Evolving Targeted Sight Reading Exercises

Intelligent Tools for Deliberate Music Practice: Evolving Targeted Sight Reading Exercises

Charlotte Pierce

A thesis presented for the degree of Doctor of Philosophy

2019

Abstract

Musical skills are generally considered to be complex and difficult to learn. Recently, efforts have been made to create digital applications for teaching these skills and enhancing or encouraging student’s deliberate practice of them. However, existing work in this space does not take advantage of the capabilities of modern technology. Often digital tools are simply screen- based translations of existing physical materials and offer no additional or ‘smart’ functionality. The purpose of this research is to determine ways in which technology can be used to enhance existing or create new digital music teaching tools and aides. This project specifically considers the learning of musical sight reading skills. There is a significant resource constraint in this area. Sight reading is the ability to perform a piece or phrase of music without having seen it before. Therefore, as soon as an exercise has been completed it can no longer be considered a sight reading exercise. This means that the traditional approach of using expert- written practice material is ineffective, as such material is expensive to produce and limited in quantity. As deliberate practice is key to gaining competence in sight reading, this resource constraint is a large barrier for musicians seeking to develop sight reading skills. The work presented in this thesis primarily aims to consider the opportunities for developing digital applications which enable user’s deliberate practice of musical sight reading. It also seeks to model an example of such an application and validate its effectiveness against existing solutions and standard practice. This application is developed with the aim of generating music that, whilst being playable by a human, is aesthetically pleasing, is adaptive in difficulty, and can incorporate specific technical skills. An application with these characteristics represents a solution to overcoming the resource constraint described above.

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Acknowledgements

First thanks must go to my advisors. To Dr. Clinton Woodward, thank you for encouraging my research endeavours from as far back as my undergraduate studies. You helped me prove to myself that I could be successful in this space and, more importantly, never seemed to doubt that I would produce results. Dr. Anthony Bartel, thank you for taking a chance on a random student you had just met, then accepting more responsibility than you originally signed up for. Your input has been invaluable. To Professor Tim Hendtlass, I can not thank you enough for joining my team. Jumping onto a project part way through is never easy, but from the moment you agreed to help you have consistently provided sound advice and guidance. As Clinton would say, you “really don’t know how to be retired”! To my parents, Dianne and Mark, thank you for supporting me throughout my education, not just this last part. Without you both I would not have had the resources to get to the start of a PhD, let alone ﬁnish it. I don’t think I can repay you, but I can try to do so in the form of free dog sitting and tech support. To my sisters, Marianne and Louise, thanks for pretending to be interested in my ‘nerd talk’. In your own ways you have both demonstrated to me the value in whole-heartedly working towards a goal, even when it’s really, really hard. I hope I can support you both in the pursuit of your goals as you have supported me with with mine. To my friends and valued members of the “Suffer’o’wave” (and any other titles we may use in the future), you are anything but normal people. Thanks for listening to my stress rants, and always responding with appropriately funny pictures and gifs. Amy, as always you have gone above and beyond the duties of an ordinary friend, but I always knew you were extraordinary. Somehow I will get you back for that (I mean this in the nicest way possible, of course). It will probably involve ﬁre. Finally, to James. You have been the chief pep talk giver, forgiver of grumpy moods, bringer of snacks, and executive in charge of Taking Breaks™. Thank you for being that person, and thank you for the thousands of other things, big and small, that you did to help me and support me over the past few years. I am beyond grateful for all of it.

Charlotte Pierce, 2019

Publications Arising from this Thesis

Some of the work described in this thesis has been published in the following paper:

Charlotte Pierce and Clinton J. Woodward. A taxonomy for describing content and activities in music education. In Proceedings of the Australian Society for Music Education (ASME) National Conference, 2017

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Declaration

I declare that this thesis contains no material that has been accepted for the award of any other degree or diploma and to the best of my knowledge contains no material previously published or written by another person except where due reference is made in the text of this thesis.

Charlotte Pierce, 2019

Contents

1 Introduction 1 1.1 Context ...... 1 1.2 Research Questions ...... 2 1.3 Key Contributions ...... 3 1.4 Thesis Structure ...... 4

2 Background 7 2.1 Overview ...... 7 2.2 Challenges in Music Education ...... 7 2.3 Use of Technology in Music Education ...... 9 2.4 Musical Sight Reading ...... 11 2.5 Software for Learning and Practicing Musical Sight Reading ...... 12 2.6 Human Algorithms for Generating Music ...... 16 2.7 Computer Music Generation ...... 18 2.8 Algorithms for Computer Music Generation ...... 20 2.9 Evolutionary Algorithms for Computer Music Generation ...... 28 2.10 Summary ...... 30

3 A Taxonomy for Describing Musical Content and Activities 31 3.1 Overview ...... 31 3.1.1 Background ...... 32 3.1.2 Chapter Structure ...... 33 3.2 Content Areas ...... 35 3.2.1 Overview ...... 35 3.2.2 Reading ...... 35 3.2.3 Rhythm ...... 35 3.2.4 Scales ...... 38 3.2.5 Elements of Harmony ...... 38 3.2.6 Harmonic Structures ...... 41 3.2.7 Style ...... 41 3.2.8 Instrument-Speciﬁc ...... 44 3.2.9 Historical and General Knowledge ...... 44 3.3 Activities ...... 47 3.3.1 Overview ...... 47 3.3.2 Recognition Activities ...... 48 3.3.2.1 Overview ...... 48

xi CONTENTS

3.3.2.2 Auditory Recognition Activities ...... 48 3.3.2.3 Visual Recognition Activities ...... 50 3.3.3 Description Activities ...... 50 3.3.3.1 Overview ...... 50 3.3.3.2 Auditory Description Activities ...... 50 3.3.3.3 Visual Description Activities ...... 53 3.3.4 Playback Activities ...... 53 3.3.4.1 Overview ...... 53 3.3.4.2 Visual Playback Activities ...... 53 3.3.4.3 Memory Playback Activities ...... 56 3.3.5 Notation Activities ...... 57 3.4 Discussion ...... 58 3.5 Summary ...... 59

4 Taxonomy Validation: Music Aptitude Tests 61 4.1 Overview ...... 61 4.2 Mapping Tests to Taxonomy ...... 61 4.2.1 Overview ...... 61 4.2.2 Seashore’s Measures of Musical Talents ...... 61 4.2.3 Revesz’s Tests of Musical Ability ...... 62 4.2.4 Kwalwasser’s Tests and Measurements in Music ...... 62 4.2.4.1 Overview ...... 62 4.2.4.2 Kwalwasser-Ruch Test of Musical Accomplishment ...... 63 4.2.4.3 Kwalwasser Test of Music Appreciation ...... 63 4.2.4.4 Kwalwasser-Dykema (K-D) Musical Talent Tests ...... 64 4.2.4.5 Kwalwasser’s Music Talent Test ...... 65 4.2.5 Schoen’s Tests of Musical Feeling and Understanding ...... 65 4.2.6 Torgerson-Fahnestock Tests ...... 65 4.2.7 Drake Musical Aptitude Tests ...... 67 4.2.8 Gordon’s Aptitude Tests ...... 67 4.2.8.1 Overview ...... 67 4.2.8.2 Gordon’s Musical Aptitude Proﬁle (MAP) ...... 67 4.2.8.3 Gordon’s Measures of Music Audiation ...... 68 4.2.9 Bentley’s Measures of Musical Abilities ...... 68 4.2.10 Wing’s Tests of Musical Ability and Appreciation ...... 69 4.2.11 Iowa Tests of Music Literacy ...... 69 4.2.12 Colwell Music Achievement Test ...... 70 4.2.13 Karma’s Test of Structure Ability ...... 70 4.2.14 Musical Aptitude Indicator ...... 70 4.2.15 The Proﬁle of Music Perception Skills (PROMS) ...... 70 4.3 Results ...... 72 4.3.1 Activity Types ...... 72 4.3.2 Content Areas ...... 75 4.3.3 Subtest Equivalence ...... 79

xii CONTENTS

4.3.3.1 Overview ...... 79 4.3.3.2 Auditory Description Activities of Reading Content ...... 79 4.3.3.3 Auditory Description Activities of Rhythm Content ...... 80 4.3.3.4 Auditory Description Activities of Scales Content ...... 80 4.3.3.5 Auditory Description Activities of Elements of Harmony Content 80 4.3.3.6 Auditory Description Activities of Harmonic Structures Content . 80 4.3.3.7 Auditory Description Activities of Style Content ...... 83 4.3.3.8 Auditory Description of Historical of General Knowledge Content 83 4.3.3.9 Visual Description Activities of Reading Content ...... 83 4.3.3.10 Visual Description Activities of Rhythm Content ...... 83 4.3.3.11 Memory Playback Activities of Rhythm Only ...... 86 4.4 Discussion ...... 86 4.5 Summary ...... 90

5 iOS Music Teaching Applications: State of the Art 91 5.1 Overview ...... 91 5.2 Method ...... 91 5.2.1 Overview ...... 91 5.2.2 Purpose ...... 92 5.2.3 Application Selection ...... 92 5.2.4 Data Collection ...... 94 5.2.4.1 Overview ...... 94 5.2.4.2 Review Template ...... 94 5.2.4.3 Content Areas and Activities ...... 104 5.2.4.4 Update History ...... 105 5.2.4.5 Characteristic Tagging ...... 105 5.2.5 Collection Process ...... 106 5.3 Results ...... 106 5.3.1 Coverage of Content and Activities ...... 106 5.3.2 Depth and Focus of Content and Activities ...... 108 5.3.2.1 Characteristics of the Depth and Focus Ratings ...... 108 5.3.2.2 Depth and Focus Ratings ...... 112 5.3.3 Co-occurrence of Content and Activities ...... 116 5.3.4 Common Application Characteristics ...... 119 5.3.5 Other Application Characteristics ...... 122 5.3.5.1 Background ...... 122 5.3.5.2 Audience ...... 125 5.3.5.3 Feedback Model ...... 129 5.3.5.4 Incentive and Achievement Model ...... 133 5.3.5.5 Progression Model ...... 135 5.3.6 Characteristic Tags ...... 135 5.3.6.1 Tag Presence ...... 135 5.3.6.2 Tag Co-occurrence ...... 136 5.4 Discussion ...... 136

xiii CONTENTS

5.5 Summary ...... 138

6 An Algorithm for Generating Musical Sight Reading Exercises 139 6.1 Overview ...... 139 6.2 Evolutionary Algorithms ...... 140 6.2.1 Introduction ...... 140 6.2.2 The Evolutionary Process ...... 140 6.2.3 Genetic Operators ...... 142 6.2.3.1 Overview ...... 142 6.2.3.2 Crossover ...... 143 6.2.3.3 Mutation ...... 143 6.3 Melody Representation ...... 143 6.3.1 Overview ...... 143 6.3.2 Melody Trees in the Literature ...... 144 6.3.3 The Case for a Novel Melody Tree ...... 148 6.3.4 Designing a Novel Melody Tree ...... 151 6.3.4.1 Supporting Compound Time Signatures ...... 152 6.3.4.2 Supporting Triplets ...... 154 6.4 Genetic Operators for Evolving Sight Reading Exercises ...... 154 6.4.1 Crossover ...... 154 6.4.2 Mutation ...... 161 6.5 Parent Selection ...... 164 6.6 Fitness ...... 165 6.7 Population Diversity ...... 168 6.8 Initialisation ...... 168 6.9 Algorithm Conﬁguration ...... 171 6.10 Summary ...... 173

7 Experimental Design 175 7.1 Overview ...... 175 7.2 A Method for Designing Algorithm Conﬁgurations ...... 175 7.3 Source Exercises ...... 176 7.3.1 Overview ...... 176 7.3.2 Characteristics of the Grade 1 Source Exercises ...... 176 7.3.3 Characteristics of the Grade 2 Source Exercises ...... 177 7.3.4 Characteristics of the Grade 3 Source Exercises ...... 177 7.3.5 Use of Key Signatures ...... 179 7.3.6 Use of Time Signatures ...... 179 7.3.7 Length ...... 182 7.3.8 Pitch Range ...... 182 7.3.9 Proportion of Notes vs. Rests ...... 185 7.3.10 Note Lengths ...... 188 7.3.11 Rest Lengths ...... 188 7.3.12 Intervals ...... 188 7.4 The Algorithm Conﬁgurations ...... 191

xiv CONTENTS

7.5 Forming A Method for Evaluating the Algorithm Output ...... 192 7.5.1 Overview ...... 192 7.5.2 Using the Fitness Measures ...... 193 7.5.3 Elements of a Good Musical Sight Reading Exercise ...... 194 7.5.4 Extracting Rules from the Literature ...... 194 7.6 A Method for Evaluating the Quality of Algorithmically Generated Musical Sight Reading Exercises ...... 197 7.6.1 General Approach ...... 197 7.6.2 Rules for Technical Appropriateness ...... 202 7.6.3 Rules for Melodic Aesthetics ...... 203 7.6.4 Rules Relating to Both Technical Appropriateness and Melodic Aesthetics204 7.6.5 Recording Broken Rules ...... 205 7.7 Summary ...... 205

8 Evaluating the Evolutionary Algorithm 207 8.1 Overview ...... 207 8.2 General Characteristics of the Generated Exercises ...... 208 8.2.1 Overview ...... 208 8.2.2 Grade 1 ...... 208 8.2.3 Grade 2 ...... 208 8.2.4 Grade 3 ...... 208 8.3 Fixed Characteristics ...... 210 8.3.1 Use of Key Signatures ...... 210 8.3.2 Use of Time Signatures ...... 210 8.3.3 Length ...... 210 8.3.4 Pitch Range ...... 212 8.4 Target Characteristics ...... 212 8.4.1 Proportion of Notes vs. Rests ...... 212 8.4.2 Note Lengths ...... 215 8.4.3 Rest Lengths ...... 217 8.4.4 Intervals ...... 219 8.5 Fitness ...... 221 8.5.1 Validating the Implementation of the Fitness Measures ...... 221 8.5.2 Fitness of the Generated Exercises ...... 221 8.5.3 Diversity of the Evolved Populations ...... 238 8.6 Likert Quality Ratings ...... 238 8.6.1 Grade 1 ...... 238 8.6.2 Grade 2 ...... 240 8.6.3 Grade 3 ...... 244 8.7 Rule Violations ...... 248 8.8 Repeatability in the Quality of Output ...... 248 8.8.1 Fixed Characteristics ...... 248 8.8.2 Proportion of Notes vs. Rests ...... 253 8.8.3 Note Lengths ...... 253

xv CONTENTS

8.8.4 Rest Lengths ...... 253 8.8.5 Intervals ...... 253 8.8.6 Likert Quality Ratings ...... 263 8.9 Summary ...... 263

9 Discussion and Future Work 267 9.1 Overview ...... 267 9.2 Research Questions in Review ...... 267 9.3 Expanding the Taxonomy ...... 269 9.4 Opportunities for Software in Music Education ...... 269 9.5 Current Capabilities of the Evolutionary Algorithm ...... 270 9.6 Future Directions for Algorithmic Development ...... 272 9.7 Building Better Models of Expert Knowledge ...... 275 9.8 Applying the Algorithm to Other Instruments ...... 276 9.9 Summary ...... 277

10 Thesis Summary 279 10.1 Research Questions ...... 279 10.2 Key Contributions ...... 280

References 281

Software References 295

A Musical Glossary 299 A.1 Deﬁnitions ...... 299 A.2 Basic Concepts ...... 300 A.2.1 Pitch ...... 300 A.2.2 Rhythm ...... 300 A.2.3 Key Signatures and Scales ...... 300 A.2.4 Intervals ...... 302

B iOS Music Teaching Applications: State of the Art Extras 303 B.1 Depth and Focus of Content and Activities ...... 303 B.1.1 Depth and Focus Ratings ...... 303 B.1.1.1 Auditory Recognition Activities ...... 303 B.1.1.2 Visual Recognition Activities ...... 303 B.1.1.3 Auditory Description Activities ...... 303 B.1.1.4 Visual Description Activities ...... 308 B.1.1.5 Visual Playback Activities ...... 308 B.1.1.6 Memory Playback Activities ...... 308 B.1.1.7 Notation Activities ...... 308 B.2 Application Structures ...... 308 B.3 Application Store Category ...... 312 B.4 Application Monetisation ...... 312

xvi CONTENTS

C Characteristics of Published Sight Reading Exercises: Grade 1 Details 323 C.1 Metadata: Key and Time Signatures, Lengths, Ranges ...... 323 C.2 Percentage of Notes and Rests ...... 325 C.3 Note Lengths in Detail ...... 326 C.4 Rest Lengths in Detail ...... 330 C.5 Intervals in Detail ...... 331

D Characteristics of Published Sight Reading Exercises: Grade 2 Details 335 D.1 Metadata: Key and Time Signatures, Lengths, Ranges ...... 335 D.2 Percentage of Notes and Rests ...... 336 D.3 Note Lengths in Detail ...... 338 D.4 Rest Lengths in Detail ...... 342 D.5 Intervals in Detail ...... 343

E Characteristics of Published Sight Reading Exercises: Grade 3 Details 347 E.1 Metadata: Key and Time Signatures, Lengths, Ranges ...... 347 E.2 Percentage of Notes and Rests ...... 349 E.3 Note Lengths in Detail ...... 351 E.4 Rest Lengths in Detail ...... 356 E.5 Intervals in Detail ...... 357

F Algorithm Parameters Used to Generate Grade 1 Exercises 361

G Algorithm Parameters Used to Generate Grade 2 Exercises 369

H Algorithm Parameters Used to Generate Grade 3 Exercises 377

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List of Figures

2.1 The interface of the videogame Rocksmith when playing a song. Taken from [45]. 10 2.2 The interface of randomsheetmusic.com [256] ...... 13 2.3 Music generated by randomsheetmusic.com using the default interface shown in Figure 2.2 ...... 14 2.4 The feedback interface of Etude Sight Reader [232]. Green indicates correctly played notes and red indicates errors. Textual markers describe the errors. . . . . 14 2.5 A level four piece for the tenor recorder generated by Sight Reading Factory [226] 15 2.6 Definition of each level of difficulty for the five musical components in PiaNote. Taken from [176]...... 15 2.7 The Arca Musarithmica device illustrated by Kircher [88] ...... 17 2.8 An example melody, ‘Push Button Bertha’, produced by the DATATRON automated composition machine in 1956 ...... 19 2.9 An advertisement for the GENIAC Electric Brain. Taken from [53]...... 19 2.10 Techniques from the field of artificial intelligence which have been applied to algorithmic composition. Recreated from Nierhaus [143]. The focus of this work, genetic algorithms, has been highlighted...... 21 2.11 An alternative summary to Figure 2.10 of techniques from the field of artificial intelligence which have been applied to algorithmic composition. Taken from Fernandez´ and Vico [58]...... 22 2.12 Tasks considered to be good candidates for evolutionary computation. Taken from Biles [22]...... 29

3.1 An overview of the taxonomy ...... 32 3.2 The colours used to visually refer to items in the taxonomy. Line colour relates to content area and text colour denotes the kind of activity...... 34 3.3 The proposed content areas in the taxonomy ...... 36 3.4 Examples of the knowledge included in the ‘Reading’ content area ...... 36 3.5 Examples of knowledge from the ‘Reading’ content area being presented in iOS applications ...... 37 3.6 Examples of the knowledge included in the ‘Rhythm’ content area ...... 38 3.7 Examples of knowledge from the ‘Rhythm’ content area being presented in iOS applications ...... 39 3.8 Examples of the knowledge included in the ‘Scales’ content area ...... 39 3.9 Examples of knowledge from the ‘Scales’ content area being presented in iOS applications ...... 40 3.10 Examples of knowledge included in the ‘Elements of Harmony’ content area . . . 41

xix LISTOF FIGURES

3.11 Examples of knowledge from the ‘Elements of Harmony’ content area being presented in iOS applications ...... 42 3.12 Examples of knowledge included in the ‘Harmonic Structures’ content area . . . . 42 3.13 Examples of knowledge from the ‘Harmonic Structures’ content area being presented in iOS applications ...... 43 3.14 Examples of knowledge included in the ‘Style’ content area ...... 44 3.15 Examples of knowledge from the ‘Style’ content area being presented in iOS applications ...... 45 3.16 Examples of knowledge included in the ‘Instrument-speciﬁc’ content area . . . . . 46 3.17 ‘Instrument-Speciﬁc’ content presented in Learn Guitar Theory [259], where the user is given a description of how to hold a guitar pick ...... 46 3.18 Examples of knowledge included in the ‘Historical or General Knowledge’ content area ...... 46 3.19 The proposed activity types ...... 47 3.20 Subtypes of ‘Auditory Recognition’ activities ...... 49 3.21 Subtypes of ‘Visual Recognition’ activities ...... 51 3.22 Subtypes of ‘Auditory Description’ activities ...... 52 3.23 Subtypes of ‘Visual Description’ activities ...... 52 3.24 Subtypes of ‘Visual Playback’ activities ...... 54 3.25 Examples of each subtype of ‘Visual Playback’ activity ...... 55 3.26 Subtypes of ‘Memory Playback’ activities ...... 56 3.27 Subtypes of ‘Notation’ activities ...... 58

4.1 The distribution of activity types across all tests of musical aptitude and ability . . 73 4.2 The distribution of content areas and playback activity types across all tests of musical aptitude and ability ...... 76

5.1 The process used to search the iTunes app store for applications to include in the analysis. The process for the next step – filtering the results of the search – is shown in Figure 5.2...... 93 5.2 The process used to filter candidate iOS applications for inclusion in the analysis, using four key criteria ...... 95 5.3 An example of local profiles as used in the iOS application Rhythm In Reach [257] 99 5.4 Possible content ratings for applications on the iTunes app store. Note that the ratings focus on age-appropriateness factors, and are not an indication of the app’s genre...... 99 5.5 The use of an on-screen instrument (piano) in Interval Ear Training [212] . . . . 101 5.6 An example of an ‘Available’ social sharing style and ‘Direct’ social sharing type in Rhythm Sight Reading Trainer [249] ...... 103 5.7 The update history shown on AppShopper for Note Brainer Pro [219]. This data is not available through the official iTunes app store...... 105 5.8 A breakdown of the content and activities in the iOS application Nota [213]. As- terisks represent single parts of the application which cover multiple content areas. Colours indicate the type of content and activities, using the colour scheme defined in Chapter 3...... 107

xx LISTOF FIGURES

5.9 The number of unique content areas covered by the applications in the sample. . 109 5.10 The number of unique activity types used by the applications in the sample. . . . 109 5.11 The number of unique content areas compared to the number of unique activity types used by applications in the sample. The bubble sizes indicate the number of applications covering a combination of number of activity types and number of content areas, with the smallest bubble representing 1...... 110 5.12 The distribution of focus ratings for the Instrument-Specific content area . . . . . 112 5.13 The distribution of depth ratings for Visual Recognition activities of Reading content113 5.14 The distribution of focus ratings for Visual Description activities of Scales content . 113 5.15 The distribution of focus ratings for Auditory Recognition activities of Elements of Harmony content ...... 113 5.16 The distribution of focus ratings for Notation activities of Elements of Harmony content ...... 113 5.17 Frequency with which each focus rating is paired with each depth rating. The bubble sizes indicate the number of times each pairing was found, with the smallest bubble representing 1...... 114 5.18 Co-occurrence of content areas amongst the sample of applications. Bubble size indicates the number of apps which cover the content area; width of edges represents the number of times the connected content areas appear on together in the same app...... 118 5.19 Co-occurrence of activity types amongst the sample of applications. Bubble size indicates the number of apps which use the activity type; width of edges represents the number of times the connected activity types appear on together in the same app...... 118 5.20 Distribution of progression styles used by the sampled iOS applications ...... 122 5.21 Primary category nominated by the developers of the sampled applications . . . . 123 5.22 The monetisation strategies used by applications in the sample ...... 123 5.23 Distribution of number of releases for applications in the sample ...... 125 5.24 Frequency and timing of updates to applications in the sample, and major updates to the iOS operating system. Version updates do not appear to correlate with iOS releases...... 126 5.25 Distribution of aggregate review scores for the applications in the sample; a score of -1 indicates that an application had an insufficient number of reviews to calculate an aggregate...... 127 5.26 Distribution of the number of reviews for the latest version of each application in the sample ...... 127 5.27 Distribution of the number of reviews for the latest version of each application in the sample, with outliers removed ...... 128 5.28 Distribution of approaches to profiles by the applications in the sample ...... 128 5.29 Distribution of approaches to using instruments as input devices across the sampled applications ...... 128 5.30 An onscreen piano keyboard used by Auralia Chord Recognition [244]. This is an example of on-screen use of instruments...... 130

xxi LISTOF FIGURES

5.31 Distributions of the styles and types of feedback used across the sample of applications ...... 130 5.32 Use of auditory and visual feedback across the sample of applications ...... 132 5.33 Comparison styles used across the sampled applications ...... 132 5.34 Evolution of user’s performance as shown in Better Ears [234] ...... 133 5.35 New high score notiﬁcation used by Bass Guitar Trainer [217] ...... 134 5.36 Score management strategies offered by applications in the sample ...... 134 5.37 Learning outcomes of the sampled applications ...... 135 5.38 Co-occurrence of characteristic tags amongst the sample of applications. The size of each bubble indicates the number of apps with a tag; the width of the edges represents the number of apps the connected tags appear on together...... 137

6.1 The general process followed by an evolutionary algorithm. Recreated from [233]. Note that the number of parent candidates selected and the number of children generated depends on the operator. This example shows two parents generating two offspring...... 141 6.2 A crossover operation between two candidates. This implementation does not preserve length...... 142 6.3 A crossover operation between two candidates where crossover points have been selected such that the results are of the same length as each other and their parents. In this case the crossover point selected is in the middle. However, other points could be selected as long as the resulting children are of the same length as the parents...... 143 6.4 The duration hierarchy typically used by tree structures which are designed to represent melodies in common time. The bottom row of semiquavers has been truncated for space, and the right-hand side of the tree is not shown to completion as it is identical to the left...... 145 6.5 A simple melody and its corresponding tree using the melody tree proposed by Rizo et al. [168] ...... 146 6.6 A melody with a dotted note and its corresponding tree using the melody tree proposed by Rizo et al. [168]. The ‘+’ symbol indicates the origin node of the combine operator...... 146 6.7 A simple polyphonic melody and its corresponding tree using the melody tree proposed by Dahlstedt [47]. ‘S’ represents the splice operator, and ‘U’ represents the union operator...... 148 6.8 Expanding a recursive melody tree using the structure proposed by Dahlstedt [47]149 6.9 A simple melody and its corresponding tree using the melody tree proposed by de Leon´ et al. [50] ...... 150 6.10 A potential duration hierarchy for fitting a compound time signature in an unmodified binary tree ...... 153 6.11 An alternative approach to fitting a compound time signature into an unmodified binary tree ...... 153 6.12 Attempting to apply the crossover operator between binary and ternary points in two parent melody trees ...... 156

xxii LISTOF FIGURES

6.13 A melody tree containing a triplet ...... 156 6.14 Applying the crossover operator where one crossover point is part of a triplet and the other crossover point is not ...... 158 6.15 Applying the crossover operator ...... 160 6.16 An example of the split mutation ...... 162 6.17 An example of the reduce mutation ...... 162 6.18 Adding a triplet to a node without any children ...... 163 6.19 Adding a triplet to a node with existing children ...... 163 6.20 Applying the add continuation mutation ...... 164 6.21 Calculating the shape of a melody. Tick marks indicate the segments which are counted as having shape, as the pitches within the segment move consistently up or down...... 167 6.22 An example melody ...... 167 6.23 An example melody and its related geometric shape ...... 169 6.24 A second example melody and its related geometric shape ...... 169 6.25 Calculating the difference between the melodies in Figures 6.23 and 6.24 . . . . . 170

7.1 The key signatures used by the Grade 1, 2, and 3 source exercises. Unless followed by an ‘m’ indicating a minor key, the key signatures are major...... 180 7.2 The number of sharps and ﬂats in the key signatures used by each of the Grade 1, 2, and 3 source exercises ...... 181 7.3 The time signatures used by the Grade 1, 2, and 3 source exercises ...... 182 7.4 Number of bars in each of the Grade 1, 2, and 3 source exercises. Lengths marked with ‘+’ contain an anacrusis...... 183 7.5 Pitch range of each Grade 1, 2, and 3 source exercise in semitones ...... 183 7.6 Range spread and pitch mode for each of the Grade 1, 2, and 3 source exercise . 184 7.7 Percentage of time in each of the Grade 1, 2, and 3 source exercises ﬁlled by notes and rests ...... 186 7.8 Amount of note time taken by each unique note length, as a percentage of time taken by all notes in the Grade 1, 2, and 3 source exercises. Rests are not included. Bubble diameter represents the number of exercises containing that proportion...... 187 7.9 Amount of rest time taken by each unique rest length, as a percentage of cumulative time taken by all rests in each Grade 1, 2, and 3 source exercise. Notes are not included. Bubble diameter represents the number of exercises containing that proportion...... 189 7.10 The percentage of intervals of each size used in the Grade 1, 2, and 3 source exercises. Intervals are represented as the distance between two adjacent notes in scale degrees. Bubble diameter represents the number of exercises containing that proportion...... 190 7.11 The number of rules for evaluating the technical appropriateness and melodic aesthetic of a sight reading exercise, and the number of those rules relating to each of the four facets...... 198

xxiii LISTOF FIGURES

7.12 The Likert rating for an exercise can be upgraded from ‘unfit’ to ‘fit for purpose’, or be improved in its fitness for purpose after a small number of repairs...... 199

