Harmonic Expectation in Twelve-Bar Blues Progressions

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2011

Harmonic Expectation in Twelve-Bar Blues Progressions Bryn Hughes

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THE FLORIDA STATE UNIVERSITY COLLEGE OF MUSIC

HARMONIC EXPECTATION IN TWELVE-BAR BLUES PROGRESSIONS

By BRYN HUGHES

A dissertation submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Summer Semester, 2011

The members of the committee approve the dissertation of Bryn Hughes defended on July 1, 2011.

___________________________________ Nancy Rogers Professor Directing Dissertation ___________________________________ Denise Von Glahn University Representative ___________________________________ Matthew Shaftel Committee Member ___________________________________ Clifton Callender Committee Member

Approved: _____________________________________ Evan Jones, Chair, Department of Music Theory and Composition _____________________________________ Don Gibson, Dean, College of Music

The Graduate School has verified and approved the above-named committee members. ii

To my father, Robert David Moyse, for teaching me about the blues, and to the love of my life, Jillian Bracken. Thanks for believing in me.

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ACKNOWLEDGEMENTS Before thanking anyone in particular, I would like to express my praise for the Florida State University music theory program. The students and faculty provided me with the perfect combination of guidance, enthusiasm, and support to allow me to succeed. My outlook on the field of music theory and on academic life in general was profoundly shaped by my time as a student at FSU. I would like to express my thanks to Richard Parks and Catherine Nolan, both of whom I studied under during my time as a student at the University of Western Ontario and inspired and motivated me to make music theory a career. I would also like to thank Matthew Royal, with whom I had the pleasure of taking a number of classes, including an introduction to the field of music cognition. Matthew Shaftel, Clifton Callender, and Denise Von Glahn each deserve utmost thanks for serving as committee members for this dissertation. I learned a great deal from each of them throughout my time spent on this project and as a student in their classes before it began. To Nancy Rogers, my dissertation advisor, I owe tremendous gratitude. My decision to pursue a music cognition topic was inspired by a doctoral seminar I took with her at the end of my second year of coursework. Among many other things, in that class I learned that designing experiments can be a creative and fundamentally rewarding experience. I am also grateful for her constructive feedback, her relentless attention to detail, and for her keen ability to concisely and elegantly solve problems. With her guidance, I know that this document is as good as it possibly could have been. I would also like to thank her for serving as an extremely helpful career mentor. Richard Parks and Catherine Nolan inspired me to make music theory a career; Nancy has helped make it a reality. I am greatly indebted to Christian Vaccaro, Ben Gaskins, Ben Zendel, and Dominique Vuvan, all of whom were extremely patient and helpful when answering numerous questions about statistics that I posed to them throughout this project. I would also like to extend thanks to Sally Gross and Lauren Smith for their administrative help during my time as a student at FSU, to Rob Bennett and Neil Anderson-Himmelspach

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for their guidance with audio editing software, and to Leah Harrison, for delivering copies of the dissertation to my committee on my behalf. I would be remiss if I didn‘t mention the overwhelming support of my family. My mother, Mair Hughes, my stepfather, John George, and my father, Robert David Moyse, have encouraged my musical endeavors for my entire life, and for that I am endlessly thankful. I would also like to thank Kathy and Doug Bracken for their support, and for welcoming me into their family, crazy academic pursuits and all. Finally, I would like to thank express boundless thanks to my spouse and the love of my life, Jillian Bracken. For her honest criticisms, her infinite support and encouragement, and for her belief in me, I am forever grateful.

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TABLE OF CONTENTS List of Tables ................................................................................................................... ix List of Figures ................................................................................................................ xiii Abstract ......................................................................................................................... xvi CHAPTER ONE: INTRODUCTION ................................................................................. 1 Jimi Hendrix‘s ―Hey Joe‖: Progression or retrogression? ................................ 1 The twelve-bar blues: a case study ................................................................. 2 Which blues?................................................................................................... 3 Prominent features of the twelve-bar blues ..................................................... 3 The V-IV-I debate ........................................................................................... 5 CHAPTER TWO: HARMONIC FUNCTION AND THE ANALYSIS OF ROCK MUSIC .... 7 What is harmonic syntax? ............................................................................... 8 Room-motion theory ........................................................................................ 8 Scale-degree theory ...................................................................................... 12 Function theory ............................................................................................. 14 Theories of voice leading .............................................................................. 18 Summary ....................................................................................................... 19 CHAPTER THREE: HARMONIC FUNCTION AS EXPECTATION ............................... 21 Musical grammar ........................................................................................... 21 Statistical learning ......................................................................................... 24 Schema theory .............................................................................................. 26 Expectation ................................................................................................... 28 Studies of harmonic expectation ................................................................... 33 Expectation and timing .................................................................................. 35 Harmonic expectation in twelve-bar blues progressions ............................... 38 CHAPTER FOUR: THE EFFECT OF STYLE-PRIMING ON HARMONIC EXPECTATION ............................................................................................................. 43 Experiment 1: Task ............................................................................................... 44 Hypotheses ............................................................................................................ 44 Participants ............................................................................................................ 45 Stimuli .................................................................................................................... 45 Equipment.............................................................................................................. 46 Design and Procedure ........................................................................................... 46 Results and Discussion ......................................................................................... 47 Root-motion theory ........................................................................................ 47 Comparison with other quantitative ratings of chord pairs ............................. 48 Chord content ................................................................................................ 51 Phrase openings ........................................................................................... 52 vi

Phrase endings ............................................................................................. 53 Conclusions ........................................................................................................... 54 Summary ....................................................................................................... 56 CHAPTER FIVE: LISTENERS‘ EXPECTATIONS OF THE TIMING OF HARMONIC EVENTS ........................................................................................................................ 57 Experiment 2A: Task ............................................................................................. 57 Hypotheses ............................................................................................................ 58 Participants ............................................................................................................ 58 Stimuli .................................................................................................................... 58 Equipment.............................................................................................................. 59 Design and Procedure ........................................................................................... 59 Results and Discussion ......................................................................................... 60 Experiment 2B: Task ............................................................................................. 62 Hypotheses ............................................................................................................ 62 Participants ............................................................................................................ 62 Stimuli .................................................................................................................... 62 Equipment.............................................................................................................. 62 Design and Procedure ........................................................................................... 63 Results and Discussion ......................................................................................... 63 General Discussion ................................................................................................ 64 Summary ....................................................................................................... 67 CHAPTER SIX: HARMONIC EXPECTATION IN TWELVE-BAR BLUES PROGRESSIONS ......................................................................................................... 68 Experiment 3 Pre-Test ........................................................................................... 69 Pre-Test Task ........................................................................................................ 69 Pre-Test Hypotheses ............................................................................................. 69 Pre-Test Participants ............................................................................................. 70 Pre-Test Stimuli ..................................................................................................... 70 Pre-Test Equipment ............................................................................................... 70 Pre-Test Design and Procedure ............................................................................ 71 Pre-Test Results and Discussion ........................................................................... 71 Experiment 3: Task ................................................................................................ 72 Hypotheses ............................................................................................................ 72 Stimuli .................................................................................................................... 72 Equipment.............................................................................................................. 73 Design and Procedure ........................................................................................... 73 Results and Discussion ......................................................................................... 74 Phrase labels ................................................................................................ 74 The effect of the variable chord on phrase labels .......................................... 75 Chord location ............................................................................................... 76 Which chords prompt listeners to abandon a schema? ................................. 78 Ratings .......................................................................................................... 85 Did variable chord affect rating? .................................................................... 85 vii

Variable chord location .................................................................................. 86 The relationship between Experiment 1 and Experiment 3 ........................... 87 Phrase labels and ratings .............................................................................. 88 Conclusions ........................................................................................................... 91 Summary ....................................................................................................... 93 CHAPTER SEVEN: CONCLUSIONS ............................................................................ 94 Comparison of experimental results with previous research ......................... 94 Opportunities for further research ................................................................. 98 Summary ..................................................................................................... 100 ILLUSTRATIONS ........................................................................................................ 102 APPENDIX A: PROCTOR‘S SCRIPTS AND RESPONSE SHEETS .......................... 200 Experiment 1: Proctor‘s script ..................................................................... 200 Experiment 2: Proctor‘s script ..................................................................... 205 Experiment 3: Proctor‘s script ..................................................................... 209 APPENDIX B: DOCUMENTATION OF APPROVAL BY THE FLORIDA STATE UNIVERSITY HUMAN SUBJECTS COMMITTEE....................................................... 215 APPENDIX C: QUESTION ORDER FOR EXPERIMENTS ......................................... 217 APPENDIX D: EXPERIMENT 1 CHORD SUCCESSION RATINGS ........................... 235 REFERENCES ............................................................................................................ 238 BIOGRAPHICAL SKETCH .......................................................................................... 247

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LIST OF TABLES 4.1

A summary of trials used in Experiment 1 ........................................................ 104

4.2

Main effect of ordered pitch-class intervals (OPCIs) between chord roots on rating (Experiment 1) ........................................................................................ 105

4.3

Mean ratings for data grouped by primary triads used in each succession in Experiment 1 .................................................................................................... 107

4.4

Main effect of primary chord(s) used on rating for data subsets grouped by ordered pitch-class interval (Experiment 1) ...................................................... 109

4.5

Main effect of OPCI on rating for successions that did not include multiple primary triads or multiple primary triad roots (Experiment 1) ............................ 114

4.6

Statistical significance of mean differences between ratings for instances of the same OPCI (Experiment 1)............................................................................... 116

4.7

Mean ratings for chords following the tonic, subdominant, and dominant (Experiment 1) .................................................................................................. 117

4.8

Mean ratings for chords approaching tonic, subdominant, and dominant (Experiment 1) .................................................................................................. 119

4.9

A comparison of ratings for diatonic successions used both in Experiment 1 and Krumhansl 1983 ............................................................................................... 121

4.10

Correlations between the different ratings of two-chord successions listed in Table 4.9 (Experiment 1) .................................................................................. 122

4.11

Correlations between Lerdahl‘s chord distance measurement and mean ratings for all successions used in Experiment 1 .......................................................... 123

4.12

A comparison of mean ratings for diatonic and non-diatonic successions (Experiment 1) .................................................................................................. 124

4.13

A Comparison of mean ratings for diatonic, mixture, and chromatic successions (Experiment 1) .................................................................................................. 126

4.14

A comparison of mean ratings for successions grouped by style and type of succession (diatonic, non-diatonic) (Experiment 1). ......................................... 128

4.15

A comparison of mean ratings for successions grouped by style and type of succession (diatonic, mixture, other chromatic) (Experiment 1) ....................... 130 ix

4.16

The effect of the type of succession (diatonic vs. non-diatonic) on ratings among successions with diatonic chord roots (Experiment 1) ...................................... 132

4.17

A comparison of mean ratings for successions grouped by first chord (Experiment 1) .................................................................................................. 134

4.18

A comparison of means for successions beginning with primary triads (Experiment 1) .................................................................................................. 136

4.19

A comparison of means for successions grouped by closing chord (Experiment 1) .................................................................................................. 138

4.20

A comparison of mean ratings for successions that close with primary triads (Experiment 1) .................................................................................................. 140

6.1

Cross-tabulation of question type (recorded or synthesized) and accuracy (correct or incorrect) for the pre-test (Experiment 3) ......................................... 155

6.2

A cross-tabulation of phrase (beginning, middle, or end) and accuracy (correct or incorrect) for the pre-test (Experiment 3) .......................................................... 156

6.3

A summary of the stimulus groups for the trials used in Experiment 3 ............. 157

6.4

A cross-tabulation of stimulus group and phrase label (Experiment 3) ............. 158

6.5

The p-values of chi-square tests of all pairs of stimulus groups (labeled A through G) (Experiment 3) ............................................................................................. 160

6.6

The p-values of chi-square tests for all pairs of listener-assigned phrase labels within stimulus groups (Experiment 3) .............................................................. 161

6.7

Overall frequency distribution of phrase labels for all variable chords (Experiment 3) ................................................................................................. 162

6.8

The p-values of chi-square tests for all variable chords in stimuli interpreted as either Phrase 2 or Phrase 3 (Experiment 3) ..................................................... 163

6.9

Distribution of phrase labels organized by Chord 1 (Experiment 3) .................. 164

6.10

Distribution of phrase labels organized by Chord 2 (Experiment 3) .................. 165

6.11

Distribution of phrase labels organized by Chord 3 (Experiment 3) .................. 166

6.12

Cross-tabulation of Chord 1 and Phrase Label for Stimulus Group A (Experiment 3) .................................................................................................. 167

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6.13

Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group B (Experiment 3) .................................................................................................. 168

6.14

Cross-Tabulation of Chord 3 and Phrase Label for Stimulus Group C (Experiment 3) .................................................................................................. 169

6.15

Cross-Tabulation of Chord 1 and Phrase Label for Stimulus Group D (Experiment 3) .................................................................................................. 170

6.16

Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group E (Experiment 3) .................................................................................................. 171

6.17

Cross-Tabulation of Chord 3 and Phrase Label for Stimulus Group F (Experiment 3) .................................................................................................. 172

6.18

Cross-Tabulation of Chord 2 and Phrase Label for Stimulus Group G (Experiment 3) .................................................................................................. 173

6.19

Ratings for stimulus groups, categorized by significant mean differences (Experiment 3) .................................................................................................. 178

6.20

Chord successions from Experiment 1 and where they appear in Experiment 3 (located by Stimulus Group) ............................................................................. 179

6.21

Correlations between mean ratings for the I-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession I-* from Experiment 1 .................................................................................................... 180

6.22

Correlations between mean ratings for the IV-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession IV-* from Experiment 1 .................................................................................................... 181

6.23

Correlations between mean ratings for the V-* succession heard in stimulus groups from Experiment 3 and the ratings for the succession V-* from Experiment 1 .................................................................................................... 182

6.24

Correlations between mean ratings for the *-I succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-I from Experiment 1 .................................................................................................... 183

6.25

Correlations between mean ratings for the *-IV succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-IV from Experiment 1 .................................................................................................... 184

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6.26

Correlations between mean ratings for the *-V succession heard in stimulus groups from Experiment 3 and the ratings for the succession *-V from Experiment 1 .................................................................................................... 185

6.27

Mean Ratings for all variable chords in Stimulus Group A, grouped by phrase label response .................................................................................................. 187

6.28

Mean Ratings for all variable chords in Stimulus Group B, grouped by phrase label response .................................................................................................. 189

6.29

Mean Ratings for all variable chords in Stimulus Group C, grouped by phrase label response .................................................................................................. 191

6.30

Mean Ratings for all variable chords in Stimulus Group D, grouped by phrase label response .................................................................................................. 193

6.31

Mean Ratings for all variable chords in Stimulus Group E, grouped by phrase label response .................................................................................................. 195

6.32

Mean Ratings for all variable chords in Stimulus Group F, grouped by phrase label response .................................................................................................. 197

6.33

Mean Ratings for all variable chords in Stimulus Group G, grouped by phrase label response .................................................................................................. 199

C.1

Question order for Experiment 1, Group 1 (Blues) ........................................... 217

C.2

Question order for Experiment 1, Group 2 (Classical) ...................................... 221

C.3

Durations in seconds for trials used in Experiments 2A and 2B ....................... 225

C.4

Question order for Experiment 2A, Group 1 (With Drums) ............................... 226

C.5

Question order for Experiment 2A, Group 2 (Without Drums) .......................... 228

C.6

Question order for Experiment 2B .................................................................... 230

C.7

Question order for Experiment 3....................................................................... 232

D.1

Mean ratings for all successions in Experiment 1 ............................................. 235

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LIST OF FIGURES 1.1

Howlin‘ Wolf/Willie Dixon, ―Little Red Rooster,‖ first verse ................................ 102

