composition major), the amount of music teaching experience, and preference for l istening to jazz accounted for over 19 percent of the variation in rhythm discrimination scores. The undergraduate coursework block of variables. Several variables provided useful predictors of ensemble error discrimination. GPA in aural training and GPA in music history accounted for roughly 21 percent of the variation in pitch discrimination scores. GPA in ensembles accounted for more than 11 percent of the variation in rhythm discrimination scores. Ensemble pitch error discrimination. Considerable redundancy was evident in the selection of variables. Of the 18 variables selected as a result of Hoip, only 10 comprised the four reduced blocks of ensemble pitch discrimination predictors. Addition of individual predictors from one block to a block accounting for more of R2, incremented R2 by at most 7 percent. In four of the six cases, none of the variables added signif icantly increased R 2 . Demographic 221 variables plus the musical background variable choral experience accounted for 42 percent of the variance in pitch discrimination scores* more than any other combination of predictors. Additional music achievement and undergraduate coursework variables did not result in a further significant increment in R 2 . The resulting regression equation was yp = -0.630 * School Three + 0.021 * extracurricular performance + 0.521 * Band instruments + 0.422 * School Two - 0.034 * age + 0.091 * choral experience An ensemble pitch discrimination value could be calculated for a hypothetical music student based upon these six variables. If this individual attended School Three, was involved in extracurricular performance twenty hours per month, chiefly played f lute, was 24 years old, and had participated in choir for five years before college, the values for this individual could be calculated by subtracting the means for these variables: School Three = 1 - 0.203 = 0.797, Extracurricular performance = 20 - 9.773 = 10.227, Band instruments = 1 - 0.304 = 0.696, School Two = 0 - 0.430 = -0.430, Age = 24 - 21.560 = 2.440, Choral experience = 5 - 2.693 = 2.307. 222 Substituting these values into the equation would produce the following predicted ensemble pitch error discrimination value for this individual: yp = -0.630 * 0.797 + 0.021 * 10.227 + 0.521 * 0.696 + 0.422 * -0.430 - 0.034 * 2.440 + 0.091 * 2.307 = 0.021 This individual would be expected to score 0.021 standard deviations above the mean in ensemble pitch error discrimination. For a 25 year-old individual attending College One, specializing in voice but having no precollege choral experience or extracurricular performance experience, the predicted ensemble pitch error discrimination value would be calculated as follows: School Three = 0 - 0 . 2 0 3 = -0.203, Extracurricular performance = 0 - 9.773 = -9.773, Band instruments = 0 - 0.304 = -0.304, School Two = 0 - 0.430 = -0.430, Age = 25 - 21.560 = 3.440, Choral experience = 0 - 2.693 = -2.693. 223 yP = -0.630 * -0.203 + 0.021 * -9.773 + 0.521 * -0.304 + 0.422 * -0.430 - 0.034 * 3.440 + 0.091 * -2.693 = -0.779 This individual would be expected to score 0.779 standard deviations below the mean in ensemble pitch error discrimination. Stepwise regression of a l l selected predictor variables of ensemble pitch error discrimination accounted for 41 percent of the variation in pitch discrimination scores. The resulting equation was as follows: yp = -0.642 * School Three + 0.208 * Band instruments played + 0.560 * School Two + 0.146 * GPA in aural training - 0.111 * GPA in music history A f ina l regression procedure was performed to predict pitch discrimination a b i l i t y when college effects were not included. This resulted in the equation: yp = 0.122 * choral experience + 0.730 * band instruments Unfortunately, this equation accounted for less than 20 percent of the variance in pitch discrimination scores. College or university 224 attended appears to be an essential predictor of pitch discrimination. Ensemble rhythm error discrimination. Of the 14 variables selected as a result of Hoie, only 7 comprised the four blocks of rhythm discrimination predictors. Addition of individual rhythm discrimination predictors to larger blocks of variables incremented R2 in five out of six cases. At most, this accounted for 7 percent more of the variance in rhythm discrimination scores. The combination representing two blocks of variables which accounted for the largest amount of R2 was rhythm plus choice of a band instrument as a major performance medium (band instruments) and choice of composition as a program major (composition major). This combination accounted for 28 percent of the variance in rhythm discrimination scores. From the precollege background and undergraduate coursework variables, only the addition of precollege band or orchestral experience (band or orchestra) provided a further significant increase in R 2 . The resulting equation was ytt = 0.328 * rhythm + 0.349 * band instruments + 0.941 * composition major + 0.063 * band or orchestra This equation accounted for over 31 percent of the variance in rhythm discrimination scores. For a trombone major specializing in 225 performance, scoring one standard deviation above the mean on the rhythm test, and with seven years of precollege band or orchestra experience, a rhythm discrimination score would be calculated as follows: Rhythm = 1.000 - 0.000 = 1.000, Band instruments = 1.000 - 0.304 = 0.696, Composition major = 0.000 - 0.063 = -0.063, Band or orchestra = 7.000 - 5.093 = 1.907 Substituting in these values, the predicted score for this individual would be y* = 0.328 * 1.000 + 0.349 * 0.696 + 0.941 * -0.063 + 0.063 * 1.907 = 0.632 Thus, this individual would be expected to score 0.632 standard deviations above the mean in rhythm discrimination. Stepwise regression of a l l rhythm discrimination predictor variables accounted for 30 percent of rhythm discrimination scores. The resulting equation was as follows: yn = 0.339 * rhythm + 0.075 * band or orchestra + 0.573 * jazz 226 Again, rhythm remained an important factor in the prediction of rhythm discrimination. The results of this study indicate that multiple l inear regression methods using selected variables can be used to predict pitch and rhythm discrimination a b i l i t y . Like the findings of previous studies, many of the undergraduate coursework variables are not s ignif icantly related to ensemble error discrimination. This seems to be part icularly true for rhythm discrimination. As mentioned in Chapter 2, l istening to music is a complex phenomena. Many enabling factors operate conjunctly during the l istening process and listeners appear to select and operate different l istening strategies under different l istening conditions. The fact that just over 42 percent of the variation in pitch discrimination scores and less than 32 percent of the variation in rhythm discrimination scores were accounted for in this study may reflect the nature of l istening to complex musical stimuli as well as the d i f f i cu l ty of designing highly rel iable tests containing complex musical excerpts. \ CHAPTER FIVE SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS Summary Studies of error detection have suggested that many variables may be related to the essential task of ensemble error detection. Studies in musical discrepancy detection and l istening to music indicate that, to consistently detect and identify errors in musical performance, the l istener must select appropriate and eff icient l istening strategies as needed from a larger repertoire of sophisticated l istening strategies. Again, many factors appear to be related to successful completion of aural-visual musical tasks. Selection and identif icat ion of predictor variables From the review of the l i terature , th ir ty-s ix variables were selected as predictors of a b i l i t y to identify pitch and rhythm errors in band performance. Including individual categorical variables, eighteen variables were found to be related to pitch discrimination at the .10 level (See Table Three, p. 139). 