8.1 The key signatures used by the generated exercises. Unless followed by an ‘m’ indicating a minor key, the key signatures are major...... 211 8.2 The time signatures used by the generated exercises ...... 211 8.3 The number of bars in each of the generated exercises ...... 211 8.4 Pitch ranges of the Grade 1, 2, and 3 source and generated exercises in semitones 213 8.5 Range spread and most common pitch for each Grade 1 source exercise ...... 213 8.6 Range spread and most common pitch for the three sets of Grade 1 generated exercises ...... 214 8.7 Range spread and most common pitch for each Grade 2 source exercise ...... 215 8.8 Range spread and most common pitch for the three sets of Grade 2 generated exercises ...... 216 8.9 Range spread and most common pitch for each Grade 3 source exercise ...... 217 8.10 Range spread and most common pitch for the three sets of Grade 3 generated exercises ...... 218 8.11 Percentage of time filled by notes and rests in each Grade 1 source exercise . . . . 219 8.12 Percentage of time filled by notes and rests for the three sets of Grade 1 generated exercises ...... 220 8.13 Percentage of time filled by notes and rests in each Grade 2 source exercise . . . . 221 8.14 Percentage of time filled by notes and rests for the three sets of Grade 2 generated exercises ...... 222 8.15 Percentage of time filled by notes and rests in each Grade 3 source exercise . . . . 223 8.16 Percentage of time filled by notes and rests for the three sets of Grade 3 generated exercises ...... 224 8.17 Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises...... 225 8.18 Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises...... 226 8.19 Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises...... 227 8.20 Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises...... 228 8.21 Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises...... 229 8.22 Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises...... 230

xxiv LISTOF FIGURES

8.23 The percentage of intervals of each size used in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises...... 231 8.24 The percentage of intervals of each size used in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises...... 232 8.25 The percentage of intervals of each size used in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises...... 233 8.26 The ‘Target note lengths’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 234 8.27 The ‘Target rest lengths’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 234 8.28 The ‘Allowable lengths’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 234 8.29 The ‘Target intervals’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 235 8.30 The ‘Allowable intervals’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 235 8.31 The ‘Melody shape’ fitness over a run of the algorithm where it is the only fitness measure used and mutation is turned off ...... 235 8.32 The fitness of the generated Grade 1 exercises over each fitness measure. Bubble diameter is relative to the number of exercises...... 236 8.33 The fitness of the generated Grade 2 exercises over each fitness measure. Bubble diameter is relative to the number of exercises...... 236 8.34 The fitness of the generated Grade 3 exercises over each fitness measure. Bubble diameter is relative to the number of exercises...... 237 8.35 A typical progression of diversity values over a single run of the algorithm. The fitness line tracks the average value of the six fitness measures for the best candidate in each generation’s population to provide a general indication of the population’s overall improvement...... 239 8.36 Fitness for purpose of the Grade 1 generated exercises before and after repair . . 239 8.37 Likert ratings of the Grade 1 generated exercises before and after repair . . . . . 241 8.38 Examples of Grade 1 generated exercises assigned each of the Likert quality ratings. An example of an exercise rated as ‘Very bad’ is not provided as none of the Grade 1 exercises were assigned this rating...... 242 8.39 Likert ratings of the Grade 1 generated exercise when viewed as Grade 2 exercises242 8.40 Likert ratings of the Grade 1 generated exercise when viewed as Grade 3 exercises243 8.41 Fitness for purpose of the Grade 2 generated exercises before and after repair . . 243 8.42 Likert ratings of the Grade 2 generated exercises before and after repair . . . . . 245 8.43 Examples of Grade 2 generated exercises assigned each of the Likert quality ratings246 8.44 Likert ratings of the Grade 2 generated exercise when viewed as Grade 1 exercises247 8.45 Likert ratings of the Grade 2 generated exercise when viewed as Grade 3 exercises247 8.46 Fitness for purpose of the Grade 3 generated exercises before and after repair . . 247 8.47 Likert ratings of the Grade 3 generated exercises before and after repair . . . . . 249 8.48 Examples of Grade 3 generated exercises assigned each of the Likert quality ratings250 8.49 Likert ratings of the Grade 3 generated exercise when viewed as Grade 1 exercises251

xxv LISTOF FIGURES

8.50 Likert ratings of the Grade 3 generated exercise when viewed as Grade 2 exercises251 8.51 The categories of rules broken by the Grade 1, 2, and 3 generated exercises . . . 252 8.52 Amount of note time taken by each unique note length in the Grade 1 generated exercises over each result set ...... 254 8.53 Amount of note time taken by each unique note length in the Grade 2 generated exercises over each result set ...... 255 8.54 Amount of note time taken by each unique note length in the Grade 3 generated exercises over each result set ...... 256 8.55 Amount of rest time taken by each unique rest length in the Grade 1 generated exercises over each result set ...... 257 8.56 Amount of rest time taken by each unique rest length in the Grade 2 generated exercises over each result set ...... 258 8.57 Amount of rest time taken by each unique rest length in the Grade 3 generated exercises over each result set ...... 259 8.58 The percentage of intervals of each size used in the Grade 1 generated exercises over each result set ...... 260 8.59 The percentage of intervals of each size used in the Grade 2 generated exercises over each result set ...... 261 8.60 The percentage of intervals of each size used in the Grade 3 generated exercises over each result set ...... 262 8.61 The Likert ratings over each result set of the Grade 1 generated exercises . . . . . 264 8.62 The Likert ratings over each result set of the Grade 2 generated exercises . . . . . 265 8.63 The Likert ratings over each result set of the Grade 3 generated exercises . . . . . 266

9.1 A transition network for key signatures by Stephen Mugglin [189] ...... 274

A.1 A piano keyboard with examples of an octave, tones, and semitones labelled. Taken from [142]...... 301 A.2 A piano keyboard with one octave of pitch classes labelled. Taken from [137]. . . 301 A.3 Common musical lengths and their symbols. ‘Value’ indicates the duration of each length type in reference to a semibreve. Adapted from [137]...... 301

B.1 Distribution of the structural breadths of the sampled applications ...... 313 B.2 Distribution of the structural depths of the sampled applications ...... 313 B.3 Structural breadth compared to structural depth across all sampled applications . 314 B.4 Percentage of application parts which present content and which provide activities. Each horizontal bar represents one application from the sample...... 315 B.5 Number of application parts covering content compared to number of parts presenting activities across all sampled applications ...... 316 B.6 Genre tree for applications with a primary genre of ‘Music’; brackets contain the iTunes genre identifiers...... 317 B.7 Genre tree for applications with a primary genre of ‘Education’; brackets contain the iTunes genre identifiers...... 318 B.8 Genre tree for applications with a primary genre of ‘Games’; brackets contain the iTunes genre identifiers...... 319

xxvi LISTOF FIGURES

B.9 Price changes made to the sample of applications over time. The bubble sizes indicate the number of applications at each price point, with the smallest bubble representing 1...... 320 B.10 Price changes made to the sample of applications costing less than $20AUD over time. Each bubble represents one price change...... 321 B.11 Distribution of number of price changes for applications in the sample ...... 322

xxvii

List of Tables

2.1 A summary of literature in algorithmic composition, sorted by year ...... 23 2.2 A summary of the ﬁtness methods used by the literature summarised in Table 2.1. Percentages are rounded to two decimal places...... 27

3.1 The most common activity style (i.e., task or exercise) for each proposed type of activity. Classiﬁcations are not absolute – generally activities of a type will be of the speciﬁed style, but there may be some which do not conform to the listed type. 48 3.2 Example activities for each auditory recognition activity subtype ...... 49 3.3 Example activities for each visual recognition activity subtype ...... 51 3.4 Example activities for each auditory description activity subtype ...... 52 3.5 Example activities for each visual description activity subtype ...... 54 3.6 Example activities for each visual playback activity subtype ...... 56 3.7 Example activities for each memory playback activity subtype ...... 57 3.8 Example activities for each notation activity subtype ...... 57

4.1 Equivalent taxonomy activities for each subtest in Seashore’s Measures of Musical Talents ...... 62 4.2 Equivalent taxonomy activities for each subtest in Revesz’s Tests of Musical Ability 62 4.3 Equivalent taxonomy activities for each subject in the Kwalwasser-Ruch Test of Musical Accomplishment ...... 63 4.4 Equivalent taxonomy activities for each subtest in Kwalwasser’s Test of Music Appreciation ...... 64 4.5 Equivalent taxonomy activities for each subtest in the Kwalwasser-Dykema Mu- sical Talent Tests ...... 64 4.6 Equivalent taxonomy activities for each subtest in Kwalwasser’s Music Talent Tests 65 4.7 Equivalent taxonomy activities for each subtest in Schoen’s Tests of Musical Feel- ing and Understanding ...... 66 4.8 Equivalent taxonomy activities for each subtest in the Torgerson-Fahnestock Tests 66 4.9 Equivalent taxonomy activities for each subtest in Drake’s Musical Aptitude Tests . 67 4.10 Equivalent taxonomy activities for each subtest in Gordon’s Musical Aptitude Proﬁle 68 4.11 Equivalent taxonomy activities for each subtest in Gordon’s Measures of Music Audiation ...... 68 4.12 Equivalent taxonomy activities for each subtest in Bentley’s Measures of Musical Abilities ...... 69 4.13 Equivalent taxonomy activities for each subtest in Wing’s Tests of Musical Ability and Appreciation ...... 69

xxix LISTOF TABLES

4.14 Equivalent taxonomy activities for each subtest in the Iowa Tests of Music Literacy 69 4.15 Equivalent taxonomy activities for each subtest in the Colwell Music Achievement Test ...... 71 4.16 Equivalent taxonomy activities for Karma’s Test of Structure Ability ...... 71 4.17 Equivalent taxonomy activities for each subtest in the Musical Aptitude Indicator . 71 4.18 Equivalent taxonomy activities for each subtest in the Proﬁle of Music Perception Skills ...... 71 4.19 The percentage of subtests of each activity type in each test of musical aptitude, sorted in ascending year of publication ...... 74 4.20 The percentage of subtests covering knowledge from each content area, or of each playback type in each test of musical aptitude, sorted in ascending year of publication ...... 77 4.21 Subtest equivalence for auditory description activities of reading content; represents equivalence, and ≈ represents partial equivalence ...... # . . . . . 81 4.22 Subtest equivalence for auditory description activities of rhythm content; represents equivalence, and ≈ represents partial equivalence ...... # . . . . . 84 4.23 Subtest equivalence for auditory description activities of scales content; represents equivalence, and ≈ represents partial equivalence ...... # ...... 85 4.24 Subtest equivalence for auditory description activities of elements of harmony content; represents equivalence, and ≈ represents partial equivalence . . . . . 86 4.25 Subtest equivalence# for auditory description activities of harmonic structures content; represents equivalence, and ≈ represents partial equivalence . . . . . 86 4.26 Subtest equivalence# for auditory description activities of style content; represents equivalence, and ≈ represents partial equivalence ...... # ...... 87 4.27 Subtest equivalence for auditory description activities of historical or general knowledge content; represents equivalence, and ≈ represents partial equivalence 88 4.28 Subtest equivalence# for visual description activities of reading content; represents equivalence, and ≈ represents partial equivalence ...... # ...... 88 4.29 Subtest equivalence for visual description activities of rhythm content; represents equivalence, and ≈ represents partial equivalence ...... # ...... 88 4.30 Subtest equivalence for memory playback activities of rhythm only; represents equivalence, and ≈ represents partial equivalence ...... # ...... 89

5.1 Descriptors collected about each iOS application. Potential values listed as ‘-’ indicate free text ﬁelds...... 96 5.2 Coverage of content areas across the sample of iOS applications ...... 108 5.3 Coverage of activity types across the sample of iOS applications ...... 109 5.4 A summary of the distribution types for the depth and focus ratings ...... 113 5.5 The depth and focus ratings for each content area in the sample of iOS applications115 5.6 The depth and focus ratings for each type of activity in the sample of iOS applications ...... 117 5.7 Common characteristics found within the sample of 175 iOS applications . . . . . 121 5.8 Application store category descriptions provided by Apple Inc. [214] ...... 123

xxx LISTOF TABLES

5.9 Co-occurrence of uses of auditory and visual feedback within the sampled applications ...... 132 5.10 Presence of characteristic tags across the sample ...... 136

6.1 A comparison of the features of the melody trees proposed in the literature . . . . 148 6.2 Categorisations of each fitness measure as time or count based ...... 166 6.3 Calculating the fitness of the melody in Figure 6.22 against an arbitrarily selected set of targets. The finally fitness value for each measure is in bold...... 167

7.1 Summary of source exercises extracted from published books ...... 177 7.2 Characteristics of the sample of published Grade 1 sight reading exercises for the flute. Ratios and proportions are represented in terms of time...... 178 7.3 Characteristics of the sample of published Grade 2 sight reading exercises for the flute. Ratios and proportions are represented in terms of time...... 178 7.4 Characteristics of the sample of published Grade 3 sight reading exercises for the flute. Pitches are represented as MIDI numbers, and ratios are represented in terms of time...... 180 7.5 Criteria for assigning each Likert rating to an algorithmically generated sight reading exercise ...... 199 7.6 Summary of rules in the ruleset for evaluating algorithmically generated sight reading exercises. Numbers refer to the rule numbers in Table 7.7...... 199 7.7 The origin of each rule in the ruleset for evaluating algorithmically generated sight reading exercises ...... 200

8.1 Typical characteristics of published and generated Grade 1 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are fixed and not expected to change...... 209 8.2 Typical characteristics of published and generated Grade 2 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are fixed and not expected to change...... 209 8.3 Typical characteristics of published and generated Grade 3 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are fixed and not expected to change...... 210 8.4 Summary of fitness values for each grade level of generated exercises. Shows that at least one exercise reached the maximum value for each fitness measure (i.e., 1.0), and that the average fitness values for each measure were high at every difficulty level...... 223 8.5 Likert ratings of the Grade 1 generated exercises before and after repair . . . . . 240 8.6 Likert ratings of the Grade 2 generated exercises before and after repair . . . . . 244 8.7 Likert ratings of the Grade 3 generated exercises before and after repair . . . . . 248

B.1 Depth and focus ratings for auditory recognition activities ...... 304

xxxi LISTOF TABLES

B.2 Depth and focus ratings for visual recognition activities ...... 305 B.3 Depth and focus ratings for auditory description activities ...... 306 B.4 Depth and focus ratings for visual description activities ...... 307 B.5 Depth and focus ratings for visual playback activities ...... 309 B.6 Depth and focus ratings for memory playback activities ...... 310 B.7 Depth and focus ratings for notation activities ...... 311

C.1 Metadata for all grace 1 source exercises ...... 323 C.2 Counts and percentages of notes and rests in each grade 1 source exercise . . . . 325 C.3 Raw count and percentage of melody time ﬁlled by each note length for all grade 1 source exercises ...... 327 C.4 Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 1 source exercises ...... 330 C.5 Number and percentage of intervals of each size for all grade 1 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes...... 331

D.1 Metadata for all grace 2 source exercises ...... 335 D.2 Counts and percentages of notes and rests in each grade 2 source exercise . . . . 337 D.3 Raw count and percentage of melody time ﬁlled by each note length for all grade 2 source exercises ...... 339 D.4 Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 2 source exercises ...... 342 D.5 Number and percentage of intervals of each size for all grade 2 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes...... 343

E.1 Metadata for all grace 3 source exercises ...... 347 E.2 Counts and percentages of notes and rests in each grade 3 source exercise . . . . 349 E.3 Raw count and percentage of melody time ﬁlled by each note length for all grade 3 source exercises ...... 352 E.4 Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 3 source exercises ...... 356 E.5 Number and percentage of intervals of each size for all grade 3 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes...... 358

F.1 Parameters used to generate Grade 1 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table C.1 when describing the Grade 1 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places...... 361

xxxii LISTOF TABLES

G.1 Parameters used to generate Grade 2 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table D.1 when describing the Grade 2 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places...... 369

H.1 Parameters used to generate Grade 3 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table E.1 when describing the Grade 3 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places...... 377

xxxiii

1 Introduction

1.1 Context

The acquisition of musical skills presents many challenges, both to educators and students [100]. As long as the field has existed there have been philosophical debates regarding the best methods of instruction, the role of teachers, and the responsibilities of students. These debates have persisted through the mentor-student style relationships of early pedagogy, where only the rich and ‘worthy’ were offered the opportunity to develop musical skills, to the modern day where musical studies are often a core component of a general education. Although there have been many strong cases throughout history for particular teaching styles and techniques, no single method has emerged as the standard. The debate has only been fuelled further with the increasingly wide availability of technology and computing devices [93, 147]. Using these devices, efforts have been made to create digital tools to teach musical skills and enhance or encourage the deliberate, self-guided practice of them. However, although the capabilities of technology continue to improve, its use in music education is not progressing at a similar rate [202]. Often, tools are no more than basic digital translations of traditional physical materials. There are many opportunities to better utilitise the capabilities of technology in music education [34, 199, 207]. For example, digital devices can be used to incorporate multimedia content into educational materials. They are also capable of engaging students with interactive and customisable features which help the student feel like they are in control of their learning. Digital tools can autonomously track student’s progress and communicate it directly to the student and their teacher. These are just a few of the many ways in which technology can be utilised in music education. In this work, focus is given to the challenge of learning and practicing musical sight reading. There is a significant resource constraint in this area, simply due to the task definition. As sight reading is the ability to perform a piece or phrase of music without having seen it before, as soon as a single exercise has been completed once by an individual it is no longer a sight reading exercise for them. Currently, practice material is written by experts and disseminated to students through online stores and physical books. This is an ineffective approach. Access to expertise is limited, and practice material is consumed much faster than it is created. This means that students often exhaust the available resources before achieving

1 CHAPTER 1. INTRODUCTION

competency. Given that deliberate practice is key to gaining competence in sight reading [94], this resource constraint is a large barrier for musicians attempting to develop the skill. The capabilities of modern technology represent an opportunity to overcome this constraint through a software system designed to generate novel sight reading exercises. These exercises would need to be playable by a human, of a nominated difﬁculty level (with respect to a particular instrument), and incorporate speciﬁc technical skills, whilst remaining aesthetically pleasing. Such a system would provide learners with access to an endless quantity of appropriate practice material.

1.2 Research Questions

The purpose of this research is to determine ways in which technology can be used to enhance and create effective digital music teaching tools and aides, with a specific focus on musical sight reading. This requires developing an understanding of music education and identifying opportunities for technology to augment the process of learning and practicing musical skills. For the practice and development of sight reading skills, this work also seeks to create a tool which is able to generate music that, whilst remaining playable by a human, is aesthetically pleasing, is of a nominated difficulty level, and can incorporate specific technical skills. To support these goals, the following research questions will be addressed:

1. How is technology currently being used in music education? To identify how technology might be better utilised, one must ﬁrst understand how it is currently being used. This involves developing an understanding not only of what the current practices are, but how they have emerged. By examining the trends in music education – both technological and not – an understanding of the priorities and different roles of music teachers and students can be gained. This understanding of the development of the ﬁeld is essential to making a valuable contribution.

2. What are the opportunities for increased or more effective use of technology in musical sight reading education? These opportunities all represent potential avenues for research, one of which – the algorithmic generation of musical sight reading exercises – was chosen as the primary focus of this work.

3. What algorithmic techniques are appropriate for generating music that is aesthetically pleasing, playable by a human, and appropriate for the development of musical sight reading skills? To build a system which generates musical sight reading exercises, appropriate algorithmic techniques for that system need to be identiﬁed. Work undertaken to address this question should take into account trends within the literature in general algorithmic composition as well as the domain-speciﬁc requirements of musical sight reading.

4. How can algorithmically generated musical sight reading exercises be measured for ﬁtness of purpose? In order to evaluate a system designed to generate musical sight reading exercises, there

2 CHAPTER 1. INTRODUCTION

needs to be a method for assessing the quality of its output. This method should consider general musical qualities such as aesthetics and grammatical correctness, as well as elements speciﬁc to musical sight reading such as difﬁculty and appropriateness for the chosen instrument.

1.3 Key Contributions

The main contributions of this thesis are:

1. A formal taxonomy for describing musical content and activities Described in Chapter 3, this taxonomy enables musical content from a diverse array of domains, including education, to be described using a common vocabulary.

2. A framework for completing structured reviews of educational applications Described in Chapter 5, this framework draws on standards in general education theory, software design principles, and musical education theory to provide a method of formally reviewing educational applications. The focus of the framework is on applications targeted to learning and practicing musical skills, but large portions apply to educational software in general.

3. An analysis of the state of the art of iOS applications for teaching and practicing musical skills Presented in Chapter 5, this describes the content covered by iOS applications designed to teach musical skills, and the activities they offer for practicing and reinforcing those skills and related knowledge. The results of this analysis can be used to identify gaps within the ﬁeld and opportunities for improvement.

4. A novel tree structure for representing musical melodies Described in Chapter 6, this novel tree structure was designed to overcome some of the limitations present in existing tree structures within the literature. These limitations include the support for triplet notes and compound time signatures.

5. An evolutionary algorithm for generating monophonic sight reading exercises Described in Chapter 6, this evolutionary algorithm is capable of generating sight reading exercises for the flute. Each exercise can be restricted to a user-specified key signature, time signature, and length. Specific targets and restrictions can be set for the desired result, including ‘legal’ note lengths and intervals, and the desired proportions of different note lengths and interval sizes.

6. A ruleset and framework for measuring the quality and fitness for purpose of algorithmically generated sight reading exercises Defined in Chapter 7, this ruleset comprises 29 individual rules extracted from a combination of scholarly works in music theory and an analysis of expert-written sight reading exercises. The ruleset covers measures relating to the melodic aesthetics and technical appropriateness of an exercise. A framework is also provided for translating the rules broken by an exercise into an overall quality rating on a five-point Likert scale.

3 CHAPTER 1. INTRODUCTION

1.4 Thesis Structure

This thesis is structured in 10 chapters. Chapter 2 explores the history of music education and algorithmic composition. The general challenges faced by music educators and students are discussed, as well as challenges specific to developing musical sight reading skills. Following this, the history of algorithmic composition is explored, from centuries-old manually executed algorithms to modern, autonomous computer-based approaches. Popular algorithms and techniques from recent literature are presented with examples, and an extended set of examples related to the chosen approach (evolutionary algorithms) is provided. These discussions dually support the second and third research questions – How is technology currently being used in music education?, and What algorithmic techniques are appropriate for generating music that is aesthetically pleasing, playable by a human, and appropriate for the development of musical sight reading skills?. In Chapter 3, a novel taxonomy for describing musical content and activities is presented. This is a key contribution of the thesis, and enables the first research question – How is technology currently being used in music education? – to be addressed. The taxonomy provides a common vocabulary which can be used to describe musical content from many domains, including music education, in a neutral and consistent way. Chapter 4 shows an example application of the taxonomy, which doubles in purpose as a validation exercise. It shows how tests of musical aptitude and ability can be translated to the common, neutral vocabulary of the taxonomy. This uncovers the frequency with which different areas of musical knowledge are covered by the tests, and enables comparisons between and within sets of assessments. In Chapter 5 the focus is placed on iOS applications for teaching and practicing musical skills, and presenting the state of the art of the field. The taxonomy presented in Chapter 3 is used as one part of a structured method for reviewing the applications, and reveals which areas of musical knowledge are covered and what activities are offered for users to practice and reinforce that knowledge and related skills. Other factors considered are the general design of the applications, their selected feedback, incentive, and progression models, and their educational outcomes. This analysis shows the current state of the field, with a view to identify areas where the technology could be better utilised. This addresses the second research question – What are the opportunities for increased or more effective use of technology in musical sight reading education?. Chapter 6 presents a novel evolutionary algorithm for generating monophonic sight reading exercises. This required the development of a new tree structure for representing musical melodies, as existing structures within the literature do not support functionality necessary for the domain. The overall goal of the algorithm is to generate new sight reading exercises that are of a specific difficulty level and which contain certain technical characteristics, whilst remaining both playable by a human and aesthetically pleasing. It achieves this by utilising models of expert-written sight reading exercises and attempting to emulate their characteristics. This approach necessitated the curation of a collection of expert-written exercises to act as target models. A structured experimental process for testing the algorithm, as well as a method for evaluating the quality and ‘fitness for purpose’ of its output is described in Chapter 7. This

4 CHAPTER 1. INTRODUCTION

process focuses on generating sight reading exercises for the flute at the Grade 1 and 2 difficulty levels. As an exploration of the extended capabilities of the algorithm, Grade 3 exercises are also generated. In order to evaluate the algorithm’s output, a ruleset and framework is presented for measuring the ‘fitness for purpose’ of exercises. This framework describes a process for assigning generated exercises an overall quality rating on a five-point Likert scale. Chapter 8 presents the results of executing the experimental design outlined in Chap- ter 7. As the algorithm attempts to emulate the characteristics of expert-written examples, this chapter includes a comparison of the characteristics of both the expert-written and generated exercises. Also discussed are the fitness scores, Likert quality ratings, and ruleset violations of the exercises. Given that evolutionary algorithms involve random elements, the repeatability of the results using different random number generator seeds is also examined. A discussion of the work presented in this thesis is provided in Chapter 9. This discussion focuses on the four research questions proposed in Section 1.2, and how addressing them has resulted in the key contributions described in Section 1.3. Avenues for future work are also identified and discussed, including those resulting directly from the work presented in this thesis and those broader within the domain of music education and technology. Finally, Chapter 10 summarises the thesis as a whole, revisiting and reinforcing the key novel contributions of the work.

2 Background

“...the Engine might compose elaborate and scientiﬁc pieces of music of any degree of complexity or extent...” — Ada Lovelace on Charles Babbage’s difference engine, 1843 [118]

2.1 Overview

The previous chapter covered the context for and overall goals of the work presented in this thesis. This chapter will discuss literature related to the ﬁeld. Although this is a multi-disciplinary work covering music theory, general education theory, music education theory, software design, mobile application design, artiﬁcial intelligence, and evolutionary algorithms, this chapter will focus only on a subset of these topics. The remaining topics will be discussed in later chapters where appropriate. The structure of this chapter is as follows. First, Section 2.2 provides an overview of the general challenges encountered by music educators. This is followed by a discussion in Section 2.3 of how technology has been applied to solve these challenges. As the goal of this work is to create a system capable of generating musical sight reading exercises, musical sight reading and the challenges it entails is discussed in Section 2.4. The ways in which technology has been used to practice and learn musical sight reading are detailed in Section 2.5. The remaining sections focus on technologies and algorithms used to generate music. First, algorithms operated entirely by humans are described in Section 2.6. Then, early computing devices designed to generate music are discussed in Section 2.7. Section 2.8 describes and discusses popular algorithms in recent literature for computer music generation. Finally, Section 2.9 focuses on the technique chosen for this work: evolutionary algorithms.

2.2 Challenges in Music Education

There are many challenges in music education. Some, such as motivating students and training good teachers, are not speciﬁc to the domain. Others are, such as managing the cognitive load of musical information, and giving students the opportunity to play in ensembles. Given the large and diverse array of potential challenges, it is not feasible to provide a complete overview here. Instead, this section focuses on a combination of the most prominent

7 CHAPTER 2. BACKGROUND

obstacles, and those which are most relevant to the work presented in this thesis. With any skill, quality instruction and guidance is key to student progress and achievement. Musical skills are no different. This phenomenon has been formally studied, with Kwal- wasser [100] stating that whilst talent sets the limit for what a student can achieve, even the most talented pupils will not be successful without proper instruction. Quality instruction must also, however, be accompanied by private practice. Both the quality and quantity of practice is key [24, 55, 100, 125], as expert abilities are achieved through “extended deliberate practice” [55, p. 1]. Quantity of practice is important as it is a known predictor of both short and long-term future performance and achievement [62, 184]. However, the quality of practice is also key. Practice should be as ‘deliberate’ as possible. That is, practice activities should be targeted towards improving specific skills in measurable ways [27]. For example, playing through the opening phrase of a piece is not deliberate practice. Playing the phrase whilst specifically focusing on executing certain technical markings would be deliberate practice. Repetitive practice is often prescribed by teachers and intuitively done by students. Whilst deliberate practice can involve repetitive elements, the key difference is that the repetition is part of a targeted strategy. For example, a student might repeat a small section of a piece five times to ensure that they can play it consistently at a particular speed. Although purely repetitive practice will lead to improvements, a student’s skill will eventually plateau below the level that they could reach if using deliberate practice [28, 206]. Two notable challenges in education arise from this:

1. Facilitating appropriate (i.e., deliberate) practice, and 2. Motivating students to practice.

These challenges relate to the quality and quantity of practice, respectively. One reason for these challenges being particularly prominent in music is lesson frequency. Commonly, students will have a weekly lesson with a trained teacher lasting between 30 and 60 minutes. During this time the student will typically show the teacher their progress since the last lesson and receive guidance regarding what they should focus on next. Given the limited frequency and length of formal instruction, the key contributing factor to a student’s overall improvement is what they do between lessons [23]. Finding the motivation to practice between lessons is difﬁcult, especially for children [127]. Many students, particularly beginners, also struggle with the discipline required for deliberate practice and with selecting appropriate practice activities. This can slow or even stall their overall progress. Another challenge resulting from the frequency and length of formal lessons is student’s access to feedback. Quality feedback is a strong motivational tool [183], but students have limited ability to receive feedback outside of lessons [43, 183, 200]. The need for feedback is captured well by Ericsson et al. [55]:

“To assure effective learning, subjects ideally should be given explicit instructions about the best method and be supervised by a teacher to allow individualized diagnosis of errors, informative feedback, and remedial part training. The instructor has to organize the sequence of appropriate training tasks and monitor improvement to decide when transitions to more complex and challenging tasks are appropriate.” — Ericsson et al. [55, p.5]

8 CHAPTER 2. BACKGROUND

It is not feasible for students to have constant access to a human instructor, or even access just for the hours when they are practicing. One way this issue is being addressed is through the use of technology. The next section will focus on this use, and other ways in which technology is being applied in music education.