2.1

Chord progression for ―(Sittin‘ On) The Dock of the Bay,‖ by Otis Redding ...... 103

4.1

Plot of mean ratings for data grouped by ordered pitch-class interval in Experiment 1 .................................................................................................... 106

4.2

Plot of mean ratings for chord successions in Experiment 1 grouped according to the number and type of primary triads used ..................................................... 108

4.3

Plot of mean ratings for data grouped by root motion by ascending minor second/descending minor seventh (Experiment 1) ........................................... 110

4.4

Plot of mean ratings for data grouped by root motion by ascending perfect fourth/descending perfect fifth (Experiment 1) .................................................. 111

4.5

Plot of mean ratings for data grouped by root motion by ascending perfect fifth/descending perfect fourth (Experiment 1) .................................................. 112

4.6

Plot of mean ratings for data grouped by root motion by ascending minor seventh/descending major second (Experiment 1) ........................................... 113

4.7

Plot of mean ratings for successions that did not include multiple primary triads or multiple primary triad roots, grouped by OPCI (Experiment 1) ......................... 115

4.8

Plots of ratings for chords following the tonic, subdominant, and dominant (Experiment 1) .................................................................................................. 118

4.9

Plots of ratings for chords approaching tonic, subdominant, and dominant (Experiment 1) .................................................................................................. 120

4.10

Plot of mean ratings for diatonic and non-diatonic successions (Experiment 1) .................................................................................................. 125

4.11

Plot of mean ratings for diatonic, mixture, and chromatic successions (Experiment 1) ................................................................................................. 127

4.12

Plot of mean ratings for diatonic and non-diatonic Successions in both blues and classical contexts (Experiment 1) ..................................................................... 129

4.13

Plot of mean ratings for diatonic, mixture, and chromatic successions in both blues and classical contexts (Experiment 1) ..................................................... 131

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4.14

Plot of mean ratings for successions with diatonic chord roots (Experiment 1) .................................................................................................. 133

4.15

Plot of mean ratings for successions grouped by opening chord (Experiment 1) .................................................................................................. 135

4.16

Plot of mean ratings for successions beginning with primary triads in both blues and classical contexts (Experiment 1) .............................................................. 137

4.17

Plot of mean ratings grouped by closing chord (Experiment 1) ........................ 139

4.18

Plot of mean ratings for successions ending with primary triads in both blues and classical contexts (Experiment 1) ..................................................................... 141

5.1

Score of the accompanying drum track used in Experiments 2A and 2B ......... 142

5.2

A summary of stimuli used in Experiments 2A and 2B ..................................... 143

5.3

A plot of mean ratings for IV, bVII, and #IV in all timing conditions (Experiment 2A)................................................................................................ 146

5.4

A plot of mean ratings for typical and atypical timing in all harmonic conditions (Experiment 2A)................................................................................................ 147

5.5

A plot of mean ratings for typical and atypical timing conditions when the data are grouped by contrasting chord (Experiment 2A) .......................................... 148

5.6

A plot of mean ratings for non-tonic chords when the data are grouped by timing (Experiment 2A)................................................................................................ 149

5.7

A plot of mean ratings for non-tonic chords in all timing conditions (Experiment 2B)................................................................................................ 150

5.8

A plot of means for ratings of typical and atypical timing conditions (Experiment 2B)................................................................................................ 151

5.9

A plot of mean ratings for typical and atypical timing when the data are grouped by non-tonic chord (Experiment 2B) ................................................................. 152

5.10

A plot of mean ratings for non-tonic chords when the data are grouped by timing (Experiment 2B)................................................................................................ 153

6.1

The structure of the standard twelve-bar blues and the excerpts from which all stimuli were constructed (Experiment 3) ........................................................... 154

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6.2

A representation of phrase label distribution for each stimulus group (Experiment 3) .................................................................................................. 159

6.3

Mean ratings for variable chords categorized by type: diatonic, mixture, and other chromatic (Experiment 3) ................................................................................. 174

6.4

Mean ratings for variable chords grouped by the ordered pitch-class interval leading into the variable chord (OPCI-to) (Experiment 3) ................................. 175

6.5

Mean ratings for variable chords grouped by the ordered pitch-class interval leading out of the variable chord (OPCI-from) (Experiment 3) .......................... 176

6.6

Mean ratings grouped by Stimulus Group ........................................................ 177

6.7

Means plot for Stimulus Group A, grouped by variable chord .......................... 186

6.8

Means plot for Stimulus Group B, grouped by variable chord .......................... 188

6.9

Means plot for Stimulus Group C, grouped by variable chord .......................... 190

6.10

Means plot for Stimulus Group D, grouped by variable chord .......................... 192

6.11

Means plot for Stimulus Group E, grouped by variable chord .......................... 194

6.12

Means plot for Stimulus Group F, grouped by variable chord ........................... 196

6.13

Means plot for Stimulus Group G, grouped by variable chord .......................... 198

A.1

Response sheet for Experiment 1 .................................................................... 202

A.2

Response sheet for Experiment 2 .................................................................... 207

A.3

Response sheet used for Experiment 3 Pre-Test and Experiment 3 ................ 211

B.1

Informed Consent Form .................................................................................... 215

B.2

IRB Approval Memorandum ............................................................................. 216

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ABSTRACT Music theorists often suggest that harmony in common-practice music is governed by syntax. Cognitive studies have shown that listeners expect chord successions that adhere to syntactical rules pertaining to chord-to-chord connections, metrical placement, and formal organization. There is less agreement among music theorists regarding rules of harmonic syntax in rock music. Some suggest that the syntax is the same for both contexts, while others propose new syntactical rules for rock music. Through three empirical studies, this dissertation addresses listener perception of harmony in rock music and examines the degree to which experimental results support the competing theories of rock harmony. For the purposes of these experiments, the twelve-bar blues scheme — a model that has greatly influenced rock music — serves as a framework for harmonic practice in the rock idiom. The experiments presented in this dissertation define harmonic syntax in terms of expectation. Although all three experiments engage different facets of expectation, they all share certain design features. Foremost is the rating scale response mode, which allows for global judgments of stimuli and addresses expectation by way of misattribution: a positive rating is understood as reflecting a predicted event. Second, because these experiments intend to investigate possible differences in the expectations produced by rock and common-practice music, the stimuli used in each experiment include several features that firmly establish stylistic context. Together, the three studies aim to contribute insight to the growing body of research that addresses the following four broad questions: 1) Does rock music elicit expectations that are different from those held for common-practice music? 2) Do listeners have graded expectations of harmony in rock music? 3) What is the relationship between expectations of temporality and harmony in a rock music context? 4) Does harmony affect expectations of musical form (or vice versa)? The results of all three experiments provide evidence that trained musicians possess specific graded expectations of harmony when engaged with musical stimuli representative of the rock genre. Although many of these expectations align with those already known for common-practice harmony, each experiment revealed subtle but significant discrepancies between expectations for these two genres of music. Experiment 1 showed that listeners are less accepting of out-of-key successions when they are primed by classical style cues than when they are primed by blues/rock cues. When primed by blues/rock cues, listeners rated primary triads equally when initiating or terminating a succession; however, in identical situations primed with classical cues, xvi

listeners showed a preference for tonic and dominant over subdominant harmony. Experiments 2 and 3 showed that listeners have strong and specific expectations of musical phrases within the context of twelve-bar blues schemata. Participants displayed sensitivity to the normative harmonic rhythm and timing in the twelve-bar blues phrase structure (Experiment 2) and largely depended on the normative events of these schemata to orient their listening within the overall twelve-bar form (Experiment 3). Experiment 3 also provided evidence that listeners prefer (presumably because they have stronger expectations for) a four-measure phrase when that phrase conveys a clear orientation within the larger twelve-bar form.

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CHAPTER ONE INTRODUCTION Jimi Hendrix’s “Hey Joe”: Progression or retrogression? The guitar riff that opens Jimi Hendrix‘s recording of the song ―Hey Joe‖ quickly orients the listener within a specific musical environment. The blues-inspired gesture begins on an anacrusis and descends through the minor pentatonic scale from top to bottom, firmly establishing E as a tonal center. E is reconfirmed with the ―bluesy‖ fivenote gesture: 5-b7-5-b7-1 before delving into the verse proper. The song‘s text poses a question of its eponymous character (―Hey Joe, where you goin‘ with that gun in your hand?‖), further rooting itself in a blues-rock setting through the initiation of a stylistically idiomatic poetic device: the presentation of a question that will likely be answered. The song proceeds in four-measure phrases.1 Hendrix delivers the vocal line in a rhythmically casual manner, aligning the climax of the poetic phrase with the arrival of the tonic. While the contour of the vocal line certainly emphasizes the arrival of the Emajor chord in m. 3, an even more salient force driving the music forward in this phrase is the ascending fifths sequence that supports it: |C-G-|D-A-|E---|E---| More broadly, we might represent this progression with Roman numerals as follows: | bVI - bIII - | bVII - IV - | I - - - | I - - - | Such an analysis suggests that this passage is entirely non-functional from the standpoint of common-practice tonality. We might describe this sequence of chords as a ―retrogression‖ or ―non-functional static harmony,‖ yet these descriptions fail to convey

Throughout this dissertation the term ―phrase‖ will be used more liberally than it would when referring exclusively to common-practice music. Rock music does not always employ conventional harmonic cadences to delineate formal units; sections are typically demarcated by some combination of textual, timbral, rhythmic, and metrical emphasis. Harmony often factors into this delineation as well (and is indeed a topic central to this dissertation); however, given that numerous chord combinations could be considered ―cadential‖ in rock music, a harmonic cadence will not be considered a requirement for a formal unit to be called a ―phrase.‖ 1

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the growing sense of expectation that an experienced listener feels as the passage transpires. Ultimately, this brief analysis of ―Hey Joe‖ reveals a seemingly dichotomous pair of perspectives regarding the role of harmonic function in rock music. In its musical context, the chord succession heard in ―Hey Joe‖ truly sounds like a progression with its connotation of perceived forward motion. Yet, through the lens of common-practice tonality, one can only view the succession as non-functional. This analytical conundrum raises the question that will remain central throughout this dissertation: does harmony convey different musical functions in different musical contexts, or does harmony behave in a universally consistent way? The current music-theoretical literature proposes two distinct answers. 1. Harmony is perceived, transformed, and construed in terms of common-practice syntax (Everett 1999 and 2004). 2. The harmonic language of rock abides by its own set of rules which the listener engages when a musical context is established (Moore 1992 and 1995; Stephenson 2002). The twelve-bar blues: a case study This dissertation investigates harmony in a small but important subset of the rock canon: works employing the twelve-bar blues progression. The twelve-bar blues includes several characteristics that make it an attractive target of study. Foremost is that its corpus features a very high degree of stylistic consistency, reducing the number of potential confounding variables in experimental studies. Additionally, as a harmonic formula with tremendous influence throughout the history of rock, the twelve-bar blues offers an opportunity to speculate about harmonic function in a more general sense as it applies to rock music as a whole. Specifically, features such as the V-IV-I chord succession and three-phrase AAB formal structure have each undergone transformations that link the blues to several pop and rock schemata (Headlam 1997; Carter 2005, 108-9; Doll 2007, 152). More generally, the twelve-bar blues provides a practical means for investigating the epistemological foundation of harmonic function. Do the rules of common-practice harmony apply to music outside of its canon, or do they depend upon cultural and/or stylistic context? The twelve-bar blues is an exemplary non-common-practice schema that is ubiquitous throughout North American 2

popular music. Thus, its study offers a unique opportunity for comparison with what we already know about common-practice tonality. It is important to understand the central criteria and common features of the twelve-bar blues, which will serve as the point of departure for later chapters. Which blues? There are certainly numerous features that might influence someone to describe a song as blues, or, more specifically, twelve-bar blues. The standard form rose to prominence in the 1930s as a result of the record industry‘s desire for a polished and consistent musical structure that fit within the three-minute time restriction of the 78 rpm phonodisc (Keil 1966, 55; Springer 1995, 62). While its roots are in blues, the twelve-bar form quickly transcended genre and eventually became an important idiom in blues, jazz, and rock. In its countless guises, the twelve-bar form offers a rich diversity of harmonic realizations across these musical genres. Some researchers have investigated variations of the twelve-bar form in jazz (Steedman 1984; Alper 2005), and several scholars have noted in a general sense that the twelve-bar form has profoundly impacted rock music from the 1950s through the present (Hamm 1979, 396; Covach 2004, 66-67; Stephenson 2002, 103; Carter 2005, 70), but specific relations to the harmonic practices of rock music have been virtually ignored. This project engages the standard twelve-bar form that directly impacted rock music, as can be heard in the music of Buddy Holly, Bill Haley, Elvis Presley, Little Richard, The Beatles, and hundreds of other musicians and bands.2 Prominent features of the twelve-bar blues The twelve-bar blues almost invariably consists of three four-measure phrases, each of which can be divided into two-measure sub-phrases. Phrases often form ―calland-response‖ patterns supported both by the melody and by the text (in the case of a song). The idea of ―call-and-response‖ is also captured within the sub-phrase. For example, in the Howlin‘ Wolf/Willie Dixon song ―Little Red Rooster,‖ each line of text transpires over the first two measures of a phrase (see Figure 1.1). Vocal ―calls‖ are 2

While an examination of the corpus of variations on the twelve-bar blues found in the jazz repertory might provide ample insight into the notion of harmonic function in this context, the stylistic differences between rock and jazz are too great to compare in detail within the scope of this project. In cases where a cross-genre comparison is apt, I will differentiate the two as jazz-blues and blues-rock as appropriate.

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―responded to‖ by instrumental riffs that close the phrase. In addition, each line is divided into two parts, resembling a ―call‖ and ―response.‖ While the twelve-bar structure of ―Little Red Rooster‖ may appear simple, there are a few analytical questions that have caused disagreement among even the most highly-trained music scholars. For instance, where does harmonic closure occur? Which factors influence closure? Which harmonies are functional, and how do they function? Using the text and melody as a guide might lead one to hear cadences in mm. 3, 7, and 11. Measure 11 offers the strongest cadence, owing to the additional closure created by the typical poetic and melodic change of the B section following two repetitions of the A section. This interpretation undermines the role of the instrumental response, essentially relegating it to the status of a post-cadential extension. Support for this reading can be found in the numerous songs that essentially follow the twelvebar form but include extended or truncated phrases (such as Johnny Cash‘s ―Folsom Prison Blues,‖ in which the last phrase of the form is only three measures long). A different interpretation of the twelve-bar form might locate closure in the fourth measure of each phrase. This reading privileges the consistent four-measure hypermeter of the twelve-bar blues, overriding any sense of harmonic closure achieved in mm.1-8. Measures 9-12 prolong dominant harmony, supported through the frequent occurrence of a V chord in m.12, serving as a ―turnaround‖ leading to the repeat of m.1. While temporary closure may occur in m. 11, the consistent repetition of the twelve-bar form overpowers this notion, inciting a strong expectation for each ensuing return to m. 1. Jazz improvisation teachers frequently reinforce this kind of phrasing, suggesting that their students play fluidly through the end of each 12-measure section to ensure a smooth connection with the return of the first phrase. Full closure is not achieved until the end of the song, at which point the dominant ―turnaround‖ is replaced by cadential motion to I (often through a chromatic ascent) in the fourth measure of the last phrase (Stephenson 2002, 62; Carter 2005, 66-70). The analytical issues discussed above can be categorized as location issues. In other words, where do important harmonic events occur? Experiment 2 in Chapter 5 examines the degree to which listeners prefer to hear harmonic events on strong beats, strong hyperbeats, or in specific locations within a twelve-bar blues phrase. Experiment 3 in Chapter 6 engages the question in a larger context, investigating whether listeners associate specific harmonic progressions with certain phrases of the twelve-bar form.