227 228 Fourteen variables were found to be s ignif icantly related to rhythm discrimination at the .10 level (See Table Six, p. 146). Music achievement scores, precollege musical background, tert iary coursework in music, and other demographic variables a l l provided useful predictors of error discrimination a b i l i t y . Individual variables generally appeared to account for small portions of the variance in pitch and rhythm discrimination scores. However, these seemingly small R2 adjusted values deserve some explanation. Although I revised the Test in Error Discrimination to improve i t s r e l i a b i l i t y , the TIED s t i l l included considerable unsystematic variance; not an unusual phenomena for tests using complex musical excerpts. As noted in Chapter 3, approximately 55 percent of the variance in pitch discrimination scores and 40 percent of the variance in rhythm discrimination scores on the TIED was generalizable to the population. When, for example, scores on the aural-visual rhythmic discrepancy subtest of the Al i fer i s -Steckle in Music Achievement Test (rhythm) were found to account for over 21 percent of the variance in rhythm discrimination scores generalizable to the population ( R 2 « < i j . ) , this variable alone accounted for over half of the generalizable variance in rhythm discrimination scores. Similarly , other variables accounted for considerable portions of the variance in pitch and rhythm 229 discrimination scores when the limitations of the TIED are considered. The R 2 adjusted values given below are not estimates of the portion of variance in sample scores that can explained by the predictor variable but estimates of the portion of variance that can be generalized to the population. Unless otherwise noted, R 2 adjusted values are hereafter referred to as R 2 . Rhythm singlehandedly accounted for most of the variance explained by the ASMAT; s l ight ly over 5 percent of the variance in pitch discrimination scores and over 21 percent of the variance in rhythm discrimination scores. Hedden (1987) has suggested that rhythmic discrepancy s k i l l i s closely related to s k i l l in pattern detection. As noted above, rhythm accounted for a considerable portion of the variation in rhythm discrimination scores. Surprisingly enough, the melodic discrepancy subtest (melody) did not account for a significant portion of variance in pitch discrimination scores when controlled for rhythm. The aural-visual chord discrepancy subtest (chords) was not s ignif icantly related to pitch or rhythm discrimination. Among precollege musical background variables, band or orchestral experience (band or orchestra) accounted for over 16 percent of the variance in rhythm discrimination scores. Addition of other variables individually fa i led to s ignif icantly increase R 2 . Although precollege choral experience (choral experience) 230 accounted for over 11 percent of the variance in pitch discrimination scores, the addition of band or orchestra to the equation increased R2 by roughly 4 percent to almost 15 percent. Other demographic variables, such as college or university, amount of extracurricular musical performance experience (extracurricular performance), major performance medium, and age col lect ive ly accounted for over 35 percent of the variation in pitch discrimination scores. No differences were noted by college or university, age, or extracurricular performance for rhythm discrimination. However, choice of a band instrument as a major performance medium was a significant predictor in both equations. Choice of composition as a major (composition major), amount of music teaching experience (teaching experience), and preference for l istening to jazz also contributed to R2 for rhythm discrimination. Together, GPA in aural training and GPA in music history accounted for almost 21 percent of the variation in pitch discrimination scores. Surprisingly, GPA in music history was negatively related to pitch discrimination. Although music history students spend much of their instructional and study time l istening to ensembles, emphasis i s , apparently, placed on aspects of musical perception other than pitch and rhythm error discrimination. Among undergraduate coursework variables, GPA in ensembles accounted for well over 11 percent of the variation in rhythm 231 discrimination scores. The individual addition of other coursework variables fa i led to s ignif icantly increase R 2 . As mentioned above, rhythm accounted for v i r tua l ly a l l of the variance in ensemble error discrimination scores related to the ASMAT. Thus, rhythm comprised the music achievement test block. For pi tch discrimination, however, rhythm accounted for less of R 2 than any other block of variables. When added to any one block or combination of these blocks of variables, rhythm did not s ignif icantly increase R 2 . In predicting pitch discrimination a b i l i t y , therefore, music achievement test variables are not essential i f undergraduate coursework, precollege musical background, or other demographic blocks of variables are included in the equation. Prediction models of ensemble rhythm error discrimination a b i l i t y The following model accounted for over 35 percent of the variance in rhythm discrimination scores for the sample' well over half of the systematic variance in discrimination scores. This model accounted for more than 31 percent of the variance in rhythm discrimination a b i l i t y in the population (See Table Twenty-Eight, p. 197). yit = 0.328 * rhythm + 0.349 * band instruments + 0.941 * composition major + 0.063 * band or orchestra 232 Rhythm accounted for more of the variance in rhythm discrimination than any other variable or block of variables. The addition of GPA in ensembles to the model did not s ignif icant ly increase the predictive power of the model. In predicting rhythm discrimination, undergraduate coursework variables need not be included when music achievement variables are already in the equation. When used in combination with rhythm, both the precollege background variable band or orchestra and the demographic variables band instruments and composition major continued to make s ignif icantly unique contributions to R 2 . When rhythm was not included in the equation, the resulting model was: yn = 0.311 * band instruments + 0.836 * composition major + 0.047 * teaching experience + 0.440 * jazz + 0.067 * band or orchestra + 0.100 * GPA in ensembles Despite the inclusion of teaching experience, jazz, and GPA in ensembles, this model accounted for approximately four percent less of the variation in ensemble rhythm error discrimination scores than the model containing rhythm. Rhythmic error discrepancy s k i l l appears to be an essential component of ensemble rhythm error discrimination. 