2.3 Use of Technology in Music Education

As with the challenges discussed in Section 2.2, there are many ways that technology is being used in music education. This section focuses on representative examples of these uses, particularly those relating to the work presented in this thesis. A clear trend in the area is that although the capabilities of technology continue to improve, its use in music education is not improving at a similar rate [202]. This is an issue as there are many opportunities for technology to advance student learning and practice. Com- pared to many other areas of study, music places a particularly high cognitive load on students. Owens and Sweller [147] believe that technology can assist in managing this load by presenting information in stages or in entirely different formats. Towards this goal, Wilson [207] developed a ‘drill and practice’ system for teaching and practicing basic music theory skills. Rather than being a standalone application, the software is intended to accompany a specific unidentified textbook. This is an example of an early approach to music education software: replicating or supplementing existing materials on a digital device. Whilst this can be of great assistance to students, it is not an approach which capitalises on the unique capabilities of technology. One of these opportunities is the capability to personalise learning [34]. Research has shown that systems which adapt to individual student’s needs can be superior to traditional methods [199]. Although this is not yet a common or well-implemented feature of music teaching and practice software, studies have shown that it is desired by both teachers and students [93]. One example of an adaptive system is that by Konecki [92], who designed an intelligent tutoring system for the piano. The software presents the user with a lesson, then generates customised exercises based on the type and number of errors in the user’s performance in that lesson. Unfortunately, the literature published on this work is not clear on the structure of the lessons, how exercises are generated, or how student’s errors are classified. Gamification is one strategy shown to strongly increase the performance and motivation of students [23]. This is not surprising when considering that feedback is a key component of gamification and, as discussed in Section 2.2, feedback is a powerful motivational and instruc- tive tool. Chapter 5 provides a discussion of where and how gamification is used in music education software. Additional and noteworthy examples can be found in the field of video games. One well-known example is Rocksmith [255]. Rocksmith is a music game where users play with a real guitar or bass. An onscreen representation of a fretboard is provided, and blocks representing notes move towards the player. The height of a block indicates a string, and the horizontal positioning of a block indicates a fret. When a block reaches the onscreen fretboard the player should play the indicated string and fret. For reference, an example of the game interface is provided in Figure 2.1.

9 CHAPTER 2. BACKGROUND

Figure 2.1: The interface of the videogame Rocksmith when playing a song. Taken from [45].

Aside from its use of a real instrument as the controller, the noteworthy feature of Rock- smith is its dynamic difficulty. Starting on the ‘easiest’ level, the game automatically adjusts the difficulty in real time based on the player’s performance. For example, the player might initially be presented with only 10% of the notes in a song, a proportion which is increased to 25% after they play the opening passage perfectly. If the player made a mistake, for example playing the wrong pitch or missing a note entirely, the game might reduce the number of notes presented to them based on the severity of their error. The dynamic difficulty offered by Rocksmith is a prominent feature of the game’s advertising. However, the developers do not provide any concrete details on how or when the difficulty is adapted. Many music video games do not teach practical skills. Even for games like Rocksmith, studies have shown that although student’s rhythmic skills often improve, their abilities in other areas tend to remain unchanged [79]. Games can, however, foster music appreciation and help players to develop auditory and listening skills [129]. In some cases they can also lead players to transition to more formal methods of instruction. Another use of technology in music education is providing feedback. The potential in this area is stated by Wilson [207]:

“Feedback in [music education] exercises is another aspect in which computers provide a distinct advantage over more traditional methods. When designed correctly, computer-based activities can provide immediate corrective and instructional feedback tailored to student responses.” — Wilson [207, p.19]

Computer-based feedback offers a number of advantages, namely that it is:

1. Consistent, 2. Efﬁcient, and 3. Unbiased.

Studies have shown that it can be used effectively at all levels of learning, not just as part of ‘drill and practice’ [123]. Additionally, automating feedback often requires the identiﬁcation of user errors, which could then be used to tailor the content of exercises to user’s weak points.

10 CHAPTER 2. BACKGROUND

MatchMySound is an example of software which provides students with automated feedback on their performance [84]. Given an ‘expert performance’, usually provided by a teacher, the software is able to compare a student’s performance to the expert’s rendition. Match- MySound provides feedback on the student’s sound (i.e., pitch, intonation, and articulation) and timing (i.e., rhythm, tempo, and speed). The focus of the work in this thesis is on one particular application of technology in music education: its use in practicing musical sight reading. Although the primary goal is to provide endless quantities of sight reading practice material, the opportunities in this space extend to many other areas. The following sections will expand on challenges speciﬁc to practicing musical sight reading, the ways in which technology has already been applied to the problem, and literature related to generating novel sight reading material.

2.4 Musical Sight Reading

Wolf [208] defines sight reading as playing a piece or part of music for the first time without the benefit of practice. It is described by Kopiez and In Lee [94, pg. 1] as being “characterised by great demands on the performer’s capacity to process highly complex visual input (i.e., the musical score) under the constraints of real time without the opportunity of error correction”. Sight reading is widely believed to be a basic skill that every musician should obtain [46, 62, 94, 107, 126, 186], and is required at most levels of formal musical achievement in many countries [13, 80, 191]. It enables musicians to learn new music quickly, to rapidly expose themselves to a variety of repertoire and musical styles, and become an independent musical learner [67]. For students specifically, good sight reading skills allow them to dedicate more lesson time to musical interpretation rather than learning notes. For music teachers, sight reading is essential for demonstrating examples to their students. As with most skills, practice is key to improving musical sight reading ability. This is shown by Kopiez and In Lee [94], who found that there is a positive correlation between the time a person has spent practicing sight reading and their level of sight reading skill. They also found that although sight reading ability improves with a musician’s general musical expertise, this only applies to pieces considered extremely easy in terms of that person’s instrumental skill. It is for these reasons that deliberate sight reading practice is essential to achieving competence. Engaging in deliberate practice of musical sight reading is particularly difficult due to the nature of the task. As sight reading is the ability to perform a piece or phrase of music without having seen it before, as soon as an exercise has been completed once by a person it can no longer be used as a sight reading exercise for them [176]. This means that the traditional approach of using books of expert-written exercises is ineffective, as such books effectively becomes single-use devices. Research supports the idea that a person’s level of experience with sight reading is a reliable predictor of their sight reading ability [16, 94, 95, 196]; that is, that practice is imperative to gaining the skill. Additionally, Galyen [62] recommends that sight reading is practiced every day. With limited practice resources, this becomes a difficult challenge. Quality feedback is also a strong learning tool for musicians wanting to improve their sight reading skills. Ji [80] studied the effect of feedback on learning sight reading, and found that students who receive feedback improve much faster than students who do not.

11 CHAPTER 2. BACKGROUND

The challenges of providing quality feedback and creating appropriate practice materials are both strong candidates for technology-based solutions. The next section will discuss some representative examples of these solutions from the literature.

2.5 Software for Learning and Practicing Musical Sight Reading

There are few cases of software designed to support the learning or practicing of musical sight reading. A large number of applications offer note identification activities, where a single note is shown on a score and the user is asked to identify what pitch that note represents. Many applications advertise this type of activity as such. However, as users are asked only to identify a single note and, in most cases, do not need to play the note on an instrument, it can not truly be classified as sight reading [196]. Random Sheet Music is an example of a web-based application which directly addresses the problem of generating infinite sight reading practice material. Last updated in 2015, Ran- dom Sheet Music provides users with the interface shown in Figure 2.2. This interface allows users to select a number of measures, any combination of four note lengths, a key signature, and a selection of pitches. Music is generated by randomly selecting pitches within these parameters. The output of the software is decidedly random. As shown in Figure 2.3, the music generated using the default configuration is unstructured, contains a large number of extreme interval sizes, and does not emphasise the selected key signature. The quality of output can be improved by further limiting the parameters, for example by selecting fewer possible pitches. However, the music generated remains overly random and unstructured. Etude Sight Reader is a desktop application targeted to piano students. The software uses a MIDI keyboard for input, and provides the user with feedback on their pitch and timing when playing through exercises. This feedback is provided through a combination of visual markers and text, as shown in Figure 2.4. Unfortunately, Etude Sight Reader does not generate sight reading material, but instead contains a predefined library of exercises. This means that although it can provide students with valuable feedback on their performance, it does not overcome the challenge of providing students with endless practice material. Sight Reading Factory [226] is the more fully formed software product of those discussed. It comes in both web and mobile variations, and is capable of generating sight reading exercises for various instruments and ensembles. Multiple difficulty levels – numbered 1 through 8 – are offered, though not all difficulties are currently available for every supported instrument. The difficulty levels do not appear to follow any particular formal curriculum. As well as selecting an instrument and difficulty level, users of Sight Reading Factory can customise a number of parameters. These parameters include the number of bars, the key signature, and maximum interval size for an exercise. The number of bars must be selected from a list of 4, 8, 12, 16, 20, and 24, and the maximum interval range allowed is one octave (i.e., intervals over an octave will never be used). Suggested values for each parameter are provided with respect to the user’s selected instrument and difficulty level. Figure 2.5 shows an example of an exercise produced by Sight Reading Factory. It is not clear how the exercises in Sight Reading Factory are generated. One potential implementation is the use of a library of motifs which are recombined, transformed, and adapted to fit within the selected restrictions. This approach is likely given the use of repeated patterns

12 CHAPTER 2. BACKGROUND

Figure 2.2: The interface of randomsheetmusic.com [256]

and phrases within the generated exercises. However, no published information can be found which conﬁrms or denies this theory. Taking a more research-based approach, Schulz [176] developed PiaNote, a web-based application capable of generating practice material for pianists. The main selling point of the software is that the content of exercises is based on the user’s past performances. When eva- luting a user’s performance, PiaNote follows a process similar to that used by James Bastien in Sight Reading, Level 2 [17]. After determining the edit distance between the user’s performance and a ‘perfect’ performance of an exercise, the software calculates a score for each of ﬁve musical elements:

Key signature The proportion of pitches which were played correctly.

Time signature The proportion of note lengths which were played correctly.

Song type A combination of the key signature and time signature scores.

Intervals The proportion of intervals which were played correctly.

Rhythms The proportion of rhythmic patterns which were played correctly.

Schulz [176] defines five difficulty levels for each of these five elements, shown in Fig- ure 2.6. PiaNote selects a difficulty level for each component based on the user’s scores in the previous exercise. It then uses the definition of each difficulty level as the parameters for generating the next exercise. For example, a user may start with an exercise generated using all the ‘Level 1’ parameters. If they played every pitch correctly but made mistakes in other areas, PiaNote may generate the next exercise with ‘level 2’ parameters for ‘Key Signature’, and the same ‘level 1’ parameters for the other four elements. One major drawback of PiaNote is that it can only generate exercises which are four bars long. Additionally, the parameters of each difficulty level in Figure 2.6 clearly show that the

13 CHAPTER 2. BACKGROUND

Figure 2.3: Music generated by randomsheetmusic.com using the default interface shown in Figure 2.2

Figure 2.4: The feedback interface of Etude Sight Reader [232]. Green indicates correctly played notes and red indicates errors. Textual markers describe the errors.

14 CHAPTER 2. BACKGROUND

Figure 2.5: A level four piece for the tenor recorder generated by Sight Reading Factory [226]

Figure 2.6: Definition of each level of difficulty for the five musical components in PiaNote. Taken from [176].

15 CHAPTER 2. BACKGROUND

software can only support generating material up to a certain level of complexity. For example, 4 3 2 whilst PiaNote can generate material using 4, 4, and 4 time, it does not support compound time 6 9 signatures such as 8 and 8. It also does not go beyond key signatures with 3 sharps or flats, nor does it use intervals greater than a 5th in size. As shown in Chapter 7, many of these features are present even in low difficulty sight reading exercises. It is clear from this discussion that whilst there are several existing software solutions for learning and practicing musical sight reading, there are many opportunities for further refinement. As this work focuses on generating endless sight reading material, the following sections will discuss literature related to the algorithmic creation of music.

2.6 Human Algorithms for Generating Music

The earliest example of an algorithmic approach to music composition comes from Guido D’Arezzo in 1026 [144]. Guido proposed a system in which alphabetical characters are mapped to musical pitches. Unfortunately, Guido’s mappings have not yet been discovered by musical scholars. Additionally, his mappings are likely based on some form of Latin, which may be dif- ﬁcult to translate to modern languages. As such, we can now only guess at how Guido’s system exactly worked. Later, in 1660, Jesuit priest Athanasius Kircher published Arca Musarithmica [88]. In this work Kircher described a device, illustrated in Figure 2.7, for algorithmically creating vocal music. Based on a given verse of poetry a series of Musarithms, or chords, are calculated to act as accompaniment [120]. To facilitate the process, the Arca Musarithmica contains a set of tariffa. Each tariffa is a wooden slat on which is written a set of numbers referring to pitches within a scale, and corresponding rhythmic patterns for those pitches. Using combinatoric techniques, music is constructed by selecting sequences of rods and combining their short musical snippets into longer phrases [29]. In total, the Arca Musarithmica is capable of producing millions of unique combinations. The Arca Musarithmica was followed by the Organum Mathematicum [175] in 1668. This device, described by Kircher’s pupil, is capable of more general purpose calculations. It also, however, offers the musical abilities of the Arca Musarithmica, though uses fewer tariffa. Between 1757 and 1812 the ﬁeld of algorithmic music was dominated by ‘musical dice games’, or Musikalisches Wurfelspiel¨ , with at least 20 unique games published during this time [71, 143]. Musical dice games are algorithmic composition processes where the outcome of dice rolls dictate the musical content of a piece. Typically, the numbers on two dice are mapped to pre-written musical phrases. Often there will be sets of phrases written for different portions of the music (e.g., opening, verses, ending), and a dice roll will be made to select a phrase for each. The earliest example of a musical dice game is Johann Philipp Kirnberger’s work Der allezeit fertige Menuetten- und Polonaisencomponist [89], which translates to “The Ever-Ready Minuet and Polonaise Composer”. Kirnberger’s game was originally published in 1757, and later revised in 1783 [143]. In 1758 Carl Philipp Emanuel Bach published the essay Einfall, einen doppelten Contrapunct in der Octave von sechs Tacten zu machen, ohne die Regeln davon zu wissen, which translates to “A method for making six bars of double counterpoint at the octave without knowing the rules” [14]. In this essay Bach summarised his musical dice game, which is

16 CHAPTER 2. BACKGROUND

Figure 2.7: The Arca Musarithmica device illustrated by Kircher [88]

capable of generating 31,381,059,609 unique counterpoint pieces. In 1780, Maximilian Stadler presented his dice game through an article titled Table pour composer des minuets et des Trios a` la infinie, avec deux dez a` jouer, which translates to “A table for composing minuets and trios to infinity, by playing with two dice” [187]. One of the most well-known instances of a musical dice game is Mozart’s musical dice game, published in 1792 [71]. However, although this game is commonly referred to as Mozart’s, and it was published by Mozart’s publisher Nikolaus Simrock, its origin has never been confirmed [42]. The game consists of a library of pre-written musical snippets, which are selected through dice rolls. Some musical snippets can only be selected at specific points in the melody (e.g., the final bar). At the end of the ‘game’, the user has created one of 45,949,729,863,572,161 possible 16 bar waltzes. In 1822 the Kaleidacousticon System parlour game was published [169]. Similar to a musical dice game, the Kaleidacousticon System comprises a deck of cards which help the player create one of 214 million possible waltzes. A similar parlor game is 1865’s The Quadrille Melodist [37]. As with the Kaleidacousticon System, The Quadrille Melodist is a deck of cards that can be combined in 428 million unique combinations. The game creates quadrilles: music suitable for a type of square dance popular in the 18th and 19th centuries. History also contains examples of novel instruments specifically built to compose music. One prominent example of this is Dietrich Nikolaus Winkel’s Componium [177]. Invented in 1821, the Componium is a type of automatic organ containing two barrels. Each barrel provides two measures of music, then passes control to the other. Whilst one barrel is playing its two measures, a roulette-like device selects two measures for the other barrel to continue with. The quantity and character of music possible when using the Componium depends on the barrels used. A more abstract form of algorithmic composition is Schoenberg’s 12 tone technique, first introduced in 1921 [9]. Schoenberg’s technique is a compositional method where each of the

17 CHAPTER 2. BACKGROUND

12 tones in the Western chromatic scale must be played before any tone can be repeated. The idea behind the technique is to write music where no pitch is emphasised more than any other, meaning that it can not be said to have been written in any particular key. More recently, computer technology has been applied to the challenge of algorithmic composition. The next sections will discuss the ﬁrst systems to emerge in this ﬁeld, and the various classes of algorithms used to drive the compositional processes.

2.7 Computer Music Generation

With the increase in technological power during the early 20th century, computer-based approaches to algorithmic composition became more popular. Although the ﬁeld has continued to grow, there are still ongoing philosophical discussions regarding what computer music actually is [41, 124]. For example, what is creativity, and are computers capable of it [138]? If so, what level of human input is required for a system to be considered a compositional tool rather than a discrete creative entity? Or, if a system primarily works by transforming and recombining human-written musical snippets, is it really creating new music? The goal of the work in this thesis is to create endless novel sight reading exercises. To achieve this goal, the need for human input must be limited, as the intended users (i.e., students) may not have the expertise to select appropriate parameters for their practice material. Beyond this requirement the solution space is unrestrained in terms of how sight reading exercises are generated. As such, these philosophical questions do not need to be addressed. An early example of a computer composing music is DATATRON [7]. This 1956 device is capable of generating ‘Tin Pan Alley’ melodies, an example of which is shown in Figure 2.8. Ames [7] describes the function of the system as follows:

“The operator inspires DATATRON by ﬁrst keying in a 10-digit random number. This causes the machine to generate and store 1000 single digits, each representing one of the eight diatonic notes in the scale with two allowable accidentals. The program then motivates DATATRON to pick successive notes at random, testing each for melodic acceptability as it goes along.” — Ames [7, p.2]

Around the same time Edmund Berkeley designed and marketed the Genius Almost- automatic Computer, or GENIAC. Although it was advertised as a computing device, GENIAC does not contain any active elements (i.e., relays, tubes, transistors), no memory, and instead relies on human operators to perform intermediary ‘computing’ steps [185]. Although GENIAC was a general purpose computer, Figure 2.9 shows that it was also advertised as being capable of composing music. The ﬁrst score generally considered to have been composed entirely by computer is the Illiac Suite [75, 172]. Composed in 1957, the suite is a four movement work for string quartet, where each movement corresponds to a different experiment in algorithmic composition:

First movement focused on generating cantus ﬁrmi (i.e., the base melody for a polyphonic piece).

Second movement focused on the generation of four-voice harmonies.

18 CHAPTER 2. BACKGROUND

Figure 2.8: An example melody, ‘Push Button Bertha’, produced by the DATATRON automated composition machine in 1956

Figure 2.9: An advertisement for the GENIAC Electric Brain. Taken from [53].

19 CHAPTER 2. BACKGROUND

Third movement focused on generating rhythmic patterns and dynamics.

Fourth movement used generative grammars and Markov chains to explore the power of stochastic processes.

The Illiac Suite was composed by the ILLIAC, a single-purpose computing device created speciﬁcally for algorithmic composition. Following ILLIAC, MUSICOMP (MUsic Simulator Inter- preter for COMpositional Procedures) was created [15]. MUSICOMP is a more general purpose composition device, offering a number of compositional subroutines which users could string together into longer musical works. As the ﬁeld of computer-based music composition has grown, certain algorithms have emerged as more popular within the literature. The next section will describe these algorithms and examples of how they have been used.

2.8 Algorithms for Computer Music Generation

Several taxonomies and categorisation systems have been developed to summarise and communicate the algorithms and techniques that have or could be applied to computer music generation [50, 58, 73, 143, 159]. The reason for the variety of systems is due to the inherent difficulty of summarising the field. This is due to the broad sample of methods that have been applied to the problem, and the fact that in practice many techniques are hybridised [143]. For example, Nierhaus [143] proposed the structure shown in Figure 2.10. This is a categorisation hierarchy which summarises techniques used in the field according to the sub-areas of artificial intelligence. Fernandez´ and Vico [58] employed a similarly hierarchical model, shown in Figure 2.11, but introduced additional sub-areas. Neither system is more or less correct than the other, but together serve to highlight the variety within the field. Other systems of summarising the field focus on what a system can do, rather than the algorithm used. For example, Quick [159] identifies four varieties of computer music generation tasks:

1. Automated Harmonisation A system is provided with a melody and must select appropriate chords to accompany that melody.

2. Automated Reharmonisation A system is given a melody and a harmony and must ﬁnd an alternative harmony that is equally appropriate.

3. Fill-in-the-Blank Problems A system is given a partially complete piece of music and must ﬁnish it in an appropriate style.

4. Generating Variations A system is given a melody or short phrase and must generate musical variations of it.

Each task can be further complicated with constraints such as a target style, genre, or instrument.

20 CHAPTER 2. BACKGROUND Rules Constraints Bayesian reasoning Abductive reasoning Propositional calculus Propositional Bayesian belief networks Reasoning with fuzzy sets Non monotonic reasoning Non monotonic First-order predicate calculus predicate First-order Scripts Frames Markov models Expert systems Traditional logic Traditional Hybrid systems Concept graphs Genetic algorithms Uninformed search Semantic networks Artificial neural nets Transition networks Transition Supervised learning Generative grammars Unsupervised learning Reinforcement learning Reinforcement Problem solving strategies Problem Informed or heuristic search Symbol-based machine learning Reasoning in uncertain situations Agents Reasoning State space of knowledge representation Machine Learning based procedures Language processing Context-related variants Context-related Production systems and rule- Production Techniques from the field of artificial intelligence which have been applied to algorithmic composition. Recreated from Nierhaus [143]. The Algorithmic Composition igure 2.10: F focus of this work, genetic algorithms, has been highlighted.

21 CHAPTER 2. BACKGROUND

Figure 2.11: An alternative summary to Figure 2.10 of techniques from the ﬁeld of artiﬁcial intelligence which have been applied to algorithmic composition. Taken from Fernandez´ and Vico [58].

There is one common theme amongst the four categories proposed by Quick [159]: all of the identiﬁed tasks require some music to have already been written. As such, these tasks can be seen more as computer-aided composition, a sub-category of computer music generation where technology is used in collaboration with a human composer. A broader categorisation is proposed by Scirea et al. [178], who deﬁnes two variations of algorithmic music generation:

1. Transformational The system is provided with some pre-existing music.

2. Generative The system starts with no pre-written music.

Using these categories, every task proposed by Quick [159] would be classiﬁed as ‘Trans- formational’. In this work the focus is on ‘Generative’ systems. This is because the goal is to create endless novel sight reading exercises. As the expected quantity of solutions is large it is not feasible to provide the system with pre-existing material. There are two reasons for this. Firstly, the availability of experts to create starter material is low. If users were able to reliably do this then they would also be able to write exercises independently of an automated system, negating the need for the system in the ﬁrst place. Secondly, the use of pre-written material introduces the risk that the system would create solutions entirely too similar to the music it was originally given.

22 CHAPTER 2. BACKGROUND rained N/A N/A N/A T Interactive Autonomous - Autonomous and Interactive Fitness N/A Autonomous - learning algorithm algorithm network ule-based system ule-based system Interprets l-system output as Algorithm R musical instructions R Neural Evolutionary Unsupervised (based on human solos) Evolutionary algorithmUnclear Autonomous Case-based reasoning Evolutionary Evolutionary algorithmEvolutionary Interactive algorithm Autonomous Random search Unclear Evolutionary algorithm Autonomous in the style of J.S. Bach, given a for classical guitar and bass, given a to compliment human solos olyphonic music olyphonic music our-part harmony our-part harmony P F Chorales human-provided soprano melody P Solos bass melody Music human-provided rhythm human-provided harmony and chord progression F progression soprano melody 2001 Monophonic melodies, given a 19631974 12-tone melodies 1988 1989 Polyphonic music 1991 1995 2000 2000 2002 2002 Polyphonic music 1994 Jazz solos over a human-provided chord 1986 Monophonic melodies 2000 Four-part harmony, given a human-provided Year Generates... 1998 Four-part harmony, given a human-provided A summary of literature in algorithmic composition, sorted by year (EMI) able 2.1: T OX POPULI ariations - MusaCazUza - CHORAL HARMONET V BoB - V Pegasus Experiments in Musical Intelligence - GenOrchestra System Name - GenJam [158] [52] and Otten [119] and Kuuskankare [102] et al. [134] et al. [166] [161] [192] [78] [40] ˘ glu et al. [74] [64] Felice et al. [49] iggins et al. [205] eference R Gill Rader Ebcio Hild Jacob Thom Laurson Moroni Prusinkiewicz Cope Biles [20] W Maddox Ribeiro De

23 CHAPTER 2. BACKGROUND rained rained rained Interactive N/A Autonomous Autonomous N/A T N/A Autonomous T Autonomous N/A T N/A Trained algorithm algorithm algorithm algorithm algorithm l-system output as network state machines and ule-based system ree-based musical algebra Evolutionary algorithm Trained Evolutionary Evolutionary Evolutionary algorithmInterprets musical instruction Autonomous Evolutionary algorithms T applied to human-provided subjects Evolutionary algorithmEvolutionary Probabilistic Autonomous grammar Neural Evolutionary Evolutionary algorithmR Autonomous Finite neural networks Markov chain Grammatical evolution Trained Evolutionary algorithm Autonomous Knowledge-based melodies melodies melodies, given a pieces wo-voice counterpoint olyphonic music olyphonic music olyphonic music olyphonic music our-part harmony human-provided chord progression P F subject, in fugue style Monophonic Monophonic P Monophonic human-provided chord progression progression T Piano P P soprano melody style 2006 Monophonic melodies, given a 2004 Countersubject for a human-provided 2007 Monophonic melodies 2007 Four-part harmony, given a human-provided 2008 Monophonic melodies of a speciﬁc musical 2008 Jazz solos using the blues scale 2003 20042004 Polyphonic piano music in a particular style2005 Unclear 2006 2007 2007 2007 Jazz solos over2007 a human-provided chord 2007 2008 2008 2006 Rhythmic lines 2007 Monophonic melodies BlueJam - ACSSM - - AMC - AMUSE NeuroComposer - ANTON - Impro-Visor Kinetic Engine ------¨ ogberg [51] [47] and Alpaslan [3] [1] et al. [81] et al. [121] and H and Rudolph [90] et al. [87] et al. [26] and [148] Erc¸al and Wagner [145] [31] et al. [56] ı ´ and Lucas [115] orth and Stepney [209] owe [170] eller and Morrison [86] ¨ Manaris Johnson W Lo Drewes Adiloglu Dahlstedt Boenn Oliwa Ozcan Chan Acevedo Klinger Eigenfeldt [54] Esp K Yi and Goldsmith [211] Khalifa R Dalhoum et al. [48]

24 CHAPTER 2. BACKGROUND rained rained rained Autonomous N/A Interactive T Autonomous Interactive Autonomous T Autonomous T Trained Trained algorithm algorithm algorithm temporal graph forest optimisation network Evolutionary algorithm Autonomous Artiﬁcial immune system N/A Evolutionary algorithm Trained Unclear Probabilistic Evolutionary Evolutionary Evolutionary Multi-agent virtual organisations Random Search parameters Neural grammars Markov chain Neural network Random selection within melodies melodies pieces olyphonic music olyphonic music op melodies for vocalists which match olyphonic music our-part harmony, given a human-provided P P Piano Monophonic F bass melody melodies P human-provided lyrics Monophonic P 2012 Jazz passages in bebop style 2016 Chorales in the style of J.S. Bach 2016 Chords to accomany human-deﬁned 2016 Monophonic melodies 2010 2013 2015 2016 2016 2016 2016 2017 2016 Polyphonic music 2015 Chord progressions 2016 Monophonic melodies S MA YSIA ulitta Virtuoso BachBot - K - - - AL MetaCompose PiaNote - MUSIC - - et al. [4] - and Loker [2] and O’Neill [116] and O’Neill [117] et al. [141] ın-Molina ´ et al. [72] et al. [136] [176] et al. [178] and Hudak [160] [109] ´ on et al. [50] ˜ noz Groux and Verschure [104] achet [149] Le Quick Loughran Loughran Mu Ackerman Scirea Hennig P Navarro et al. [140] Liang Albarrac Navarro de Le Schulz

25 CHAPTER 2. BACKGROUND

Table 2.1 summarises notable literature within the field of algorithmic music composition. Both generative and transformational systems are covered. One clear trend is the popularity of four-part harmonisation as a test problem. This is likely because it is a musical task with well-defined rules [119], to the point where it is considered ‘solved’ in terms of the ability to algorithmically generate musically correct solutions [151]. Another popular test problem is the generation of counterpoint. This is also a well-defined task – Fux [60] wrote a seminal book on the topic in 1725, and his work is still being used today. Some solutions rely on human input. This could be for fitness evaluation [104], the curation of training data [153], the composing of ‘starter’ musical material [166], or to arrange the output for actual musical instruments [64, 166]. Other systems, after being provided with appropriate parameters, operate largely by themselves. Many early examples of systems for computer-based music generation take a rule-based approach. For example, Rader [161] used a collection of rules to generate melodies appropriate for rounds1. Although the system was considered successful, even the authors note that the melodies generated by it are not interesting outside of the context of a round. Additionally, the rule-based approach restricted the solution space such that the generated melodies did not exhibit much variety. Overall, rule-based systems are not known for producing particularly varied music [26]. This is because the rulesets need to be restrictive enough to produce musically valid output. Often, this results in a ruleset that is so restrictive the system is unable to produce consistently interesting results [56]. Many early systems alternatively employ the use of Markov models [146]. For example, Pinkerton [155] created the Banal Tune-Maker in 1956. Using a training set of 39 nursery rhymes, the Banal Tune-Maker was designed to generate novel melodies in the same style. Other examples include systems which use Markov models to generate counterpoint melodies [57], four-part harmony [211], and even ‘virtuosic’ bebop jazz phrases Pachet [149]. Markov models remain a popular technique for style imitation [143]. Transition proba- bilities can be set by hand [58] or learned from a corpus of training data [143]. One issue with the technique is the curation of a training set which is both appropriately large and sufficiently broad [153]. Additionally, there is a trade-off when considering the order of chain to use. For example, low-order chains are limited in their capabilities because they don’t consider enough context. Higher-order chains, however, are computationally expensive and have been known to repeat, verbatim, segments of the training data [58]. Managing these issues is a point of difficulty when applying the technique. Another technique prominent in the literature is generative grammars. For example, Sundberg and Lindblom [190] used a generative grammar to create 8-bar folk songs. Similarly, Steedman [188] used the same approach to create 12-bar blues progressions. A popular sub- field of generative grammars is the Lindenmayer system (l-system) [113]. The most common approach with l-systems is to interpret its output symbols as a sequence of musical parameters [48, 158, 209]. For example, some symbols might indicate an upwards movement in pitch, and others might indicate a downwards movement. These types of systems have achieved some success, but are mostly known for being computationally expensive and having a low hit rate of

1Rounds are a type of musical composition where the same melody is played by multiple people who start at different times.