4

The V-IV-I debate The third phrase in a blues progression typically contains the most harmonic activity in the form, and there is widespread agreement that the third phrase provides a local climactic moment within each verse. Which harmonies are functional in the third phrase of a twelve-bar blues? This question resides at the center of nearly every scholarly debate regarding harmonic function in rock music. Several analysts argue that the V chord found in m. 9 is functional: it prepares the return to I in m. 11, and in combination these chords provide the necessary musical gesture to evince closure. The stepwise voice leading and root motion by descending fifth/ascending fourth made possible through the connection of these two chords supports this notion of closure. This interpretation dismisses the IV chord in m. 10 as an incomplete neighboring embellishment of V that softens the resolution to tonic (Covach 2004; Everett 2001, 61; Doll 2007, 151-2). Essentially, this analysis indicates that the harmony in the third phrase of a twelve-bar blues mirrors common practice.3 However, many musicians contend that interpreting V as the functional dominant misappropriates the rules of common-practice harmony. Could we not consider the V chord a neighboring embellishment of the IV chord? The direct resolution of the IV to the I chord also aligns with the cadential goals of the melody and text. Discussing the Beatles‘ song ―You‘ll Be Mine,‖ in which this particular harmonic convention plays an important role, Mark Spicer suggests that V is subservient to the IV chord [which] is ―clearly in the driver‘s seat‖ (Spicer 2005, ¶8). Given that blues emanated from a different musical tradition, is it not plausible that its harmonic events abide by different syntactical rules? Ken Stephenson (2002, 103) goes as far as to assert that this particular cadence represents a ―new harmonic standard for rock music‖ in which root progressions contrary to the idioms of the common practice, such as V-IV, are customary. Each argument has weaknesses. Misappropriation aside, interpreting V as the operative chord suggests a substantial misalignment of the melodic and harmonic components of the cadence. As David Temperley (2007) points out, this may be an instance of melodic and harmonic independence (―the melodic-harmonic divorce‖) 3

Carter 2005 (71) argues that at the background level, V controls the entire harmonic structure of the third phrase. This notion is supported in examples that include a dominant turnaround gesture at the end of phrase 3 (typically in m.12). Furthermore, he asserts that the harmonic trajectory of the twelve-bar form is a large-scale I-IV-V progression that propels the music through the repeat to the beginning of the next verse. Each of these background harmonies serve as goals, supported by their presence on hypermetrical downbeats.

5

commonly found throughout the rock repertory. Nevertheless, several songs utilizing the twelve-bar form exhibit melodies that are supported by the IV chord in m. 10. In these cases, interpreting a misaligned cadence would seem to ignore the obvious stability of the IV chord. Conversely, if the motion from IV to I in mm. 10-11 fulfills the structural requirements of a harmonic cadence, how does one differentiate it from the clearly less important but identical gesture found in mm. 6-7 (or even mm. 2-3, given that IV is commonly found in m. 2)? This interpretation suggests that V is superfluous and could be replaced with another chord.4 Through three empirical studies, this dissertation addresses listener perception of harmony in rock music and examines the degree to which experimental results support the competing theories above. For the purposes of these experiments, the twelve-bar blues scheme — a model that has greatly influenced rock music — will serve as a framework for harmonic practice in the rock idiom. Chapter 2 provides an overview of the preeminent theories of harmonic function pertaining to common-practice tonality and discusses numerous instances in the literature in which these theories have been applied to rock music. Chapter 3 reframes the notion of harmonic function within theories of expectation drawn from cognitive psychology. Following a survey of the relevant music cognition and psychology literature, I outline the methodological framework used for each of the three experiments. Chapter 4 investigates the issue of whether or not musical style affects listeners‘ expectations of two-chord successions. Chapter 5 addresses the issue of timing in harmonic expectation. Building on the foundation laid by the first two experiments, Chapter 6 engages harmonic expectation and how it influences our sense of form. Chapter 7 presents a summary of the conclusions drawn from each of the three experiments, and reflects upon their implications within the fields of music theory, music cognition, and rock music analysis.

4

Of course, in common-practice music, not all V-I progressions are considered authentic cadences. Cadences require a combination of melodic, harmonic, and metrical features to truly communicate a sense of ―closure.‖ In the case of the twelve-bar blues, however, the previously mentioned IV-I progressions all occur in the same metrical location (mm.2-3 of a four-bar phrase), and often support similarly constructed melodic lines.

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CHAPTER TWO HARMONIC FUNCTION AND THE ANALYSIS OF ROCK MUSIC As Walter Everett (2004) has shown, popular music from the last fifty years displays a wide range of harmonic tendencies. Amidst this diversity, Everett nevertheless asserts that ―the tonal norms basic to the pop music from which rock emerged are the same norms common to the system of common-practice tonality‖ (Everett 2004, ¶3). Indeed, much of Everett‘s analytical work is grounded in Schenkerian practice and unsurprisingly reflects this assertion. 5 In some cases, Everett expands his conception of harmonic function to include a greater variety of chords within common-practice functional categories.6 Most times, however, Everett considers non-common-practice harmonic successions to be byproducts of voice leading or instances of non-functionality. For example, Everett remarks that the dominant harmony in the traditional V-IV-I twelve-bar blues cadence is ―mitigated by an intervening subdominant, which ... has no harmonic value but merely softens the resolution to tonic with its contrapuntal stepwise descent‖ (Everett 2004, ¶18). Importantly, Everett dismisses theories of ―retrogressive‖ harmonic function as ―…discredited concepts [that] leave unconsidered the ramifications of voice leading upon chord identity, function, embellishment, and harmonic expansion‖ (Everett 2004, ¶2 footnote). Several authors have stated opposing views. Most adamant among them is Ken Stephenson, who proposes that the harmonic language of rock music is ―diametrically opposed‖ to the common practice, citing the V-IV-I cadence in particular as an exemplar of this standard (Stephenson 2002, 103-104). He suggests that in blues, and to a greater extent rock music, harmonic progression is created through chord-root motion by descending second, ascending third, and descending fourth—in other words, root motion contrary to the tonal norms of the common practice. Setting aside their differing opinions and methodologies, both Everett and Stephenson imply that listeners—at least those who are highly trained—possess specific expectations of harmonic succession in rock music. In other words, both Everett and Stephenson believe that harmonic function exists in some capacity in rock This is best illustrated in Everett‘s monumental two-volume book The Beatles as Musicians (1999), which teems with analyses clearly inspired by Schenkerian theory.

5

6

See the appendix in Everett 1999 (309-313), for example.

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music. In contrast, a skeptic might suggest that the harmonic practice of rock music is not at all governed by syntax. Before sorting out the differences between harmonic practices in rock and common-practice music, it is necessary for us to consider exactly what is meant by ―harmonic syntax.‖ What is harmonic syntax? Principles of harmonic syntax have been presented from various perspectives by numerous authors throughout the history of music theory. Regarding the music of the common practice, four perspectives on harmonic syntax stand out in the literature: rootmotion theory, scale-degree theory, function theory, and voice-leading theory. In order to provide context for later discussions of harmonic theory in rock music, each of these approaches is briefly summarized below. Root-motion theory Rameau‘s Traité de l’harmonie (1722/1971) was the first of many theoretical works to propose that syntactical chord progressions are the result of an appropriate succession of fundamental bass notes, or chord roots. Simply put, Rameau‘s theory states that chord roots should progress by certain intervals: the descending fifth, descending third, and ascending second (in order of preference). Root motion by ascending fifth, third, or descending second is increasingly undesirable, with the last expressly forbidden by Rameau (Lester 2002, 766-8). Nicholas Meeùs (2002) connects Rameau‘s work with the theoretical writings of Arnold Schoenberg (1954/1969) and Yizhak Sadai (1980), both of whom similarly categorize chord progressions according to root motion. Meeùs simplifies the ideas posed by these authors and presents them as two categories: ―dominant‖ progressions typified by descending-fifth root motion, and ―subdominant‖ progressions typified by ascending-fifth root motion. Meeùs allows descending-third and ascending-second progressions to ―substitute‖ for descending-fifth progressions. Likewise, he allows ascending-third and descending-second progressions to substitute for ascending-fifth progressions (Meeùs 2000, ¶7). He rationalizes third substitutions by identifying the parsimonious voice-leading connection between chords with roots a third apart (Meeùs 2000, ¶6). For instance, the progression I-vi is an acceptable substitute for the stronger descending-fifth progression iii-vi, since I and iii share and can be connected by efficient voice leading. He justifies the second type of substitution (root motion by 8

second) by invoking Rameau‘s double emploi. For Meeùs (and Rameau), progressions by ascending second are understood as instances of harmonic elision. For example, the progression IV-V is considered an elision of the progressions IV-ii (a third substitute) and ii-V (a descending-fifth progression). As Dmitri Tymoczko (2003) points out, implicit to the theory of root motion is the notion that all diatonic harmonies participate equally in the same set of allowable root motions (Tymoczko 2003, 3). Tymoczko finds this problematic because such theories fail to account for the fact that ―normal tonal phrases tend to begin and end with the tonic chord‖ (Tymoczko 2003, 5). Indeed, Rameau‘s and Meeùs‘s theories only withstand collapse when the status of the V-I progression is elevated among other descending-fifth progressions, a point which Rameau justifies through a supplemental discussion of its characteristic voice leading (Tymoczko 2003, 3). Likewise, a pure root-motion theory lacks the discretion necessary to subvert uncommon progressions such as V-iii-I, ii-iii-I, and viio-iii-I (Tymoczko 2003, 5). Tymoczko rectifies this flaw with a caveat requiring progressions to begin and end on tonic, and he removes the anomalous iii chord altogether.7 Through a statistical analysis of several tonal Bach chorales and modal Palestrina mass movements, Tymoczko confirms that dominant progressions (as defined by Meeùs) are more typical of tonal music than are subdominant progressions. By contrast, modal music (such as the Palestrina movements) is characterized equally by dominant and subdominant harmonic motions (Tymoczko 2003, 9-10). To some extent, Tymoczko‘s survey supports Meeùs‘s original claim that common-practice harmonic syntax originated from a growing preference among composers for dominant progressions (Meeùs 2000, ¶17). 8 A handful of contemporary music theorists have used principles of root motion to describe harmonic function in rock music. Interestingly, a few of the criticisms aimed at root-motion theory are less problematic when engaging rock music. When arguing about the fundamental differences between common-practice and rock music, Allan Moore (1992) states that common-practice harmony is ―linear‖ while rock harmony is ―cyclic‖ (Moore 1992, 74). By ―linear,‖ Moore means ―goal-oriented‖ in the sense that 7

However, Tymoczko does allow the mediant triad to be used as part of an elision (Tymoczko 2003, 6).

Tymoczko‘s data reveal three exceptions to Meeùs‘s assertion that well-formed progressions consist entirely of dominant progressions: I-V, IV-I, and V-IV6 (essentially a substitute progression for the more common V-vi). Together, these three progressions account for 87% of subdominant progressions found in Tymoczko‘s data. Although Tymoczko uses these examples as a means of questioning the theoretical completeness of Meeùs‘s work, he admits that, in a general sense, there is ―something right‖ about Meeùs‘s theory regarding the prevalence of dominant progressions in tonal music and the freedom with which tonal composers use them (Tymoczko 2003, 10).

8

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common-practice phrases tend to convey a sense of motion toward the harmonic terminus of the phrase (usually tonic). As Tymoczko mentions, root-motion theories are less convincing for tonal music because they necessitate the use of a caveat: phrases must end (and usually begin) on tonic harmony. Rock music, on the other hand, tends to be ―cyclical,‖ in the sense that formal sections (or sometimes entire songs) are structured in small repeated units of four or eight measures (or occasionally two measures).9 Since these sections repeat frequently throughout a song, it is less likely that listeners will hear the ends of sections as harmonic goals. Moreover, the identification of tonic is often determined by rhythmic, metrical, or durational emphasis, instead of information gleaned from the operating pitch collection (Moore 1992, 77). Since tonic harmony seems to hold a less prominent (often even ambiguous) place in rock, the restrictions it places upon a root-motion theory of harmonic progression are much less relevant. Chord progressions are more likely to be governed by principles pertaining only to immediately contiguous chords. Thus, in the context of rock music, the use of a root-motion theory may be apt when describing principles of harmonic succession. While Moore poses a convincing argument for using root-motion theory as a guiding principle of rock harmony, he fails to provide a specific description of how such a system would work. He alludes to the lack of tension and release in rock music (an oft-used description of common-practice harmonic function) and how that is represented by rock‘s preponderance of ―flatwise‖ harmonic motion (Moore 1992, 80); presumably Moore refers to ascending-fifth progressions from the flat-inflected circle of fifths, such as bVII-IV-I, which occur frequently in rock music.10 Moore continues by suggesting that many rock sequences could be formed ―from fifth cycles by … substitution of modal-mediant-related chords and elisions of consecutive cyclic steps‖ (Moore 1992, 80). This description neatly coincides with Nicholas Meeùs‘s rules for subdominant progressions. Incidentally, Meeùs‘s speculation that subdominant progressions might be better suited to modal music than to tonal music aligns with Moore‘s claim that rock‘s musical language is primarily a modal one as opposed to a tonal one (Moore 1992, 76). Several other authors purport that the cyclic nature of rock‘s formal units nullifies any sense of direction in its harmonic progressions. In his book What to Listen for in Rock, Ken Stephenson posits that most phrases in rock music end with 9

Moore (1992) calls these ―patterns‖ (77).

Everett (1999, 312) calls this particular progression ―rock defining.‖ Carter (2005, 139) calls it a ―staple of the repertoire.‖ 10

10

harmonically-open gestures that lack the ability to signify the end of a formal unit or song (Stephenson 2002, 70).11 Due to this avoidance of harmonic closure, Stephenson recommends identifying chord successions rather than chord progressions (69). Similarly, Alf Björnberg speculates that chord successions are used as ―harmonic ostinati‖ that are repeated to create a ―harmonic field‖ within which melodic improvisations may freely operate (Björnberg 1989/2001, ¶4). Björnberg argues that these ostinati ―lack the forward-directed teleological character of tension-resolution [in] progressions of common-practice harmony‖ (Björnberg 1989/2001, ¶14). Philip Tagg takes a clearer stance, suggesting that ―guitar-based harmony‖ serves ―neither to provide long-term harmonic direction nor to construct musical narrative but rather to provide a fitting tonal dimension to underlying patterns of rhythm, meter, and periodicity … [and] to generate an immediate sense of ongoing tonal movement‖ (Tagg 2003, 13-14; emphasis mine).12 While some scholars (Everett 2004, Doll 2007) claim that harmonic function is generated by an expected stepwise resolution of specific chord members, Stephenson argues that tendency tones have little influence upon listeners‘ expectations of that chord‘s harmonic target. He refers specifically to secondary dominant chords in this regard. For instance, Stephenson claims that V/V is ―seldom followed by V‖ in rock music (Stephenson 2002, 114). He cites several compelling examples in support of this claim. The Beatles‘ ―Eight Days A Week‖ features a V/V that moves up by minor third to IV. In the Byrds‘ ―I‘ll Feel A Whole Lot Better,‖ V/V moves directly to the tonic. ―Bad, Bad Leroy Brown‖ by Jim Croce includes a V/V that moves to V/vi. According to Stephenson, most other secondary dominants found in rock music behave in a similarly erratic fashion. His culminating example, ―(Sittin‘ On) The Dock of the Bay‖ by Otis Redding, includes several non-traditional uses of secondary dominants (see Figure 2.1). Stephenson‘s examples show that chromatically altered chords such as secondary dominants do not resolve in a consistent way throughout the rock repertoire. Stephenson‘s argument inherently makes a good case for root-motion theory, in which predictions are unaffected by the quality of the chords in question. Even though its #5 does not resolve to the root of the following chord, V/vi-IV is an ascending-second progression that is no more anomalous than its diatonic counterpart iii-IV. Simply put, if 11

Presumably, closure and formal delineation are created through other musical means.