233 A different equation resulted when a l l predictor variables were considered and entered according to their a b i l i t y to account for more of the variance in discrimination scores! y* = 0.339 * rhythm + 0.075 * band or orchestra + 0.573 * jazz Jazz replaced the variables band instruments and composition major in the f i r s t model. The new-model s t i l l accounted, however, for over 30 percent of the variance in rhythm discrimination scores. Prediction models of ensemble pitch error discrimination a b i l i t y Demographic variables comprised the largest block of ensemble pitch error discrimination predictors (See Table Thirty-Three, p. 213). Attendance at School Two or School Three, extracurricular performance, band instruments, and age accounted for over 35 percent of the variance in pitch discrimination scores. Choral experience and GPA in aural training both s ignif icantly increased R2 when the demographic block of variables was already in the equation. This model accounted for over 42 percent of the variance in pitch discrimination a b i l i t y generalizable to the population (See Table Twenty-Three, p. 183): 234 yp = -0.630 * School Three + 0.021 * extracurricular performance + 0.521 * band instruments + 0.422 * School Two - 0.034 * age + 0.091 * choral experience With choral experience and demographic variables already in the equation, the addition of GPA in aural training did not s ignif icantly increase R2. A s l ight ly different equation resulted when variables were entered individually by their a b i l i t y to improve the predictive a b i l i t y of the model. The new equation contained one less variable and accounted for approximately 1 percent less of the variance in pitch discrimination scores. yp = -0.642 * School Three + 0.208 * band or orchestra + 0.560 * School Two + 0.146 * GPA in aural training - 0.111 * GPA in music history The variables extracurricular performance, band instruments, age, and choral experience were replaced by the variables band or orchestra, GPA in aural training, and GPA in music history in this equation. College or university attended, however, accounted for a major portion of the variation in pitch discrimination scores. 235 School Three alone accounted for approximately 18 percent of the variation in pitch discrimination scores. College or university attended was not s ignif icant ly related to rhythm discrimination. For pitch discrimination, however, i t provided the most important predictor. Elimination of college attendance variables resulted in the following model: yp = 0.122 * choral experience + 0.730 * band instruments Choral experience and band instruments s t i l l entered the model but, co l lect ive ly , accounted for less than 20 percent of the variation in pitch discrimination scores. Extracurricular performance, age and the 12 other predictor variables were individually unable to s ignif icantly increase R 2 . Clearly, pitch discrimination is strongly related to the college or university attended. Selection of Levels of S ta t i s t i ca l Significance As mentioned in Chapter 3, I chose the .10 level of significance to reduce the r isk of rejecting variables which are related to pitch or rhythm error discrimination. In making this decision I increased the l ikelihood of accepting variables which are not related to pitch or rhythm discrimination. At any rate, I suspect that the variables retained in the multiple regressions were essentially those that would have been obtained i f the c r i t e r i a for 236 selecting individual variables during the i n i t i a l screening had been that they were s ignif icantly related to the cr i ter ion variables at the .05 l eve l . Eleven variables comprised the blocks of selected pitch discrimination variables. Of these, 10 were individual ly significant at the .05 level (See Table 3, p. 139). Extracurricular performance, the other variable, became significant at the .001 level when a model of selected demographic variables was constructed (See Table 13, p. 162). Seven variables comprised the blocks of selected rhythm discrimination variables. Of these, a l l but composition as a chosen major were significant at the .05 level (See Table 6, p. 146). Composition was significant at the .01 level when the other three selected demographic variables were included in the model (See Table 14, p. 164). Conclusions and Recommendations 1. Each of the following four blocks of variables can be used as predictors of pitch and rhythm error discrimination a b i l i t y for undergraduate music students: musical achievement variables; precollege musical background variables; undergraduate musical coursework variables; and other demographic variables. 237 2. Multiple l inear regression techniques can be used to predict ensemble pitch and rhythm error discrimination a b i l i t y . Ensemble rhythm error discrimination. 3. Scores on the aural-visual rhythmic discrepancy subtest of the Al i fer i s -Steckle in Music Achievement Test (rhythm) provided the best single predictor of rhythm discrimination a b i l i t y . Even when a l l other blocks were entered into the model, the addition of rhythm substantially increased the amount of variance explained by the model. It is recommended therefore that generalized measures of rhythmic achievement be included in future models of ensemble rhythm error discrimination. 4. Prom the precollege musical background block, band or orchestra experience was the single best predictor of rhythm discrimination a b i l i t y . It i s recommended that, for future studies, previous experience at l istening to the type of ensemble under consideration be included when predicting musical discrimination a b i l i t y . 238 5. Demographic variables comprised an important block of predictor variables. Even when the other three blocks were entered into the model, the addition of this block substantially increased the amount of variance explained by the model. It i s recommended therefore that appropriate demographic variables pertaining to famil iar i ty with the performance medium, l istening preferences, choice of musical major, and types of extracurricular musical involvement be included in future models of ensemble rhythm error discrimination. 6. Undergraduate coursework variables accounted for less of the variance in rhythm error discrimination scores than any other block of variables. GPA in ensembles provided the best single predictor of rhythm discrimination a b i l i t y . It is recommended that GPA, rather than quantity of tert iary coursework in ensembles, be used a predictor of ensemble error discrimination in future studies. Ensemble pitch error discrimination. 7 . The musical achievement test variables melody and rhythm accounted for a significant portion of the variance in pitch discrimination scores; with rhythm being the best single predictor 239 from this block. However, this block did not s ignif icant ly improve the predictive a b i l i t y of the model when any of the other three blocks of variables were already in the model. Therefore, when the other blocks of variables are included musical achievement variables are not essential to the model. 8. The precollege musical background variables choral experience and band or orchestra experience comprised an important block of predictor variables. Choral experience and other demographic variables provided the best predictive model of pitch discrimination a b i l i t y . When demographic variables, such as choice of band instruments as one's major performance medium, were entered in the model, the amount of precollege experience in band or orchestra did not substantially increase the amount of variance explained by the model. 9. Demographic variables comprised the best single block of predictors of pi tch discrimination a b i l i t y . The music inst i tut ion attended should be considered in future studies because i t can be a strong predictor of pitch discrimination. The amount of extracurricular performance experience and the choice of band instruments as one's major performance medium are both posit ively related to pitch discrimination a b i l i t y . Surprisingly, younger 240 students tended to be better at discriminating pitch errors than older students. 10. Undergraduate coursework variables accounted for a significant portion of the variance in pitch discrimination a b i l i t y . GPA in aural training is posit ively related to pitch error discrimination a b i l i t y and GPA in music history i s negatively related to pitch error discrimination a b i l i t y . Early musical training In this study, precollege musical background variables were found to be related to both pitch and rhythm discrimination. Even when other variables were considered, the amount of precollege choral experience remained one of the best predictors of pitch discrimination. If the extent of precollege musical experience can be shown to posit ively effect the musical development of undergraduate music students, and, i f latency periods exist for the development of musical discrimination s k i l l s , then: 11. It is essential that young music students receive sufficient musical instruction which is appropriate to their current levels of musical development. 