26 CHAPTER 2. BACKGROUND

acceptable solutions [153]. Recent work has focused primarily on using l-systems to generate rhythmic sequences [82, 83, 114]. Although they emerged later than other techniques in the field, neural networks are another popular approach to computer-based composition. Todd [193] is the first example of their use, focusing on the creation of small melodies which emulate the characteristics and style of melodies in a training corpus. Other examples of neural networks include the creation of two-voice counterpoint [3] and chorales in the style of J. S. Bach [72]. Given that neural networks are generally considered to be inefficient at producing musical content in isolation [153], they are often used as fitness evaluators in combination with some other technique [58]. HARMONET [74] and CONCERT [135] are examples of such systems. Combining a neural network with a rule-based system, HARMONET takes a given melody and creates a harmony for it in the style of J. S. Bach. CONCERT also operates in the style of Bach, using a different rule-based system to generate novel melodies and harmonic progressions based on Bach’s chorales, folk songs, and waltzes. Both systems are successful within their chosen tasks, but do not easily generalise to other styles due to their need for significant quantities of training data [145]. Other less prominent techniques which have been applied in the field include transition networks [39, 70], chaos systems [18], and cellular automata [132]. None of these approaches are recognised as being particularly effective [58, 143]. Deep learning techniques are a more recent advancement in the field. One application of these techniques is in creating fitness functions. A significant challenge in the field is evaluating the fitness (i.e., quality) of the generated music. This is an inherently complex task given the subjective nature of creative evaluation [50, 61, 159]. Table 2.2 shows how the systems summarised in Table 2.1 approach the problem. Some systems, such as those based on l-systems, do not require fitness evaluation. These are labelled as ‘N/A’. Of those systems where fitness evaluation is necessary, the least popular approach is interactive. Interactive fitness is where candidate solutions are manually evaluated and rated by a human listener. There are a number of issues with this approach. First, the process is time intensive [21, 58]. To deal with this issue the number of human evaluators could be increased, but this introduces a new problem of ensuring that the different human raters are consistent in their ratings. Secondly, finding a suitable rater can be difficult. The person needs to understand what characteristics they are looking for, how those characteristics should be measured, and how those measurements should translate to an overall rating. Lastly, continuous listening causes significant fatigue, thus inconsistency even in ratings made by the same person [122, 194].

Table 2.2: A summary of the ﬁtness methods used by the literature summarised in Table 2.1. Percentages are rounded to two decimal places.

Fitness Method % of Literature

Trained 25.53 Interactive 10.64 Autonomous 38.3 N/A 25.53

27 CHAPTER 2. BACKGROUND

The next most common approach is to train an algorithmic fitness evaluator such as a neural network. This can be an effective solution, but does require a non-trivial quantity of training data. Additionally, it can result in a system where the generated music is driven to emulate the training data too closely, or in some cases exactly as written. Autonomous fitness evaluation is the most popular approach, as it does not overly influence the solution space or require the use of human evaluators. Although it avoids these pitfalls, autonomous fitness evaluation represents a different set of challenges. These challenges almost entirely relate to the intended scope of the solution space. Clear boundaries for the solution space need to be established, and the fitness criteria needs to meet these boundaries as closely as possible. A thorough understanding of the problem space is required to both establish these boundaries and devise appropriate fitness criteria. Within this section, many notable and popular approaches to algorithmic computer music generation have been discussed. One approach, evolutionary algorithms (EAs), has been neglected. This is because EAs are the chosen algorithm in this work. The reasons for this are that evolutionary algorithms:

1. have been applied to algorithmic computer music generation more often and with more success than any other technique [22, 133, 148],

2. are well-suited to navigating the large solution space of music generation [81, 148], and

3. allow for speciﬁc goals to be set for solutions whilst still providing space for novel and emergent behaviours to appear [143, 148].

The next section provides an overview of notable evolutionary systems within the ﬁeld.

2.9 Evolutionary Algorithms for Computer Music Generation

In his work, Biles [22] identified a number of key areas of computer music generation suitable for evolutionary algorithms. These areas, shown in Figure 2.12, cover the generation of simple melodies, musical variations, harmonisations and chord progressions, arrangements of music, and larger musical structures. The goal of this work, to generate sight reading exercises, falls strictly within the category of ‘Generate melodic motifs/ideas’. Within this category, the goal is to create ‘Sequences with both pitch and rhythm’. In terms of summarising the field of evolutionary algorithms for music generation, San- tos et al. [173] identified five unique types of systems:

1. Interactive Systems which require a human critic to rate the ﬁtness of candidate solutions.

2. Based on Examples Systems which require a training corpus to be provided. Often uses a neural network as a ﬁtness rater.

3. Rule-based The ﬁtness of candidate solutions is based on a set of rules.

28 CHAPTER 2. BACKGROUND

Figure 2.12: Tasks considered to be good candidates for evolutionary computation. Taken from Biles [22].

4. Autonomous Systems where no human input is required beyond setting initial parameters.

5. Hybrid Systems which combine two or more of the above approaches.

Santos et al. [173] states that early systems tended to use non-hybrid approaches, not because they are superior but because computational power was limited. Now that computational power is more readily available, he recommends that a hybrid approach be taken in almost all cases. One example of a hybrid approach is by Towsey et al. [195], who extracted a set of statistics from the analysis of existing musical material over 21 unique criteria. These statistics were then used as a fitness function. Lo and Lucas [115] took an alternative approach, training a grammatical model to evaluate the fitness of candidate solutions. However, this model was shown to be better at classifying inputs (e.g., identifying the composer of a piece) than evaluating the fitness of generated material. Loughran and O’Neill [116] also took a grammatical approach, using a context-free grammar to evaluate the fitness of generated piano pieces. This method does not make use of a training set. Instead, the user is required to define which notes from the target scale are acceptable, which interval sizes are acceptable, and the desired likelihood of occurrence for each of those notes and intervals. De Felice et al. [49] adopted an uncommon approach when creating GenOrchestra, combining both interactive and automated fitness measures. GenOrchestra first uses a ruleset to ensure that the rules of harmony are followed. If they are, candidate solutions are presented to human listeners for aesthetic evaluation. Rather than using interactive and autonomous fitness, Scirea et al. [178] used a combination of ‘soft’ and ‘hard’ requirements in their system MetaCompose. MetaCompose maintains two evolutionary populations: one containing infeasible solutions, and the other containing only feasible solutions. Each population is evolved independently using three negotiable and three non-negotiable rules, and candidate solutions are moved between the two populations

29 CHAPTER 2. BACKGROUND

when appropriate. Another approach is to define a set of criteria that candidate solutions need to meet. These criteria can be combined using a weighted sum as in AMUSE [148], or as part of a more complex points system. A points system, such as that used by Johnson et al. [81], rewards ‘positive’ elements of a melody (e.g., using an interval of a third) with points. Elements of a melody seen as ‘negative’ (e.g., using an interval over a fifth) are penalised by taking points away. The work of Acevedo [1] uses a similar system, but positive and negative elements are assigned positive and negative weightings instead of point values. Some systems take advantage of the domain. For example, Papadopoulos and Wiggins [152] created a system to generate melodies for given chord progressions. To achieve this goal, they used domain-specific operators such as transposition, inversions, and rearranging pitch sequences in ascending and descending order. Rowe [170] also used domain-specific knowledge in his system BlueJam. Given that the goal of BlueJam is to generate solos in a jazz style, Rowe [170] used the knowledge that jazz solos do not contain many long notes to restrict the evolutionary process. An example of a system which diverges from the traditions of the field is GenDash [201]. Instead of each candidate in the evolutionary population being an independent solution, each candidate in GenDash represents a single bar, and the entire population is the solution. In GenDash the first x bars of music are chosen by a human. These bars then form the initial population, and the next y bars of music result from applying genetic operators to that population. The quality of output using this approach is highly dependent on the initial human-selected bars.

2.10 Summary

This chapter has discussed key aspects of the literature related to the work presented in this thesis. This includes the general challenges faced in music education, and the use of technology in the field. Also discussed was the concept of musical sight reading and how technology has been used to enable deliberate practice of the skill. Algorithms executed by humans to generate music were detailed, as well as their contemporary computer-based equivalents. A number of algorithms popular in the field were identified, and the technique chosen for this work – evolutionary algorithms – was discussed. The next chapter will shift the focus to developing a taxonomy for categorising musical content and activities. It is through this taxonomy that materials for music education can be formally described and analysed.

30 3 A Taxonomy for Describing Musical Content and Activities

3.1 Overview

The previous chapter provided a discussion of literature relevant to the work presented in this thesis, from general music education to algorithms for computer music generation. This chapter describes a taxonomy for categorising both the principles of musical knowledge and activities where they are applied. This taxonomy will facilitate formal analyses of educational musical materials, including those for sight reading. The following deﬁnitions, introduced by Grant [66], are used:

Aspect A characteristic, dimension, or element forming a part of music; a.k.a., a rudiment.

Parameter Any aspect that can be altered independently of other aspects.

Principle Any parameter that can be independently focused on in an educational context.

Although there is little dispute regarding the central aspects of music (e.g., pitch, rhythm), subject matter experts disagree on their exact deﬁnitions [63]. Similarly, there is disagreement about the total number of aspects and their names. In this work an attempt has been made to cover each of the commonly accepted central aspects and principles, and some additions. The taxonomy is intended to provide a common vocabulary across and within previously dichotomous musical domains. It also enables the analysis of existing musical teaching tools, by allowing one to see the coverage of content areas and types of activities both within a single tool and across multiple tools. Similarly, it also represents a framework for creating new teaching tools. When designing the taxonomy, the four following goals were deﬁned:

1. The taxonomy should be instrument-agnostic1

1The ‘Instrument-Specific’ area of the taxonomy may appear to violate this goal. However, this area of the taxonomy makes no specific reference to any particular instrument(s), but rather is named ‘Instrument-Specific’ as it can be applied to any instrument. This is further discussed in Section 3.2.8.

31 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

This relates to a larger unwritten goal of making the taxonomy as general as possible. Doing so allows it to be applied in more situations and domains than if the categories were restricted by references to speciﬁc instruments or instrument families.

2. The taxonomy should not consider human characteristics such as sound perception and cognition These characteristics describe physical abilities commonly measured in psychological tests of musical aptitude [103]. As this taxonomy classiﬁes and describes knowledge and tasks which can be learned and improved upon, these abilities are irrelevant as they are static within a person [85, 98].

3. The taxonomy should not imply any speciﬁc teaching approach Although the taxonomy can be used to describe teaching tools and curriculums, it is not itself intended to be a teaching tool. Were it to prescribe or promote a particular teaching approach it would no longer be able to act as a neutral vocabulary across domains.

4. The taxonomy should not suggest an order of delivery for teaching concepts There is no standard order of delivery in the literature for teaching musical concepts, and this work makes no attempt to deﬁne one.

Attending to these goals resulted in a structure, illustrated in Figure 3.1, where musical principles are separated into a number of content areas and activities. Activities, which involve the application of musical principles, are further separated into a hierarchical collection of tasks and exercises. Each content area groups a number of related topics, and each task and exercise type describes both the structure of an activity, the question format of the activity, and the area of knowledge (i.e., content area) required to successfully complete the activity. There has been no clear attempt in the literature to create a taxonomy of this type in the past. However, taxonomies have been used in the musical domain for other purposes. The next section discusses some key examples of these uses.

3.1.1 Background

The literature provides many examples of taxonomies being used in the musical domain. For example, multiple proposals have been put forth regarding the aspects of music. These proposals often exhibit some crossover, but eventually diverge from one another either in the names

Content Areas

used to Taxonomy complete Tasks Activities Exercises

Figure 3.1: An overview of the taxonomy

32 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

or definitions of aspects. For example, Meyer [128] suggests that musical aspects are limited to melody, rhythm, timbre, and harmony. White [203] also proposes these four aspects, but adds dynamics and texture. Narmour [139], however, submits that musical aspects include, at a minimum, melody, rhythm, timbre, harmony, dynamics, texture, tempo, and meter. Other classification systems tend to be quite specific in terms of their purpose. For example, there are numerous cases where a taxonomy has been proposed – either formally or informally – for the organisation of concepts within a curriculum. These taxonomies often focus on the specifics of their related curriculum, frequently involving categorisations based on subjective characteristics such as order of presentation or perceived difficulty. Being specific to only a single curriculum, these types of taxonomies also regularly miss some of the aspects or activity types proposed in this work. One example of such a taxonomy is the Trinity College music knowledge curriculum [38]. This taxonomy organises concepts in terms of what an examiner may ask a student about the music they have played during a practical examination. A single level of categorisation is used – the grade at which a concept may be asked – and no other factors are considered. More general taxonomies have been proposed by various education-focused branches of governments at the state or country-wide levels. Although these systems are intended to be more generic than those which apply to only a single curriculum, they tend to organise knowledge into broad, poorly-defined groups. They also tend to separate concepts into difficulty levels for which there is little empirical justification. For example, the US teacher certification exams split knowledge into four categories [157]:

1. Music history and literature, 2. Theory and composition, 3. Performance, and 4. Pedagogy, professional issues, and technology.

Similarly, the Victorian Ministry of Education defines twelve areas of learning and skill development, which are then further split into five difficulty levels [131]. These patterns are repeated in informal taxonomies such as those frequently seen in online learning support tools and massively online open courses [223, 231, 239, 250]. In non-academic contexts taxonomies have been defined for categorising musical instruments [179, 180], describing musical genres [108, 150], processing musical information from the semantic web [163], and even describing the areas of the computer music field itself [156].

3.1.2 Chapter Structure

The proposed taxonomy is split into two distinct sectors: content areas and tasks and exercises (i.e., activities). Each of these will be presented separately. The content areas will be described ﬁrst in Section 3.2, as this knowledge is required to understand the tasks and exercises. Sec- tion 3.3 will detail each of the proposed tasks and exercises. A single colour code will be used to visually describe both content areas and tasks and exercises. This colour key is provided in Figure 3.2 – the colour of a line describes the content type, and the text colour indicates the kind of activity.

33 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Reading content

Rhythm content

Scales content

Elements of Harmony content Content (line colour) Harmonic Structures content

Style content

Instrument-speciﬁc Instruction content

Historical or General Knowledge content

Auditory Recognition activity

Recognition activity Visual Recognition activity

Auditory Description activity

Activities (text colour) Description activity Visual Description activity

Playback activity Visual Playback activity

Notation activity Memory Playback activity

Figure 3.2: The colours used to visually refer to items in the taxonomy. Line colour relates to content area and text colour denotes the kind of activity.

34 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

3.2 Content Areas

3.2.1 Overview

In this taxonomy, content areas are defined as the categories into which musical knowledge can be placed. Each category contains a subset of topics, all of which relate to the same broad area. The content areas proposed in this taxonomy are shown in Figure 3.3. The type of knowledge classified by content areas is factual only. This knowledge can be applied or demonstrated when completing the tasks and exercises (a.k.a. activities) described in Section 3.3. For example, the pattern of a harmonic minor scale would fall under the ‘Scales’ content area, and this knowledge could be demonstrated by notating a harmonic minor scale in a particular key. Similarly, the appearance and uses of the repeat symbol would be ‘Rhythm’ content, which might be applied by identifying the repeat symbol from some set or collection of symbols. Sections 3.2.2 through 3.2.9 will describe the proposed content areas. The order in which the categories and their topics are presented is not intended to imply any recommendations for the order of their delivery when being taught. However, in some cases there are clearly more ideal sequences than others. For example, it would be difficult to explain the writing of key signatures (part of the ‘Scales’ content area) to a person who does not yet understand the stave or clefs (elements from the ‘Reading’ content area). Similarly, a person would struggle to write chord progressions (a topic from the ‘Harmonic Structures’ content area) without first understanding individual chord types (part of the ‘Elements of Harmony’ content area). There has intentionally been no attempt made to sort the concepts into difficulty levels. This is largely due to the purpose of the taxonomy being to act as a common vocabulary between musical domains, but also because there currently exists no standard for making such classifications.

3.2.2 Reading

The ‘Reading’ content area covers the aspects of musical knowledge needed to understand, from musical notation, what pitch to play and its intended length relative to other pitches. Representative examples of this type of content are listed, but not limited to, those in Figure 3.4. These are the most basic elements needed to visually communicate a sequence of notes – both monophonic and polyphonic – in such a way that they can consistently be reproduced. Some examples of how content from the ‘Reading’ category can be presented are shown in Figure 3.5. Basic pitches and their positions on the stave are shown in Figure 3.5(a), with Figure 3.5(b) taking a more abstract view by describing where ‘high’ and ‘low’ notes are placed. An example of instructional material relating to the interpretation of accidentals is shown in Figure 3.5(c), which describes how long an accidental applies to a given pitch.

3.2.3 Rhythm

‘Rhythm’ content is deﬁned as the aspects of musical knowledge related to the grouping of notes. For example, bar lines show how notes are grouped into measures, the sizes of which are deﬁned by time signatures. Figure 3.6 shows some examples of topics found in this content

35 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Reading

Rhythm

Scales

Elements of Harmony Content Harmonic Structures

Style

Instrument-speciﬁc Instruction

Historical or General Knowledge

Figure 3.3: The proposed content areas in the taxonomy

Staves

Clefs

Notes

Reading Rests

Accidentals

Slurs

Tie

Figure 3.4: Examples of the knowledge included in the ‘Reading’ content area

36 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(b) ‘Reading’ content presented in Music (a) ‘Reading’ content presented in Jelly- Theory for Beginners [240], showing how bean Tunes [225], showing the positions low and high pitches are notated on the of pitches stave

(c) ‘Reading’ content presented in Musition Note Reading [246], explaining the interpretation of accidentals in musical notation

Figure 3.5: Examples of knowledge from the ‘Reading’ content area being presented in iOS applications

37 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Bar lines

Measures

Time signatures

Repeats

Rhythm Anacruses

Da Capo

Dal Segno

Rhythmic placement

Syncopation

Figure 3.6: Examples of the knowledge included in the ‘Rhythm’ content area

area. Whilst topics directly related to musical notation (e.g., bar lines, repeat symbols) are included, ‘Rhythm’ also covers more abstract concepts such as syncopation, ‘up’ and ‘down’ (or ‘on’ and ‘off’) beats, rhythmic styles (e.g., swung, straight), and rhythmic placement. Figure 3.7 shows some examples of how content from the ‘Rhythm’ category can be presented. An introduction to time signatures is shown in Figure 3.7(a), and an example of how rhythmic placement may be described is provided in Figure 3.7(b).

3.2.4 Scales

The content covered by the ‘Scales’ content area is defined as the patterns of scales, structure of key signatures, and knowledge that can be inferred directly from this information. For example, as shown in Figure 3.8, the category also covers knowledge of the circles of fourths and fifths. This is because the circle’s structures are derived from the number of sharps and flats in each musical scale. Moreover, understanding the construction of the circles enables one to compute the key signature of a specific scale from any other scale of the same type. Examples of how ‘Scales’ content has been presented in iOS applications are shown in Figure 3.9. The first, Figure 3.9(a), shows the description of a common piece of ‘Scales’ knowledge – the pattern of a musical scale. Another common area – key signatures – is presented by the application shown in Figure 3.9(b). Finally, Figure 3.9(c) shows how the concept of the circle of fourths and fifths might be illustrated.

3.2.5 Elements of Harmony

The ‘Elements of Harmony’ content area is deﬁned as covering knowledge of foundational harmonic concepts such as those listed in Figure 3.10 – interval types, chord types, and their inversions. These concepts are central to the more advanced topics covered in the ‘Harmonic Structures’ content area described in Section 3.2.6.

38 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(a) ‘Rhythm’ content presented in Theory Lessons [241], showing a description of time signatures

(b) ‘Rhythm’ content presented in Musition Rhythm Notation [247], providing an explanation of rhythmic placement

Figure 3.7: Examples of knowledge from the ‘Rhythm’ content area being presented in iOS applications

Scale types and patterns

Key signatures

Scales Labelling scale degrees

Circle of fourths

Circle of ﬁfths

Figure 3.8: Examples of the knowledge included in the ‘Scales’ content area

39 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(a) ‘Scales’ content presented in Auralia Scales [245] showing the pattern of the blues scale

(b) ‘Scales’ content presented in Better Ears [234], deﬁning the concept of a ‘key signature’ and its proper location within musical notation

Figure 3.9: Examples of knowledge from the ‘Scales’ content area being presented in iOS applications

40 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Interval types

Interval inversions Elements of Harmony Chord types

Chord inversions

Figure 3.10: Examples of knowledge included in the ‘Elements of Harmony’ content area

Some examples of how ‘Elements of Harmony’ content is commonly presented in iOS applications are shown in Figure 3.11, with Figure 3.11(a) illustrating a perfect ﬁfth and Fig- ure 3.11(b) showing a description of the major and minor chord structures.

3.2.6 Harmonic Structures

Knowledge falling under the ‘Harmonic Structures’ content area is deﬁned as that which enables one to break down the structure of existing pieces, and that which is needed to create new, harmonically valid musical material. As shown in Figure 3.12 these concepts include, but are not limited to, the use of chord progressions and cadences, the rules of harmony, and the use of passing notes. The content area also includes the knowledge of how to identify and label cadence and chord types, and the proper arrangement of concurrent notes within a group of instruments (i.e., voicing). Two examples of how knowledge from the ‘Harmonic Structures’ content area may be presented are shown in Figure 3.13. The ﬁrst, Figure 3.13(a) shows how one particular iOS application chooses to introduce a subset of chord labels and their harmonic uses. Figure 3.13(b) shows a more concrete example of chord labelling, describing the appropriate way to differen- tiate between ‘minor’ and ‘major’ when assigning labels.

3.2.7 Style

The ‘Style’ content area contains knowledge of concepts which are intended to add auditory interest to both individual notes and sequences of notes. This is a broad category, with Figure 3.14 showing only a small list of the knowledge it describes. Within each of the listed items there can be a large set of knowledge. For example, ‘Dynamics’ includes both single instructions that take immediate effect (e.g., ff, mf, ppp) and those which apply over a period of time (e.g., crescendos and diminuendos). ‘Articulation’ and ‘Ornamentation’ similarly describe several aspects, including articulation markings such as staccato and legato, and ornamental markings such as trills and grace notes. ‘Style descriptions’ and ‘Tempo descriptions’ refer to the text often found at the beginning of a piece describing the intended style or speed for the performer to follow. Figure 3.15 shows examples of ‘Style’ content being presented in iOS applications.

41 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(a) ‘Elements of Harmony’ content pre- (b) ‘Elements of Harmony’ content presented in Music Intervals [238], showing sented in Chordelia Triad Tutor [224] de- the identiﬁcation of a perfect ﬁfth as op- scribing the interval structures that composed to a perfect fourth prise major and minor chords

Figure 3.11: Examples of knowledge from the ‘Elements of Harmony’ content area being presented in iOS applications

Chord progressions

Chord labelling

Cadence types Harmonic Structures Voicing

Passing Notes

Harmonisation

Figure 3.12: Examples of knowledge included in the ‘Harmonic Structures’ content area

42 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(a) ‘Harmonic Structures’ content presented in Music Theory and Practice [253], describing some basic chord types, their labels, and their purposes

(b) ‘Harmonic Structures’ content presented in Theory Lessons [241], showing the identiﬁcation and labelling of chords using each note in the C major scale as the root

Figure 3.13: Examples of knowledge from the ‘Harmonic Structures’ content area being presented in iOS applications

43 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Tempo markings

Tempo descriptions

Style descriptions Style Dynamics

Articulation markings

Ornaments

Figure 3.14: Examples of knowledge included in the ‘Style’ content area

3.2.8 Instrument-Speciﬁc

Knowledge covered by the ‘Instrument-Specific’ content area is as the name suggests – information specific to the playing of a particular instrument. This makes it one of the broadest categories, especially as the exact content is entirely dependent on the instrument being taught. There is little knowledge applicable to all instruments and only some common knowledge across instruments in the same family (e.g., strings), meaning that each sub-category contains layers of information. Knowledge which is described as ‘Instrument-Specific’, some of which are listed in Figure 3.16, center around concepts such as physical positioning, tuning, and maintenance.

Figure 3.17 shows some ‘Instrument-Speciﬁc’ content being presented in the iOS application Learn Guitar Theory [259]. However, given the scope of the content area this should not be taken as a representative example.

3.2.9 Historical and General Knowledge

As with the ‘Instrument-Speciﬁc’ content area, the ‘Historical and General Knowledge’ content area is reasonably broad. It is deﬁned as containing knowledge that, whilst essential to in- forming the context and background of a piece or a person’s general musical framework, is not fundamental to one’s ability to play it. For example, although knowing the time period or era in which a piece was written can help a player’s interpretation, lacking this knowledge does not present an impenetrable barrier to its performance.

The content covered by this category is not limited to any particular musical style, culture, instrument, or time period. Figure 3.18 shows some areas of knowledge that are included. For example, the content area covers the identiﬁcation of composers based on their image, a description, or their works. Similarly, it also includes the knowledge of concert halls and works generally considered to be ‘well-known’.