12

Some authors, such as Björnberg, propose (perhaps inadvertently) that harmonic function does not exist in rock music. Instead, sections of music are defined by particular chord progressions, but the transitions between chords within those sections are not governed by any specific set of principles and do not incite any particular expectations of listeners beyond the maintenance of an established pattern.

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two chords have the same root, Stephenson‘s theory predicts that they will behave in the same way. Like Stephenson, Paul Carter (2005) presents a theory of ―pop-rock‖ harmony founded upon fundamental bass lines. Carter differentiates progressive from retrogressive motion and suggests that their combination characterizes harmonic practice in pop-rock music.13 Carter‘s definition of progression aligns with Meeùs‘s and Rameau‘s, but Carter assigns numbers to root motions representing their predictability: P3 for descending fifth, P2 for descending third, and P1 for ascending second. Following Stephenson, Carter proposes that retrogression is commonplace in pop-rock music and is defined by root motions complementary to those used in progressions. Appropriately, Carter also quantifies the predictability of retrogressive motions: R3 for ascending fifth, R2 for ascending third, and R1 for descending second. Thus, chains of chord roots ascending or descending by fourth would yield the most predictable successions, while chains of roots ascending or descending by second would result in unpredictable successions. Overall, root-motion theory is more robust when applied to rock music. The theory‘s central premise—that listeners privilege chord roots over the voice leading of individual parts when hearing harmonic progressions—is strongly supported by the preponderance of root-position triads and parallel voice leading in guitar-based repertoire. As Stephenson‘s examples suggest, the strength of our preference for hearing chord roots even seems to outweigh the presence of secondary leading tones. While its simplicity may not allow for particularly compelling or descriptive analyses, it presents a viable option for explaining our perception of harmonic successions in rock music. Scale-degree theory Scale-degree theory was established by Georg Vogler (1749-1814) and Gottfried Weber (1779-1839) in the early nineteenth century. In their respective theoretical works, Vogler and Weber each ascribed Roman numerals to chords built upon members of the diatonic scale (Bernstein 2002, 779-88). Simon Sechter applied the nomenclature put forth by Vogler and Weber to Rameauvian fundamental bass theory (Bernstein 2002, 788-9). This theoretical infusion made explicit the notion that diatonic Carter (2005) refers to retrogressive motion as ―regressive‖ motion—he uses the terms interchangeably (1). For the sake of clarity, I will only refer to ―retrogressive‖ motion when discussing Carter‘s work.

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chords are arranged hierarchically, and that each chord in the system has its own characteristic behavior. Sechter‘s writings laid the foundation for twentieth-century harmony treatises by Schoenberg, Schenker, and others (Bernstein 2002, 788-9). In contemporary theory textbooks, the tendencies of chords built upon specific scale degrees are often summarized by charts that reveal subtleties simple root-motion theory cannot; for instance, I-V is an acceptable ascending-fifth progression while V-ii is not. Dmitri Tymoczko likens these chord progression charts to first-order Markov models, which, in probability theory, describe the ―probability of transitions from one ‗state‘ of a system to another‖ (Tymoczko 2003, 13).14 Tymoczko provides a ―rational reconstruction‖ of scale-degree theory that consists of a set of probabilities representing the likelihood that any single diatonic chord will move to any other. He obtains his probabilities through a statistical analysis of the Bach chorales, and his results largely support the principles of elementary diatonic harmony (Tymoczko 2003, 15).15 With a few exceptions, random progressions generated by the model emulate those found in Bach‘s chorales. While more discriminating than root-motion theory, Tymoczko‘s model is not flawless. As he admits, the model is prone to generating unstylistic progressions such as I-vi-V-vi-V-vi-V-I. In this example, the presence of a single deceptive resolution is unaffected by any immediately preceding deceptive resolutions. We might describe this theory as having no memory: the probabilities of future events are independent of past events.16 Similarly, location-specific progressions such as IV-I are also susceptible to misrepresentation by the model. Generated progressions are as likely to include IV-I at a phrase‘s beginning as at its end. Tymoczko posits that a potential solution would be to add additional states to the model that would account for these and other irregularities (such as idiomatic progressions that are inversion-specific or grammatically unorthodox). Of course, the constant addition of new states to the system complicates the model. Moreover, Tymoczko fails to acknowledge the possibility that harmonic syntax is linked to independent expectations of timing and location. Such factors deserve considerable thought and exceed the explanatory power of a pure scale-degree theory.

14

When applied to harmonic theory, we can interpret ―state‖ to mean ―chord.‖

One might choose to criticize Tymoczko‘s conclusions, since his statistics are drawn from a single musical source.

15

16

This is true of all first-order Markov models.

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To my knowledge, there has been no attempt at a formal and exhaustive scale-degree-theoretical approach to harmony in rock music. One issue (among many) is that stylistically-consistent investigations, such as Tymoczko‘s statistical survey of the Bach chorales, are almost impossible when virtually no two scholars agree on a corpus that codifies ―standard rock harmony‖ similar to the way that Bach‘s chorales represent ―standard diatonic harmony.‖ Walter Everett‘s work on the music of the Beatles includes a table of chord tendencies as they appear throughout The Beatles‘ catalog (Everett 1999, 309-13). In his 2004 article, Everett begins the requisite legwork for a more generalized theory of rock harmony, suggesting six categories for rock music based upon the degree to which a song displays the norms of tonal harmony. David Temperley and Trevor De Clercq‘s (2011) recently published corpus analysis of rock harmony provides statistical analyses of harmonic progressions used in 100 rock songs. Temperely and De Clercq‘s findings suggest that rock‘s harmonic profile differs somewhat from common-practice music; however, the authors admit that the relatively narrow corpus chosen for study may not be entirely representative of rock music as a whole (Temperley and De Clercq 2011, 69). More generalized theories, such as rootmotion theories and function theories, are therefore currently preferred for approaching rock‘s idiosyncratic harmonic language. Function theory Originally developed by Hugo Riemann (Bernstein 2002, 796), function theory proposes harmonic categories by grouping chords that, while literally constructed of different notes, sound and behave alike (Harrison 1994, 37). Specifically, Riemann‘s three functional categories were defined by the three primary triads: tonic, subdominant, and dominant. Each category was filled out with diatonic chords that shared two common tones with its constituent primary triad.17 While the chords consist of distinct elements, the ―sense of function [that] they communicate is identical‖ (Harrison 1994, 38). As Daniel Harrison explains, function is not something tangible, but rather the ―result of perceptual judgment on the part of the listener in response to hearing chords‖ (Harrison 1994, 38). Importantly, function is a musical phenomenon entirely dependent upon context: it is meaningless without an established tonal center (Harrison 1994, 37). Typically, functional groups must proceed from subdominant to dominant to tonic. The identification of patterns of functional progression, resulting in 17

Agmon (1995) calls this ―a prototype-theoretic account of harmonic functions‖ (199).

14

the codification of permissible successions, occurred independently in the development of the theory (Tymoczko 2003, 18). The grounds for categorical inclusion in most interpretations of Riemannian function theory are based upon the idea that members of the same category exhibit a certain degree of aural similarity. While this definition allows for a relatively clear rubric for inclusion, it inappropriately equates normative progressions with problematic ones (for instance, ii-iii-I vs. IV-V-I.) An alternative perspective, as Tymoczko points out, would be to group chords according to their most typical targets of resolution. In his reconstruction of function theory, Tymoczko defines categories by again observing the statistical frequency of two-chord diatonic successions in Bach‘s chorales. For each diatonic chord, Tymoczko supplies a vector of six probabilities that represent the likelihood of that chord moving to any of the remaining diatonic chords. He creates functional categories through a simple comparison of the probability vectors: if two chords‘ vectors show a strong correlation, Tymoczko deems them members of the same functional group (Tymoczko 2003, 19). While Tymoczko‘s groups avoid the problems encountered in a pure function theory, they also have deficiencies—most notably their inability to deal with chords such as IV that commonly serve multiple harmonic roles. In Bach‘s chorales, IV has a tendency to proceed either to I (as part of a plagal motion) or to V (as a pre-dominant harmony). Its probability vector therefore does not strongly correlate with that of the ii chord, which does not share the same plagal tendencies. Tymoczko‘s solution is to define two types of IV chords: those that serve a plagal role and those that serve a predominant function. Logically, this results in a strong correlation between the vectors of pre-dominant IV chords and ii chords. To some degree, however, Tymoczko is begging the question: he has parsed the probability vector until it resembles something suitable for a pre-dominant chord because he knows that IV should be pre-dominant. Moreover, the addition of exceptional cases for inclusion into functional groups, such as predominant IV and plagal IV, renders the groups less robust and weakens their explanatory power. Seen in this light, Tymoczko‘s perspective of function as categories of chords that share the same harmonic targets is merely a simplification of his reconstructed scale-degree theory.18 Consequently, one could direct the same criticisms of scale-degree theory, discussed above, toward Tymoczko‘s reconstructed function theory.

18

Tymoczko freely concedes this point in his article (22).

15

In his book Harmonic Function in Chromatic Music (1994), Daniel Harrison presents an interpretation of function theory that accounts for the sometimes dual nature of chords‘ functional allegiances. Harrison writes that ―harmonic function might be not the property of the chordal community as a whole but rather that of the individual constituents of that community‖ (Harrison 1994, 43) – in other words, harmonic function is conveyed by scale degrees rather than by chords. For example, the supertonic chord contains two subdominant scale degrees, 4 and 6, that assign it a relatively strong subdominant function. This is especially useful for functionally ambiguous chords such as the submediant and mediant triads, as well as the numerous chromatic chords on which Harrison focuses, such as augmented-sixth chords. Christopher Doll‘s theory of rock harmony borrows heavily from function theory. Like Harrison, Doll posits that scale degrees, not chords, are the purveyors of harmonic function. Although he acknowledges that the predictive strength of a chord is undeniably tied to numerous musical details, Doll‘s theory ascribes function according to abstract voice leading in scale-degree space (Doll 2007, 17). Most of Doll‘s analyses are based on the voice-leading potential projected by the scale-degree content of successive chords, which often goes unrealized on the musical surface. Doll‘s use of abstract voice-leading allows him to account for the idiomatic parallel motion used to connect chords in guitar-based music. Thus, Doll‘s theory is more akin to Harrison‘s work than to the Schenker-inspired analyses of Walter Everett (1999 and 2004), Lori Burns (2000), and others. Doll applies function theory idiosyncratically, suggesting new roles for functional categories, as well as presenting them hierarchically. To Doll, dominant, subdominant, and mediant chords predict tonic chords, and are thus each captured in a higher-level general category called pre-tonic function. Likewise, pre-subdominant, pre-dominant, and pre-mediant chords predict subdominant, dominant, and mediant chords, respectively. Doll permits a chord‘s membership in a functional category based upon its potential for stepwise resolutions of particular scale degrees. For instance, the motion from 6-5 corresponds to a chord with subdominant function resolving to tonic, while the combined motions of 7-1 and 2-1 or 2-3 correspond to a chord with dominant function resolving to tonic. A chord with mediant function resolves to tonic with the resolution of 7-1 (but not 2-1 or 2-3). Finally, the adjectives authentic, plagal, and mediant are applied to progressions in which the resolutions of chord members emulate his subdominant, dominant, and mediant functions but resolve to non-tonic chords. For example, using Doll‘s terms, an authentic pre-dominant includes the same pair of ascending and descending steps to the root and third as a dominant to tonic progression, but it moves 16

to a dominant chord instead of a tonic. Likewise, a plagal pre-dominant features the same descending step to the fifth of the chord found in subdominant to tonic progressions. Recognizing the ubiquitous b7-1 voice leading heard throughout the rock repertoire, Doll allows the pattern to be included in progressions identified as having dominant function. He calls these rogue dominants to distinguish them from tonal dominants which feature the leading-tone. Similarly, Doll allows b3-1 to substitute for 2-1 in songs that feature harmony drawn exclusively from the minor pentatonic scale. For example, the progression D7-B7 is a rogue dominant progression because its b3 (D) predicts a fall to 1 (B) while its b7 (A) predicts an ascent to 1 (B) (Doll 2007, 24-25).19 The flexibility of Doll‘s theory is enticing: it allows for non-common-practice progressions to attain functional status rather than being cast aside as retrogressions. Nevertheless, Doll doesn‘t simply suggest that every chord has functional value. Indeed, he describes chords with a ―non-predictive‖ character as neighboring or passing (and thus non-functional). He views retrogression as the delay or softening of a particular progression by an intervening non-functional chord (Doll 2007, 39-41). Depending on the musical situation, the same chords may be assigned different functions. For example, the succession IV-bVII-I could be interpreted authentic predominant, dominant, and tonic. In a different musical situation, the bVII chord could be heard as ornamental within a retrogression: subdominant, non-functional lower neighbor, tonic. Obviously context is highly important when determining harmonic function in Doll‘s system.20 Scale-degree and function theories are philosophically different from root-motion theories because they ascribe agency to chords rather than to root relationships. These theories are therefore more discriminating than are root-motion theories: they are able to recognize important differences between successions that have otherwise identical root relationships.21 Scale-degree and function theories are also much more descriptive than root-motion theories, potentially making them more useful for music analysis.

19

Evidently Doll considers only chord roots when defining exclusively minor pentatonic space. Otherwise, the D# in the B major-minor seventh chord would contradict his categorization of this example. Furthermore, Doll provides no opinion of the seemingly more intuitive voice leading which would maintain A as a common tone between the two chords. 20

Like Walter Everett (2004), Doll develops his theory thorough analysis of numerous musical examples. Similar to Everett‘s work, Doll‘s work may be best interpreted as a ―developing theory,‖ as he does not provide distinct guidelines for determining a chord‘s function. 21

For instance, scale-degree and function theories do not equate I-V with V-ii, discussed previously.

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Theories of voice leading Several scholars have applied techniques drawn from Schenkerian theory to the analysis of rock music.22 Chief among them is Walter Everett, who claims that harmony in most rock music features an underlying tonal hierarchy that is embellished through voice-leading patterns, which he often reveals through Schenkerian analyses (Everett 2004, ¶6). In his 2004 article ―Making Sense of Rock‘s Tonal Systems,‖ Everett divides the corpus of rock music from the early 1950s through the present into six categories (labeled 1-6), which he defines by the degree to which their music features commonpractice harmonic and contrapuntal tendencies. Everett considers these features, specifically leading-tone resolution, to be the primary means by which rock music conveys a sense of progression.23 In his first category, Everett includes music that features ―thoroughly major-mode or minor-mode systems‖ that resemble those used in the common practice (Everett 2004, ¶7). Category 2 includes music that is governed exclusively by ―functional‖ counterpoint. Everett asserts that category 2 chord successions (such as the ―Hey Joe‖ ascending-fifth sequence) use stepwise voice leading, enabling the music to sound highly deterministic without being truly functional (Everett 2004, ¶11). Music in Everett‘s third and fourth categories bear only a fleeting surface-level resemblance to common-practice contrapuntal and harmonic behavior. Finally, Everett places songs that exclusively utilize blues-influenced minor-pentatonic harmonic systems in his categories 5 and 6. In these categories, Everett describes the harmony as ―entirely non-functional‖ and the voice-leading as ―severely compromised,‖ stating that tonal centers are established through ―assertion rather than syntax‖ (Everett 2004, ¶20).24 In defining his six categories, Everett purports that as rock music moves further from common-practice tonality, chords become more interchangeable, and harmonic function ceases to impact on our musical expectations. The use of Schenkerian and other reductive techniques in theoretical and analytical writings about rock music has been met with some criticism. Both Allan Moore and Richard Middleton, for instance, claim that Schenkerian analyses privilege 22

In addition to Everett (1999, 2000, 2004), these include Matthew Brown (1997), Lori Burns (1997, 2000), and Timothy Koozin (2000), among many others. This definition was gleaned from Everett‘s discussion of Paul Simon‘s ―The Sounds of Silence,‖ in which he suggests the absence of the leading tone accounts for the lack of pull to the tonic, and the overall absence of ―any harmonic function at all‖ (Everett 2004, ¶10).