241 Tertiary musical training This study concerned prediction; not causation. Nevertheless, I had suspected that various forms of tert iary musical coursework would contribute to improved error discrimination a b i l i t y . If so, significant and positive correlations should exist between these variables and the two error discrimination variables. Only four of the 18 variables met these c r i t e r i a for pitch discrimination; GPA in aural training, coursework in band instrument techniques, GPA in ensembles, and GPA in orchestration and arranging. Only three of the 18 variables met these c r i t e r i a for rhythm discrimination; GPA in aural training, GPA in ensembles, and coursework in music history. 12. If improving the ab i l i t y of undergraduate students to discriminate pitch errors in band music is an objective of coursework in applied lessons, composition, conducting, music history, or music theory, then efforts should be made to include practice in pitch error discrimination in these areas of study. 13. If improving the a b i l i t y of undergraduate students to discriminate errors in band music i s an objective of coursework in applied lessons, band instrument techniques, composition, conducting, music theory, or orchestration and arranging, then 242 efforts should be made to include practice in rhythm error discrimination in these areas of study. When implementing musical discrimination training, instructors should consider several important factors. As noted in Chapter 2, various researchers have suggested that higher order thinking s k i l l s are related to success at ensemble error discrimination. MacKinnon (1986), however, found that the majority of students entering college were incapable of formal thought. Therefore, those in charge of teaching musical discrimination should use approaches in keeping with their students' current levels of mental maturity. One frequent complaint about aural training offered at post-secondary institutions is that i t is irrelevant to other musical act iv i t ies (Ashley, 1982; Pratt , 1987). Block (1981) reported that: The l istening tasks associated with tradit ional beginning l i terature and theory courses exhibit a divis ion of labor along two extremes, usually experienced simultaneously by the college music major. On the one hand, in l i terature courses, l i s tening tasks begin with the experience of the whole, and any growth in structural awareness is expected to be gained only from exposure to complete compositions. 243 On the other hand, analytical and ear training tasks begin with the smallest details in order to work out, ostensibly, to the level of whole compositions. The problem with the tradit ional approaches is that they do not work effectively toward each other, and a large gap remains, (p. 41) Pratt (1987) fe l t that, as a result , students do not consciously apply the s k i l l s acquired in aural training to their other musical act iv i t ies (p. 8). To avoid this problem, I recommend that musical error discrimination and other forms of aural training be taught in musical contexts. Likewise, l istening tasks in l i terature courses should encourage students to build upon the perceptual s k i l l s developed in music theory and aural training. Limitations to memory and attention res tr ic t the a b i l i t y to process aural information (Mount (1982). Therefore, i t i s imperative that students develop effective l istening s k i l l s . It i s common for students to shift their focus of attention from one musical event to another, never completely perceiving any aspect of a musical event. Students need to be taught to attend to images in some organized fashion so that complete conceptions can be b u i l t , relationships recognized, and associations formed. 244 This takes a conscious concentrated effort because there are so many events competing for attention (Horning, 1982, p. 205). . . Students must be taught when and what to select in l i s tening, performing or composing, and, when the selection is made, to concentrate on attention. Students need to be taught how to select information which is pertinent to the l istening task at hand. (p. 207) Brink (1980) recommended that students f i r s t learn to master re lat ive ly simple aural-cognitive tasks before attempting more advanced tasks. Horning's approach to aural instruction emphasizes that such study should occur in musical contexts: In teaching students l istening s k i l l s , for example, we must f i r s t help them distinguish musical elements such as melody, harmony, rhythm, timbre, dynamics, tempo, and form. When they have clearly distinguished these elements, they w i l l have more clear images of these elements in mind. When an image is clear, i t can be processed in less time, leaving more room and time in the memory system for succeeding images. Processing becomes more automatic and requires fewer conscious decisions. Then, we must help students to associate, categorize, and store musical images so that they can form complex images. 245 Through an analysis of many musical melodies, for example, students can learn the kind of things that melodies do. When they learn this , they know what to expect of melodies in certain situations, and when the melody goes according to expectation, very l i t t l e processing time or space is needed. Since melodies follow certain grammatical and syntactical patterns in most musical situations, psychological processing is greatly fac i l i t a t ed . Next, we can help students to develop more complex images, by helping them to perceive the relationship between melody and harmony, for example. By showing students how harmonies are implied in melodies and how harmonies suggest melodies, and then how melodic, harmonic, and rhythmic movement are related, a teacher is helping students to form complex images which can be processed quickly and even automatically. (1982, p. 198) Because most students can not attend to the large number of musical events occurring in a work at one time, they must be taught to attend to those elements in the music which are most l ike ly to be important for an understanding of the piece. Lester (1987) noted, for example, that a student whose attention is focussed on the rhythms in a work, perceives that piece in a way that is quite different from a person who is focusing on the themes. Listeners need to learn what to focus their attention on at a given time in a 246 given piece. Such strategies w i l l enable the l istener to get the most out of a single hearing of a work. Ashley recommends that students develop basic l istening strategies which are useful over a wide range of musical situations, especially in re lat ive ly novel situations (1982, p. 98). Other strategies, presumably, should be applied during subsequent hearings of the work. Discrepancy tasks offer an advantage over sight singing in that compositions may include a great variety in texture, timbre, style , and complexity. One could be asked to identify discrepancies in pi tch, rhythm, timbre, and dynamics. Errors of omission as well as commission could be included. Another advantage is that the student can add information upon successive hearings. The greatest advantage of a l l is an immensely pract ical one. Teachers and conductors are constantly faced with situations in which they need to correct faulty readings on the part of performers. A b i l i t y to quickly pinpoint the discrepancy between performance and score is an indispensible s k i l l , one that demonstrates that the score