44 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

(a) ‘Style’ content presented in Musition Symbols [248] showing descriptions of common articulation symbols

(b) ‘Style’ content presented in Music Theory Tutor [251], where the user is given examples of symbols and phrases relating to dynamics

Figure 3.15: Examples of knowledge from the ‘Style’ content area being presented in iOS applications

45 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Tuning

Hand position

Instrument-speciﬁc Instruction Embouchure

Cleaning

Assembly and disassembly

Figure 3.16: Examples of knowledge included in the ‘Instrument-speciﬁc’ content area

Figure 3.17: ‘Instrument-Speciﬁc’ content presented in Learn Guitar Theory [259], where the user is given a description of how to hold a guitar pick

Composers

Time periods Historical or General Knowledge Concert halls

Well-known works

Figure 3.18: Examples of knowledge included in the ‘Historical or General Knowledge’ content area

46 CHAPTER 3. A TAXONOMYFOR DESCRIBING MUSICAL CONTENTAND ACTIVITIES

Auditory

Recognition Visual

Auditory

Tasks/Exercises Description Visual

Playback Visual

Notation Memory

Figure 3.19: The proposed activity types

3.3 Activities

3.3.1 Overview

Whilst the content areas described in Section 3.2 allow one to categorise the areas of musical knowledge, ‘Activities’ allow one to consistently describe and group activities where this knowledge is applied. Two separate activity styles, Tasks and Exercises, are deﬁned:

Task An activity for which there is a single binary answer, and the solution can be discovered or identiﬁed with one step (e.g., by choosing from a list of options). For example, identifying which of four images is the treble clef.

Exercise An activity requiring multiple steps to complete. Solutions are more complex than for tasks, and can be partially correct. For example, writing the notation for one ascending octave of the A major scale in the treble clef.

Figure 3.19 shows the major types or categories of activities, each of which defines a set of problem structures. Individual activities are classified as tasks or as exercises on a case-by- case basis. That is, each activity type can contain both tasks and exercises, not just one or the other. Each activity type is also further split into subtypes. These subtypes relate to the content areas defined in Section 3.2. Combined, the activity type and content area describe the problem structure of an activity and the area of knowledge needed to complete it. Although each activity type can contain both tasks and exercises, each category strongly tends towards one of the two. These tendencies are described in Table 3.1. Sections 3.3.2 to 3.3.5 describe the activity types proposed in this taxonomy. Through- out, the person completing the task or exercise will be referred to as a ‘participant’, ‘student’, or ‘user’.

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Table 3.1: The most common activity style (i.e., task or exercise) for each proposed type of activity. Classiﬁcations are not absolute – generally activities of a type will be of the speciﬁed style, but there may be some which do not conform to the listed type.

Activity Type

Auditory Recognition Task Visual Recognition Task Auditory Description Task Visual Description Task Visual Playback Exercise Memory Playback Exercise Notation Exercise

3.3.2 Recognition Activities

3.3.2.1 Overview

Recognition activities all require the participant to identify some musical element. Two variations of recognition activities are deﬁned:

Auditory Question content is primarily presented through an auditory medium (recorded or live), but may be accompanied by some written material, and

Visual Question content is largely visual (i.e., drawn), but may be accompanied by some auditory stimulus.

Auditory and visual recognition activities are described further in Sections 3.3.2.2 and 3.3.2.3, respectively.

3.3.2.2 Auditory Recognition Activities

As described in Section 3.3.2.1, ‘Auditory Recognition’ activities are defined as those where question content is presented primarily through an auditory medium, either pre-recorded or performed live. Eight types of auditory recognition activities are defined, listed in Figure 3.20. Example activities for each subtype are provided in Table 3.2. Excepting ‘Pure’, each example relates to the identification of content from a specific content area. For example, an ‘auditory recognition of scales content’ activity may ask the participant to identify a major scale from four different scales played to them. Similarly, ‘auditory recognition of elements of harmony content’ might require users to select the type of interval being played from a list of options. Pure auditory recognition, on the other hand, does not relate to any particular content area. These activities may involve students being asked to identify a random pitch or sequence of pitches that is played to them. Such questions may ask for answers to be given either as pitch names (e.g., C, D, E), or Solfége (e.g., Do Re Mi). Given that auditory recognition questions generally require participants to identify only one thing, they are mostly described as being tasks. However, in some cases an activity is better described as an exercise – for example, when the participant is asked to identify a sequence of notes rather than just a single pitch.

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Pure

Reading content

Rhythm content

Scales content Auditory Recognition Elements of Harmony content

Harmonic Structures content

Style content

Historical or General Knowledge content

Figure 3.20: Subtypes of ‘Auditory Recognition’ activities

Table 3.2: Example activities for each auditory recognition activity subtype

Auditory Recognition Activity Subtype Example Activity

Pure A single note is played and the user is asked to name the pitch Rhythm content A series of clicks are played at consistent intervals and the student is asked to nominate an appropriate tempo marking Scales content A single scale is played and the user is asked to select the scale type from a list of options Elements of Harmony content A single interval is played and the participant is asked to select its label (e.g., perfect fourth, minor third) from a list of options Harmonic Structures content A single cadence is played and the student is asked to identify its label (e.g., plagal, perfect) from a list of options Style content A short melodic phrase is played and the student is asked to tick whether it was played with a crescendo or diminuendo Historical or General Knowledge content An excerpt from a piece is played and the user is asked to identify the composer from a short list

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3.3.2.3 Visual Recognition Activities

‘Visual Recognition’ activities, as deﬁned in Section 3.3.2.1, are those where question content is presented visually. This taxonomy proposes eight subtypes of visual recognition activities, listed in Figure 3.21. For example, an activity for ‘visual recognition of reading content’ may present the user with images of a semibreve, a crotchet, a quaver, and a semiquaver and ask them to identify the crotchet. Alternatively, an activity for ‘visual recognition of historical or general knowledge content’ may require the participant to identify the picture of Mozart from four images of different composers. Example questions for each subtype of visual recognition activity are provided in Table 3.3. Visual recognition activities mostly ask participants to identify some musical element from a set of options. As such, they can almost always be categorised as tasks. The only exception to this is if the user is asked to identify multiple items in the same question, in which case the activity would be better described as an exercise. This is because the user’s answer in this case could be only partially correct (e.g., by correctly identifying some but not all of the elements).

3.3.3 Description Activities

3.3.3.1 Overview

Description activities require the user to explain some part of a concept, usually in terms of a single characteristic. Two variations of description activities are deﬁned:

Auditory Question content is primarily presented through an auditory medium (recorded or live), but may be accompanied by some written material, and

Visual Question content is largely visual (i.e., written), but may be accompanied by some auditory stimulus.

Auditory and visual description activities are described further in Sections 3.3.3.2 and 3.3.3.3, respectively.

3.3.3.2 Auditory Description Activities

As deﬁned in Section 3.3.3.1, auditory description activities are those where question content is largely auditory. These activities can be one of the eight subtypes listed in Figure 3.22. For example, an activity for ‘auditory description of reading content’ may play the user two pitches and ask them to state which was higher. Alternatively, an ‘auditory description activity for style content’ may require the participant to characterise a sound as ‘loud’ or ‘soft’. Example activities for all of the proposed activity subtypes are provided in Table 3.4. Auditory description activities mostly ask participants to describe a single characteristic of a single musical element. As such, they can generally be characterised as tasks. In cases where the participant is asked to describe multiple items in the same activity, however, that activity would be better described as an exercise.

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Reading content

Rhythm content

Scales content

Elements of Harmony content Visual Recognition Harmonic Structures content

Style content

Instrument-speciﬁc content

Historical or General Knowledge content

Figure 3.21: Subtypes of ‘Visual Recognition’ activities

Table 3.3: Example activities for each visual recognition activity subtype

Visual Recognition Activity Subtype Example Activity

Reading content A picture of a semibreve, a minim, a crotchet, and a quaver are displayed and the user is asked to identify the crotchet Rhythm content A picture of a time signature, a repeat symbol, and a bar line are displayed and the student is asked to identify the repeat symbol Scales content They key signatures for A major, C] major, F major, E major and B major are displayed and the user is asked to identify which is the key signature for E major Elements of Harmony content Augmented major, minor, diminished 7th, and minor 7th chords are written in the key of D and the student is asked to identify which is the diminished 7th chord Harmonic Structures content Chords IV, II, VI, and V and notated in the key of E minor with no labels, and the participant is asked to identify which chord would be labelled with “II” Style content Staccato, tenuto, accent, and sforzando marks are displayed, and the user is asked to identify which mark is the sforzando Instrument-specific content A single pitch is notated and four clarinet fingering charts are shown, and the participant is asked to identify which fingering chart matches the notated pitch Historical or General Knowledge content Pictures of Mozart, Beethoven, Brahms, and Bach are displayed, and the user is asked to identify which image depicts Brahms

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Reading content

Rhythm content

Scales content

Elements of Harmony content Auditory Description Harmonic Structures content

Style content

Historical or general knowledge content

Figure 3.22: Subtypes of ‘Auditory Description’ activities

Table 3.4: Example activities for each auditory description activity subtype

Auditory Description Activity Subtype Example Activity

Reading content Two pitches are played and the user is asked to state whether the second pitch was higher or lower than the first Rhythm content Two short rhythmic phrases are played and the student is asked whether they were the same or different Scales content AE[ minor scale is played for one octave ascending with a single note missing and the user is asked to describe which note was missing Elements of Harmony content A single interval is played and the student is asked whether it would be best described as consonant or dissonant Harmonic Structures content A single chord is played and the student is asked whether it would be best described as consonant or dissonant Style content A pitch is played at a ‘moderate’ volume, then repeated at a louder or softer volume. The participant is asked whether the repeated pitch was louder or softer than the first Historical or General Knowledge content A short phrase is played on a flute, and the student is asked to identify whether the sound was a clarinet, flute, bassoon, or piccolo

Reading content

Rhythm content

Scales content

Elements of Harmony content Visual Description Harmonic Structures content

Style content

Instrument-speciﬁc content

Historical or general knowledge content

Figure 3.23: Subtypes of ‘Visual Description’ activities

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3.3.3.3 Visual Description Activities

As defined in Section 3.3.3.1, visual description activities are those where question content is largely visual. Eight subtypes of visual description activities are defined. Shown in Figure 3.23, each subtype describes activities which require the description of knowledge from a one content area. For example, the iOS application Glossary of Music Quiz [236] provides users with a description of some musical element and asks them to select the element matching that description from a large list. This type of activity is classified as a visual description task as the question content is visual (a.k.a., written), and the question is centered around describing a musical element, not simply identifying its image. Alternatively, in the iOS application Ultimate Music Theory - Smart Audio Flashcards [218], users are presented with a single musical element and asked to describe it. This application uses a flash card approach, so once the user believes they have come up with an accurate description of the element they may tap the screen to flip the flash card and reveal the application’s description. They may then compare the description provided by the application against their own. Table 3.5 provides an example activity for each activity subtype. As with auditory description activities, visual description activities mostly ask participants to describe a single characteristic of a single musical element. Again as with auditory description activities, this means that they can generally be characterised as tasks. This is not the case when the activity requires the description of multiple elements within the same question, in which case it would be better described as an exercise.

3.3.4 Playback Activities

3.3.4.1 Overview

Playback activities require users to play a single note or a series of notes on an instrument. The instrument can be digital (e.g., an on-screen keyboard in an iOS application) or physical (e.g., a violin). Two variations of playback activities are deﬁned:

Visual The user is provided with some visual stimulus (e.g., notation) to guide their playing.

Memory The user is given no visual cue(s) to indicate what they should be playing.

Visual and memory playback activities are described further in Sections 3.3.4.2 and 3.3.4.3, respectively.

3.3.4.2 Visual Playback Activities

As described in Section 3.3.4.1, a visual playback activity is one where the user is given some visual stimuli to guide their playing. Three subtypes of visual playback activities are deﬁned, listed in Figure 3.24. Each subtype refers to how much musical information the student is asked to interpret. For example, in ‘Rhythm only’ activities participants are asked to play a rhythmic phrase with no melodic information (i.e., all on the same pitch or on a non-pitched instrument). Alternatively, in ‘Pitch only’ activities participants only play the melodic information

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Table 3.5: Example activities for each visual description activity subtype

Visual Description Activity Subtype Example Activity

Reading content Two pitches are notated and the user is asked to state which would be better described as the higher sound Rhythm content A textual description of a time signature is given, and the student is asked to select the concept that best matches the description out of a list concepts Scales content An incomplete circle of ﬁfths is displayed, and the user is asked to complete it Elements of Harmony content An interval description is provided – for example, ‘What is a minor 2nd above B?’ – and the student is asked to provide the answer Harmonic Structures content The student is asked to list all of the closely related keys to F major, according to the western rules of harmony Style content A text description of the term ‘allegro’ is given, and the student is asked to select the concept that best matches the description from a list of terms Historical or General Knowledge content A text description of the term ‘concerto’ is given, and the student is asked to select the concept that best matches the description from a list of concepts

Rhythm and pitch

Standard Playback Pitch only

Rhythm only

Figure 3.24: Subtypes of ‘Visual Playback’ activities

(i.e., pitches), with no rhythmic aspects (i.e., the pitches are all played to whatever length the user desires). Only ‘Rhythm and pitch’ activities ask the user to interpret both rhythmic and melodic instructions. In each activity there may be information to consider in addition to the melodic or rhythmic markings. For example, notes may be accessorised with style markings such as those described in the ‘Style’ content area in Section 3.2.7. If a question includes these markings, a student’s correctness in interpreting them would be taken into account when their performance was evaluated or scored. Table 3.6 describes an example activity for each visual playback activity subtype. Fig- ure 3.25 illustrates how these activities may look when presented in iOS applications. Most visual playback activities would be characterised as exercises, as they commonly involve the interpretation of a sequence of notes. Even in cases where a single note were given, it may have one or more style markings for the student to consider, in which case their answer can still be only partially correct (e.g., the note was correctly played staccato, but at the wrong pitch). Only a small number of visual playback activities would be characterised as tasks, as they would have to involve only playing a single note at once with no stylistic information.

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(a) A ‘visual playback of rhythm and pitch’ activity from the iOS application Sight Read Plus [228]

(b) A ‘visual playback of pitch only’ activity from the iOS application NoteWorks [222]; the rhythm at which the user plays the notes does not matter – only that they play the correct pitch before the note scrolls to the left-hand side of the screen

Figure 3.25: Examples of each subtype of ‘Visual Playback’ activity

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Table 3.6: Example activities for each visual playback activity subtype

Visual Playback Activity Subtype Activity

Rhythm and pitch A short melody is notated and the student is asked to play it with the correct pitches and rhythms; example provided in Figure 3.25(a) Pitch only A short melody is notated and the student is asked to play the pitches with any rhythm they like; example provided in Figure 3.25(b) Rhythm only A short rhythmic phrase is notated and the student is asked to tap it; example provided in Figure 3.25(c)

3.3.4.3 Memory Playback Activities

As described in Section 3.3.4.1, memory playback activities provide the user with no stimuli or cues to indicate what they should be playing. Six subtypes of memory playback activities are deﬁned, listed in Figure 3.26. An example activity for each of these types is provided in Table 3.7. As with visual playback, there are memory playback activity subtypes referring to each of the different kinds of musical information the student may be asked to interpret (pitch only, rhythm only, rhythm and pitch). Questions for these subtypes typically involve the user being played some musical phrase – either live or through a recording – and then being asked to repeat it on a digital or physical instrument. In addition to these, there are also memory playback activity subtypes for some content areas. These subtypes relate to activities where a user is asked to play something, from memory, from a particular content area. For example, they may be asked to play a B[ harmonic minor scale ascending over two octaves. Successfully completing this request would require the participant to recall information directly from the ‘Scales’ content area (i.e., the pattern of a harmonic minor scale), thus would be assigned to the ‘memory playback of scales content’ activity subtype. Questions relating to content areas will generally be descriptive – instead of being played a phrase to repeat, the user will instead be given a description of what they are to play. The interpretation of this description (and thus the successful completion of the activity) will rely on the user’s ability to recall the relevant information from the related content area. As with visual playback, most memory playback activities would be characterised as exercises as they typically require the user to playing a sequence of notes.

Rhythm and pitch

Pitches only

Rhythm only Memory Playback Scales content

Elements of Harmony content

Harmonic Structures content

Figure 3.26: Subtypes of ‘Memory Playback’ activities

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Table 3.7: Example activities for each memory playback activity subtype

Memory Playback Activity Subtype Example Activity

Rhythm and pitch A short melody is played to the student, and they are asked to repeat it with the correct pitches and rhythms Pitch only A short melody is played to the student, and they are asked to repeat the pitches that were played with any rhythm they like Rhythm only A short rhythmic phrase is played to the student, and they are asked to repeat it by either tapping or playing each note on a single pitch Scales content The user is asked to play two octaves of an A[ minor scale ascending and descending Elements of Harmony content The user is asked to play an augmented 6th interval starting on a C] Harmonic Structures content The user is asked to play a perfect cadence in the key of G

3.3.5 Notation Activities

Notation activities require users to write down a musical phrase in some communicable way such that it can be consistently reproduced by others. Questions may be answered using West- ern notation, fingering charts, or some other form of visual representation. Seven subtypes of notation activities are defined, listed in Figure 3.27, with Table 3.8 giving an example activity for each. As with the playback activities described in Sections 3.3.4.2 and 3.3.4.3, there are notation activity subtypes referring to each of the different kinds of musical information the student may be asked to consider. As well as these activity subtypes, there are notation activities for some content areas. These subtypes relate to questions where the user is asked to write music based on a description of knowledge from a content area rather than a phrase played to them. For example, students might be asked to write a perfect cadence in the key of C major. Successfully doing this would require knowledge from the ‘Harmonic Structures’ content area, thus is categorised as a ‘notation of harmonic structures content’ activity. Notation activities would typically be classified as exercises. This is due to the fact that they tend to involve notating more than a single piece of musical information, and therefore answers could be only partially correct.

Table 3.8: Example activities for each notation activity subtype

Notation Activity Subtype Example Activity

Rhythm and pitch A short melody is played to the student, and they are asked to notate what was played with the correct pitches and rhythms Pitch only A short melody is played to the student, and they are asked to notate the pitches that were played, in the order they were played Rhythm only A short rhythmic phrase is played to the student, and they are asked to notate the rhythm that was played on any single pitch Scales content The student is asked to write a B[ harmonic minor scale descending one octave Elements of Harmony content The student is asked to write a major 7th chord in the key of D Harmonic Structures content The student is asked to write a chord progression of I-V-VI-II-IV-I in the key of E Style content The student is given the notation for a short melodic phrase. This phrase is then played with some articulation, which the student is asked to add to the provided notation

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Rhythm and pitch

Pitch only

Rhythm only

Notation Scales content

Elements of Harmony content

Harmonic Structures content

Style content

Figure 3.27: Subtypes of ‘Notation’ activities

3.4 Discussion

Although the goals described in Section 3.1 have been successfully fulfilled by the proposed taxonomy, there are some trade-offs that were made in its design. In order to remain as generic as reasonably possible, none of the content areas or activities were written with respect to a specific teaching or delivery method. However, the definitions of the activities may imply some necessary limitations or resources. For example, by nature, playback exercises require either a physical or digital instrument on which the user can play a musical phrase2. Similarly, auditory recognition and auditory description activities are defined by their question content being presented through an auditory medium. This would mean that some method of playing either live or recorded audio to students would be required for all activities of these types. A trade-off was also made between the complexity and brevity of the taxonomy. This trade-off applies primarily to the ‘Instrument-specific’ and ‘Historical and General Knowledge’ content areas, both of which are especially broad. Although further categorisation of the knowledge contained in these content areas is out of scope within the original goals of creating the taxonomy, this may be an avenue for future work. It may be noted that although many of the activities have subtypes relating to several of the content areas, not all content areas are represented in all activity types. Content areas were omitted for activity types where it made no sense to create such a subtype. For example, the ‘Notation’ activity type does not contain a subtype for ‘Historical and General Knowledge’. Further work may involve creating optional characteristics for certain activities. For example, ‘Playback’ exercises could optionally be described as ‘stylistic’ in cases where students are asked to play a phrase in a certain way (e.g., with a crescendo or with some notes accented). Additional further work may involve aligning the tasks and exercises with the cognitive processes defined in Bloom’s [25, 96], Anderson and Krawthwoh’s [8], or Rifkin and Stoecker’s [167] taxonomies. This would enable educators to assess the educational value of tasks, and select appropriate activities based on the cognitive needs of their curriculum [68]. One potential limitation of the taxonomy is the author’s strong background in Western

2It should be noted that this instrument may be the voice, in which case no additional equipment is required.

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music and Western music education. This has biased its design. However, a conscious effort was made to design the content areas and activity types in a generic manner, and although the given examples invariably come from Western applications it should be possible to appropriately assign labels to both knowledge and activities from other cultures.

3.5 Summary

This chapter has described a novel for categorising both the principles of music and the activities where these principles are applied. The two complementary portions of the taxonomy – content areas and activities – were described. Examples of knowledge included in each content area were given, as well as instances of how this knowledge has historically been presented. The general structure of each proposed activity type was given, as well as an example of a question for each activity subtype. The following chapter will present an example application of the taxonomy.

4 Taxonomy Validation: Music Aptitude Tests

4.1 Overview

In the previous chapter a taxonomy for describing musical content and activities was deﬁned. This chapter will present an example application of this taxonomy, showing how it allows historical tests of musical aptitude and abilities to be described using a common, neutral vocabulary. This can be considered an exercise in validating the taxonomy. By converting the original vocabulary used by test proponents to the proposed nomenclature, one can identify the frequency with which activity types and content areas are used, trends within and across tests, and similarities between subtests from different test batteries. Section 4.2 will identify the taxonomic equivalents for all available parts of each test. This knowledge is then used in Sections 4.3 and 4.4 to identify the most frequently used activity types and content areas, and the similarities between tests across the history of the ﬁeld.

4.2 Mapping Tests to Taxonomy

4.2.1 Overview

Sections 4.2.2 to 4.2.15 show how key tests of musical ability and aptitude translate to the activity types proposed in Chapter 3. In some cases, a subtest (i.e., activity) will cover multiple content areas. This is generally due to the exact question content being unavailable, requiring an informed guess to be made from what description(s) were available.

4.2.2 Seashore’s Measures of Musical Talents

As can be seen in Table 4.1, every subtest in Seashore’s Measures of Musical Talent is classiﬁed as an ‘auditory description’ activity. This is a direct result of all question content being played to the learner rather than being presented visually (e.g., on paper). Three content areas are covered over the four activities – reading, rhythm, and style – leaving ﬁve additional content areas unaddressed.

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Table 4.1: Equivalent taxonomy activities for each subtest in Seashore’s Measures of Musical Talents

Seashore’s Measure of Musical Talent Taxonomy Mapping

Sense of Pitch Auditory description of reading content Sense of Intensity Auditory description of style content Sense of Time Auditory description of rhythm content Tonal Memory Auditory description of reading content

Table 4.2: Equivalent taxonomy activities for each subtest in Revesz’s Tests of Musical Ability

Revesz’s Test of Musical Ability Taxonomy Mapping

Rhythmic Sense Memory playback of rhythm only Absolute Pitch Memory playback of pitch only Relative Pitch Memory playback of elements of harmony content Harmonic Sense Memory playback of elements of harmony content Melodic Memory Memory playback of rhythm and pitch Playing by Ear Memory playback of rhythm and pitch

4.2.3 Revesz’s Tests of Musical Ability

Table 4.2 shows that all of the individual tests in Revesz’s Tests of Musical Ability are classiﬁed as memory playback activities. This shows that all of the tests involve playing some auditory stimulus to the user and having them replicate it. Four different types of memory playback activities are exhibited over the six tests. De- spite ‘Melodic Memory’ and ‘Playing by Ear’ activities being described differently in Revesz’s test manual, they are both ‘memory playback of rhythm and pitch’ activities. The only difference between them is that ‘Melodic Memory’ asks users to sing or hum a melodic line played to them, and ‘Playing by Ear’ asks them to repeat a melodic line on some other instrument. Similarly, the ‘Relative Pitch’ and ‘Harmonic Sense’ activities are both ‘memory playback of elements of harmony content’ activities. However, in this case the activities are notably different, as each relates to different parts of the elements of harmony content area (intervals and chords, respectively).

4.2.4 Kwalwasser’s Tests and Measurements in Music

4.2.4.1 Overview

Despite originating largely from the same person, each of the batteries devised by Kwalwasser and his collaborators are quite different in their chosen activities. For example, Kwalwasser’s Test of Music Appreciation is entirely composed of activities testing historical or general knowledge content, either through visual description or an unknown format. In contrast to this, every subtest in Kwalwasser’s Music Talent Tests is described as an ‘auditory description’ activity, generally of either reading or rhythm content. The tests are not completely dissimilar, however, focusing almost entirely on visual and auditory description activities. Only in two cases – both in the Kwalwasser-Ruch Test of Musical Accomplishment – are recognition activities employed, both of which cover the reading content area.

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Sections 4.2.4.2 to 4.2.4.4 show how each of the test batteries developed by Kwalwasser and his collaborators can be described using the taxonomy.

4.2.4.2 Kwalwasser-Ruch Test of Musical Accomplishment

The Kwalwasser-Ruch Test of Musical Accomplishment is described only in terms of the subjects in which participant’s knowledge is assessed. For example, the ﬁrst test is described as assessing participant’s knowledge of “Musical symbols and terms” [99]. As such, exact mappings to the taxonomy can not always be made. This is illustrated in Table 4.3, showing that only half of the subject areas are able to be translated into activities from the taxonomy, with the other half being of an unknown type. In all cases the equivalent content areas for each subject have been identiﬁed. The Kwalwasser-Ruch test focuses heavily on the reading content area, with seven of the ten subtests assessing this knowledge. One subject area, ‘Musical symbols and terms’, appears to cover two content areas. This is due to its vague wording – whilst it is likely that ‘musical symbols’ refers to basic elements of notation (i.e., concepts from the reading content area), ‘musical symbols and terms’ could also include those more abstract concepts that indicate the style in which a piece should be played (i.e., concepts from the style content area). Without further information it is assumed that concepts from both content areas are included in this subtest.

4.2.4.3 Kwalwasser Test of Music Appreciation

Every subtest in Kwalwasser’s Test of Music Appreciation assesses knowledge from the historical or general knowledge content area. Excluding the three subtests for which activity types can not be identified, the subtests are invariably visual description activities. This is because each of these subtests visually (i.e., through text or an image) presents a single musical item (e.g., an instrument or a composer) and asks the user to describe a characteristic of that item. For example, participants may be asked to name a well-known composition by a certain composer or whether a specified instrument is blown, struck, or bowed. The subtests for which an activity type could not be defined all involve answering binary ‘true or false’ questions. These could not be mapped to the taxonomy because their format is

Table 4.3: Equivalent taxonomy activities for each subject in the Kwalwasser-Ruch Test of Mu- sical Accomplishment

Subject tested in the Kwalwasser-Ruch Test of Musical Accomplishment Taxonomy Mapping

Musical symbols and terms Unknown activity of reading content Unknown activity of style content Recognition of syllable names from notation Visual recognition of reading content Detection of pitch errors in notation of a known melody Visual description of reading content Recognition of time errors in notation of a known melody Visual description of rhythm content Pitch names in the bass and treble clefs Visual recognition of reading content Time signatures Unknown activity of rhythm content Key signatures Unknown activity of scales content Note values Unknown activity of reading content Rest values Unknown activity of reading content Recognition of familiar melodies from notation Visual recognition of reading content

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Table 4.4: Equivalent taxonomy activities for each subtest in Kwalwasser’s Test of Music Appre- ciation

Kwalwasser’s Subtest Taxonomy Mapping

Classiﬁcation of artists Visual description of historical or general knowledge content Nationality of composers Visual description of historical or general knowledge content Composers of famous compositions Visual description of historical or general knowledge content Classiﬁcation of composers by composition types Visual description of historical or general knowledge content General historical and biographical knowledge Unknown activity of historical or general knowledge content Producing tones on orchestral instruments Visual description of historical or general knowledge content Classifying orchestral instruments Visual description of historical or general knowledge content General knowledge of instrumentation Unknown activity of historical or general knowledge content Musical structure and form Unknown activity of historical or general knowledge content

not known, making it impossible to say whether the activities are visual or auditory or whether they involve recognition or description.

4.2.4.4 Kwalwasser-Dykema (K-D) Musical Talent Tests

As seen in Table 4.5, the Kwalwasser-Dykema Musical Talent Tests feature a subtest, ‘Melodic Taste’, which can not be assigned a content area. This subtest involves playing participants a number of melodic phrases and asking them to rate their preferences for each. Given that the question content is auditory, this can be described as being an auditory description activity. However, as the answer is entirely subjective and dependent on the participant’s personal taste, it is not possible to assign a content area. This does not represent a failing of the taxonomy, however, as it is designed to classify activities which require the use of teachable knowledge and skills, not personal preferences. Activities in the K-D Musical Talent Tests are largely of the auditory description variety, and touch on a number of content areas. Reading content is particularly prominent, as many of the tasks require the identiﬁcation of errors in basic notation. One subtest, ‘Rhythm Imagery’, may potentially cover reading or rhythm content. This subtest asks users to identify mismatches between provided rhythmic notation and a short rhythmic phrase that is played to them. With- out knowing the parts of the notation that may be incorrect it is not possible to say whether

Table 4.5: Equivalent taxonomy activities for each subtest in the Kwalwasser-Dykema Musical Talent Tests

Kwalwasser-Dykema Subtest Taxonomy Mapping

Pitch Discrimination Auditory description of reading content Intensity Discrimination Auditory description of style content Time Discrimination Auditory description of rhythm content Quality Discrimination Auditory description of historical or general knowledge content Rhythm Discrimination Auditory description of rhythm content Tonal Memory Auditory description of reading content Pitch Imagery Visual description of reading content Rhythm Imagery Visual description of reading content Visual description of rhythm content Tonal Movement Auditory description of style content Melodic Taste Auditory description of no content

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the subtest requires knowledge of reading content, or rhythm content, or both. For example, if the note duration values were incorrect, knowledge from the reading content area would be required. However, if the notation included errors in time signatures or the placement or bar lines, knowledge from the rhythm content area would be necessary.