23

Remarkably, Everett‘s descriptions of categories 5 and 6 align quite well with Björnberg‘s (1989/2001) harmonic theory.

24

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harmony and counterpoint over rhythm and meter, which are often the sole determinants of a tonal center in rock music (Moore 1992, 77; Middleton 1990, 193). 25 As mentioned above, several scholars suggest that much of rock‘s harmonic palette is modally derived (Moore 1992 and 1999; Björnberg 1989/2001; Tagg 2003; Biamonte 2008) and transpires in repeated cycles that do not allow for the harmonic closure required by Schenkerian theory (Moore 1995, 186-7; Stephenson 2002, 70; Björnberg 1989/2001, ¶14). Specifically, Moore claims that closure in common-practice music is achieved by the stepwise resolutions of 2 and 7 at cadences. In rock music, these resolutions are often heavily obscured by a misalignment of melody and harmony, 26 and they are notably absent in the numerous songs that use subtonic and/or subdominant harmony as cadential agents (Moore 1995, 186-7). Perhaps most convincing is Moore‘s contention that rock musicians conceive of harmonies as ―indivisible units‖ that are rarely governed by principles of voice-leading (Moore 1995, 181)—a conjecture recognizing that most composers of rock music are guitarists who frequently connect chords with parallel motion for reasons of convenience and ease of performance on their instrument (Moore 1995, 190). For this reason, Moore considers interior voiceleading strands to be incidental parts that ―rarely have a linear role‖ (Moore 1995, 190). This belief is echoed by Paul Carter (2005, 133-4) who states that pop-rock music is ―composed vertically‖ as justification for emphasizing root motion rather than voice leading. Summary In this chapter, I have laid out the main premises of several competing theories of rock harmony. Stephenson and Carter (and, to a lesser extent, Moore) present root-motion theories with three central claims: 1. We attend to a chord‘s root when listening to harmony in rock music. 2. Harmonic syntax is governed by common intervals formed between successive chord roots. 3. Most importantly, musical style determines which root successions will generate listener expectations. Everett refutes this, suggesting that such claims have been ―disproved‖ through examples such as the important dominant anacruses in Billy Joel‘s ―She‘s Always a Woman‖ (2004, ¶7). 25

Moore calls this the ―melodic-harmonic divorce‖ (1995, 189). The concept was more thoroughly investigated by Temperley 2007.

26

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Conversely, Everett‘s and Doll‘s theories propose that: 1. Counterpoint (perhaps in an abstract guise) is rock‘s most salient harmonic feature. 2. Harmonic syntax is controlled by voice-leading tendencies determined by tonal hierarchy 3. Rock and common-practice music have similar rules of harmonic syntax.27 In addition, Björnberg proposes that individual chords possess no inherent functional information and are interchangeable in exclusively modal and pentatonic harmonic systems.28 While the remainder of this dissertation will engage and scrutinize these premises, it is important to acknowledge the differences in scholarly aims motivating this study and those pursued by the authors surveyed in this chapter. In most cases, the work reviewed above centers on music analysis. This is certainly evident among the Schenker-inspired authors such as Everett, and one could argue that both Stephenson‘s and Carter‘s theories are analytically oriented. Christopher Doll‘s work, although seemingly fueled by the predictive power of functions, essentially requires listeners to make retrospective judgments of abstract voice leading. Thus, Doll‘s theory is also primarily an analytical endeavor. Analysts tend to publish highly complex, nuanced interpretations of specific musical works that, with careful study, can provide readers with a compelling and enriched musical experience. The experiments presented in this dissertation do not intend to either debunk or to validate analyses. Rather, the goal of this study is to address the fundamental assumptions that lie behind the theories that drive these analyses: do we have harmonic expectations, and if so, what are they? The perspectives reviewed in this chapter suggest some factors that might produce such expectations. The experiments presented in Chapters 4-6 of this dissertation attempt to evaluate the relative merit of each of these claims.

As discussed earlier, Doll‘s theory is clearly more flexible than Everett‘s. Nevertheless, Doll‘s functions subsume those recognized in common-practice tonality.

27

Everett‘s (2004) theories of harmony depend on the style of rock in question. Since his first four categories are firmly based in common-practice tonality, it can be generally said that Everett views rock through a tonal lens. Nevertheless, much like Björnberg, Everett proposes that individual chords are interchangeable in rock music that exclusively uses minor pentatonic harmony.

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CHAPTER THREE HARMONIC FUNCTION AS EXPECTATION In the previous chapter, I outlined several theories of harmony and their applicability to the analysis of rock music. Each theory proposed an analytical explanation of why one chord can move to another. For all of their explanatory power, however, these theories don't attempt to reflect the listener's perspective. How is harmonic knowledge gained? How do harmonic ―rules‖ manifest themselves in the listening experience? In this chapter, I will review three theories that address the epistemology of music: musical grammar, the theory of statistical learning (specifically the Hick-Hyman law), and schema theory. These theories are not mutually exclusive; parts of each will be used to contextualize my empirical investigation of harmonic function as harmonic expectation. Following a brief survey of pertinent empirical scholarship, I present the experimental framework for the studies of twelve-bar blues progressions that appear in the ensuing chapters. Musical grammar In 1973, Leonard Bernstein delivered a series of lectures about music at Harvard University. He campaigned for a new discipline of music scholarship that engaged the structure of music from the perspective of linguistics. In particular, Bernstein was inspired by the system of generative-transformational grammar championed by Noam Chomsky. Chomskian linguistics attempts to characterize the knowledge required to speak a language. How can we understand a sentence we have never heard before? According to linguistic theory, we have an unconscious knowledge of a system of rules, called a ―grammar,‖ which enables us to ―generate‖ possible sentences in a language. Our knowledge of grammar allows us to process and assign meaning to the unfamiliar sentence. Bernstein felt that this theory could potentially offer profound insight into music. The lectures galvanized new interest in interdisciplinary studies combining music and linguistics, perhaps best represented in the music-theoretical literature by Fred Lerdahl and Ray Jackendoff's landmark 1983 publication A Generative Theory of Tonal Music (henceforth, GTTM). In this work, Lerdahl and Jackendoff attempt to describe what we know when we understand ―the language of music.‖

21

Lerdahl and Jackendoff's theory of musical grammar presumes that we unconsciously understand a set of rules that ―generates‖ all possible musical structures. Importantly, Lerdahl and Jackendoff qualify their intended meaning of the verb ―generate‖ in this sense. Chomsky's generative theory does not provide an algorithm that manufactures all grammatical sentences; rather, it assigns structure to sentences. Likewise, Lerdahl and Jackendoff's theory does not compose all possible pieces of tonal music; rather, it provides a structural description of what an experienced listener infers while hearing of a piece of tonal music (Lerdahl and Jackendoff 1983, 6). Such a theory explains what enables us to ―understand‖ music that we haven't heard before. Moreover, it reflects our ability to identify violations of musical grammar—our ability to point out ―mistakes.‖ This ability is honed with experience gained through our exposure to the ubiquitous music of our culture, which Lerdahl and Jackendoff suggest is common-practice Western tonal music (Lerdahl and Jackendoff 1983, 3-4). The relationship between language and music has also been a central concern among cognitive neuroscientists and cognitive psychologists. Several studies have illustrated that syntactical and harmonic incongruities elicit similar neurophysiological responses in similar locations in the brain (Besson et al 1998; Patel et al 1998). In his review of the corpus of comparative studies of linguistic and musical syntax, Aniruddh Patel suggests that language and music share a common set of syntactical processes (Patel 2003, 674). He claims we have implicit knowledge of principles of syntax which govern our ability to combine structural elements (words) into sequences (sentences) and allow us to detect incongruities in novel sequences. Patel proposes that sentence comprehension involves two distinct components: one that keeps track of predicted syntactic categories (―structural storage‖) and one that connects incoming words to their dependent elements heard earlier in the sentence structure (―structural integration‖). Both of these components consume neural resources, and this consumption is affected by the distance between elements in the structural hierarchy. Elements close in proximity consume fewer neural resources compared to those that are more distantly connected in the syntactic structure. Moreover, these distances can be quantified, allowing for empirical tests to confirm the system‘s predictions (Patel 2003, 677). According to Patel, the best music-theoretical parallel to this quantification of our consumption of neural resources during linguistic processing is Fred Lerdahl‘s model of tonal pitch space (Lerdahl 1988; 2001). In GTTM, Lerdahl and Jackendoff proposed that tonal hierarchy is formed through an understanding of musical events as recursive moments of tension and release—specifically, the authentic cadence (Lerdahl and Jackendoff 1983, 214). The tonal pitch space model uses this hierarchy to quantify the 22

―psychological distance between musical objects‖ (Bigand, Parncutt, and Lerdahl 1996, 127). Among other things, Lerdahl‘s model represents the distance between any two musical events with a single integer that combines information about pitches, chords, and keys. Moreover, musical events are parsed with tree structures (like diagrams of sentence structures in linguistics) which affect distance measurements in a manner reflecting the music‘s hierarchy. In any given key, the most important chords are the ones closest in proximity on Lerdahl‘s model (Bigand, Parncutt, and Lerdahl 1996, 127). The model‘s distance metric reflects ―degrees of perceived musical tension‖ (Bigand, Parncutt, and Lerdahl 1996, 128), which, like our processing of linguistic syntax, Patel speculates will correspond to our consumption of neural resources. Most pertinent to the present studies is the distance metric provided by Lerdahl‘s model. The metric is easily subjected to empirical testing, as demonstrated in a 1996 study reported by Emmanual Bigand, Richard Parncutt, and Fred Lerdahl. Participants were asked to rate the tension produced by the middle chord in a series of three-chord successions that always began and ended with a C-major triad. The results of this experiment showed a significant correlation between the participants‘ ratings of tension and the distance in tonal pitch space between the second chord and the C-major tonic triad (133). While these results are by no means comprehensive or conclusive, they do suggest that Lerdahl‘s measurements could feasibly represent the processing differences we experience when listening to various chord progressions. The studies discussed above provide some insight into how rules of harmony are manifest in a listening experience. In language and in music, the rules of syntax allow us quickly and accurately to identify grammatical errors. We learn linguistic syntax through exposure and past experience (Lhost and Ashley 2006,1283). As Lerdahl and Jackendoff suggest (1983, 3-4), the ubiquity of common-practice tonal music has nurtured in us a similar understanding of music. Is it possible that other culturally pervasive musics could engender a similar knowledge of syntax? Both Mark Steedman (1984; 1996) and Richard Middleton (1990) speculate that this could be possible for rock music. Borrowing from Lerdahl and Jackendoff, both Steedman and Middleton even suggest that, in rock, the plagal cadence could supplant the authentic cadence at the highest level of recursion. How do listeners gain this knowledge? This question will be addressed in the remaining sections of this chapter.

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Statistical learning Attempting to understand how we obtain knowledge, philosophers throughout history have generally debated from two wide-ranging perspectives: induction and deduction (Huron 2006, 59). Deduction proposes that knowledge is gained by deriving statements from a set of axioms. If the axioms are true, then the derived statements should also be true, as long as one arrives at those statements by logical means. Mathematics is founded upon deductive reasoning, and many music theories also purport to use deductive logic.29 General statements and axioms formalize these theories; supporting evidence from the repertoire is gathered afterward. Conversely, the process of induction constructs principles through multiple observations of events. Inductive reasoning is plagued with a fundamental problem: no number of consistent observations can absolutely confirm a statement. Despite being inherently fallible, inductive reasoning has its advantages, foremost the ability to adapt to additional experiences and observations. Throughout our lives we experience countless sound events. Over time, we become sensitive to the rates at which these events occur. By induction, we develop an understanding of probabilities for these events, which helps shape our expectations about the future (Huron 2006, 60). Throughout the last fifty years, experimental research has shown that humans are keenly aware of the degree to which various stimuli are present in their environment. W.E. Hick and Ray Hyman studied this phenomenon, independently discovering a relationship between the frequency of occurrence of some stimulus in our environment and the speed at which we are able to process it. For instance, if you were asked to identify the sex of people in a series of photographs, your response time would be fastest when looking at pictures of people you know, slightly slower for pictures of people from your culture that you don‘t know, and slowest for people from outside of your culture. The reason for this is that we are able to process more familiar, or more frequently occurring, stimuli faster than unfamiliar stimuli. Known as the Hick-Hyman law, this principle can be generalized to many types of stimuli, including musical ones (Huron 2006, 63). The theory of statistical learning suggests that much of our musical knowledge is gained from the frequency of certain musical events in our environment. 30 Several Some examples that come to mind are numerous tuning systems derived from the ―perfect‖ consonances, Schenkerian theory, and more abstract theories such as Forte‘s (1973) set theory, and Callender, Quinn, and Tymoczko‘s theory of chord geometry (2006). 29

30

In this case, ―our environment‖ refers to all of our musical experiences, conscious and subconscious.