conveys an aural conception which must match the aural conception of the performance... The cognitive requirements for discrepancy tasks are demanding due to the need to process and relate both aural and visual 247 information. The student must form an aural conception of what he has heard and instantaneously compare that conception with another based on the reading process in which precise information must be gleaned from abstract and discrete visual symbols. (Brink, 1980, p. 92). Aural training programs should include the aspects of sound which are most important for musicians to perceive accurately. From an analysis of current music tests i t would appear that these aspects include pitch, rhythm, overall volume, timbre, the density or transparency of musical textures, and the relative volume of individual voices (Pratt, 1987). "While some aural s k i l l s may be needed by a l l musicians, different act iv i t ies demand different stresses and probably different training programs altogether" (Pratt, 1987, p. 5). Ashley (1982) also noted the need to develop specific l istening procedures "which may not be as widely applicable but which are better suited to some restricted domain. These w i l l prevent the l istener from having to spend a great deal of attention on early selection of attributes for analysis" (p. 99). Specialized aural training could be made available to students who have selected specialized areas of training. For example, students planning to direct ensembles after graduation w i l l presumably f i r s t take some training in conducting. Error 248 discrimination act iv i t ies could be a course requirement. Alternatively, the conducting instructor could require that students be tested in error discrimination s k i l l s . Students needing remedial practice could then be encouraged to use programmed materials to help develop their ensemble error discrimination s k i l l s . Horning (1982) and DeCarbo (1984) not only recommended that instructors help their students to develop error discrimination s k i l l s , but also that they show their students how to structure musical rehearsals so that musical problems can be solved one at a time. Knowing which problem to solve and in which order to solve i t , helps a student to focus attention and fac i l i ta tes the processing of musical information (p. 201). Further research. The following recommendations are made for future studies in ensemble error discrimination: 14. that hierarchies of common performance errors be developed so that students can practice systematic detection and timely correction of performance errors. 15. that further research be performed to identify the mental processes involved in error detection. 249 16. that further research be performed to identify the inte l lectual and experiential prerequisites for ensemble error discrimination. 17. that further research be performed to identify relationships between the structural characteristics of works, processes in musical l i s tening, and success in ensemble error discrimination. 18. that intercorrelations between predictor variables be considered in developing new models of ensemble error discrimination. In this study many predictors were selected and identif ied as individually accounting for significant portions of R2 . However, when several variables were already in the equation a new variable was often unable to make a significant unique contribution to R 2 . Willemsen (1974) suggests that the ideal prediction model consists of predictors that correlate moderately with the cr i ter ion variable and that show a low correlation among themselves. When high correlations exist among the predictors, R2 i s only marginally increased by adding more than two predictors to the regression equation (p. 146). To some extent, this may be what happened with regard to ensemble pitch error discrimination. Once School Two and 250 School Three were eliminated from the equation, only two of the remaining sixteen variables, choral experience and band instruments, entered the new equation' and accounted for less than 20 percent of the variance in ensemble pitch error discrimination scores. In developing new models of ensemble error discrimination i t would be useful to be able to identify moderately strong predictors of ensemble error discrimination that are weakly intercorrelated. 19. that highly rel iable tests of ensemble error discrimination be constructed and validated. Although the new Test in Error Detection proved useful in this study for identifying other variables as predictors of pitch and rhythm discrimination, i t s level of r e l i a b i l i t y was not high enough to permit precise prediction of ensemble error discrimination s k i l l for individuals . Within the f i e l d of music education such tests might be comprised of high f ide l i ty recordings of band, choral, stage band, and orchestral excerpts containing selected embedded errors. 20. that future studies attempt to improve upon the prediction models produced in this study. 251 McClave and Benson (1982) emphasize the need for establishing c r i t e r i a when building mathematical models of the relationship between predictor variables and a cr i ter ion variable: "The biggest problem in building a model . . . i s choosing the important variables to be included in the model. The l i s t of potentially important variables is extremely long, and we need some objective method of screening out those that are not important. The problem of deciding which of a large set of independent variables to include is common" (p. 570). Because ensemble error discrimination is a complex musical act iv i ty (Colwell, 1987), i t is l ike ly that satisfactory explanatory models of music error detection and identif icat ion w i l l also be complex. If explanatory models of ensemble error discrimination can be developed and ver i f ied , i t may be possible in future studies to select more appropriate combinations of predictor variables. In this study, readily obtainable data representing undergraduate coursework, precollege musical background, and other demographic factors were collected. This pool of variables accounted for over 42 percent of the variance in pitch discrimination scores but accounted for less than 32 percent of the variance in rhythm discrimination scores. The advantage of this 252 group of variables was that i t only took about ten minutes for students to complete the precollege musical background and other demographic variables sections of the Musical Background Questionnaire. The undergraduate coursework information was, of course, obtained via analysis of transcript information. However, although many of the variables i n i t i a l l y selected were found to be related to pitch or rhythm discrimination, considerable intercorrelation of variables was present. As a result , re lat ive ly few of these variables were needed to account for most of the variance explainable by these blocks of variables. At the same time, most of the variance in ensemble error discrimination scores remained unaccounted for by the models. It is recommended, that, to increase the amount of variance accounted for in future models, other variables also be considered. Two subtests of the Al i fer i s -Steckle in Music Achievement Test were found to be related to ensemble error discrimination. Melody was related to pitch discrimination and rhythm was related to both pitch and rhythm discrimination. It is recommended, that future studies attempt to identify relationships between aspects of musical a b i l i t y and ensemble error discrimination. The use of music achievement tests alone to predict ensemble error discrimination a b i l i t y is not advised. A test of error discrimination a b i l i t y would probably be more useful. However, i f music achievement test scores are to be used in predicting of other 253 desirable musical competencies, this could just i fy the re lat ive ly lengthy time of administration and the controlled environment necessary for the administration of aural tests. Future attempts to produce error discrimination models should use larger sample sizes. If a large number of variables are, in fact , involved in error discrimination, larger sample sizes w i l l be needed to improve estimates of R 2 , effect sizes, and confidence intervals for predictive purposes. 