4.2.4.5 Kwalwasser’s Music Talent Test

Every subtest in Kwalwasser’s Music Talent Test involves detecting changes between the ﬁrst and second times a short phrase or pattern is played. As the question content is invariably presented through an auditory medium, this means that all of the subtests map to auditory description activities. This is shown in Table 4.6. As with the Kwalwasser-Dykema Music Talent Tests, one subtest (‘Changes in rhythm’) can be described as requiring the use of reading or rhythm content. This is due to the vague- ness of the task description in the available literature. The change in rhythm may involve altering note durations, in which case the activity would be covering knowledge from the reading content area. However, alterations may be made to the time signature, or the placement of repeats, in which case the activity would be covering knowledge from the rhythm content area.

4.2.5 Schoen’s Tests of Musical Feeling and Understanding

As shown in Table 4.7, all of the subtests in Schoen’s Tests of Musical Feeling and Understanding translate to auditory description activities. As with the Kwalwasser-Dykema Music Talent Tests and Kwalwasser’s Music Talent Test, one subtest, ‘Rhythms’, could potentially require the use of reading or rhythm content. The subtest description states that during this task participants are asked to state whether the second of two rhythmic phrases is different to the ﬁrst and, if so, how it is different. Following this description, alterations could reasonably be made to elements such as note durations or time signatures, which are concepts from the reading and rhythm content areas, respectively. Without further information it is not possible to say which content area (or if both content areas) best match this subtest.

4.2.6 Torgerson-Fahnestock Tests

The Torgerson-Fahnestock tests are split into two parts – A and B. Each part has a different focus, which is clearly reﬂected when translating the subtests to activities from the taxonomy. As can be seen in Table 4.8 part A concentrates entirely on the user’s ability to recognise various musical symbols, touching mostly upon concepts from the reading and rhythm content areas. Part B places a focus on musical dictation, which translates to notation activities of

Table 4.6: Equivalent taxonomy activities for each subtest in Kwalwasser’s Music Talent Tests

Kwalwasser’s Subtest Taxonomy Mapping

Changes in pitch Auditory description of reading content Changes in time Auditory description of rhythm content Changes in rhythm Auditory description of reading content Auditory description of rhythm content Changes in volume Auditory description of style content

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Table 4.7: Equivalent taxonomy activities for each subtest in Schoen’s Tests of Musical Feeling and Understanding

Schoen’s Subtest Taxonomy Mapping

Relative Pitch Auditory description of elements of harmony content Rhythms Auditory description of reading content Auditory description of rhythm content Tonal Sequence Auditory description of style content

Table 4.8: Equivalent taxonomy activities for each subtest in the Torgerson-Fahnestock Tests

Torgerson-Fahnestock Test Taxonomy Mapping

Part A Note values Visual recognition of reading content Rest values Visual recognition of reading content The pause symbol Visual recognition of rhythm content Time signatures Visual recognition of rhythm content Pitch names Visual recognition of reading content Repeat marks Visual recognition of rhythm content Slurs Visual recognition of rhythm content Chromatic marks Visual recognition of reading content Dynamics signs Visual recognition of style content Major and minor key signatures Visual recognition of scales content Neutral and harmonic minor scales Visual recognition of scales content Part B Test 1 Notation of rhythm and pitch Test 2 Notation of rhythm and pitch Test 3 Visual description of reading content Visual description of rhythm content Visual description of style content

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rhythm and pitch. Test 3 from Part B asks students to listen to a melody and make note of where it differs from provided notation. The test description states that the melody may be ‘played differently’ to the notation. This could incorporate any of several alterations, including changes to note durations, time signatures, and dynamics. As such, this activity could potentially cover multiple content areas.

4.2.7 Drake Musical Aptitude Tests

Although Drake’s Musical Aptitude Tests comprise only two subtests, Table 4.9 shows that they cover four different activity types. This is due to the breadth of content tested in the ‘Musical Memory’ activity, where participants are asked to describe changes to a melody that may include alterations of pitch, time signature, or key (i.e., concepts from the reading, rhythm, and scales content areas, respectively). ‘Rhythm’ is an abstract activity, asking users to continue counting at a consistent speed, as set by a series of metronome clicks, until they are asked to stop. This can be considered a memory playback activity of rhythm content, where the metronome clicks represent the example rhythm the user must play from memory.

4.2.8 Gordon’s Aptitude Tests

4.2.8.1 Overview

Sections 4.2.8.2 and 4.2.8.3 describe the mapping of Gordon’s Musical Aptitude Proﬁle and Measures of Musical Audiation to activities in the taxonomy. In both cases, the subtests are invariably described as auditory description activities. However, the Musical Aptitude Proﬁle features a wider variety of content areas, touching upon concepts from reading, rhythm, scales, harmonic structures, and style. The Measures of Music Audiation, however, assess only knowledge from the reading content area.

4.2.8.2 Gordon’s Musical Aptitude Proﬁle (MAP)

Table 4.10 shows that every subtest in Gordon’s Musical Aptitude Proﬁle is a type of auditory description activity. This is because each subtest asks the user to describe whether anything has changed between two performances of the same melody or, in the case of the ‘Musical Sensitivity’ subtests, describe which of two options was more stylistically appropriate. The ‘Melody’ subtest for ‘Tonal Imagery’ covers multiple content areas, as the potential alterations are only described as ‘melodic’. This could include changes in pitches or pitch durations (i.e,. reading content), a change in key signature (i.e., scales content), or an alteration in

Table 4.9: Equivalent taxonomy activities for each subtest in Drake’s Musical Aptitude Tests

Drake’s Subtest Taxonomy Mapping

Musical Memory Auditory description of reading content Auditory description of rhythm content Auditory description of scales content Rhythm Memory playback of rhythm only

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Table 4.10: Equivalent taxonomy activities for each subtest in Gordon’s Musical Aptitude Proﬁle

Musical Aptitude Taxonomy Mapping Proﬁle Subtest

Tonal Imagery Melody Auditory description of reading content Auditory description of scales content Auditory description of style content Harmony Auditory description of harmonic structures content Rhythm Imagery Tempo Auditory description of style content Meter Auditory description of rhythm content Musical Sensitivity Phrasing Auditory description of style content Balance Auditory description of style content Style Auditory description of style content

how the melody is played (i.e., style content). Without further information it is not possible to say which content area(s) are most appropriate for this activity.

4.2.8.3 Gordon’s Measures of Music Audiation

As illustrated in Table 4.11, all subtests in Gordon’s Measures of Music Audiation represent auditory description activities of reading content. This is because all of the subtests involve playing users either a tonal or rhythmic sequence twice and asking then to describe whether the pitch durations were altered in the second performance. The only difference between each of the test levels (i.e., primary, intermediate, and advanced) is the difﬁculty of the questions.

4.2.9 Bentley’s Measures of Musical Abilities

Table 4.12 shows that every subtest in Bentley’s Measures of Musical Abilities translates to an auditory description activity of reading content. This is due to the similarity of the subtests, which mostly involve identifying differences between individual notes or sequences of notes. For example, in the ‘Pitch Discrimination’ subtest two notes are played and participants are asked if they would be best described as the same or different. Similarly, the ‘Rhythmic Memory’ subtest involves participants being played a four-beat rhythm twice, then asked if the note durations were altered between the two performances.

Table 4.11: Equivalent taxonomy activities for each subtest in Gordon’s Measures of Music Audiation

Level Measures of Music Taxonomy Mapping Audiation Subtest

Primary Tonal Auditory description of reading content Rhythm Auditory description of reading content Intermediate Tonal Auditory description of reading content Rhythm Auditory description of reading content Advanced Tonal Auditory description of reading content Rhythm Auditory description of reading content

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Table 4.12: Equivalent taxonomy activities for each subtest in Bentley’s Measures of Musical Abilities

Measures of Musical Abilities Subtest Taxonomy Mapping

Pitch Discrimination Auditory description of reading content Tonal Memory Auditory description of reading content Chord Analysis Auditory description of reading content Rhythmic Memory Auditory description of reading content

Table 4.13: Equivalent taxonomy activities for each subtest in Wing’s Tests of Musical Ability and Appreciation

Wing’s Subtest Taxonomy Mapping

Chord Analysis Auditory description of reading content Pitch Change Auditory description of elements of harmony content Memory Auditory description of reading content Rhythmic Accent Auditory description of style content Harmony Auditory description of harmonic structures content Intensity Auditory description of style content Phrasing Auditory description of style content

4.2.10 Wing’s Tests of Musical Ability and Appreciation

All of the subtests in Wing’s Tests of Musical Ability and Appreciation involve asking users to describe changes between two musical items. Table 4.13 shows that this results in them invariably being classiﬁed as auditory description activities. Style content is heavily featured, with multiple subtests (‘Rhythmic Accent’, ‘Intensity’, and ‘Phrasing’) asking users to identify changes in how a musical phrase was played rather than what was played. Wing’s is one of the only test batteries to touch on harmonic structures content. It does so in the ‘Harmony’ subtest, which asks participants to describe whether two performances of a melody used the same or different harmonisation.

4.2.11 Iowa Tests of Music Literacy

Most of the subtests in the Iowa Tests of Music Literacy involve describing whether some given notation matches an auditory stimulus (i.e., a visual description activity of reading content), or selecting the correct notation for a melody from a set of options (i.e., a visual recognition activity of reading content). Interestingly, despite the second part of the test being referred to as tests of ‘Rhythm Concepts’, Table 4.14 shows that two of the three subtests actually cover

Table 4.14: Equivalent taxonomy activities for each subtest in the Iowa Tests of Music Literacy

Iowa Music Literacy Subtest Taxonomy Mapping

Tonal Aural Perception Auditory description of scales content Concepts Reading Recognition Visual description of reading content Notational Understanding Visual recognition of reading content Rhythm Aural Perception Auditory description of rhythm content Concepts Reading Recognition Visual description of reading content Notational Understanding Visual recognition of reading content

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reading content. This is because these subtests involve only recognising and describing note durations, rather than working with more strictly rhythmic concepts such as time signatures and syncopation.

4.2.12 Colwell Music Achievement Test

Table 4.15 shows that all activities in the Colwell Music Achievement Test are auditory – that is, they all present question material through an auditory medium. The subtests are split between auditory recognition and auditory description activities, and cover a variety of content areas. One subtest – ‘Auditory-Musical Discrimination’ – potentially touches on three content areas. This test asks participants to listen to a phrase and mark any bars in some provided notation where the audio does not match what is written. Without being able to access the exact test questions, it must be assumed that the pitches, their durations, the time signature, and how the phrase is played could all change. In other words, participants may need knowledge from the reading, rhythm, and style content areas.

4.2.13 Karma’s Test of Structure Ability

Karma’s Test of Structure Ability contains only one subtest, as shown in Table 4.16. The test involves playing the user a phrase three times, then playing a second phrase and asking the user to describe whether that phrase is equivalent to the ﬁrst. As the question content is auditory and the comparisons between the two phrases are made in terms of their sequences of notes, this test is an auditory description activity of reading content.

4.2.14 Musical Aptitude Indicator

Despite their names suggesting otherwise, Table 4.17 shows that all of the subtests in the Mu- sical Aptitude Indicator are auditory description activities of reading content. All of the subtests involve the participant being played two notes (or two sequences of notes) and being asked to describe whether they are different or the same. As no alterations are made to anything but the pitches or durations of the notes, these activities exclusively cover knowledge from the reading content area.

4.2.15 The Proﬁle of Music Perception Skills (PROMS)

The subtests in the Proﬁle of Music Perception Skills invariably ask users to compare two items and describe whether they are the same or different. Table 4.18 shows that this results in all the subtests being auditory description activities. Reading content is most frequently covered, as many of the subtests involve comparing either a sequence of notes or two individual notes. Style content is next frequently addressed. In the activities, participants are asked to describe how the second performance of a sequence of notes was altered from the ﬁrst (e.g., in tempo, accents, or volume). A single subtest – ‘Timbre’ – covers historical or general knowledge content, requiring participants to identify changes in the instrumentation of a piece between two performances.

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Table 4.15: Equivalent taxonomy activities for each subtest in the Colwell Music Achievement Test

Colwell Music Achievement Subtest Taxonomy Mapping

Test One Pitch Discrimination Auditory description of reading content Interval Discrimination Auditory description of elements of harmony content Meter Discrimination Auditory description of rhythm content Test Two Major-Minor Mode Discrimination Auditory description of elements of harmony content Feeling for Tonal Center Auditory description of elements of harmony content Auditory-Visual Discrimination Auditory description of reading content Test Three Tonal Memory Auditory description of reading content Melody Recognition Auditory recognition of reading content Pitch Recognition Auditory recognition of reading content Instrument Recognition Auditory recognition of harmonic structures content Test Four Musical Style Auditory recognition of historical or general knowledge Auditory-Musical Discrimination Auditory description of reading content Auditory description of rhythm content Auditory description of style content Chord Recognition Auditory recognition of elements of harmony content Cadence Recognition Auditory recognition of harmonic structures content

Table 4.16: Equivalent taxonomy activities for Karma’s Test of Structure Ability

Karma’s Test Taxonomy Mapping

Test for Structure Ability Auditory description of reading content

Table 4.17: Equivalent taxonomy activities for each subtest in the Musical Aptitude Indicator

Musical Aptitude Indicator Subtest Taxonomy Mapping

Pitch Auditory description of reading content Rhythm Auditory description of reading content Tunes Auditory description of reading content

Table 4.18: Equivalent taxonomy activities for each subtest in the Proﬁle of Music Perception Skills

PROMS Subtest Taxonomy Mapping

Melody Auditory description of reading content Standard Rhythm Auditory description of reading content Rhythm-to-melody Auditory description of reading content Accent Auditory description of style content Tempo Auditory description of style content Pitch Auditory description of reading content Timbre Auditory description of historical or general knowledge content Tuning Auditory description of reading content Loudness Auditory description of style content

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4.3 Results

Translating the subtests in the tests of musical aptitude and ability to activities from the proposed taxonomy allows one to more clearly describe their similarities and differences. This enables the identification of trends, developments, and constants throughout the history of the field. Sections 4.3.1 to 4.3.3 describe the results of such comparisons, and Section 4.3.3 shows how translating the tests to a common, neutral vocabulary enables the identification of equivalent subtests from different batteries.

4.3.1 Activity Types

Figure 4.1 shows the distribution of activity types across all of the tests. There is a clear strong skew towards auditory description activities, with approximately 55% of the subtests being of this type. Auditory recognition activities, however, are relatively unused, forming only 5% of all subtests. The next most frequent activity type is visual recognition. However, its prevalence is much lower than auditory description, representing just 13% of the subtests. Unlike the auditory activities, where description is utilised far more often than recognition, visual description activities comprise a similar percentage of tests to their visual recognition counterpart. Not insigniﬁcantly, 7% of subtests were unable to be mapped to the taxonomy. However, this outcome is not due to a failure of the taxonomy, but rather a lack of available published information regarding the structure of some tests. Only 2% of subtests translate to notation activities, and there are no cases where a subtest could be described as a visual playback activity. The Kwalwasser-Ruch Test of Musical Accomplishment is the least clearly described, with approximately 55% of its subtests unable to be translated. Kwalwasser’s Test of Music Appreci- ation is the only other battery where this difﬁculty was encountered, with 33% of its subtests unable to be translated. Table 4.19 breaks this information down in terms of the individual test batteries. Again, a strong tendency towards auditory description activities can be seen. However, it is also shown that many tests use only auditory description activities, neglecting to employ any other activity types. Ten of the eighteen test batteries are exclusively comprised of auditory description activities, and a further three are comprised of over 50% auditory description activities. A total of four batteries do not include any auditory description activities, and, with the exception of Revesz’s Tests of Musical Ability, tend to use the visual description activity type instead. The small percentage of auditory recognition and notation activities shown in Figure 4.1 is a result of only one test battery exhibiting subtests of each of these types. However, auditory recognition activities do form 43% of the subtests in the Colwell Music Achievement Test, and 13% of the Torgerson-Fahnestock Tests are notation activities. There are no cases where a battery contains activities of more than three types. Three batteries cover three activity types each, four cover two activity types each, and a further eleven exclusively using only one activity type. Where two or three activity types are used, there is either a strong preference for one (i.e., at least 50% of the subtests are of that type), or a relatively even split between them. Neither of these distribution patterns is particularly favoured.

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Visual Playback (0%)

Notation (~2%)

Auditory Recognition (~5%) Memory Playback (~6%)

Unknown (~7%)

Visual Description (~12%)

Visual Recognition (~13%)

Auditory Description (~55%)

Figure 4.1: The distribution of activity types across all tests of musical aptitude and ability

73 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ~55% ------~33% - - - - - Notation Unknown ------~13% ------Memory Playback 100% ------50% ------Visual Playback - - - - - Visual Description - ~18%- - 20% ------~19% - ~67% - - 100% 80% 100% 100% 100% ~57% 100% 100% Auditory Description 100% - 50% - 100% - 100% - - 100% - ~69% - - ~33% ~33% ~33% ------Visual Recognition ------~27% - Auditory Recognition ------~43% - - 10 - Tests 6 3 10 2 7 7 14 2 9 No. 4 - 46 - - 2 - 3 - 4 - 9 - 1 - The percentage of subtests of each activity type in each test of musical aptitude, sorted in ascending year of publication Musical Talent Tests (1930) able 4.19: T uch Test of Musical Accomplishment Music Talent Test (1953) Test of Music Appreciation (1927) Measures of Musical Talents (1919) Tests of Musical Feeling and Understanding Musical Aptitude Proﬁle (1965) Measures of Music Audiation (1979) Measures of Musical Abilities (1966) Test of Structure Ability (1973) Aptitude Indicator (2002) Music Achievement Test (1970) Musical Aptitude Tests (1957) Tests of Music Literacy (1970) Proﬁle of Music Perception Skills (2012) ing’s Tests of Musical Ability and Appreciation (1968) evesz’s Tests of Musical Ability (1919) est orgerson-Fahnestock Tests (1930) (1924) T Seashore’s R Schoen’s (1925) Kwalwasser-Dykema Kwalwasser’s Gordon’s W Colwell Gordon’s The Kwalwasser-R Kwalwasser T Drake Bentley’s Iowa Karma’s Musical

74 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

4.3.2 Content Areas

As with the distribution of activity types discussed in Section 4.3.1, the distribution of content areas covered by the tests of musical aptitude and ability shows a strong skew towards one area – in this case, reading content. This is shown in Figure 4.2, which illustrates the distribution of content areas and playback/notation activity types across all test batteries. In other words, it shows how many of the subtests assess each kind of knowledge or skill defined in the taxonomy. Reading content is assessed by 41% of the subtests. The next most frequently assessed areas of knowledge are style and rhythm content, each of which comprise approximately 15% of all subtests. The remaining nine areas each encompass less than 10% of the subtest population, with six each occupying between 1 and 5% of the distribution. Instrument-specific instruction is not covered by any of the test batteries. A very small proportion of the subtest (1%) are described as assessing ‘None’ – that is, they do not assess any knowledge or skills defined in the taxonomy. This does not represent a gap in the taxonomy, but rather the use of questions for which the answers are entirely rooted in personal preference. The question “Do you prefer the works of Beethoven or Mozart?” is an example of this. Table 4.20 shows the distribution of content areas and playback/notation activity types on a test-by-test basis. Again, the skew towards assessing reading content is clear, with only two of the eighteen batteries choosing to omit this area entirely. Four of the tests address knowledge from the reading content area exclusively, and a further four assess reading content in over 50% of their subtests. When a battery covers more than one activity type, it tends to address either 3 or 4. Two batteries each cover 5 unique activity types. In one instance, namely Kwalwasser’s Test of Music Appreciation, two activity types are employed. Another isolated case, the Colwell Music Achievement Test, touches upon 6 different activity types. Aside from ‘None’, there are no areas which are covered by only one test battery. The areas with low prevalence shown in Figure 4.2 are due to their being relatively unfavoured by the test batteries that use them, as well as being used by batteries with a comparatively small number of subtests.

75 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

Instrument-Speciﬁc Instruction (0%)

None (~1%)

Pitch Only (~1%) Rhythm Only (~2%) Rhythm and Pitch (~3%) Harmonic Structures (~3%) Scales (~5%) Elements of Harmony (~6%)

Historical or General Knowledge (~9%)

Rhythm (~15%)

Style (~15%)

Reading (~41%)

Figure 4.2: The distribution of content areas and playback activity types across all tests of musical aptitude and ability

76 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS None - 10% ------Rhythm and Pitch ~33% - - - - Rhythm Only ~17% - - - - Activity Types Pitch Only --- 90% -- - -- ~13% 25% - - --- ~17% - - - - Playback and Notation Historical or General Knowledge - - - - 10% - - - - - Speciﬁc Instruction - - - - - Style Instrument- ~9% - -- ~13% - -- 25% - - 25% 20% 20% ~56% Areas Harmonic Structures - - - - ~11% - - - - - Content of Harmony ~33% 25% ------~11% - 25% 30% 40% ~11% Reading Rhythm Scales Elements - 25% 40% 40% ~11% Tests No. 9 - - - - 10 ~64% ~18% ~9% - 6 3 10 42 ~31% ~31%2 ~13%7 - 25% 25% 25% - 4 50% 25% - - Musi- The percentage of subtests covering knowledge from each content area, or of each playback type in each test of musical aptitude, sorted in Music Talent uch Test of Test of Music Measures of Mu- Musical Aptitude Tests of Musical Musical Aptitude able 4.20: T ascending year of publication evesz’s Tests of Musical orgerson-Fahnestock Tests Test Appreciation (1927) Kwalwasser-R Musical(1924) Accomplishment Feeling and Understanding (1925) Kwalwasser T Drake Seashore’s R Ability (1919) Schoen’s Kwalwasser-Dykema Kwalwasser’s Gordon’s Tests (1957) Proﬁle (1965) (1930) sical Talents (1919) Test (1953) cal Talent Tests (1930)

77 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS None ------Rhythm and Pitch - - - - Rhythm Only - - - - Activity Types Pitch Only ------Playback and Notation Historical or General Knowledge - - ~6% - - ~11% - - Speciﬁc Instruction - - - - Style Instrument------~43% ~6% - ~33% Areas Harmonic Structures ~14% ~13% ------Content of Harmony ~14% 25% ------~13% - - Reading Rhythm Scales Elements ~29% ~38% 100% ~56% Tests No. 7 614 ~67% ~17% ~17%2 - 39 100% - - - 1 100% - - - 4 100% - - - Measures of Musi- Test of Structure Measures of Music Aptitude Indicator Music Achievement Tests of Music Literacy Proﬁle of Music Percep- ing’s Tests of Musical Abil- Test Iowa Karma’s Musical tion Skills (2012) Audiation (1979) Bentley’s W Colwell Gordon’s (2002) The (1970) ity and Appreciation (1968) Ability (1973) Test (1970) cal Abilities (1966)

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4.3.3 Subtest Equivalence

4.3.3.1 Overview

It is reasonable to assume that subtests that are of the same activity type and cover the same content could possibly be equivalent to one another. As such, translating the tests of musical aptitude and ability to activities from the taxonomy allows one to more easily identify which subtests could be described as being equivalent. For this analysis, two types of equivalence are deﬁned:

Full Equivalence The two subtests are identical, only differing in the speciﬁc item(s) chosen. For example, two tests which ask the participant to identify pitches on the treble staff, but do not necessarily present the exact same pitches as questions.

Partial Equivalence The two subtests share signiﬁcant similarities. For example, two tests which both ask participants to identify dynamic markings, but one of which offers no prompts where the other provides four options from which to select an answer.

If neither type of equivalence applies to a pair of subtests, they are described as having no equivalence. Sections 4.3.3.2 to 4.3.3.11 show the equivalence matchings between several activity subtypes over the population of test batteries. Not all activity subtypes in the taxonomy are included. This may be because there are no tests of a particular subtype, or because there are no equivalence relations within that area. For example, there is only one memory playback activity of pitch, so no equivalence relations are possible. Alternatively, whilst there are six visual description activities of historical or general knowledge content, there are no equivalence relations amongst them.

4.3.3.2 Auditory Description Activities of Reading Content

By a wide margin, ‘auditory description of reading content’ activities represent the highest number of subtests in the tests of musical aptitude and ability. As such, this area contains the largest number of potentially equivalent subtests. Table 4.21 shows how these subtests compare to one another. Overall, Drake’s Musical Memory test ({10}), is the most well-matched, with 2 fully equivalent and 11 partially equivalent subtests. Conversely, {18}, {22}, {23}, {24}, {25}, and {31} – most of which are subtests of the Colwell Music Achievement Test – are the least well-matched, with no fully or partially equivalent subtests. Over the 33 subtests of this subtype, the existence of a fully equivalent match tends to correspond with some partially equivalent matches as well. This is true for all of the subtests excluding {16}, {19}, {27}, and {33}, which have only partially equivalent matches. Overall, there are far more partially than fully equivalent matches throughout the population. It does not appear that the existence of equivalence of either type is particular to any time period. Excluding the gap presented by the Colwell Music Achievement Test, the density of equivalent subtests is fairly consistent throughout the history of the ﬁeld.

79 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

4.3.3.3 Auditory Description Activities of Rhythm Content

Table 4.22 shows the equivalence ratings for all auditory description activities covering rhythm content. In this population, very few subtest pairs can be described as fully equivalent, and few subtests have more than one or two partially equivalent matches. Two subtests, {10} and {21}, have no fully or partially equivalent matches. The most well-matched subtest by far is {11}, Drake’s Musical Memory subtest, which has 2 fully and 9 partially equivalent matches. Overall, when equivalence is present, a subtest tends to have only 1 or 2 partial matches. However, in one case (subtest {8}) two matches exist, and two subtests ({9} and {11}) have a total of 9 partial matches. Earlier test batteries tend to exhibit slightly more equivalence than later tests. These generally have at least 2 matches rather than the 1 typically found in later work. However, the ﬁrst full equivalence match is not found until {11}, and the remaining two do not appear until {23} and {24}, both of which are subtests from relatively recent batteries.

4.3.3.4 Auditory Description Activities of Scales Content

As shown in Table 4.23, subtest equivalence for auditory description activities of scales content centers heavily on the Musical Memory subtest from the Drake Musical Aptitude Tests. Musical Memory has 2 fully and 10 partially equivalent matches, with only two of the other subtests not being equivalent to it in any way. Only one subtest in the population, Tonal Concepts (Aural Perception) from the Iowa Tests of Music Literacy, has no equivalence to any other subtest. Amongst the remainder of the population, excluding the partial match between tests {8} and {9}, the only equivalence matches are those with Drake’s Musical Memory subtest.

4.3.3.5 Auditory Description Activities of Elements of Harmony Content

Table 4.24 shows that amongst the auditory description activities of elements of harmony content there are no fully equivalent subtests. Furthermore, there is only ever one partially equivalent match for any one activity, and two of the six activities are not fully or partially equivalent to any others.

4.3.3.6 Auditory Description Activities of Harmonic Structures Content

There are very few ‘auditory description of harmonic structures content’ activities across the test batteries. Within these subtests no one test structure has been exactly repeated (i.e., there are no fully equivalent matches). However, Table 4.25 shows that there is partial equivalence between the Tonal Imagery (Harmony) activity from Gordon’s Musical Aptitude Proﬁle, and the Tonal activity from Gordon’s Measures of Music Audiation. This is a result of the Measures of Mu- sic Audiation being developed after and taking inspiration from the Musical Aptitude Proﬁle. The only other subtest in this area, Harmony from Wing’s Tests of Musical Ability and Appreciation is neither partially or fully equivalent to this preceding work.