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music scholars have studied the statistics of music in various ways. Research by Ken‘ichi Miyazaki (1990) and David Huron and Jasba Simpson (1994) has shown that absolute pitch possessors are able to process the pitch classes associated with white keys on a piano more quickly, presumably because those pitch classes occur more frequently in music—a musical instance of the Hick-Hyman law. Jenny Saffran et al (1999) found that participants were quicker and more accurate when identifying the three-pitch sequences that occurred most frequently in seven-minute pitch successions. Other expectations derived from music‘s statistical regularities include pitch proximity (melodies employ sequences of tones that are close in pitch), step declination (large melodic intervals tend to ascend while small intervals tend to descend), step inertia (melodic steps are followed by steps in the same direction), melodic regression (melodic leaps reverse direction and move towards a mean pitch), and melodic arch (melodies descend at the end of a phrase) (Huron 2006, 73-89). Carol Krumhansl (1990) and Bret Aarden (2003) have both documented that listeners are sensitive to the frequency distribution of scale degrees in tonal music. Krumhansl (1990) extended her investigation to include chord sequences and again revealed a remarkable correlation between listeners' harmonic expectations and the most frequent chords in the common practice. The studies cited above provide simple, well-documented accounts of how statistics can explain our culturally learned musical knowledge. Might certain events occur in rock music more frequently than in common-practice music? I speculate that that they do. Have these events pervaded our musical experience to the point of affecting our understanding and expectations of music? This question is much more difficult to answer. In Western culture, rock music has been ubiquitous for the better part of sixty years, and the blues became increasingly widespread early in the twentieth century. The musical properties upon which most of the aforementioned studies are based have been consistent for much longer and have pervaded a greater number of musical cultures. Nevertheless, other than common-practice Western tonal music, the genre most likely to have influenced the twenty-first-century North American listener's statistical understanding of music is rock. Both a comparison of the relative frequency of harmonic events in rock and classical music and an investigation of whether listeners have different harmonic expectations when listening to rock are warranted. Even if the theory of statistical learning can account for a unique set of harmonic expectations in rock music, it does not offer an explanation of why some people are potentially able to speak two ―musical languages‖ with different grammatical systems. 25

More importantly, how do we know when to activate one musical language over another? Schema theory offers a possible answer to this question. Schema theory In his book A Classic Turn of Phrase, Robert Gjerdingen engages the notion of interpretive context and its significant role in our understanding of music. Musically, ―interpretive context‖ is perhaps best explained by a (relatively) simple example: stability and instability. Stability and instability are entirely dependent upon context. In certain situations (such as a passage in C major), a C-major triad is highly stable, while in others (such as a passage in B minor), the chord is quite unstable. From a cognitive perspective, how do we understand musical context? Gjerdingen suggests the application of schema theory. Schemata are defined differently in the numerous disciplines in which they are employed. Among psychologists, schemata are considered cognitive structures that are formed ―on the basis of past experience with objects, scenes, or events and consisting of a set of (usually unconscious) expectations about what things look like and/or the order in which they occur‖ (Gjerdingen 1988, 4; after Jean Mandler). Gjerdingen highlights six characteristics that all schemata share:      

they have variables they can embed within one another they represent knowledge at all levels of abstraction they represent knowledge rather than definitions they are active processes they function by processing data and evaluating its goodness of fit within the schema itself

The ―input data‖ upon which a schema bases its evaluation of context can otherwise be referred to as a ―feature.‖ While some features are innately recognized by all people around the world, others are learned through cultural experience (Gjerdingen 1988, 5). Western listeners might learn to identify specific sounds of instruments, chord qualities, scale types, and so on. There are many musical features that are highly context dependent, such as harmonic relationships. For example, if we hear a triple suspension at a final cadence in a chorale, how do we know that the suspended pitches are not part of the cadential tonic chord? According to schema theory, we know this 26

because such a chord (root plus the suspended notes) does not exist as a harmonic feature in this particular musical genre. At the outset of the musical experience, various features of the chorale motivated us to invoke common-practice schemata, including harmonic syntax and voice leading, which provide us with a larger interpretive context. Features and schemata have a reciprocal relationship. Features inform schemata selection, which in turn helps to detect additional features. Cognitively, this works like a logical process of elimination. When we encounter a feature, we eliminate all schemata with which that feature is not associated. We continue to accumulate features and eliminate schemata until an appropriate schema becomes apparent. Once this occurs, our chosen schema allows us actively to seek out the remaining features. At this point, the schema achieves a ―higher level‖: having established a context for our experience, we are able to begin the process of ―filling in the blanks‖ (Gjerdingen 1988, 6-7). This process represents our activation of expectations. Studies have shown that listeners activate common-practice schemata in anticipation of musical stimuli. In other words, listeners have certain musical expectations even before hearing a sound. For instance, David Huron studied listeners' interpretations of a single imagined tone. His results showed that in the absence of any musical context, listeners assumed the imagined tone to be the tonic note of a major key (Huron 2006, 207). In a similar experiment, Huron played a single pitch for his participants and asked them to imagine a harmonization of that pitch. The vast majority of listeners imagined an equal-tempered major triad (Huron 2006, 207). Huron's results reveal that most North American listeners preemptively activate representative schemata of the common practice.31 David Huron explains schema theory from the perspective of evolutionary biology. Recall that schemata represent different sets of expectations that we apply in particular situations. In dire circumstances, quickly and accurately predicting the outcome of events may be a matter of life and death. From a biological standpoint, if expectations are enabled though the implementation of specific schemata, we must quickly apply and (when necessary) switch schemata in response to any given situation. If listeners possess two or more distinct genre-specific sets of musical expectations, how do they know when to apply one particular set rather than another? Schema theory suggests that listeners attend to contextual cues (or features) that eventually influence the

31

It should be noted that major keys and triads are also features present in many non-common-practice musical styles. Indeed, identifying the degree to which these features overlap stylistic boundaries is one of the aims of this dissertation.

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implementation of a particular schema. In these terms, harmonic expectation is represented by the listener's enabling of a higher-level schema activated by the presence of numerous musical features or lower-level schemata. Thus, if distinct harmonic expectations exist for blues and common-practice music, those expectations should be triggered by the presence of idiom-specific musical features. Thus far, I have made little mention of the specific musical features that may trigger various schemata. One reason is that schemata are complex hierarchical models that sometimes defy concrete definitions (consider, for example, ―common-practice tonal music‖). While conceding that high-level schemata may forever remain vague theoretical constructs, we can certainly identify some of their most characteristic and concrete features. In the case of common-practice tonal music, these features would likely include tertian harmony, diatonicism, and the major scale. In contrast, low-level schematic features of blues might be instrumentation (guitar, bass, drums, and a vocalist), so-called ―blue notes,‖ a shuffle rhythm, and so on. Note that the features at the lowest level of the hierarchy are those that can be most quickly processed. In a fascinating study, Robert Gjerdingen and David Perrott (2008) showed that listeners require as little as 250 milliseconds to correctly identify musical genre, suggesting that the most important information for invoking schemata occurs within the first second of hearing the music and is most likely communicated through features such as timbre, instrumentation, and tuning. Expectation In 1956, Leonard Meyer speculated that music‘s meaning and emotional content are communicated through the fulfillment and/or denial of expectations (Meyer 1956, 34). Although his investigations were driven by psychological research, including Gestalt principles, his claims remained purely speculative at the time (Huron 2006, 2). When Meyer published his influential book Emotion and Meaning in Music (Meyer 1956), the mind was considered a ―black box‖ among psychologists (Margulis 2007, 197-198). Fortunately, Meyer‘s work has inspired numerous studies of expectation over the last fifty years, many of which aim to support and/or recast his theories with empirical evidence (Huron 2006, 3). Studying expectation poses several problems that must be addressed. First, definitions of expectation can be tenuous or vague. Throughout the music theory literature, authors routinely refer to musical expectations as a means of supporting their analytical arguments. While these observations often allow for compelling analyses, 28

seemingly ad hoc definitions of ―expectation‖ can sometimes lead to confusion. In a recent article, Elizabeth Margulis (2007) presents a taxonomical framework with five defining criteria for considering expectation in music (198)32: 1. The origin of an expectation may arise from reflexes, conceptual knowledge, mechanisms of statistical learning (as discussed above), logic, or hard-wiring (205). 2. The nature of the expectation can be either conscious or unconscious. Are you aware of the expectation while you‘re experiencing it, or do you only realize it after that expectation has been violated? (205). 3. The time course of an expectation refers to its duration and temporal specificity. For instance, one could have a long-range expectation for a piece of tonal music to have closure in the home key. The time course of this expectation is long and unspecific regarding the exact moment at which it might be fulfilled. Alternatively, one could have a momentary, time-specific expectation that a dominant seventh chord on the last beat of a measure will resolve to a tonic chord on the first beat of the next measure (206). 4. The object is targeted by the expectation, and could include chords, phrases, melodic pitches, motives, topics, tempi, etc. (206) 5. The fulfillment or denial of an expectation can yield a consequence that impacts our thoughts, emotions, behaviors, or other expectations (206). In his book Sweet Anticipation, David Huron (2006) presents a formal model of expectation abbreviated as the ITPRA model. While the model represents a general theory of expectation, Huron almost exclusively uses musical examples to support his claims. The five components of Huron‘s model represent the psychological and biological responses that occur when we process an event, musical or otherwise (Huron 2006, 12-14). 1. Imagination Response (pre-outcome). A long-term prediction of the outcome of a future event. Biologically, this forecasting is accompanied by a feeling generated by the body in response to ―previewing‖ the outcome of a future event. A musical

32

Margulis continues with several analytical examples that promote more thorough discussions of each of these criteria.

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example of this would be our expectation that a tonal piece will end in the home key, and we may imagine the last cadence long before it actually happens. 2. Tension Response (pre-outcome). The mental and corporeal preparation for an anticipated event. Huron describes watching someone who is about to pop a balloon with a needle. One often undergoes motor preparation by tensing up, and perceptual preparation by paying closer attention to all things involved with the anticipated event. In music, a good example would be when a concerto soloist is playing the cadential trill prior to the end of the cadenza. 3. Prediction Response (post-outcome). When a stimulus is accurately predicted, the body provides the reward of a positive (or positively valenced) emotional response. Conversely, when the stimulus is not predicted, the emotional response is negatively valenced. Importantly, confirmation of expected outcomes usually induces a positively valenced response, even when the expected outcome is bad. This facet of Huron‘s model will be explained in more detail below. 4. Reaction Response (post-outcome). The onset of this response occurs shortly (approximately 150ms) after the outcome of the event and produces an emotional response to the worst-case assessment of the outcome. Huron cites reflexes, such as the startle response or the orienting response, as instances of reaction responses (Huron 2006, 418). 5. Appraisal Response (post-outcome). This is the final and most complex assessment of the outcome that involves conscious thought. It is independent of and not necessarily consistent with the reaction response. Expectation is at least as difficult to measure as it is to define. While numerous methods have been used to investigate expectation,33 I will only discuss the two that are most pertinent to my study of harmony and the scholarly literature from which it is drawn. Recall the Hick-Hyman law that states ―the speed of processing a stimulus is inversely proportional to the familiarity of that stimulus‖ (Huron 2006, 415). In addition to providing support for the theory of statistical learning, the law also presents a more general fact about expectation: accurate prediction facilitates perception. In other 33

These include non-verbal response modes such as head turning paradigms, heart-rate monitoring, and brainwave monitoring such as the evoked response potential (ERP) (Huron 2006, 49-52). Other response modes include method of production (Schmuckler 1988, 1989; Larson 1997, 2002) and betting paradigms (Huron 2006, 53-55).

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words, if participants are required to perform some task in response to an event, accurate predictions of that event will enhance their speed and precision when performing the task. Music cognition experiments that measure reaction time tend to present stimuli in two phases: primes and targets. The prime establishes a musical context; the target event immediately follows the prime and is assessed by the listener according to some criterion. For example, in a classic priming experiment, participants hear stimuli consisting of two chords and are asked whether the second chord is in tune or out of tune. In this case, the second chord is the target while the first chord is the prime. On the surface, it may seem that this experiment aims to investigate participants‘ perception of intonation. The real goal, however, is to see whether the relationship between the prime and target chords affects participants‘ ability to make intonation judgments. Since prediction facilitates perception, participants should more quickly and accurately judge the intonation of highly predictable targets. When primed by a G major-minor seventh (GMm7) chord, for instance, a participant might predict that a C-major triad will follow. It is far less likely that this GMm7 chord would lead the participant to predict a C#-minor triad to come next. Asking participants to convey their predictions directly would be complicated and potentially misleading because these predictions are often unconscious and difficult to articulate. Judging the intonation of a chord is a clear forced-choice response that can easily be measured in terms of accuracy and speed. In the above example, if the participant has strong expectations for a C-major target to follow a G Mm7 prime, it will be reflected by the speed and accuracy with which the participant assesses the intonation of the C-major triad. The converse would be true for the C#-major triad: the participant would be slower and less accurate when judging its intonation because it is highly unexpected when following a G-major triad. While several studies have measured the reaction time of listeners asked to judge the intonation of the target chord (Bharucha and Stoeckig 1986 and 1987; Justus and Bharucha 2001), the response task for this approach is not restricted to an intonation judgment. Other investigators have asked participants whether the target chord was consonant or dissonant (Bigand and Pinaeau 1997; Bigand et al 1999; Poulin-Charronat et al 2005), or to identify the timbre of the target chord (Tillman and Lebrun-Guillaud 2006). In each case, chords widely considered to be closely related to the prime were processed faster and with more precision than were unrelated chords. With a few exceptions, each of the studies mentioned above measures a listener‘s expectations at a specific moment. In Margulis‘s terms, the time course of these expectations is very specific and very short in duration. The results likely measured expectancy at the prediction phase of Huron‘s ITPRA model. Experiments investigating 31

harmonic expectation in longer musical events, in contrast, are likely assessing participants' appraisal responses. For instance, one might be interested in how the second chord of a five-chord succession impacts a listener's response to the entire stimulus. The investigator would likely want the listener to wait until the five-chord succession transpired before providing a response. A reaction time measurement would be inappropriate in this case, since the time separating the onset of the second chord and the response is so long (recall that reaction response occurs approximately 150ms after the outcome of the event). Reaction time measures are therefore not well suited for these types of experiments, nor are they useful for investigating expectations with longer and less specific time courses. In 1979, Carol Krumhansl and Roger Shepard conducted an experiment in which listeners were presented with a musical context—the first seven notes of a C-major scale—and assessed the ―goodness of fit‖ of a single note (the ―probe tone‖) that followed the scale. The results showed that experienced listeners consistently preferred specific pitches (especially members of the tonic triad) in a manner that reflected the traditional models of tonal hierarchy (Krumhansl and Shepard 1979, 592). This was the first of many music cognition experiments that asked listeners to provide ratings in response to musical stimuli. In subsequent studies of harmony, the ―goodness of fit‖ question has been recast as ―degree of tension‖ (Bigand, Parncutt, and Lerdahl 1996), the ―degree of belonging,‖ and ―degree of completion‖ (Bigand and Pineau 1997; Tillman and Lebrun-Guillaud 2006). One might reasonably wonder what these rating scales have to do with expectation. Recall that in the prediction phase of Huron‘s ITPRA model, the body produces a positively valenced emotional response when the prediction is correct. In effect, we are rewarded for easily processing a stimulus. When we provide a qualitative assessment of a stimulus, part of our subjective rating reflects this emotional response to the prediction. Although we think we have assessed the stimulus itself, we‘ve actually confused it with our processing of that stimulus. Psychologists refer to this phenomenon as misattribution (Huron 2006, 135). Our ratings are directly linked with our ability to predict targets, as both Huron (2006; 45, 136) and Aarden (2003, 2) point out.34 When we claim that a stimulus ―sounds good,‖ presumably hearing it produced a positive emotional response. While ―degree of tension‖ and ―degree of belonging‖ do not directly ask for qualitative judgments, it is plausible that listeners could interpret ―less tense‖ and ―belongs‖ as good qualities, while ―more tense‖ and ―doesn‘t belong‖ might have more negative connotations. If participants interpret these descriptions in this way, they may be misattributing their positively or negatively valenced responses as they would with more overt descriptors such as ―good‖ and ―bad.‖

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Both Huron (2006) and Aarden (2003) identify difficulties with probe-tone designs and with the rating scales that accompany them. One problem with this method is that it is quite tedious, requiring a large number of trials (Huron 2006, 46). This can lead to long experiments in which participants could easily fatigue. Using Shepard tones (Shepard 1964) may reduce the number of possible trials by eliminating distinctions in voicing and register among stimuli; on the other hand, the experimenter cannot observe the potential impact of these factors. Perhaps more problematic is the fact that probetone designs require the music to stop and wait for a response, making it difficult for the investigator to discern whether a listener‘s rating refers to the musical connection between the context and stimulus or to perceptual closure (Huron 2006, 46). Aarden (2003) compared the scale-degree profiles from Krumhansl‘s early experiments with the distribution of scale degrees throughout a large body of tonal music. He found a strong correlation between Krumhansl‘s profiles and with the occurrence rates of phrase-terminating scale degrees (Huron 2006, 152). While Krumhansl‘s profiles do reflect listener‘s expectations for pitch continuations, it is unclear whether these expectations apply to mid-phrase contexts. In spite of the methodological problems just mentioned, experimental designs using post hoc ratings have been employed successfully by several researchers. In addition to Krumhansl and her collaborators, Bigand, Parncutt, and Lerdahl (1996), Bigand and Pineau (1997), and Tillman and Lebrun-Guillaud (2006) used post hoc rating systems in experimental studies of harmonic expectation. Indeed, Tillman and Lebrun-Guillaud suggest that post hoc judgments may be a better means of revealing interactions between pitch and time (Tillman and Lebrun-Guillaud 2006, 350-351), since these parameters are initially processed independently and are only integrated during later stages of cognitive processing.35 In Margulis‘s terms, the nature and time course of our expectations might be more appropriately measured using a subjective assessment. Studies of harmonic expectation Empirical studies of harmony have provided evidence supporting some of the most basic claims of common-practice music theory. In 1982, Carol Krumhansl, Jamshed J. Bharucha, and Edward Kessler reported an experiment in which listeners 35

Tillmann and Lebrun-Guillaud base these claims on their interpretation of research by Peretz and Morais (1989).