254 BIBLIOGRAPHY A l i f e r i s , J . , & S t e c k l e i n , J . E. (1962). 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No. 17. 271 APPENDIX A Appendix A Musical Background Questionnaire Student identif icat ion number Precollege Musical Background Total years of applied music lessons Number of band instruments played Number of years of band or orchestral experience Number of years of choral experience Number of courses in music theory or ear training completed before entering university Related Current Information Age Amount of extra-curricular musical performance experience (in hours per month) Major performance medium Program major (eg. composition, music education, performance, general or undeclared) School of music attended Sex Year in undergraduate program 273 Type of music you most enjoy l istening to (Circle one) Classical Country Easy Listening Jazz Popular Rock Other (Please specify) Type of musical ensemble you l i s ten to most (Select one) Singer (Unaccompanied) Instrumentalist (Unaccompanied) Soloist with instrumental and/or choral accompaniment Small choral ensemble (6 members or less) Small instrumental ensemble (6 members or less) Large choral ensembles Large instrumental ensembles Other (Please specify) Equivalent of full-t ime music teaching experience (10 months can be considered as equivalent to one year) Years plus Months APPENDIX B Appendix B 275 Selection of New Test In Error Detection Items Items for the new version of the Test in Error Detection have been selected based upon three c r i t e r i a : type of error, relative proportion of errors by different instruments, and item d i f f i c u l t y . The types of errors were determined by examination of Ramsey's 135 excerpts (See Table One below). Having identified types of pitch and rhythm errors (See Table Two), a representative number of medium d i f f i c u l t items were selected for different instruments. In addition, attempts were made to consider the relative occurrence of pitch errors by concert pi tch, instrument and part, composition, and even the measure of the excerpt in which the error occurred. Pitch errors outnumbered rhythm errors by 93 to 42 in Ramsey's pool. However, since this study w i l l treat the ab i l i t y to detect pitch and rhythm errors in ensemble performance as different s k i l l s , 15 pitch and 15 rhythm items were selected for the new version of TIED (See Table Three below). 276 TABLE ONE RAMSEY'S TEST IN ERROR DETECTION It«. C o m p o s i t i o n Segment M e a s u r e o f E r r o r t n s t r u i s e n t K a t u r e o f t h e E r r o r D i f f i c u l t y C o e f f i c i e n t 1 The Orsgoons o f V l l l a r a 79-82 1 C t a r . ( I p i . T . d Jinnn 1.000 : O v e r t u r e In Bb 138-141 : Tuba p l a y e d J » i ' J - J v 1.000 3 T o c c a t a f o r Band m - m * T r p t . 1 o i a y e d nn 1.000 • A a e r l c a n Folk. Rhapsody '1 i S n a r e 0ru« p l a y e d e r a s u r e e v l t t t n g r e s t i 1 .CCO s A r i a ( o r V l n d s 33-56 3 Cyeibal p l a y e d o n s e c o n d count 1.000 « K e n t u c k y 1300 SJ-3» «• C o r n e t I p l a y e d J*aa J on count t h r e e I.POO 7 T o c c a t a f o r Band »o-63 ' T i e ? ant p l a y e d ) ) r a t h e r 4 h e n r J J * t.roo % Tha Dragoons o f V l l l a r t 7-10 j Beasoon p l a y e d J " ' " - - / 1.000 7 Tht Dragoons o f V l l t a r a l - i i C l a r i n e t I p l a y e d J r a t h e r tftae J X l.ooa 10 The 9rageone o f ' V l l l a r a 3 Co rnee I p l a y e d J _ / U /T3 .9JJ3 11 Ttie Dragoons o f V l l l a r * 16-19 3 B a r l i o n e p l a y e d A k r a t h e r t h a n A,». -•313 12 A r i a f o r Winds 4J-46 C o r n e t I p l a y e d C*3 r a t h e r than OP .St 66 13 The Dragoons o f V I l i a r s 14-19 3 F l u t e p l a y e d 5» r a t h e r *hen .8646 14 ? l c a s a n t V a l l e y 150-15} 2 Snare Pru» P l a y e d ,/?2 d« fTj .S6»o IS A r i a f o r v l n d s 62-65 «• K e r n I t o r IV pl . i y e d r a t h e r than g\ • ittt 16 A r i a f o r I f l n d l 42-46 * C o r n e t I I p l a y e d S* r j r h e . - t h a n sS .tat 17 The Oragoons o f V l l l a r * ) S - 6 l 1 Horn 1 p l a y e d ,T> • .JT) • Sbtl 18 O v e r t u r e In B b 1-4 1 P i c c o l o p l a y e d C on - f o u r t h count . JCCC 1» The o r j g o o n a o f V i l l a r s 16-10 1 F l u t s p l a y e d r a t h e r t h a n A.M • 100C :o K o n t e Y l j t a 77-80 A l t o Sax. p l a y e d F» r a t h e r t h a n fS .(CCO I t e a C o m p o s i t i o n Segment Measure of E r r o r I n s t r u m e n t K a t u r e of E r r o r O K f t c u l t y C o e f f i c i e n t 21 A m e r i c a n F o l k Rhapsody *1 57-63 3 Oboe p l a y e d A S r a t h e r t h a n A b .8009 u M e x i c a n f o l k , f a n t a s y 206-211 2 T l n p a n l p l a y e d on dovnbeat .SOOO 13 A r i a f o r w i n d s 22-26 } F l u t e p l a y e d o\ r a t h e r than 0* .8000 24 A m e r i c a n F o l k Rhapsody 11 64-67 I B a r i t o n e p l a y e d J3 r a t h e r than J3 .8000 21 H i c k o r y K i l l s 21-26 J B a r i t o n e p l a y e d EH r a t h e r than E? .8009 ;» F l a a s a n t V a l l e y 114-1 IT 6 Oboe p l a y e d A* r a t h e r than A* .7.'33 27 M e x i c a n F o l k F a n c a s y 142-167 J T r b . I £ I I p l a - e d r a t h e r t h a n a* . 7 3 3 J it f t e x l c a n F o l k F a n t a s y 94-98 » C o r . 1 p l a y e d Fa* r a t h e r t h a n F*t .'333 i9 A e t t r l c a n f o l k Rhapsody ' l 64-67 2 B a r i t o n e p l a y e d /) r a t h e r t h a n Si . 7333 30 The Dragoons o f V l l l a r s 23-26 1 C o t . t p l a y e d C r a t h e r than C . 7 3 « 31 H o m e V i s t a l - > 1 Tuba p l a y e d A* r a t h e r t h a n y t * .7333 32 A n e r l e a n r o l k f h a p e o d y #1 16-91 1 T r b . I t l p l a y e d E* r a t h e r than F> . 7333 33 K e n t u c k y 1900 J 7-61 t Horn I p l a y e d A* r a t h e r t h a n * V .6666 3» O v e r t u r e I n 8^ 86-90 4 Hern p l a y e d fH r a t h e r t h a n F# .6666 35 A l c a l a 11-16 : C l a r i n e t 1 p l a y e d S b r a t h g r ehan »*: .6666 16 H i c k o r y i l l U s 11-16 3 P l c c o l p p l a y e d A* r a t e e r i f l a n A^ .616ft 37 P l e a s a n t " a l l e y 62-6} i B a r i t o n e p l a y e d r a t h e r th«o 8^ .6666 38 H i c k o r y HI l i s 81-66 2 Bar t t o n e p l a y e d A S r a t h e r th>n A * .6666 39 O v e r t u r e i n B° 6-10 C l a r . I l l p l a y e d 0' r a t h e r t h a n BH .6666 •9 A r i a f o r Winds i 7 - : o 6 C o r . I I P l a y e d - J3 V .6666 + 1 P l e a s a n t V a l l e y 70-74 1 C l a r . 1 p U y e d F^ t a t h e r t h a n F * .6000 Three M e n d e l s s o h n C h o r a l e s 1-4 T r b . 1 p l a y e d A * r a c i e r khaa AH .63?0 277 I c e * C o n p u a l t l o n | | Segment • Meaaure ; cl C r r o r | t n t t r u n e n c j t u r e of t h e t r r c r ? l f f U u l t j r C o e f f i c i e n t -3 A r i a ( o r Wind* ! 22-71, i | C l - r , 11 • p l a y e d r a t h e r t h a n t b . »coo A r i a f o r Wlnda | J-8 2 | T. * a * r l a y e d f\ r a t h e r t h a n t* .6000 A m e r i c a n F o l k Rliapaody *1 j C8-91 I j Cor. 1 | p i a y e d rS r a t h e r t h a n f* .r000 H i c k o r y HI 11* 9-11 - j M u t e I I p l a y e d A** r a t h e r t han AS .6000 17 A l c a l a 97-95 J • r i c e r l o ntriyi'd r a t b e r tb.-.n AH .6000 ;s M e x i c a n f o l k F a n t a s y 78-81 3 1 f l u t e i • p i a y e d J J J , . , TJJ" .'000 i» T o c c a t a f o r Band 186-189 i j T r b . l i t \ p l a y e d t 1 , r a t h e r t h a n C*\ ; .6000 50 Three 7>ndcla»ohn C h o r a l e a 10-11 : | C U r . I I \ p i a y e d B^ on f o u r t h count • .f-OOO 51 M e x i c a n F o l k F a n t a s y :0!