80 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ≈ No. # No. - 1 - 4 4 - 1 4 - 2 3 ≈ ≈ # ≈ - - - - 9 - - - 1 3 - - - - 4 - - - - 5≈ 3 - - - - 5- 4 - - - -- 8 - - -- 2 - - 11 - 1- 8 - - - 2 6 # ≈ ≈ ≈ # -- # ≈ ≈ ## ≈ ≈ ≈ ≈ ------≈ ----- ≈ # ≈ # represents partial equivalence ≈ ------# ------≈ ------≈ # # ≈ ≈ ≈ ≈ ------1------# ------≈ - ≈ ------# represents equivalence, and ------# # ------≈ ≈ ≈ ------# # ------≈ ------1 ------≈ - -- ≈ - ≈ ≈ # ≈ - ≈ ≈ ≈ ------2 ------3 ≈ ≈ ------≈ ≈ - ≈ ≈ 2 ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ ≈ - ≈ ≈ ------≈ ≈ ------≈ ≈ - ≈ ---- ≈ ≈ ≈ ≈ ≈ --- # # - # -- ≈ ≈ --- ≈ - - ≈ ------≈ - - -- ≈ -- - # - ≈ # ------≈ ≈ ≈ ≈ ≈ 1 2 3 4- 5 6 7 8 9 10 11 12 13 14 15 16 17 18## 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 # Musical Memory Tonal Imagery (Melody) - - - - -Rhythm - - - - - Tonal Memory Chord AnalysisRhythmic Memory ------Tonal Pitch Discrimination Chord AnalysisPitch Change ------Tonal Memory Rhythm Discrimination - -Changes in Pitch - Sense of Pitch Pitch Discrimination Changes in TimeChanges in Rhythm ------Tonal Memory Rhythms { 2 } { 4 } { 6 } { 10 } { 1 } { 3 } { 7 } { 8 } { 11 } { 13 } { 15 } { 16 } { 17 } { 5 } { 9 } { 12 } { 14 } { 18 } { 19 } Subtest Subtest equivalence for auditory description activities of reading content; Measures of Musi- able 4.21: T est Kwalasser’s Music Talent Test Drake Musical Aptitude Tests K-D Musical Talent Tests Gordon’s MusicalProﬁle Aptitude cal Talents T Seashore’s Schoen’s Tests of Musical Feel- ing and Understanding Gordon’s Measures ofAudiation Music Bentley’s Measures of Musical Abilities Wing’s Tests of Musical Ability and Appreciation

81 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ≈ No. # No. - 1 - 1 4 - 2- 3 - 2 3 ≈ ----- ≈ ------3- 3 - 5 - 1 3 - - - - - 2 6 ≈ - - - - 1 7 - - ≈ - ≈ -- ≈ ≈ -- - ≈ ------≈ ≈ ------≈ ------# ------≈ ≈ ------≈ ------≈ ≈ ------≈ ------≈ ≈ ------≈ # --- ≈ ------# ≈ ≈ ≈ - - - ≈ # # ------≈ ≈ ------≈ ≈ # # ≈ ≈ ------≈ ≈ -- -- # -- # ≈ - - # ------# ------# ≈ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Auditory-Musical Dis- Pitch Discrimination Tonal Memory Test for Structure Ability - -Pitch ------Tuning ------Memory Tunes Standard RhythmRhythm-to-melodyPitch ------Rhythm Melody Auditory-Visual Discrimi- { 21 } { 22 } nation { 23 } { 24 } crimination { 25 } { 26 } { 33 } { 20 } { 28 } { 30 } { 31 } { 32 } { 27 } { 29 } Subtest est Colwell MusicTest Achievement Karma’s Test of Structure Abil- ity Musical Aptitude Indicator T The Proﬁle of Music Perception Skills

82 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

4.3.3.7 Auditory Description Activities of Style Content

It can be seen in Table 4.26 that equivalence matches between auditory description activities of style content are sparse throughout the subtest population. Most subtests have only a single partial match, and only three have 2 partial matches. One subtest, {4}, has a total of 3 partially equivalent counterparts. There are very few cases where subtests are fully equivalent to one another. Two of these are early within the development of the ﬁeld, between the Sense of Intensity subtest from Seashore’s Measures of Musical Talents, and the Intensity Discrimination subtest from the K-D Musical Talent Tests. Following these, a fully equivalent match is not found again until the recent Proﬁle of Music Perception Skills battery, whose Loudness subtest is fully equivalent to K-D’s Intensity Discrimination. One subtest, Auditory-Musical Discrimination from the Colwell Music Achievement Test, has no fully of partially equivalent matches.

4.3.3.8 Auditory Description of Historical of General Knowledge Content

Table 4.27 shows the small population of two subtests in the auditory description of historical or general knowledge content category. Both of these subtests are partially equivalent to one another.

4.3.3.9 Visual Description Activities of Reading Content

As shown in Table 4.28, 2 of the 9 visual description activities of reading content are not fully or partially equivalent to any other subtest from the same area. Of the remaining subtests, four have one fully equivalent match, and seven have at least one partially equivalent match. The most common number of partially equivalent matches is 2, with four subtests having this number of counterparts. There is also one subtest with each of 1, 3, and 6 partially equivalent matches. Matches are most frequently found in older test batteries, with Test 3 from the Torgerson- Fahnestock Tests being the most well-matched subtest overall.

4.3.3.10 Visual Description Activities of Rhythm Content

Table 4.29 shows that across the population of visual description activities of rhythm content, there is only one pair of subtests which are fully equivalent. There are no completely unique subtests, as all of them are at least partially equivalent to at least one other. Generally a subtest has only one or two partially equivalent matches, but there is one case where a subtest has 3 matches and another instance where 5 matches for a subtest exist. Aside from the increased density of equivalence matches found for subtest {10} (Test 3 from the Torgerson-Fahnestock Tests), there is no particular time period or test battery in which a higher number of equivalence matches can be found.

83 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ≈ No. # - 1 No. - 9 - 2 9 ≈ -- 1 - - - - 1 - ## ------1 ≈ ------1 ------1 - ≈ ------≈ - - - - - 1 ≈ ------1 - ≈ ------1 represents partial equivalence ------2 - ≈ ------1 ≈ ≈ ≈ ≈ ------2 ------1 ------≈ ------2 ------2 ------1 2 # ≈ ≈ ------≈ ≈ ≈ ≈ # 3 ≈ ≈ ≈ ------2 ------≈ ≈ ≈ ≈ -- ≈ - ≈ ≈ ≈ - ≈ ≈ ≈ - - - - ≈ ≈ - represents equivalence, and - ≈ ----- # ≈ ≈ ≈ ------1 ≈ ≈ ------≈ ≈ ------≈ ≈ ------≈ - 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Rhythm Slurs Melody Auditory-Musical Discrimination - - -Standard - Rhythm ------Musical Memory Rhythm Imagery (Meter) Tonal Rhythm Tonal Memory Memory Rhythm Concepts (Aural Perception) -Meter Discrimination - -Rhythm - -Tunes ------Rhythmic Memory Time Discrimination Rhythm Discrimination Changes in Time Sense of Time Tonal Memory Tonal Memory Changes in Pitch Rhythms Changes in Rhythm Subtest { 12 } { 3 } { 4 } { 10 } { 24 } { 7 } { 21 } { 25 } { 1 } { 2 } { 5 } { 6 } { 9 } { 11 } { 13 } { 14 } { 15 } { 16 } { 18 } { 19 } { 20 } { 22 } { 23 } { 8 } { 17 } Subtest equivalence for auditory description activities of rhythm content; able 4.22: Measures of Musical Talents T est K-D Musical Talent Tests Torgerson-Fahnestock Tests The Proﬁle of Music Perception Skills Schoen’s Tests ofstanding Musical Feeling and Under- Drake Musical Aptitude Tests Gordon’s Measures of Music Audiation Bentley’s Measures of Musical Abilities T Seashore’s Kwalwasser’s Music Talent Test Gordon’s Musical Aptitude Proﬁle Wing’s Tests of Musical Ability andIowa Appreciation Test of Music Literacy Colwell Music Achievement Test Musical Aptitude Indicator

84 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ≈ No. # 1 - 2 10 No. - 1- - - ## ------1 - - - - - 1 - represents partial equivalence ≈ ------1 1 ------2 ≈ ≈ ≈ ≈ - ≈ ------1 ------1 ------1 ---- 1 ------1 1 ------≈ ≈ ≈ ≈ ≈ - ≈ ≈ ≈ ≈ ≈ ≈ # # ------≈ ≈ ≈ ≈ ≈ ≈ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ------represents equivalence, and # Tonal Memory Memory Rhythm Tonal Concepts (Aural Perception) -Tunes -Melody ------Tonal Imagery (Melody) Tonal Memory Changes in Time Rhythms Tonal Tonal Memory Changes in Pitch Changes in Rhythm Musical Memory { 8 } { 2 } { 4 } { 6 } { 9 } { 11 } { 12 } { 1 } { 3 } { 5 } { 7 } { 10 } { 13 } { 14 } { 15 } Subtest Measures of Musical Talents Subtest equivalence for auditory description activities of scales content; est Gordon’s Musical Aptitude Proﬁle K-D Musical Talent Tests Schoen’s Tests of Musical Feeling and Understanding Gordon’s Measures of Music Audiation Bentley’s Measures of Musical Abilities Wing’s Tests of Musical Ability and Appreciation T Seashore’s Kwalwasser’s Music Talent Test Drake Musical Aptitude Tests Musical Aptitude Indicator The Proﬁle of Music Perception Skills Iowa Tests of Music Literacy able 4.23: T

85 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

Table 4.24: Subtest equivalence for auditory description activities of elements of harmony content; represents equivalence, and ≈ represents partial equivalence # Test Subtest No. No. ≈ 1 2 3 4 5 6 #

Schoen’s Tests of Musical Feeling and Un- {1} Relative Pitch -- ≈ - - - - 1 derstanding Wing’s Tests of Musical Ability and Appre- {2} Pitch Change - ---- ≈ - 1 ciation Colwell Music Achievement Test {3} Interval Discrimination ≈ ------1 {4} Major-Minor Mode Discrimination ------{5} Feeling for Tonal Center ------The Proﬁle of Music Perception Skills {6} Tuning - ≈ --- - - 1

Table 4.25: Subtest equivalence for auditory description activities of harmonic structures content; represents equivalence, and ≈ represents partial equivalence # Test Subtest No. No. ≈ 1 2 3 #

Gordon’s Musical Aptitude Proﬁle {1} Tonal Imagery (Harmony) - ≈ - - 1 Gordon’s Measures of Music Audiation {2} Tonal ≈ - - - 1 Wing’s Tests of Musical Ability and Appreciation {3} Harmony -- ---

4.3.3.11 Memory Playback Activities of Rhythm Only

Table 4.30 shows that across the population of test batteries, only three subtests are ‘memory playback of rhythm only’ activities. Amongst these three subtests, Rhythmic Sense from Revesz’s Tests of Musical Ability is entirely unique in its structure, having no equivalence to the other subtests. The remaining two subtests – Time Discrimination from the K-D Musical Talent Tests, and Rhythm from the Drake Musical Aptitude Tests – are partially equivalent to one another.

4.4 Discussion

The results presented in this chapter clearly show that most test batteries heavily favour one particular type of activity or content area. Whilst without further investigation this finding can not lead to any statements about the quality of the batteries, it could be indicative of their purpose. Not all of the batteries have a specifically published statement of their intended purpose or use, but when they do it is often that they are designed to assess the musical aptitude of children with the aim of prioritising musical lessons for those who would most benefit from them (i.e., those with high measured aptitude). As such, test designers are unlikely to want to measure a wide variety of skills, but only those abilities which they believe to be fundamental. It is likely that notation and visual playback activities are unpopular for similar reasons. Given that the tests are generally attempting to identify students with high musical aptitude at a young age, it is unlikely that the intended participants will have strong skills in writing or reading musical notation, or playing any particular instrument. As such, both notation and visual playback activities are not well suited. Memory playback activities, however, can provide some utility, as tasks such as mimicking a rhythm through clapping or a melody through humming can be performed by those with little to no formal musical training.

86 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS ≈ No. # 1 1 No. 12 2 1 - - 1 ≈ # - - 1 -- - 2 ≈ - - - 1 ≈ - -- - 1 ≈ ------1 -- - - - 1 ≈ ------1 represents partial equivalence ------3 - --- ≈ ------1 ≈ ------≈ - - 1 ≈ ------≈ ------2 ------1 ≈ ------≈ ------≈ ---- ≈ ------1 ------≈ ≈ ------≈ ≈ ≈ ------≈ ------represents equivalence, and # - # # - # ≈ ≈ ≈ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 ------Tonal Intensity Auditory-Musical Discrimination ------Phrasing Musical Sensitivity (Style)Rhythmic Accent - - - - -Accent -Tempo - -Loudness - Rhythm Imagery (Tempo) ------Tonal Movement Changes in Volume Musical Sensitivity (Balance) - - - - Sense of Intensity Intensity Discrimination Tonal Sequence Musical Sensitivity (Phrasing) ------Tonal Imagery (Melody) - - - - - { 13 } { 3 } { 8 } { 10 } { 17 } { 18 } { 7 } { 11 } { 4 } { 9 } { 15 } Subtest { 1 } { 2 } { 5 } { 14 } { 6 } { 12 } { 16 } Subtest equivalence for auditory description activities of style content; Measures of Musical Talents able 4.26: est T Gordon’s Measures of Music Audiation Kwalwasser’s Music Talent Test Colwell Music Achievement Test K-D Musical Talent Tests Schoen’s Tests of Musical Feeling and Understanding T Seashore’s Gordon’s Musical Aptitude Proﬁle Wing’s Tests of Musical Ability and Appreciation The Proﬁle of Music Perception Skills

87 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

Table 4.27: Subtest equivalence for auditory description activities of historical or general knowledge content; represents equivalence, and ≈ represents partial equivalence # Test Subtest No. No. ≈ 1 2 #

K-D Musical Talent Tests {1} Quality Discrimination - ≈ - 1 The Proﬁle of Music Perception Skills {2} Timbre ≈ - - 1

Table 4.28: Subtest equivalence for visual description activities of reading content; represents equivalence, and ≈ represents partial equivalence #

Test Subtest No. No. ≈ 1 2 3 4 5 6 7 8 9 # Kwalwasser-Ruch Test of Musical {1} Detection of Pitch Errors in Notation -- ≈ - ≈ ≈ - - - - 3 Accomplishment of a Known Melody {2} Recognition of Time Errors in Nota- - -- ≈ ≈ - - - - - 2 tion of a Known Melody K-D Musical Talent Tests {3} Pitch Imagery ≈ - -- ≈ - - - 1 2 {4} Rhythm Imagery - ≈ - - ≈ #-- - 1 2 Torgerson-Fanestock Tests {5} Test 3 ≈ ≈ ≈ ≈ - ≈ - #≈ - - 6 Iowa Tests of Music Literacy {6} Tonal Concepts (Reading Recogni- ≈ - - ≈ - - - - 1 2 tion) # {7} Tonal Concepts (Notational Under------standing) {8} Rhythm Concepts (Reading Recogni- --- ≈ -- - - 1 1 tion) # {9} Rhythm Concepts (Notational Un------derstanding)

Table 4.29: Subtest equivalence for visual description activities of rhythm content; represents equivalence, and ≈ represents partial equivalence #

Test Subtest No. No. ≈ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 # Seashore’s Measures of Musical {1} Sense of Time --- ≈ ------≈ - - - 2 Talents Kwalwasser-Ruch Test of Musical {2} Detection of Pitch Errors in ------≈ - - - - - 1 Accomplishment Notation of a Known Melody {3} Recognition of Time Errors ------≈ -- ≈ - - - - - 2 in Notation of a Known Melody K-D Musical Talent Tests {4} Time Discrimination ≈ ------1 {5} Rhythm Discrimination ------≈ ------1 {6} Pitch Imagery ------≈ - 1 {7} Rhythm Imagery -- ≈ ------≈ --- 1 2 Kwalwasser’s Music Talent Test {8} Changes in Rhythm - - - - ≈ -- - ≈ - ≈ - - -# - 3 Schoen’s Tests of Musical Feeling {9} Rhythms ------≈ ------1 and Understanding Torgerson-Fahnestock Tests {10} Test 3 - ≈ ≈ --- ≈ -- --- ≈ ≈ - 5 Drake Musical Aptitude Tests {11} Musical Memory ------≈ ------1 {12} Rhythm ≈ ------1 Iowa Tests of Music Literacy {13} Tonal Concepts (Reading ------≈ -- - - - 1 Recognition) {14} Rhythm Concepts (Reading ----- ≈ -- ≈ --- - 1 2 Recognition) #

88 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

Table 4.30: Subtest equivalence for memory playback activities of rhythm only; represents equivalence, and ≈ represents partial equivalence #

Test Subtest No. No. ≈ 1 2 3 # Revesz’s Tests of Musical Ability {1} Rhythmic Sense ----- K-D Musical Talent Tests {2} Time Discrimination - - ≈ - 1 Drake Musical Aptitude Tests {3} Rhythm - ≈ - - 1

Many of the test proponents also designed their work to be used on a wide scale – for example, measuring the abilities of an entire incoming class at once. This is likely the reason why auditory description is such a popular activity. Being able to play questions through an auditory medium limits the audience only in terms of the range from which the audio can be heard, and avoids issues where participants may be too young to read and interpret questions on their own. Description activities also lend themselves well to pictorial answer cues (e.g., ‘up’ and ‘down’ arrows which can be circled to indicate whether a tone was higher or lower than its predecessor), which also avoids text comprehension issues for younger participants. It is likely for this reason that visual activities – both of the description and recognition types – are the next most frequently used. When question content is visual, participants do not need to understand the written word to partake in the assessment process. The process of determining subtest equivalence revealed that many fully and partially equivalent subtests have names that would not suggest such similarities. For example, equivalence was frequently found between subtests containing the word ‘melody’ and those containing the word ‘rhythm’, despite these words intuitively indicating separate areas of knowledge. This results from a combination of the subtest names generally being vague and non-specific, and many subtests covering multiple content areas. One example of this is Drake’s Musical Memory subtest, which touches on no fewer than three content areas (reading, rhythm, and scales). Overall, there is a large disparity between the number of fully equivalent and the number of partially equivalent subtests. Unsurprisingly, partial equivalence is significantly more common. This reveals the inspiration of earlier works on their later counterparts, but also that test proponents were hesitant to directly include work proposed by their predecessors or com- petitors in their own batteries. Conversely, a subtest with little to no equivalent counterparts represents a departure from the norm. This is particularly true when an entire battery contains few subtests with equivalence matches, such as the Colwell Music Achievement Test. It should be noted that when a test is described as assessing knowledge from a content area, this does not mean it assesses all knowledge from that content area. For example, Bentley’s Measures of Musical Abilities assess reading knowledge by asking students to identify whether the second of two tones was higher or lower, but does not assess whether the student can identify the correct location for that pitch on a musical stave. Although two subtests may be of the same activity type and may cover the same content area, it can not be assumed that they are equivalent. As such, the identification of equivalent subtests requires manual verification. Automating this process is an avenue for further work. Some of the popular test batteries within the field were not translated. These batteries include the Silver Burdett Music Competency Tests, Lowery’s Test for Cadence, the Mosher Group Test, Gildersleeve’s Music Achievement Tests, and the Beach Standardized Music Tests. This is

89 CHAPTER 4. TAXONOMY VALIDATION:MUSIC APTITUDE TESTS

entirely due to a lack of available information surrounding the structure and content of their subtests.

4.5 Summary

This chapter has presented an example application of the taxonomy deﬁned in Chapter 3. It has shown how the taxonomy can be used to describe tests of musical aptitude and ability in a common, neutral language, despite the test developers intentionally using different terminolo- gies. The next chapter will use the taxonomy in combination with other techniques to analyse the state of the art of iOS applications designed to teach musical skills.

90 5 iOS Music Teaching Applications: State of the Art

5.1 Overview

Before proposing new ways in which technology can be utilised for teaching and practicing musical skills, it is important to understand what has already been done in the space. To this end, this chapter will discuss the state of the art of music teaching and practice applications (i.e., ‘apps’) on the iOS platform. Several characteristics of the applications will be examined, including their general design, coverage of musical knowledge and activities1, use of feedback, and the educational outcomes users are likely to achieve. This allows for the identiﬁcation of gaps within the ﬁeld, both in terms of what could be improved and what is not yet being done. The chapter is organised as follows. Section 5.2 provides a detailed description of the method used to analyse the state of the art, and Section 5.3 provides an overview of the results of this analysis. A discussion of the major results and their meaning within the context of this thesis is given in Section 5.4.

5.2 Method

5.2.1 Overview

This review will cover music teaching and practice applications on Apple’s iOS application store. Mobile applications were selected as the focus for two reasons. Firstly, many desktop applications in this space have related iOS applications which have either feature parity or more functionality than their desktop counterparts. Secondly, tablet applications and devices are becoming increasingly popular as teaching aids due to their mobility, ease of use, and interaction modes. Within the mobile space, the iOS platform was chosen as it features the largest library of applications designed to teach or assess musical skills compared to other platforms such as Android. However, many of these applications are also available on other mobile platforms.

1The areas of musical knowledge and activity types are taken from the taxonomy deﬁned in Chapter 3.

91 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART

Sections 5.2.2 to 5.2.5 describe the method followed for this analysis. This includes the purpose of the analysis, the selection process for applications, and all collected data.

5.2.2 Purpose

The purpose of this review is to analyse skill-based iOS applications. These are deﬁned by Cherner et al. [32] as being applications which aim to help a learner build basic abilities and fundamental knowledge in a subject area. Generally this is accomplished by focusing on recall, rote memorisation, and skill-and-drill instruction – activities which fall under the ‘Remember- ing’ and ‘Understanding’ parts of Bloom’s taxonomy [25]. The general process used for data collection was that deﬁned by Leedy and Ormrod [106], which involves the following four steps:

Step 1: Identify sample The identiﬁcation and selection process of applications, described in Section 5.2.3, used domain keywords and a recursive search process to ﬁnd candidate applications from the iTunes app store.

Step 2: Deﬁne characteristics to be examined A number of characteristics and features were identiﬁed for describing both the content and general features of each application. Broadly, these characteristics related to the background and general metadata for the application (e.g., who was the developer?, how much does it cost?), the knowledge the app covers, and how learners progress through the content.

Step 3: Break down larger characteristics into measurable items The characteristics and features identiﬁed in Step 2 were broken down and de- ﬁned such that they can be measured. This is described further in Section 5.2.4.

Step 4: Measure Each of the selected applications was systematically surveyed. This process is described in Section 5.2.5.

5.2.3 Application Selection

As this review focused on applications available on the iOS platform, the iTunes app store2, maintained by Apple Inc., was used to select a representative sample. First, the following search phrases were deﬁned:

• music theory • music theory tutor • music tutor • sight reading • music sight reading

2http://www.apple.com/au/itunes/

92 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART

Start Search item

Add item to list

Is there No another search phrase?

Open related apps list Yes

Use next search phrase

Are there apps No not already considered?

No Are there apps not already Yes considered?

Pick next result Yes

Pick next result Search item

Search item Finish

Finish

Figure 5.1: The process used to search the iTunes app store for applications to include in the analysis. The process for the next step – ﬁltering the results of the search – is shown in Figure 5.2.

93 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART

A recursive process, detailed in Figure 5.1, was then applied in order to expand the results from searching these phrases in the app store to a larger list of apps to consider for inclusion in the analysis. This process relies on Apple’s algorithm for identifying related apps, given the limited number of results the iTunes app store returns for individual search queries. After searching a phrase, each app in the results list was considered in turn. If the app was not already in the list of candidates, it was searched. Searching involved adding the app to the list of candidates, opening the list of apps related to it, then searching each of the unseen apps from that list. This process iteratively expanded the space of connected apps, meaning a large number of candidates could be identified from only a small number of search phrases. Once a list of candidates was found, it was filtered according to the criteria illustrated in Figure 5.2. The first key selection criterion was that the application must be available on the Australian iOS app store, as this is the only version of the store accessible from Australia. If this was true, the app description and screenshots were perused in an attempt to identify whether the app was skill-based or not. Once past this stage, the app’s rating and reviews (both positive and negative) were briefly considered. This was done in an effort to identify any obvious issues (e.g., frequent crashing, catastrophic bugs) that would prevent the app from being properly assessed. In cases where an app clearly had such issues it was omitted. Finally, the app was checked for compatibility with the review hardware – a first generation iPad Mini and an iPhone 5. This process of selection and filtering resulted in a final sample of 175 of 313 iOS applications being selected.

5.2.4 Data Collection

5.2.4.1 Overview

Data collection followed a three part process. The first part was to fill in a review template for each application. This involved the collection of various descriptors such as the application developer, feedback style, and learning outcome. Descriptors were either free text or one of a defined set of values. The second part was to use the applications and determine which content areas and activities they use. Each application was then assigned both a focus and depth rating for each of its content areas and activities. Finally, applications were assigned tags to indicate whether they exhibit certain characteristics. Tags are binary as applications either do, or do not have the characteristic. That is, it is not possible for a characteristic to be partially present. Sections 5.2.4.2, 5.2.4.3, and 5.2.4.5 describe the review template, focus and depth ratings, and set of characteristic tags, respectively. Once collected, this data was analysed to compile a rich view of the state of the art.

5.2.4.2 Review Template

A broad range of data was collected about each of the selected apps. In order to maintain a consistent format, a review template was devised. This template includes ﬁelds for collection of background data as well as descriptors for how each app provides feedback, represents achievement, and progresses the user through its content.

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Select application

Is the app available in the No (a) Australian store?

Yes

Is the app No (b) skill-based?

Yes

Are there any Yes (c) obvious issues?

Will the app run on the No (d) review hardware?

Yes

Selected Rejected

Figure 5.2: The process used to ﬁlter candidate iOS applications for inclusion in the analysis, using four key criteria

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Table 5.1 lists the complete set of descriptors in the review template. Each descriptor can be assigned one or more of a given set of values, or ﬁlled with free text. For those with pre-deﬁned values the value type may be exclusive or inclusive. For example, the project status of an application is exclusive as it can be either ‘active’ or ‘inactive’ but not both. In contrast, the comparison style of an application could be any combination of the values listed, as different areas of an application may employ different styles. Further descriptions of the descriptors are provided below.

Table 5.1: Descriptors collected about each iOS application. Potential values listed as ‘-’ indicate free text ﬁelds.

Category Descriptor Potential Values Value Type

Background Developer - - [33, 105] Version - - Application Store Category - - App Store Average Rating 0 - 5 stars Exclusive Project Status Active Exclusive Inactive Monetisation Model Free Inclusive Ad-supported In-app purchases Paid Subscription Cost - - Total Reviews - - Current Version Reviews - -

Audience [33, 105] Content Rating 4+ Exclusive 9+ 12+ 17+ Use of Proﬁles Single Exclusive Local Online Use of devices None Single-device Multi-device Use of Instruments None Exclusive Real On-screen Both

Feedback Model Feedback Style None Inclusive [97, 123, 182] Veriﬁcation Elaboration - directive

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Elaboration - facilitative Feedback Type No-feedback Inclusive Knowledge-of-response Answer-until-correct Knowledge-of-correct-response Error-ﬂagging Topic-contingent Response-contingent Hints-cues-prompts Bug-related Attribute-isolation Informative-tutoring Auditory Feedback No Exclusive Yes Yes-inconsistent Visual Feedback No Exclusive Yes Yes-inconsistent Feedback timing Immediate Inclusive Delayed Comparison Style None Inclusive Past-self Local-users Global-users

Incentive and Achievement Style None Inclusive Achievement Model Scored Starred Competitive Score Management None Exclusive Reset-single Reset-all Both Social Sharing Style None Exclusive Available Encouraged Social Sharing Type None Exclusive Direct Broadcast

Progression Model Progression Style None Exclusive [19] Linear Manually-adaptive Adaptive Answer Revealable No Exclusive

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Yes With-consequence Question Skippable No Exclusive Yes With-consequence Learning Outcome Pre-structural Exclusive Uni-structural Multi-structural Relational Extended abstract

Background The background material focuses on general information about the app and its developer. Information collected includes the name of the developer, the category and rating listed for the app in the iTunes store, the app’s monetisation model, and the cost of the app. Also included is the version of the app that was assessed in this work and the number of public reviews the application has received in total and for the latest version. It is also noted whether the project is being actively developed, where an app is considered to be ‘actively developed’ if it has been updated within the last six months.

Audience The audience information collected includes the app’s target age(s) and skill level. Unless specifically defined by the app or its supporting documentation, the ‘target age group’ field is left blank. The ‘Content Rating’ for an application is taken from its page on the app store. Descriptions of the possible ratings can be found in Figure 5.4. The ‘use of profiles’ characteristic indicates whether multiple users can independently track their progress on a single installation of the application and, if so, if that progress can be transferred between instances of the application. Three values are possible:

Single The application supports only a single user on any one device.

Local The application supports multiple users, but user proﬁles are stored locally. Figure 5.3 shows an example of an application which supports local user proﬁles.

Online The application supports multiple users and user data is stored online.

The ‘use of devices’ characteristic indicates whether an application supports syncing user data between separate devices. Three values are possible:

None The application does not support user proﬁles.

Single-device User data is stored locally and can not be transferred to another device or instance of the application.

Multi-device User data is stored either locally or online and can be transferred to another device or instance of the application.