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assessed the relatedness of chord pairs in C major, G major, and A minor. Their results revealed that listeners considered chords constructed on the same contextual scale degree to be ―functionally equivalent.‖ Across keys, chord pairings were rated similarly, regardless of whether the chords or even chord qualities literally matched (Krumhansl, Bharucha, and Kessler 1982, 30). Bharucha and Krumhansl (1983) found similar results in a thorough study of two-chord successions in C major and F-sharp major contexts. In their study, listeners‘ preferences gave more weight to the second chord in the succession and depended strongly on that chord‘s frequency of occurrence in the tonal repertoire (Krumhansl 1990, 193). These results give credence to the notion that our knowledge of common-practice harmony is a function of statistical learning. More interestingly, Krumhansl assigned values to chord pairs found on Walter Piston‘s table of root progressions and found a significant correlation between Piston‘s evaluations and the rating data from her and Bharucha‘s experiment (Krumhansl 1990, 195), indicating that listeners have a ―systematic preference for chord progressions considered by Piston to be most common‖ (Krumhansl 1990, 195). In a series of experiments, Bharucha and Stoeckig (1986 and 1987) measured reaction time to investigate harmonic expectancy in two-chord successions. Their results revealed that listeners perform faster and more accurate intonation judgments when chords are in tune and closely related to the prime, and also when chords are mistuned and distantly related to the prime. Given that accurate expectation facilitates perception, Bharucha and Stoeckig ascertained that listeners have strong expectations for well tuned closely related chords. Moreover, listeners showed a bias toward closely related chords, often inaccurately judging them as in tune.36 The studies discussed above all investigated harmonic expectation in two-chord successions. More recent studies have broadened this context and engaged longer stimuli. Bigand and Pineau (1997) examined the effect of ―global context‖ on harmonic expectancy by creating stimuli that included the same prime and target pair at the end of an eight-chord sequence. Since stimuli could only be distinguished by the harmonic context created by the first six chords in the sequence, the results could not be attributed to sensory priming. Specifically, each stimulus ended with a G-major triad followed by a C-major triad and the preceding six chords determined the degree to which those chords sounded like a conventional phrase ending (V-I in C major), or an unconventional phrase ending (I-IV in G major). In this case, the prime consisted of all but the final chord and established the musical context in which the participants‘ assess 36

In other words, listeners associated good intonation with ―goodness of fit.‖

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the final chord. In a fast-reaction judgment, participants processed conventional progressions more quickly and accurately, suggesting that the ―influence of global harmonic context may be better understood in the light of current models of tonal cognition‖ instead of sensory priming (Bigand and Pineau 1997, 1105). In other words, our ability to anticipate the next chord in a succession is influenced to some extent by all of the preceding chords that form the tonal context. In a series of follow-up studies, Bigand, Madurell, Tillman, and Pineau (1999) investigated the effect of duration, temporal regularity, and long-range closure on global contexts that again terminated with identical two-chord successions. The results of their first two experiments (addressing duration) showed that the context effect diminished as the length of the prime decreased. This suggests that the processing of the target chord depends on all of the information accumulated from the beginning of the sequence (190). Bigand et al‘s (1999) culminating experiment engaged expectancy for long-range closure. Chord sequences were split into two phrases separated by a fermata. In all cases, chord sequences ended with a D-major triad followed by a G-major triad. As projected, listeners‘ fastest processing occurred in contexts in which both phrases were firmly in G major and the slowest processing occurred for sequences entirely in D major. In the middle were contexts that began in G major and modulated to D major. The authors claim that this means expectancy occurs at multiple levels: facilitation is best when the target chord is expected at both the high and intermediate levels, reduced when the target chord is expected solely at the high level, and reduced further when it is not expected at either level (193-4). The results of this experiment lend some support to hierarchical theories of tonal music, such as Lerdahl and Jackendoff‘s GTTM (1983). Expectation and timing In the early development of her model of dynamic attending, Mari Riess Jones claimed that models of expectation (developed prior to her publication in 1981) focused too much on ―what‖ and not enough on ―when‖ (Jones 1982a, 36). Generally, Jones argues that these two facets of expectation are inseparable and directly interact with one another. Regarding musical expectation, Jones suggests that listeners can more easily attend to temporally predictable melodic events (Jones 1982b, 11). Similarly, certain melodic events involving contour, melodic interval, and tonal stability combine with rhythmic and metrical accent patterns to create hierarchical temporal regularities or which Jones calls Joint Accent Structures (Jones 1987, 625). While this may seem 35

obvious, it touches upon the difficult question of whether temporal events and tonal events interact when listeners form expectations about music. If this is the case, do listeners weigh these factors equally when forming expectations? Furthermore, are listeners‘ expectations formed by a simple additive combination of these factors, or does the musical whole invoke stronger expectancies than the sum of its parts? Several other researchers addressing these questions have reached conflicting conclusions. Gabrielsson (1973) and Monahan and Carterette (1985) found that the effects of rhythmic and pitch dimensions were negatively correlated when listeners judged the similarity of two melodies, suggesting that listeners attend to these musical dimensions separately. Palmer and Krumhansl (1987a) asked listeners to rate the quality of fugue subjects and found that pitch and temporal components had an additive but independent influence on listeners‘ ratings. In a later study, Palmer and Krumhansl (1987b) asked listeners to rate the quality or completeness of a musical phrase presented in either a strictly pitch (isochronous), strictly rhythmic, or a combined pitch/rhythmic domain. They determined that ratings in the combined domain could be predicted as a function of listeners‘ ratings of the same phrases heard in either the separate pitch or rhythmic contexts, again suggesting that these musical domains have an additive relationship as opposed to an interactive one. All of these authors demonstrated that temporal and melodic factors independently influence listeners who are asked to provide similarity or qualitative judgments for a musical stimulus. However, several other researchers have found evidence suggesting an interactive relationship between the temporal and pitch domains. Jones, Boltz, and Kidd (1982) showed that listeners more adeptly discriminated pitch changes when they occurred at important temporal events. Deutsch (1980) showed that participants‘ memory for melodies was enhanced by coinciding pitch and temporal structures; when the pitch and rhythm contexts conflicted, participants were less successful. In a melody-recognition task, Jones (1987) showed that rhythm and contour interact to impact listeners‘ feeling of familiarity with a tune. Marilyn Boltz (1989) attempted to determine whether timing, tonality, or their interaction impacted the perceived completion of a melody. Her results showed main effects both for tonality and for timing, as well as an interaction of those two factors in judgments of completeness. In a 1993 experiment, Boltz again asked listeners to rate the sense of closure conveyed by melodies with variant or invariant metrical structures. In this experiment, Boltz examined the effects of timing and melody on longer-range expectations and found that anticipatory attending only occurred when invariant periodicity coincided with appropriate ending pitches (Boltz 1993, 593). To summarize, the findings of these 36

authors suggest that joint expectancies of pitch and timing are stronger than either of those expectancies alone.37 The majority of experimental studies investigating both pitch and temporal domains have specifically used melodies as musical stimuli. Research pertaining to the potential interaction of harmony and timing is much less widespread. In a 1994 study, Schmuckler and Boltz investigated the influences of the temporal and harmonic domains on expectation. In a series of four experiments, participants heard four-chord phrases that featured common-practice cadences. The phrases were varied with regard to the timing and type of closing chords and also the phrase‘s temporal periodicity. Depending on the iteration of the experiment, participants responded to these stimuli either rating the ―fit‖ of the final chord or by indicating (through a two-option forced-choice question) whether or not the final chord belonged in the phrase. Among the most pertinent of Schmuckler‘s and Boltz‘s findings was a three-way interaction of ending time, temporal periodicity, and closing chord. In contexts with invariant periodicity, early endings received lower ratings than on-time and late endings, but, perhaps more interestingly, ending time only affected ratings in phrases that concluded with high-expectancy chords. In stimuli with tenuous periodicity, the timing of closing chords had no effect on participants‘ ratings. Similarly, there was a significant interaction between cadence type, periodicity, and ending time. Half and deceptive cadences were judged as more appropriate when they occurred on time or late, while late-arriving authentic cadences actually received slightly higher ratings than on-time authentic cadences. Schuckler and Boltz speculate that this occurs because the strong sense of completion conveyed by the authentic cadence overrides the influence of periodicity or timing. In a 1999 study, Bigand et al investigated the effect of temporal organization on longer-range harmonic expectation. Participants were asked to judge the intonation of the final chord in several two-phrase excerpts that were designed to invoke low-, medium-, and high-level harmonic expectancies. Their results did not show a main effect of temporal organization, but an interaction occurred between temporal organization and harmonic structure. Participants took longer to process chords if those chords were both harmonically and temporally unexpected. The authors interpreted this result as supporting the notion that music cognition is a ―dynamic context-specific

37

This was first hypothesized by Boltz prior to undertaking her studies (Boltz 1989,15).

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activity‖ that is not guided solely by abstract knowledge of the tonal hierarchy (Bigand et al 1999, 194).38 Tillman and Lebrun-Guillaud (2006) presented participants with eight-chord successions that varied in harmonic context,39 periodicity, and timing of the final chord. Participants were asked to judge the timbre of the final chord. The authors‘ results showed that aberrations from the prevailing periodicity, certain harmonic contexts, and early endings caused participants to respond more slowly and less accurately; however, there was no interaction between any of these factors (Tillman and Lebrun-Guillaud 2006, 350). In a series of follow-up experiments, the authors found that the absence of periodicity made future-oriented attending almost impossible. Likewise, the authors speculated that when participants are asked to focus on local-level events (as they were in the first experiment‘s timbre judgment task) they tend not to be influenced by the global context. When asked to provide subjective judgments of completion, participants are able to better reflect on the musical whole, and their judgments are thus appropriately influenced by an interaction of harmonic context and timing (Tillman and Lebrun-Guillaud 2006, 355). The numerous studies discussed above employed different designs and response modes. It is certainly possible their inconsistent results simply reflect the fact that our cognition of melody, harmony, and rhythm functions according to the specific task at hand. With Palmer‘s and Krumhansl‘s work (1987a and 1987b) as a notable exception, experiments that utilized subjective, post-hoc judgment tasks as response modes demonstrated interactive relationship between temporality and pitch (Jones, Boltz, and Kidd 1982; Boltz 1989, 1993; Schmuckler and Boltz 1994; Tillman and Lebrun-Guillaud 2006). Experiments utilizing more objective response modes, such as those that measured reaction time or tested memory, suggested that temporality and pitch have an additive relationship (Gabrielsson 1973; Deutsch 1980; Monahan and Carerette 1985; Tillman and Lebrun-Guillaud 2006). Harmonic expectation in twelve-bar blues progressions The experiments presented in the following three chapters were influenced by many of the studies and theories discussed in this chapter. Although all three 38

This theory is one of the core arguments for Jones‘s theory of dynamic attending (Jones 1987).

39

In this experiment, all stimuli used the same penultimate and final chords. The harmonic function of these chords was altered by the context established by the first six chords of the succession.

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experiments engage different facets of expectation, they all share certain design features. Foremost is the rating scale response mode, which allows for global judgments of stimuli and addresses expectation by way of misattribution: a positive rating will be understood as reflecting a predicted event. Second, since these experiments intend to investigate possible differences in the expectations produced by blues and common-practice music, the stimuli used in each experiment include several features that firmly establish stylistic context. As Gjerdingen and Perrot (2008) demonstrated, stylistic features quickly activate musical schemata, presumably prompting listeners to engage the appropriate set of stylistically associated expectations. Together, the three studies aim to contribute insight to the growing body of research that addresses the following four broad questions. Does rock music elicit expectations that are different from those held for common-practice music? This question is central to this dissertation and will serve as the driving force for its inquiries, speculations, and conclusions. It certainly lies behind the music-theoretical arguments discussed in Chapter 1; additionally, it remains the ―elephant in the room‖ for conclusions drawn by much of the aforementioned theoretical and empirical work discussed in this chapter. Lerdahl and Jackendoff claimed that our ability to identify violations of musical grammar is honed by our exposure to the ubiquitous music of our culture (Lerdahl and Jackendoff 1983, 3-4). Common-practice music has undoubtedly pervaded our culture for hundreds of years. Is it possible that alternate musical systems could have reached the same status? Empirical studies have shown that our identification of syntactical errors in music relates to the distributional frequency of events found in the style in which the music is presented. Very few studies have addressed expectations for music with a hierarchy differing from that of commonpractice tonal music. Studies have shown participants to be sensitive to the distribution hierarchy in their native non-European music (Castellano et al 1984; Von Hippel, Huron, and Harnish 2006; Khrumhansl et al 2000). While the expertise of these participants had likely been cultivated by a lifetime of musical experience, both Castellano et al (1984) and Krumhansl et al (2000) found that even non-experts attended to the distributional hierarchy present in the stimuli, even when doing so required them to suppress their prior musical knowledge. Jonaitis and Saffran (2009) found that participants were able to detect mistakes in novel musical systems learned entirely through exposure during the course of an experiment. As a culture, we certainly have been exposed to a greater amount of common-practice music than we have rock music. Nevertheless, rock music has been at the forefront of our musical culture for over sixty years, and, as the experimental evidence suggests, this amount of exposure may be 39

sufficient for us to engender an understanding of rock‘s distributional hierarchy of musical events. It is the aim of this dissertation to investigate whether the idiosyncrasies of rock‘s harmonic language have impacted our musical expectations to a degree that separates them from those held for common-practice music. Do listeners have graded expectations of harmony in rock music? The majority of studies of harmonic expectation include relatively few chords as stimuli. In priming paradigms, chords used as targets are either very closely or very distantly related to primes.40 While this allows for a sound experimental design, conclusions have typically been limited to claiming that listeners expect closely related targets to follow closely related primes. However, it has also been demonstrated—albeit in decidedly fewer studies—that we have graded expectations when presented with various combinations of diatonic triads (Krumhansl 1990; Lhost and Ashley 2006). Bigand, Parncutt, and Lerdahl (1996) included non-diatonic triads and seventh chords along with diatonic triads in their study; however, these chords were always preceded and followed by tonic harmony. The first experiment presented in this dissertation takes these studies as a point of departure. Stimuli include both diatonic and non-diatonic triads preceded or followed by a single primary triad (I, IV, or V). One of its aims is to provide a more detailed description of listeners‘ expectations of harmony when presented with a wider variety of chords than have previously been investigated. The aforementioned results published by both Krumhansl (1990) and Bigand et al (1996) correlated with quantitative models of tonal hierarchy.41 These metrics will provide a means of comparing the findings of this experiment with those demonstrated by previous empirical studies and illustrated by music-theoretical models. What is the relationship between expectations of temporality and harmony in a rock music context? Some scholars have suggested that rock music operates in fouror eight-measure phrase units within which the harmonic behavior is relatively free (Björnberg 1989/2001). This implies that the structural boundaries of these phrase units should be perceptually salient events demarcated by a change in harmony; a fact that is evident in a vast majority of twelve-bar blues songs (Lhost and Ashley 2006, 1284). 40

Among the most obvious examples of such studies are those by Jamshed Jay Bharucha and his numerous collaborators (Bharucha and Stoeckig 1986; Tekman and Bharucha 1998; Justus and Bharucha 2001). However, even in experiments that did not use a priming paradigm, it has been most common for stimuli used in studies of harmony to include only two levels of this variable (a common chord and an uncommon chord), such as Schmuckler 1989, Steinbaus et al 2006, and others. Krumhansl‘s metric was based on Piston‘s table of chord-root progressions. While Piston‘s table was not expressly quantitative, his strict categorization of chord pairs was suitable enough for calculating statistical correlation. 41