-205 I j l l o r r [ a l a y e d on t h e heat .6000 5; O v e r t u r e I n B^ 96-100 1 | Oboe p l a v e d In (/( l i n e • .6^00 j ) A r i a f o r U l n d s 1-4 I ! Oboe • p l a v e d 8^ r a t h e r t h a n BS .6100 K e n t u c k y 1800 : i - : * 3 | R a c o o n p i a v e d P*1 r a t h e r t h a n OS . 6 ™ 0 » K e n t u c k y 1900 a 9-i A I | C o r . t ; p 1 ay c d 8 r a t h e r t h a n 8S • 5 M 1 H H i c k o r y III 11* 11-16 I j G»r. 1 r I aved tfi c a l S e r l h a n J<5 . M i l J - K e n t u c k y IkOO 1-1: 2 ; T r h . 1 M « Y , . | A 1 , r a t h e r l l . n n Ak( . ) l \ ! SS r i e a i a n t V a l l e y 78-B: A J l U r t t o n e r l i v h i t* r a t i . , r lh«" I N 5'* O w v r u i r r In B U 67- 70 2 1 C U r . l i t C *>n «*(pn.l T not r .1)11 t ; l i K k u r v 1,1 M a • 76-no p.ir 1 l o n e C h rall.»r t h a n r.kj .1)11 ( i A l c a l a Trumpet I M.ived B*' r a t h e r t h a n BS .55)1 *: 1 A l c a l a C l a r . I p 1 Avnl B*S rath.'r lli.»n T\r .5)11 6 ) | P l e a a a n t V a l l e y 5 l - » : Trr<r»bone p l a y v d A*l r a t h # r th.^n A** .5111 n i 1 A m e r i c a n F o l k Rhapeody *1 33- 11* 4 1 C l a r . I I r* 1 «>••*<! r * r a t h e r IS.n r*. .5)11 65 • A l e x i a 1 I A. S.i* 1 r S r a t h e r lh..r T' .'.1 66 I t c c 1 C e o p o a l t l o n 1 Sett>ent ; o f . r r o r ( l n a t r u r w n t N a t u r e ©f the E r r o r • C o e r r t r l e n 66 i H i c k o r y H l l l a 1 1-* • 1 | S n a r e ?rur» p l a y e d / . i f 6 6 67 A l e x i a 15-19 | J •-.lor. 11 P l a y e d • J ) D \JT) ..<.66 60 | K e n t u c k y 18000 l-» | . 1 A. Sax p l a y o d F H r a t h e r t h a n f * .4*60 *9 Itonte V t a t a 31-36 ; 1 l C o r . 1 p l a y e d B^ r a t h e r t h a n 8*1 .-(»f-70 P l e a s a n t V a l l e y io:-ios , I ' I C o r . 1 p l a y e d B P r a t h e r t han BS . J6:-6 71 r i e a a a n t V a l l e y 63-65 1 F l u t e p l a y e d A* r a t h e r t h a n A*1 .i66» J : ; A r i a f o r Irtnds «l-4« 5 C o r . I l l p l a y e d t\ r a t h e r t han F- . 1666 >3 | P l e a s a n t V a l l e y : 9 - 3 ' F l u t e p l a y r d AH r a t h e r t h a n AO .(666 7* J A m e r i c a n F o l k Rhapsody *1 188-191 1 • U c o l n p l a y e d A* r a t h e r t h a n A™ . ( ( 6 6 7J j H i c k o r y H l l l a 76-80 ; A l t o Sax n l a y e d F^ r a t h e r t h a p F" .(*6« 76 j O v e r t u r e I n B° 6-10 Oboe p l a y e d T on devnbeat .4 666 77 • T o c c a t a f o r Band • 80-83 Horn I I p l a y e d BFC r a t N e r than B V .1666 7C T h r e s H e n d a l e l o h n C h o r a l a a »7-S0 T l r e t a n ! p l a y e d /. J[g .46(6 7? ! M e x i c a n F o l k F a n t a a y I J 7 - 1 6 0 C o r . 11 1 I I I p l a y e d r a t h e r t h a n t s . '.000 80 ' A l c a l a 37-tO C l a v e s p l a y e d X'. J*l/* .4000 81 I O v e r t u r e . I n 8^ 8«-87 T r b . 1 p l a y e d C s r o t h e r t han .4000 87 | A r i a f a r V l n d i 57-60 4 S n a r e 9 r u * | p l i y e d "JJ- . 0 1 0 S3 ' H i c k o r y H l l l a 8 9 - 1 J r i r c o l o \ p t a v e d AS r a i h e r t h a n A' 4000 S i : H i c k o r y H l l l a 1 ( 1 - 1 ( 7 Cy»hal ' playrtl .*n d ' v n h r a t .4900 «5 A r i a f o r U l n d a 13-46 B a a . Ort.n | n l a . e d ^ ) ^ ^ . C0'> 86 P l e a a . i n t V a l l e y 96-101 ; C l a r l n e l 1 ' ol.iv.'.! r n l h e r t han F' . S0 r t? 67 j O v e r t u r e I n B*1 ( 5 - ( S I A. S a . J Plowed T ^ r a l h e r than r * . lO^O SS A r x r l c a n f o l k Rhapsody i '1 1-1 1 I Sn.ire DruP i j M.-vrd J » T . if^ O 278 t t t n C o m p o s i t i o n j Seenant r " Stature o f C r r o r I n s t r u m e n t N a t u r e e f t h e t r r o r D i f f i c u l t y C o e f f i c i e n t 8? H i c k o r y H U i f ? - i : J Trombone I p l a y e d A b r a t h e r t h a n A^ .4000 TO O v e r t u r e In 8° i : - : i Trombone p l a y e d r a t h e r t h a n r- .4100 11 A m e r i c a n F o l k Rhapacdy '1 16C-16J I Oboe F l a y e d r a t h e r t h a n Pr .1351 92 rlr-.tt.tnt V a l l e y 70-74 1 C l a r i n e t I I r l a v c d f S r a t h e r t h a n Tf .3313 • J r i c a a a n t V a l l e y 114-117 » Horn I t p l a v e O F ' r a t h e r that. F*. , 111.1 94 H i c k o r y H l l l a 1 1-16 T t m r a n l p i ayed »-eaa . ^ I n " v a * . T .I'll 93 A l c a l a 1-8 4 T rm-bone 1 p l a y e d r a t h e r t h a n t > . 1)1) 96 The> Dragoon* o f V l l t a r a J8-41 1 n* i * Pl*ved /-•ern . 1111 97 A n e r l c a n F o l k Rhapsody * l 1-4 3 T r o r b o n e 11 p l a v e d fS r a t h e r t h a n t*< . 33)1 98 K e n t u c k y 1S0C i 7 - : o I B a r i t o n e p l a y e d 13 r a t h e r than D . 1 ) 1 1 99 A l c a l a 37-61 Cor. 1 p i t y e d B* r a t h e ; t h a r .1.13' 100 A r i a f o r Wind* 1 - i A l t o 5 a * rl<yed CV r a t h e r than Cf .133) 101 P l e a a a n t V a l l e y 2)-:a * e a r l . Sax F ' r a t h e r than F*< .1)13 102 The Dragoon* o f V I U a r * 43-46 j B a r i t o n e p l a y e d B H r a t h e r t h a n . 3 ) 3 1 101 A r i a f o r Wlnda 1-4 1 C l a r i n e t I p I a y e d r a t h e r t h - r »> . 2666 104 Three Mendelaechn C h o r a l e * 1-4 I A l t e Sax 11 p l a y e d F H r a t h e r t h a n F ' .261* 10* The Dragoon* o f V l l l a r * 38-42 J Trumpet p l a y e d xh jh & .2646 10( A m e r i c a n F o l k r.hapaody *1 9-12 1 Trombone I p l a y e d Ah rfl:h«T tha?. A*| .2666 107 A n e r l c a n F o l k Rhapsody *1 117-127 9 C l a r i n e t I I I P l a y e d «*• rather thar 8* .2666 10C P l e a s a n t V a l l e y 41-46 2 Horn 1 p l a y e d ravhrr than .26»(. 109 H i c k o r y H i l l s 91-84 2 Cor. t Pl.-yed rather than .:«*6 110 A l c a l a 76-81 3 C o r . 1 o l a v e d T> rather than . r*6f 111 K e n t u c k y 16.00 3 > ) 7 1 j Trombone 111 p l a y e d *\\ r»t:»cr than A^  . T66# 112 P l e a s a n t V a l l e y j 1*4-168 I 4 j Snare Orum p l a y e d i as / ..•6r.6 r Iteat C o m p o s i t i o n Segment r Measure o f t r r o r I I n s t r u m e n t ' N a t u r e of the t r r o r 1 D i f f i c u l t y C o e f f i c i e n t 113 A r i a f o r Wlnda 2-26 4 C l a r i n e t I p l a y e d Ft* r a t h e r t h a n . :oo? 114 A m e r i c a n r.»lk Rhapsody f l 57-60 3 B. T r b . p l a y e d T\ r a t h e r t h a n D© .:ooo 113 H i c k o r y H i l l s 45-50 6 Horn 1 p l a y e d Cf r a t h e r t h a n c\ .2000 116 T o c c a t a f o r Band 73-7* 1 Horn t p l a y e d C*l r a t h e r t h a n P .2000 117 T h r e e M e n d e l t e o h n C h o r a l e * 32-36 3 Tuba p l a y e d A B r a t h e r t h a n .1333 118 A l c a l a 82-83 3 Snare Dr-rn p l a y e d J J J r a t h e r t h a n J J / .1333 119 A l c a l a 72-76 4 B a r i t o n e M a y e d J j j r a t h e r -San^JJjJ .13)3 120 A l c a l a 26-29 I A. Sax 11 p l a y e d r a t h e r t h a n F< .11)3 121 A l c a l a 5 1 - 5 * J F l u t e I p l a y e d A* r a t h e r t h a n A H .1111 122 Monte V l s t * 14-17 Horn* p l a e e d JJJ .1311 121 A l c a l a 31-36 4 Bass p l a y e d t b r a t h e r t h a n t\ .0600 124 A n e r l c a n F o l k Rhapsody # 1 3-8 2 F l u t e p l a y e d t S r a t h e r t h a n t\ .06 JO 12} M e x i c a n F o l k F a n t a s y 179-162 1 C o r . 