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Another ubiquitous feature of rock music is the prevalence of common time, with quarter-note beats emphasized by the consistent presence of drums. This emphasis on rhythmic periodicity perhaps explains why melodic and harmonic onsets and termini in rock music are often slightly misaligned with the metrical framework of the song and/or with each other. David Temperley (2007) refers to this phenomenon as the ―melodicharmonic divorce‖ in rock music. As discussed previously in this chapter, the body of research that has investigated expectation of periodicity, timing, and harmony together has found that disrupted or absent periodicity negates expectations for all but the most salient harmonic events—namely authentic cadences (Schmuckler and Boltz 1994; Tillman and Lebrund-Guillaud 2006). Early event onsets are least expected (Tillman and Lebrund-Guillaud 2006) and also affect expectations for long-range temporal regularity, specifically cadences occurring on strong beats in successive phrases (Bigand et al 1999). The second experiment in this dissertation explores the potential effects of periodicity and timing on harmonic expectation in the first two phrases of a twelve-bar blues song. It investigates whether listeners‘ temporal expectations are rigid (strictly adhering to the metrical structure of the schema), graded (higher ratings for metrically strong events among stimuli with atypical timing), or non-existent (no preference for timing among all stimuli). Moreover, it addresses whether temporal disruptions affect listeners‘ harmonic expectations. Is it possible that our expectation for a chord change to occur at a specific location outweighs our expectation of what that chord will be? In other words, is our expectation of timing stronger than our expectation of harmony? Does harmony affect expectations of musical form (or vice versa)? While several studies have investigated the impact of harmony in longer musical contexts (Smith and Melara 1990; Bigand and Pineau 1997; Bigand et al 1999), very few have used contexts that potentially elicit strong expectations themselves. In a 2006 experiment, Elizabeth Lhost and Ric Ashley investigated the impact of chord substitutions on harmonic expectation in twelve-bar blues songs. Stimuli consisted of complete twelve-bar patterns that included a single diatonic chord substitution in one of three locations: m.5, m.9, and m.11. Three substitutions were used in each location and were categorized by the authors as ―expected,‖ ―acceptable,‖ or ―unacceptable‖ chords in these locations. The chords were chosen based on their frequency of occurrence in a corpus of blues songs. ―Expected‖ chords occurred frequently and consistently in the same location, while ―unacceptable‖ chords rarely occurred throughout the corpus. Chords were categorized as ―acceptable‖ if they occurred relatively frequently in the repertoire, but not at that corresponding location. Lhost and Ashley demonstrated that participants had 41

graded harmonic expectations, consistently differentiating among the three chord categories. They also found that participants made faster judgments when the chord substitution occurred later in the excerpt, suggesting that harmonic expectations are narrowed when contextual evidence is increased. Participants‘ response times were impacted by location and chord type, though the effect was not consistent across type or location. Nevertheless, Lhost and Ashley concluded that judgments of fit (expectations) are affected by contextual information (the presence of a known musical schema such as a twelve-bar blues form) and not solely by general schematic expectations of Western tonal music (Lhost and Ashley 2006, 1287). Lhost and Ashley‘s findings raise two points pertinent to the final experiment in this dissertation. The first is that expectations of specific schemata can override more general musical expectations. In their experiment, this was reflected by participants‘ higher ratings for chords expected in specific contexts (such as IV in m.5) over chords that generally receive high ratings in goodness of fit judgments (such as V). My experiment investigates this issue more closely by using as stimuli a greater number of replacement chords (all major and minor triads) in more locations within the twelve-bar blues form. Furthermore, since these stimuli all feature harmonic motion to or from primary triads, the data is apt for comparison with the results of my first experiment. The comparison of ratings for two-chord successions heard in the abstract with ratings for the same successions heard in a longer and more specific musical context will allow for a greater understanding of the role that context plays in harmonic expectation. Second, the experiment investigates whether harmony shapes our expectations of form within the twelve-bar blues. Lhost and Ashley found that participants were more sensitive (and thus reacted more quickly) to harmonic events in the last phrase of the twelve-bar form. Since they only used three chords in each location (and did not use the same chords in each location), Lhost and Ashley were unable to investigate the relationship between these domains in greater detail.42 Is it possible that specific chords serve to orient the listener within the larger musical structure? For instance, does the presence of V serve as a structural marker for the last phrase in the form, or does it simply sound good in any location because it is highly predictable? To my knowledge, an empirical investigation such as this has yet to be undertaken, and would provide insight into our understanding of multiple levels of harmonic expectation in a form central to the rock idiom. 42

Lhost and Ashley admitted that they may have inappropriately categorized some of the chords used in their experiment (Lhost and Ashley 2006, 1287). My experiment will have no such difficulty, since it uses all major and minor triads as stimuli.

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CHAPTER FOUR THE EFFECT OF STYLE-PRIMING ON HARMONIC EXPECTATION Music theorists, as discussed in previous chapters, often suggest that chord successions in common-practice music are governed by syntax, and cognitive studies have confirmed that listeners expect chord successions that adhere to these syntactical rules. There is less agreement among music theorists regarding principles of chord succession in non-common-practice music, such as blues or rock. Some suggest that the syntax is the same for both contexts, while others propose new syntactical rules for blues/rock music. This study investigates whether listeners have different expectations for chord successions when the chords are presented in two different stylistic contexts: blues/rock music and classical music. Harmonic expectation can be influenced by numerous factors, including chord relatedness (Bharucha and Stoeckig 1986 and 1987; Krumhansl 1990), global harmonic context (Bigand and Pineau 1997), temporal organization (Bigand et al 1999; Tillman and Lebrun-Guillaud 2006), and voice leading (Poulin-Charronnat et al 2005). While the question of stylistic context is not explicitly raised in these studies, it is likely that participants in these experiments interpreted the stimuli as representing common-practice music. As David Huron has noted (Huron 2006, 207), North American listeners tend to activate common-practice musical schemata even in the absence of stylistic context. The current study has two aims. First, it examines listener expectations of two-chord successions that include the so-called ―primary‖ triads (I, IV, and V); that is, all major and minor triads preceding I, IV, and V, and all major and minor triads following I, IV, and V.43 Primary triads are central to the harmonic structure of both the twelve-bar blues and common-practice music. Second, the experiment investigates the effect of stylistic context on listeners‘ expectations. To create this musical context, the key for each trial is established by a commercial recording that activates the appropriate stylistic schema. Recall that listeners require less than 200 milliseconds to identify a 43

The decision to limit stimuli to these combinations was one of practicality. It would have been too taxing for participants to hear all possible combinations of major and minor triads. Chromatic chords could have been excluded; however, modally inflected scale degrees (and the chords they are built upon) are important to the blues and rock aesthetic. Given the prominence of the primary triads in the twelvebar blues structure, this was a reasonable compromise.

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musical genre (Gjerdingen and Perrot 2008). Presumably, when participants hear a stylistically clear excerpt, they should be inclined to assess the ensuing harmonic progression in the context provided by the recording. If the data exhibit differences between ratings of identical two-chord successions it would support the theory that listeners may possess two (or more) distinct sets of harmonic expectations.

EXPERIMENT 1 Task In this experiment, two groups of subjects (N = 56) listened to pairs of triads and rated how good each harmonic succession sounded. Each triad pair was primed by a brief key-confirming excerpt of either blues/rock or classical music drawn from commercial recordings, always establishing the key of Eb major. Stimuli were presented in blocks corresponding to the musical style of the prime to strengthen listeners‘ notions of stylistic context.

Hypotheses Participants will provide high ratings for successions that feature common-practice characteristics such as typical root motion. While both blocks will receive high ratings for this type of harmonic motion, ratings will be higher when these progressions are primed by classical music cues. In common-practice theory, chords with dominant function incite strong expectations for a tonic chord to follow. Christopher Doll describes bVII and bIII (which contain the subtonic rather than the traditional leading tone) as ―rogue dominants‖ in the rock idiom (Doll 2007, 24-25). If these chords have a similar function in rock music, then they should pique the same expectations. Thus, idiomatic blues/rock progressions such as bVII-I, V-IV, and bIII-I will receive higher ratings when primed by blues/rock cues. More broadly, a wider variety of chords often lead to tonic harmony in blues/rock music. Thus, in this experiment, successions that end on tonic will receive higher ratings when primed by blues/rock cues. As discussed in Chapter 2, ratings will be interpreted as levels of expectancy in accordance with the concept of misattribution.

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Participants All participants were volunteers enrolled in Music Theory 3 (a required course for undergraduate music majors) at Florida State University. The 33 female and 23 male participants ranged in age from 18 to 23 years (average of 19.56 years).

Stimuli Four representative recordings, two each from the blues/rock and classical repertories, served as contextual cues for the experiment. ―Boot Hill‖ and ―Give Me Back My Wig,‖ both by Stevie Ray Vaughn and Double Trouble, were chosen as the representative blues/rock recordings. The first movement of Mozart‘s Concerto for Two Pianos and Orchestra No. 10 in Eb Major K. 365 and the first movement of Mozart‘s Symphony No. 1 in Eb major K. 16, recorded by the English Baroque Soloists (conducted by John Eliot Gardiner) and the Academy of St. Martin-in-the-Fields (conducted by Neville Marriner) respectively, were chosen as the representative classical recordings. All recordings included an extended passage that clearly established Eb major as the tonal center. Within stylistic groups, selections were made based on consistency of timbre and idiomatic features. Between stylistic groups, the recordings were chosen for their disparity in this same regard. One excerpt was selected from each recording and edited to a length of 24 seconds. Single two-second clips were selected from each of the 24-second excerpts to be used as shorter cues. The triads that followed these contextual cues were constructed with three Shepard tones to control for any influence of chord inversion or register.44 Each chord was 750ms in length; successive chords were separated by 500ms of silence. Question prompts, contextual cues, and chord successions were combined with multi-track audio editing software. Any volume differences between the recordings and the synthesized chords were normalized

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Shepard tones are complex tones that consist of ten octave-related sine tones sounded together. The amplitudes of the sine tones share a logarithmic relationship that results in a fusion that makes it nearly impossible for listeners to discern the sounding octave (Shepard 1964). When triads are constructed with Shepard tones, it is unlikely that listeners can distinguish inversion.

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Equipment Question prompts were synthesized using the MARY Text-to-Speech System. Recordings were transcoded from CD to .wav files with Exact Audio Copy and edited with Audacity. Shepard tones were synthesized with Csound and combined into chords with Audacity.45 Each stimulus element was then combined, edited, and rendered in REAPER, a multi-track audio editing environment. Finally, all stimuli were compiled and burned onto CD. All of these tasks were completed on a Lenovo R61i laptop computer. During the experiment proper, stimuli were played for participants over a high-quality stereo system in a quiet classroom.

Design and Procedure Table 4.1 outlines the design of this experiment. Participants were randomly assigned to one of two groups: group 1 heard only blues/rock cues while group 2 heard only classical cues. Before the experiment proper, participants heard a brief description of the procedure, followed by two practice questions that allowed them to grow accustomed to the speed of the trials and to the rating scale.46 Trials were presented to listeners in blocks of 67 or 69 trials corresponding to the recordings used in the stimuli.47 The first key- and style-establishing cue of each block lasted 24 seconds. Subsequent trials in each block used a single two-second cue drawn from the same excerpt. The two-chord successions used in each group were presented in random order across both blocks. The chords used in this experiment included all non-redundant successions of major and minor triads to and from each of the primary triads (I, IV, or V). Overall, 132 successions were used as stimuli.48 With the inclusion of four non-data questions, 136 trials were heard in each group. Following each trial, participants were given four seconds to rate how good the chord succession sounded on a scale from 1(―sounds bad‖) to 6 (―sounds good‖). After 45

Clifton Callender graciously provided the Csound Shepard tone templates.

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A transcript of the instructions for this experiment is included in Appendix A.

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There were 66 trials in each block. In addition, three non-data trials were heard in the first block and one non-data trial was heard in the second block, resulting in 69 and 67 trials per block, respectively. 48

There are three primary triads, twenty-three remaining major and minor triads, and two orderings: 3*23*2=138. Six of these combinations occur twice in the collection of 138: IV-I, I-IV, V-I, I-V, IV-V, and V-IV. The redundancies were removed from the stimuli, leaving 132 unique successions.

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the experiment, participants completed a survey of basic biographical information as well as time spent in university, musical training, primary instruments played, and secondary instruments played. The survey also asked participants to indicate their time spent listening to, performing, composing or arranging, and general interest in ten different musical genres.

Results and Discussion The observations presented below are organized in relation to the theoretical systems discussed in Chapters 2 and 3. In each case, the effects of stylistic context are also observed to ascertain any differences in listeners‘ expectations when primed with blues or classical music. Root-motion theory A one-way analysis of variance (ANOVA) revealed a main effect of root motion (p < .001).49 Table 4.2 and Figure 4.1 show that listeners gave high ratings for successions that included one of the three most prevalent root motions found in major-key common-practice music: descending fifth, descending minor third, and ascending major second. Root motion by ascending perfect fifth and ascending major third also received high ratings; however, it is important to realize that two successions producing ascending fifth root motion involved exclusively primary triads (I-V and IV-I). Overall, listeners strongly preferred successions that included multiple primary triads (p < .001; see Table 4.3 and Figure 4.2); when individual relevant data subsets are grouped by ordered pitch-class interval (OPCI), we can see that successions containing multiple primary triads were rated significantly higher in each case. Table 4.4 and Figures 4.3-4.6 depict the overall ratings grouped by the number of primary triads used as well as the ratings for the individual relevant data subsets grouped by OPCI. Table 4.5 and Figure 4.7 show that, among successions that do not include multiple primary triads or multiple primary triad roots (such as i-IV or v-I), there was a main effect of root

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Since the chord successions were constructed with Shepard tones, it is perhaps most accurate to refer to the intervals formed between chord roots as ordered pitch-class intervals (OPCIs). For the purpose of drawing a parallel between these results and the idioms of common-practice harmony, I will sometimes refer to root motion by common intervals, such as descending fifths, even though pitch height (and thus, interval ―direction‖) in these successions has no objective meaning.

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motion on ratings (p < .001).50 Note that these results are nearly identical to those presented in Figure 4.2, suggesting that the presence of multiple primary triads was not solely responsible for listeners‘ high ratings of successions that included common root motion. None of these main effects interacted with stylistic context at the level of significance. While the results revealed that listeners have heightened expectations for certain root progressions, these expectations were significantly affected by scale-degree context. A series of one-way ANOVAs revealed a main effect of first chord on ratings across all data grouped by OPCI. The p-values for these tests are summarized in Table 4.6 and indicate that there were significant differences between ratings within all OPCI groups. These results show that listeners discriminate among specific instances of the same root motion.51 For instance, descending fifth progressions that began on II, ii, or V (yielding the progressions, II-V, ii-V, V-i, and V-I, respectively) were rated significantly higher than those that began on any other chord. There was no interaction between first chord and style among any of these groups of data. In Chapter 1, I suggested that root motion absent of scale-degree context52 was a plausible foundation for a theory of rock harmony, since rock progressions tend to be less dependent upon a goal-oriented motion toward the tonic. The significant differences among mean ratings for particular instances of root progressions indicate that successions with equivalent root motion do not incite the same level of expectancy in listeners. Moreover, the lack of significant interaction between first chord and style suggests that root motion alone does not provide a good model for listeners‘ expectations of two-chord successions when primed by either a classical or blues context. Comparison with other quantitative ratings of chord pairs Given that listeners distinguished among specific instances of root progressions, a more detailed statistical analysis of chord combinations was performed. A univariate ANOVA reveals a significant preference for specific chord successions (p