1 p l a y e d r a t h e r t h a n tS .06 00 126 A r i a f o r V l n d a 13-16 3 Horn I I p l a y e d TS r a t h e r t h a n ft .0600 127 P l e a a a n t V a l l e y 70- 74 1 A. Sax 1 p l a y e d C*, r a t h e r t h a n C* .0600 128 A l e x i a 57-70 3 B. Sax p l a y e d t * l r a t h e r :han 3* .0600 129 T o c c a t a f o r Band 34-17 3 T r o r b c n * 1 n l a y e d 8** r a t h e r t h a n tS .0000 130 I l o n t e V l a t * 10-13 2 Tubs p l a y e d J3 aa .0000 131 A l c a l a 1-4 1 A. Sax ! p l a y e d f r a t h e r t h a n F H .Of 00 132 T o c c a t a f o r Band 171-174 1 Tlejpant | p l a y e d a-d-a r a t h e r t h a n d-a-d .0000 133 I l e a l can F o l k r a r t t a e y 191-1P4 2 B a r i t o n e j p l a y e d £** r a t h e r t h a n C*l .0000 134 K e n t u c k y 1600 98-101 4 Snare T r u e [ e t o p p e d one f-eae. e a r l y • 0000 135 O v e r t u r e I n 6^ 154-157 1 T i m p a n i plav*»d A-0 r a t h e r t h a n IVA i I .0000 279 TABLE TWO CLASSIFICATION OF PITCH AMD RHYTHM ERRORS PITCH ERRORS Iristnjnent Part Piccolo Flute Clarinet II I I III I I I II II III I III II I Item Type of Error  Nuriber 36 47 74 83 13 23 19 46 71 121 73 124 35 39 103 41 86 92 43 59 62 107 64 113 Played A f l a t rather than A natural ti it it •• II •• ti Played A natural rather than A f l a t Played D natural rather than D f l a t it ti it ti tt •• •• Played A f l a t rather than A natural ti it it it ti it it Played A natural rather than A f l a t Played E f l a t rather than E natural Played B f l a t rather than B natural D i f f i c u l t y Coefficient .6666 .6000 .4666 .4000 .8666 .8000 .8000 .6000 .4666 .1333 .4666 .0600 Played F natural rather than F sharp it it ti it it ti Played Played Played Played II E natural rather than E f l a t C on second sixteenth note B natural rather than B f l a t •t ti ti it •• it F sharp rather than F natural ,6666 .6666 .2666 .6000 .4000 .3333 .6000 .5333 .5333 .2666 .5333 .2000 Oboe 21 Played A natural rather than A f l a t .8000 26 •t •• ti it it ti it .7333 53 Played B f l a t rather than B natural .6000 91 Played D natural rather than D f l a t .3333 Bassoon 54 Played D f l a t rather than D natural .6000 280 PITCH ERRORS Saxophone A. Cornet Trunpet Horn Part Item Type of Error D i f f i c u l t y Nunber Coefficient 20 Played F sharp rather than A natural .8000 A. I 131 it II tt it tt ti ti .0000 B. 101 II I I it it it it II .3333 T. 44 Played F natural rather than F sharp .6000 A. I 65 •i ti II •t it it it .4666 A. 68 II it ti it it ii tt .4666 A. 75 ti it ti it ti it •• .4666 A. 87 II •• tt tt tt ti ti .4000 A. II 104 II ti it it it ti tt .2666 A. II 120 it tt tt tt ti it it .1333 A. 100 Played G natural rather than G sharp .3333 A. I 127 II it I I ti it it it .0600 B. 128 Played B natural rather than B f l a t .0600 12 Played C natural rather than C sharp .8666 II 16 Played B f l a t rather than B natural .8666 I 55 •i it it it it tt it .5333 I 56 •t tt tt tt tt it it .5333 I 69 •• tt ti ti tt ti it .4666 I 70 II tt ti it tt it it .4666 I 99 I I tt •t •i tt ti ti .3333 I 28 Played F sharp rather than F natural .7333 I 30 Played E rather than G .7333 I 45 Played F natural rather than F sharp .6000 III 72 I I ti it it it it it .4666 I 109 Played B natural rather than B f l a t .2666 II&III 79 Played E natural rather than E f l a t .4000 I 110 it •t it it it it •• .2666 1 125 Played E f l a t rather than E natural .0600 I 61 Played B f l a t rather than B natural .5333 II or IV 15 Played B f l a t rather than B natural .8666 II 77 II it •t •t II tt ti .4666 I 33 Played A f l a t rather than A natural .6666 34 Played F natural rather than F sharp .6666 II 126 I I tt it it it tt it .0600 II 93 Played F sharp rather than F natural .3333 I 108 Played B natural rather than B f l a t .2666 I 115 Played C sharp rather than C natural .2000 I 116 Played C rather than D .2000 281. PITCH ERRORS Instrument Part Item Type of Error D i f f i c u l t y Trcnibane Baritone Tuba Number Coefficient I & II 27 Played D natural rather than D f l a t .7333 B. 114 it it •t it it it it .2000 I l l 32 Played E f l a t rather than E natural .7333 III 49 tt tt tt tt ti ti tt .6000 I 81 it II it ti II tt II .4000 I 95 it ti •t it ti it II .3333 II 97 •i II II it II it tt .3333 I 42 Played A f l a t rather,than A natural .6000 I 57 it it tt tt II it it .5333 I 89 ti it it tt it tt it .4000 I 106 it ti n tt it ti it .2666 63 Played A natural rather than A f l a t .5333 III 111 ti it II II it •• it .2666 90 Played E f l a t rather than D f l a t .4000 1 129 Played B f l a t rather than B natural .0000 11 Played A f l a t rather than A natural .9333 25 Played E natural rather than E f l a t .8000 37 Played E f l a t rather than E natural .6666 58 it it II it II it II .5333 133 it •t •i it it it it .0000 38 Played A natural rather than A f l a t .6666 60 Played G f l a t rather than G natural .5333 102 Played B natural rather than B f l a t .3333 31 Played A f l a t rather than A natural .7333 117 ti ti tt ti ti it ti .1333 Bass 123 Played E f l a t rather than E natural .0600 282 RHYTHM ERRORS Instrument Part Piccolo Flute Clarinet II Oboe Bassoon Cornet Trtinpet II II II Item  Number 18 48 1 9 50 67 52 76 8 10 40 3 105 Type of Error Played C on fourth count Played t r i p l e t quarter note as eighth-quarter-eighth Played measure as repeated dotted eighth-sixteenth D i f f i c u l t y  Coefficient .8000 .6000 1.0000 Played a half note rather than a quarter note tied to an eighth note 1.0000 Played B natural on fourth count .6000 Played eighth rest-two sixteenths, two eighths, quarter tied to an eighth plus two sixteenths .4666 Played i n 4/4 time .6000 Played F on dc*nibeat .4666 Played eighth note-eighth rest, quarter rest, eighth rest-eighth note 1.0000 Played eighth note as a quarter note on count three 1.0000 Played half note tied to sixteenth plus eighth and sixteenth, sixteenth-eighth-sixteenth .9333 Played half rest, two eighths, quarter rest .6666 Played two eights, two eighths 1.0000 Played repeated t r i p l e t eighth tied to t r i p l e t eighth plus t r i p l e t eighth .2666 283 RHYTHM ERRORS Instrument Part Horn Baritone Tuba Bass Item  Number 17 51 122 24 29 98 119 2 130 96 Type of Error D i f f i c u l t y  Coefficient Played eighth note-eighth rest, quarter rest, eighth rest-eighth note, eighth rest-eighth note .8666 Played on the beat .6000 Played t r i p l e t quarter notes .1333 Played two eighths rather than dotted eighth-sixteenth .8000 Played dotted eighth-sixteenth rather than two eighths .7333 Played dotted quarter-eighth rather than two eighths .3333 Played eighth-quarter-eighth rather than t r i p l e t quarters .1333 Played repeated eighth note-eighth rest 1.0000 Played dotted eighth-sixteenth as two eighths .0000 Played eighth note-eighth rest, quarter rest, eighth rest-eighth note, eighth rest-eighth note .3333 284 RHYTHM ERRORS Instrument Part Snare Drum Claves Cymbal Bass Drum Timpani Item  Number 4 14 66 82 88 112 118 134 80 5 84 85 Type of Error 22 78 94 132 Di f f i cu l ty  Coefficient Played measure omitting rests 1.0000 Played tr ip le t eighths as sixteenth-eighth-sixteenth .8666 Played as a rol led half note .4666 Played as eighth rest, eighth r o l l t ied to quarter note, half rest .4000 Played quarter note, quarter rest, quarter rest .4000 Played half note r o l l as an eighth note r o l l .2666 Played tr ip le t quarters rather than eighth-quarter-eighth .1333 Stopped one measure early .0000 Played eighth note-eighth rest, eighth rest-eighth note, quarter rest, eighth note-eighth rest .4000 Played on second count 1.0000 Played on downbeat .4000 Played quarter rest, quarter note, quarter rest, quarter rest .4000 Played two quarter notes rather than eighth rest-quarter note-eighth note 1.0000 Played on downbeat .8000 Played dotted half r o l l , quarter r o l l t ied to whole note r o l l .4666 Played measure 3 in measure 2 Played A-D-A rather than D-A-D .3333 .0000 285 T A B L E T H R E E ITEMS S E L E C T E D FOR THE NEW T E S T IN ERROR DETECTION 286 PARTIAL COPYRIGHT LICENSE I hereby grant the right to lend my dissertation (the t i t l e of which is shown below) to users of the University of Br i t i sh Columbia Library, and to make single copies only for such users or in response to a request from the l ibrary of any other university or similar inst i tut ion , on i ts behalf or for one of i t s users. I further agree that permission for extensive copying of this dissertation for scholarly purposes may be granted by me or by a member of the University designated by me. It is understood that copying or publication of this dissertation for financial gain shall not be allowed without my written permission. T i t l e of Dissertation ENSEMBLE PITCH AND RHYTHM ERROR DISCRIMINATION:  THE IDENTIFICATION AND SELECTION OF PREDICTORS Author DENNIS RICHARD VINCENT SEPTEMBER 1990 

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