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Figure 5.3: An example of local proﬁles as used in the iOS application Rhythm In Reach [257]

Figure 5.4: Possible content ratings for applications on the iTunes app store. Note that the ratings focus on age-appropriateness factors, and are not an indication of the app’s genre.

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‘Use of instruments’ refers to the input method(s) supported by the application. Four values are possible:

None The application does not support instrument input.

Real A physical instrument can be used with the application. Input may be processed through a MIDI interface or the device’s microphone.

On-screen A digital replica of an instrument is provided, which the user can interact with by tapping or swiping the device’s screen. An example of this is shown in Figure 5.5.

Both The application supports input from a physical instrument, but also provides a digital replica. Users may choose which they wish to use.

Feedback Model Feedback is deﬁned by Mason and Bruning [123] as being any message provided in response to a learner with the purpose of helping them identify their errors and misconceptions. Two types of feedback styles were originally deﬁned by Kulhavy and Stock [97]:

Veriﬁcation Indicating to the learner whether their answer is correct or incorrect.

Elaboration Providing the learner with cues to lead them towards a correct answer.

Elaboration was later split into two types by Shute [182]:

Directive Elaboration Addresses the learner’s response and their particular errors. Also known as speciﬁc elaborative feedback.

Facilitative Elaboration Provides worked examples or information related to the topic. Also known as general elaborative feedback.

These two styles of feedback are not mutually exclusive. For example, they can be combined by telling the user that their answer is incorrect (verifying) as well as providing them with guidance to help them find the correct answer (elaborating). The feedback style used by each app (i.e., verification or elaboration) was measured and, if elaborative, the type of elaboration (directive or facilitative). In some cases an application may exhibit no feedback style. This is true of Brainscape’s Ultimate Music Theory – Smart Audio Flashcards [218]. In this application, users are presented with a series of flash cards, each of which contains a musical question. Users are asked to think of an answer to the presented question, then tap the screen when they are ready to flip the card and reveal the solution. They can then compare their own answer to the provided one and rate their confidence in that piece of knowledge. This is an entirely self-managed process, with the user providing their own form of verification in comparing their answer to that provided by the software. At no point does the application provide any feedback to the user; as such, this app is described as providing ‘no feedback’.

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Figure 5.5: The use of an on-screen instrument (piano) in Interval Ear Training [212]

In addition to the feedback style, the template also captures the speciﬁc feedback type. Again, these values are not mutually exclusive – a single app can utilise multiple feedback types either in the same or in separate areas. The possible feedback types are those deﬁned by Mason and Bruning [123] and Shute [182]:

None No feedback is given.

No-feedback Individual answers are not addressed. For example, the learner is given an overall score but is not told which questions they got correct or incorrect.

Knowledge-of-response Individual answers are labelled as correct or incorrect.

Answer-until-correct Individual answers are labelled as correct or incorrect, and if incorrect the user is required to repeat the question.

Knowlege-of-correct-response Individual answers are labelled as correct or incorrect, and if incorrect the correct answer is provided.

Error-ﬂagging Mistakes in individual answers are highlighted, but not ex- plained or corrected.

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Topic-contingent Individual answers are labelled as correct or incorrect, and if incorrect the user is directed towards learning material that will help them identify the correct answer.

Response-contingent Individual answers are labelled as correct or incorrect, and if incorrect the correct answer is provided. Explanations are given in all cases – for example, “Your answer was incorrect because ...”; “Your answer was correct because ...”.

Hints-cues-prompts Individual answers are labelled as correct or incorrect, and if incorrect hints are given as to the correct answer. The correct answer is not explicitly given.

Bug-related A ‘bug library’ is maintained, and examples are retrieved relating to a user’s error(s) when they nominate an incorrect answer.

Attribute-isolation Individual answers are labelled as correct or incorrect, and the central attributes of the target concept are highlighted.

Informative-tutoring Individual answers are labelled as correct or incorrect, and, if incorrect, mistakes are highlighted and hints as to the correct answer are provided. The correct answer is not explicitly given.

The ‘Auditory Feedback’ and ‘Visual Feedback’ categories record whether or not auditory and visual feedback was utilised in an application and, if so, whether the feedback given is inconsistent. For example, an application that emits a sound to indicate a correct answer, but gives no sound for an incorrect answer would be exhibiting inconsistent auditory feedback. The template also notes whether feedback is provided immediately after nominating users input, or after some time (i.e., whether the feedback timing is immediate or delayed). Additionally, the template contains a ﬁeld for the comparison style used by the app. This indicates whether the app compares a user’s performance with their own past performances, the performances of other users on the same device (local users), or the performances of users on other devices (global users). As with the other aspects of the feedback model, this is inclusive. That is, one or more comparison styles may be used.

Incentive and Achievement Model The incentive and achievement model deﬁnes how the user’s level of success completing the activities in an app is shown and how they are encouraged to share their success. First, the app’s achievement style is recorded. This indicates how the user’s performance on an activity is communicated to them. For example, they may be provided with a numerical score, a number of stars, or with some kind of ranking against their past self. These methods are not exclusive, as a single app may use multiple of them. The score management style an application follows indicates whether users can reset their scores and, if so, whether scores can be reset across all activities, for individual activities, or both. The social sharing style of an app indicates whether users are able to share their progress with others (e.g., through an e-mail, a Twitter post, or on Facebook) and, if possible, whether doing so is encouraged. For example, an app that allows you to share your progress would have

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Figure 5.6: An example of an ‘Available’ social sharing style and ‘Direct’ social sharing type in Rhythm Sight Reading Trainer [249]

an ‘Available’ social sharing style. However, if the app had a pop-up after each key achievement asking you to share your progress, it would have an ‘Encouraged’ social sharing style. In addition to the social sharing style, the social sharing type is also deﬁned. This may be one of three values:

None No social sharing is available.

Direct Users may share their performance or progress, but must speciﬁcally nominate recipients of the message. E-mail is an example of a direct type of sharing.

Broadcast Users may share their performance or progress publicly without nominating any speciﬁc recipients. Examples of broadcast sharing types include Twitter and Facebook.

Figure 5.6 displays a screenshot from Rhythm Sight Reading Trainer, showing how users are able to use the ‘direct’ social sharing type by sending an e-mail summarising their performance on an exercise. In this case the user must navigate a series of menus to share this information, meaning it falls under the ‘Available’ social sharing style. As the user must nominate recipients for their e-mail this app is further described as having a ‘direct’ type of social sharing.

Progression Model The progression model deﬁnes how users work through the content and activities of an app. This is an exclusive category, as only one progression model can be used at any one time. Four progression models are deﬁned:

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None There is no content to progress through. For example, a game with one level.

Linear There is only one path through the content.

Manually-adaptive The user can alter some or all aspects of the content. For example, a quiz game which allows the user to select the topics and concepts they will be quizzed on.

Adaptive The app automatically alters some or all aspects of the content. For example, a quiz game which presents more questions from subject areas in which the user has performed poorly.

The ‘Answer Revealable’ and ‘Question Skippable’ characteristics define whether users are able to view the answer for a question without having first submitted an answer of their own, or skip a question entirely. This may either be possible (i.e., ‘Yes’), not possible (i.e., ‘No’), or only possible with some consequence (i.e., ‘With-consequence’), such as a reduction in their score. The progression model also includes the type of learning outcome of the app, as defined by the SOLO taxonomy (Structure of the Observed Learning Outcome [19]) developed by Biggs. Five levels of outcomes are possible:

Pre-structural Indicates no understanding of the topic; the student hasn’t un- derstood the point of the task and uses simple methods for completing it.

Uni-structural Indicates understanding of one aspect relevant to the topic; learner has a basic understanding.

Multi-structural Indicates understanding of multiple aspects relevant to the topic, but in isolation; assessment is mostly quantitative.

Relational Indicates an ability to connect multiple aspects relevant to the topic; student somewhat understands the topic.

Extended abstract Indicates an ability to generalise or extend knowledge of the topic to a new area.

5.2.4.3 Content Areas and Activities

The taxonomy presented in Chapter 3 was also used to describe each application. As an app was assessed, each part was matched to either a content area or activity from the taxonomy. This was done with a high level of granularity, splitting games into their individual levels and textbook-style apps into their individual chapters. Once the parts of an app were matched to appropriate content areas and activities, the entire app was rated for its depth of coverage and level of focus in each part of the taxonomy. In accordance with recommendations made by Lee and Cherner [105] in their work developing rubrics for assessing instructional applications, ratings followed a ﬁve-point Likert scale, using the categories ‘very low’, ‘low’, ‘medium’, ‘high’, and ‘very high’.

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Figure 5.7: The update history shown on AppShopper for Note Brainer Pro [219]. This data is not available through the ofﬁcial iTunes app store.

5.2.4.4 Update History

To gain a deeper appreciation of the history of development for each application, data from AppShopper3 was also used. AppShopper records both version and pricing changes, noting the date and relevant details (e.g., version number, new price) of each event. An example of this is shown in Figure 5.7. This data was collected for every application in the sample.

5.2.4.5 Characteristic Tagging

In addition to the characteristic descriptors described in Section 5.2.4.2, a number of tags were applied to each application to further describe their functionality. These tags are entirely binary, allowing only for exclusive ‘yes’ or ‘no’ values. The following tags were deﬁned:

rh-friendly Is the application useable for users who are right handed?

lh-friendly Is the application useable for users who are left handed?

content-only Does the application contain only instructional content without any interactive activities?

push-notiﬁcations Does the application use push notiﬁcations?

game-center-integrated Does the application use iOS’s game center?

internet-required Is the internet required to use the application?

unstable Is the application unstable (i.e., did it crash at least once during evaluation)?

handles-rotation Does the application change orientation when the user ro- tates their device?

repeats-questions Does the application frequently repeat a question within a short time frame (i.e., within ﬁve questions)?

3http://appshopper.com/

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saves-scores Does the application keep a record of users scores?

ipad-support Does the application run on an iPad?

iphone-support Does the application run on an iPhone?

5.2.5 Collection Process

The data collection process was the same for each of the apps in the review sample. Firstly, the parts of the app were broken down to create a structure chart. Each part was then examined, an appropriate content area or activity type from the taxonomy was identified, and the related colour(s) were applied to that area of the chart. This information was also textually coded for easier analysis. Figure 5.8 shows an example of a structure chart resulting from this process for the iOS application Nota [213]. In this case the application is split into two main areas – ‘Piano’ and ‘Quiz’ – with an additional ‘Reference’ section. The content in the ‘Piano’ section is all instructional, with each part relating to a single content area from the taxonomy (instrument- specific, elements of harmony, and scales content areas for the notes, chords, and scales parts, respectively). The ‘Quiz’ section contains two areas, both of which are best described as visual recognition activities of reading content. Finally, the ‘Reference’ area, whilst being only one section of the application, covers multiple content areas. To reflect this, the structure chart contains an entry for each content area covered (reading, style, elements of harmony, harmonic structures, and scales), and the section name in each label is followed by an asterisk. Once this breakdown was complete the review template described in Section 5.2.4.2 was filled out and the appropriate characteristic tags from those described in Section 5.2.4.5 were recorded.

5.3 Results

5.3.1 Coverage of Content and Activities

Key Outcomes:

• Applications generally cover zero or one content area • The large majority of applications use only one activity type • Reading and Instrument-specific are the most popular content areas • Visual Recognition is the most popular activity type The applications do not present a broad range of content or activity types, tending to focus on teaching or supporting the practice of one specific aspect of musical knowledge. Most applications focus on teaching either basic note reading skills or specific instrument-related content, and the large majority of applications exclusively use the Visual Recognition activity type when testing or supporting the application of user’s knowledge. Visual Recognition is likely a popular activity type as it is simple to im-

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Notes

Piano Chords

Scales

Quiz Easy

Reference* Advanced

Content Reference*

Reference*

Figure 5.8: A breakdown of the content and activities in the iOS application Nota [213]. As- terisks represent single parts of the application which cover multiple content areas. Colours indicate the type of content and activities, using the colour scheme deﬁned in Chapter 3.

plement. Questions of this type require users to identify some musical element from a set of visual options, meaning that algorithmically determining the correctness of a user’s answer is trivial. It also restricts the complexity of potential questions to those where answers can be represented visually, which simpliﬁes the process of algorithmically generating activities. This is particularly true when the activity requires knowledge of Reading content (i.e., one of the two most popular content areas), as the question parameters can be as simple as the range of notes or list of notation symbols to test the user on. Whilst this likely accounts for some of the popularity of the Reading content area, there are other potential reasons. For example, it is also probable that Reading content is popular as it is seen as a fundamental skill, thus likely to have a higher perceived utility and larger potential market than applications focusing on other content areas. Reading knowledge also traditionally relies on rote learning and repetitive practice, which means applications do not have to provide a large amount of instructional content which can be time-consuming and difﬁcult to design well. Instead, they can focus on providing practice tools which are, as already mentioned, reasonably trivial to implement.

Figures 5.9 and 5.10 show the number of unique content areas and activity types used by the sampled applications. Figure 5.9 shows that the majority of applications do not cover any content areas, and those that do tend to touch only upon one. Very few applications cover two or more content areas, and at most they will present information from ﬁve different areas. Figure 5.10 shows a similar lack of broadness, revealing that the majority of applications use only one activity type. A small number cover two or three, and very few use between four and ten different activities. Almost no applications use zero activity types (i.e., only present

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content). This data reveals that the applications tend to focus strongly on just one aspect of musical knowledge. The most common structure is to exclusively present one activity type with no instructional content. Figure 5.11 shows this clearly. The largest points are for applications which cover one or two content areas and only one activity type. When more activity types are used, most applications cover no content areas. Overall, only a small subset of the sampled applications cover any one of the content areas. This can be seen in Table 5.2, which shows that the most popular content areas are Instrument-Speciﬁc and Reading. The least popular content area is Historical and General Knowl- edge, which is touched on by just one application. Table 5.3 shows the number of applications which cover each activity type. The most popular activity is, by a wide margin, Visual Recognition, used by 87 applications. This is followed by Visual Playback, which is used by 53 applications. The least popular activity types are Auditory Description, Memory Playback, and Visual Description, which are used by 8, 11, and 13 applications respectively.

5.3.2 Depth and Focus of Content and Activities

5.3.2.1 Characteristics of the Depth and Focus Ratings

Key Outcomes:

• Most focus ratings are relatively high • Most depth ratings are relatively low • The most common pattern for both the depth and focus ratings is for there to be one dominant rating • When there is one dominant depth or focus rating for a category, it can be of any value • When there are two dominant depth or focus ratings for a category, they tend to be contiguous within the rating scale The applications tend to focus narrowly on one activity type or content area. However, at the same time, the content and activities they present are not

Table 5.2: Coverage of content areas across the sample of iOS applications

Category Covered? No Yes

Reading 142 32 Rhythm 158 16 Scales 159 15 Elements of Harmony 155 19 Harmonic Structures 169 5 Style 168 6 Instrument-Speciﬁc 140 34 Historical and General Knowledge 173 1

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Figure 5.9: The number of unique content areas covered by the applications in the sample.

Figure 5.10: The number of unique activity types used by the applications in the sample.

Table 5.3: Coverage of activity types across the sample of iOS applications

Category Covered? No Yes

Auditory Recognition 133 41 Visual Recognition 87 87 Auditory Description 166 8 Visual Description 161 13 Visual Playback 121 53 Memory Playback 163 11 Notation 149 25

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Figure 5.11: The number of unique content areas compared to the number of unique activity types used by applications in the sample. The bubble sizes indicate the number of applications covering a combination of number of activity types and number of content areas, with the smallest bubble representing 1.

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covered in a great deal of depth. This means that the applications only help users learn the basics of any particular topic. By covering content at a low depth the applications are often limited to knowledge that can be taught through rote learning and repetitive practice. This typically means that the activities are simple enough to be algorithmically generated with little issue. Consequently, answers can also be algorithmically assessed with ease. This significantly simplifies the complexity of implementation and time commitment developers face before they can publish their work. The applications are frequently highly focused, as they often cover just one or two aspects of musical knowledge. It is likely that developers create such highly focused applications simply because they only implement support for the musical knowledge they consider to be important or relevant to their target audience. In some cases this is themselves, a family member, or a friend. Adding additional knowledge (and supporting activities) increases the development time and complexity of an application, which developers generally consider to be undesirable without significant justification. In some cases developers create multiple applications, each of which focuses on a different area of musical knowledge. This may be an effort to simplify each application, or it could be an attempt to increase their chances of finding paying users by having multiple low-cost offerings rather than one higher-cost application with more functionality.

Applications were assigned depth and focus ratings in a total of 55 unique categories. These categories cover each of the content areas, and each activity subtype from the taxonomy presented in Chapter 3. When examining the distributions of ratings for these 55 categories over the entire sample, 6 patterns were found:

1. One dominant rating The applications have a variety of depth and focus ratings, but one rating is particularly popular. For example, Figure 5.12 shows the distribution of focus ratings for the Instrument-Speciﬁc content area. Although ratings have been given at almost all levels of the scale, ‘High’ ratings are clearly dominant.

2. Two dominant ratings The applications have a variety of depth and focus ratings, but two ratings are particularly popular. For example, Figure 5.13 shows the distribution of depth ratings for Visual Recognition activities of Reading content. Although ratings have been made from ‘Very Low’ to ‘High’, the ‘Medium’ and ‘Low’ ratings dominate.

3. Even split The applications have a variety of depth and focus ratings in approximately equal amounts. For example, the distribution of focus ratings for Visual Description activities of Scales content – shown in Figure 5.14 – reveals that applications covering this activity are rated at either a ‘Medium’, ‘Low’, or ‘Very low’ depth, in equal amounts across the sample.

4. Generally higher ratings The applications have a variety of depth and focus ratings, but ratings tend to be higher up the scale. For example, the distribution of focus ratings for Auditory Recognition activities of Elements of Harmony content – shown in Figure 5.15 – generally fall in the upper bracket of possible values (i.e., ‘Medium’ to ‘Very high’).

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5. Generally lower ratings The applications have been given a variety of depth and focus ratings, but ratings tend to be lower down the scale. For example, Figure 5.16 shows that the depth ratings for Notation activities of Elements of harmony generally fall in the lower bracket of possible values (i.e., ‘Medium’ to ‘Very low’).

6. One application in category Only one application in the sample covered the category. For example, only one application has a Memory Playback activity of Elements of Harmony content.

A summary of the number of distributions ﬁtting each of the 6 patterns identiﬁed is provided in Table 5.4. The most commonly found pattern, both for the focus and depth ratings, is for there to be one dominant rating. Next most common is for there to be only one application representing a category, followed by there being two dominant ratings. Few categories present with an even split of ratings or a tendency towards higher or lower rating values. When only one application is in a category, focus ratings tend to be high. However, depth ratings for categories with only one application never go above the ‘Medium’ level. For the ‘One dominant rating’ pattern the dominant rating can be from any level of the scale. When two dominant ratings are present they tend to be contiguous within the rating scale (e.g., ‘High’ and ‘Very high’; ‘Low’ and ‘Medium’). Figure 5.17 shows the correlation between depth and focus ratings in the same categories. It shows that a ‘Very low’ focus will never be paired with a ‘High’ or ‘Very high’ depth in the same category, and that a ‘Low’ focus will never be paired with a ‘Very high’ depth. All other pairings of ratings are seen at least once. Figure 5.17 also shows the general trend of ratings. For example, most of the focus ratings fall in the higher bracket of the ratings scale, with a large number being ‘Very high’. This outcome matches the results discussed in Section 5.3.1 (i.e., that most applications cover only one activity type), as an application which only covers one activity type would naturally have a high focus in that area. Unlike the focus ratings, the depth ratings tend to fall into the lower bracket of the ratings scale, with very few reaching the ‘High’ and ‘Very high’ levels.

5.3.2.2 Depth and Focus Ratings

Key Outcomes:

• The large majority of content areas and activity types show high focus ratings but low depth ratings • High depth ratings are rare The applications tend to focus highly on one particular aspect of musical

Figure 5.12: The distribution of focus ratings for the Instrument-Speciﬁc content area

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Figure 5.13: The distribution of depth ratings for Visual Recognition activities of Reading content

Figure 5.14: The distribution of focus ratings for Visual Description activities of Scales content

Figure 5.15: The distribution of focus ratings for Auditory Recognition activities of Elements of Harmony content

Figure 5.16: The distribution of focus ratings for Notation activities of Elements of Harmony content

Table 5.4: A summary of the distribution types for the depth and focus ratings

Characteristic Number of Categories Exhibiting the Distribution Type Focus Ratings Depth Ratings

One dominant rating 20 28 Two dominant ratings 11 9 Even split 8 4 Generally higher ratings 4 - Generally lower ratings 1 3 One application in category 11 11

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Figure 5.17: Frequency with which each focus rating is paired with each depth rating. The bubble sizes indicate the number of times each pairing was found, with the smallest bubble representing 1.

knowledge but do not cover that knowledge to a high level of depth. The lack of high depth is likely because deep coverage of even one aspect of musical knowledge is difﬁcult, whether it’s teaching students or designing activities to test their knowledge. Developers would need an ability to create content that effectively teaches or assesses knowledge at a deep level. This is not an easy task, and in many cases would require the applications to go beyond the rote learning and simple feedback structures they tend to currently follow. High focus ratings, on the other hand, are not difﬁcult to achieve. In fact, as focus is an indication of how varied an application is in its content and activities, a high focus rating is easier to achieve than a low focus rating as it simply means that the developer covers less content or fewer activities.

Table 5.5 shows that there are only two ‘Very High’ depth ratings across the sample, in the Reading and Instrument-Specific content areas. There are also only two instances of ‘Very High’ focus ratings, both of which are for the Instrument-Specific content area. The Instrument-Specific content area contains significantly more ‘High’ focus ratings than other content areas. However, depth ratings for Instrument-Specific are generally low, with the large majority of ratings being ‘Low’. This suggests that although applications which cover Instrument-Specific content tend to do so almost exclusively (i.e., with a very high focus), they do not cover the content to a particularly high depth (i.e., with a low depth). This pattern, though less pronounced across the other content areas, can be seen throughout the sample. For example, both the Reading and Rhythm content areas tend to be covered with either a ‘Low’ or ‘Medium’ focus, but only at a ‘Very Low’ or ‘Low’ depth. Table 5.6 shows the level to which the applications focus on each activity type, and the depth of knowledge assessed with that activity. Three activity types – Auditory Recognition, Visual Recognition, and Visual Playback, have a majority of ‘Very High’ focus ratings, meaning that applications tend to use this activity type exclusively, or almost exclusively. However, as with the content areas, a high focus does not indicate a high level of depth. Both Auditory Recognition and Visual Recognition have mostly ‘Very Low’ or ‘Low’ depth ratings, and Visual

114 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART 2 1 1 - 1 - - 1 -- 1 - -- -- 5 1 Depth Ratings 4 4 6 6 29 13 1 - 6 4 - 1 3 - 7 6 3 11 - 4 4 3 2 2 - -- 3 - 23 -- -- 1 - -- 2 11 Focus Ratings 13 12 12 - 1 5 9 3 1 - 2 - 3 6 The depth and focus ratings for each content area in the sample of iOS applications able 5.5: T Covered? No Yes Very Low Low Medium High Very High Very Low Low Medium High Very High 173 1 - 142 32 5 158 16 2 159 15 1 155 19 2 169 5 3 168 6 4 140 34 - eading Rhythm Scales Elements of Harmony Harmonic Structures Style Instrument-Speciﬁc HistoricalKnowledge and General Category R

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Playback largely receives ‘Medium’ depth ratings. This pattern of higher focus ratings and lower depth ratings can again be seen across the other activity types, though to a lesser degree. A breakdown of this data on a per-activity-type basis is provided in Appendix B.

5.3.3 Co-occurrence of Content and Activities

Key Outcomes:

• Reading + Rhythm, and Reading + Scales are the most commonly seen pairs of content areas • Visual Recognition + Auditory Recognition is the most commonly seen pair of activity types • No particular combination of activity types or content areas is typical across the sample The applications tend to present combinations of content areas appropriate for teaching users to read music notation (i.e., Reading, Rhythm, and Scales content). These content areas go well together and match well with Recognition-style activities, which are also particularly popular. When asking users to apply their knowledge, Recognition-style activities are most often used together. Both of these activity types are relatively simple conceptually, and fairly trivial to implement. As they involve asking the user to identify some element from either a visual or auditory list of options they are also easy to algorithmically assess. In terms of implementation, very little needs to change in the user interface between Visual and Auditory recognition activities – this may also be a reason for their high level of co-occurrence.

Figure 5.18 shows the co-occurrence of content areas within the sample. Overall, the links are weak, with very few content areas appearing together in the same application. The most frequently co-occurring content areas are Reading and Rhythm, and Reading and Scales. Rhythm and Scales, however, have only a moderate connection. Historical and General Knowl- edge does not co-occur with any other content areas. The co-occurrence of activity types, shown in Figure 5.19, follows a similar structure. Visual Recognition and Auditory Recognition activities are most commonly seen together, closely followed by both Recognition activities and Notation. Links between the remainder of the activity types are weak, generally with fewer than ﬁve instances of co-occurrence found. None of the activity types were found in isolation. These two co-occurrence graphs indicate that although there are a few strong pairings (i.e., Reading and Rhythm content, Visual Recognition and Auditory Recognition activities), there are no particular combinations of content areas or activity types that could be considered typical throughout the sample.

116 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART 2 1 1---- - 2---- - 5 36 Depth Ratings 14 1725 3 2 1 8 1 5 1 2 19 66 5 7 13 2 17 48 41 3 11 15 19 127 1 - 3 9 5 Focus Ratings 5 7 613 10 3 4 2 2 7 2 3 4 The depth and focus ratings for each type of activity in the sample of iOS applications able 5.6: T Covered? No Yes Very Low Low Medium High Very High Very Low Low Medium High Very High 121 53149 25 - 2 Recognition 133 41 3 Category Auditory Visual RecognitionAuditory DescriptionVisual Description 87Visual 166 Playback Memory Playback 8 87 161Notation 13 4 163 1 3 11 1

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Figure 5.18: Co-occurrence of content areas amongst the sample of applications. Bubble size indicates the number of apps which cover the content area; width of edges represents the number of times the connected content areas appear on together in the same app.

Figure 5.19: Co-occurrence of activity types amongst the sample of applications. Bubble size indicates the number of apps which use the activity type; width of edges represents the number of times the connected activity types appear on together in the same app.

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5.3.4 Common Application Characteristics

Key Outcomes:

• There are 25 characteristics exhibited by a large majority of the applications • Only one application had adaptive features The applications have several common features, including their achievement styles, progression styles, and use of feedback. This indicates that there is not a large amount of variety amongst the sample in terms of application design both generally and educationally. When completing activities it is most common for users to be able to set parameters to adjust the questions that they will see (e.g., “Only test my recognition of key signatures up to 4 sharps”). That is, most applications follow a manually adaptive progression model. This is not a result of non-adaptive models being superior but rather a side-effect of adaptive progression being more difficult to implement. Adaptive progression, if done well, would result in application content being tailored to the needs of each individual user, which would enhance or speed their learning. Only one application in the sample has an adaptive progression model. However, its implementation is simple and relies on using a set of predefined questions. As such, it exhibits few of the benefits of a more sophisticated adaptive model. Feedback is typically immediate. This could be for one of two reasons. Firstly, some studies have shown immediate feedback to be beneficial for learning, particularly in rote learning activities such as those often seen in the sampled applications. Alternatively, immediate feedback is simple to implement and can typically be shown as an augmentation on the user interface. Delayed feedback would require the creation of a summary screen, which adds both development time and complexity. Users are often shown a score to indicate their performance. As with immediate feedback, scores are simple to implement and can be shown as an annotation on existing user interfaces. They also require little explanation as most users would implicitly understand the concept of a score even if they don’t know exactly how points are assigned.

Several characteristics, shown in Table 5.7, were found to be common amongst the sampled applications. Each of the characteristics identified are supported, on average, by approximately 88% of the sample. The lowest level of support found is ~82%, and four characteristics are supported by 100% of the applications. Progression style is the least consistently supported characteristic. Although a significant proportion (i.e., ~73%) of the applications use the Manually-adaptive style, ~27% utilise other methods. Figure 5.20 shows the distribution of progression styles used, revealing that applications which do not use a Manually-adaptive style tend to have no progression or follow a linear model. Exactly one application in the sample – Music Reading Essentials [216] – is described as having an adaptive progression style. Music Reading Essentials contains a finite set of pre-written questions and uses the number of times a user has answered a question incorrectly to deter-

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mine the frequency with which that question should be repeated. This approach relies on the existence of a set of pre-defined questions within the application. As such, this implementation of the adaptive progression style does not represent a particularly significant enhancement over the manually adaptive alternatives. Although the identified characteristics receive strong support from the sample, there are outliers that go against the trends set by the large majority of applications. For example, two applications – Piano Dust Buster [229] and Piano Genius [254] – require an internet connection. Both applications are heavily based on users competing with other users from around the world or downloading core content (e.g., songs) on demand. Similarly, although a large number of applications include activities for users to complete, three applications in the sample contain only instructional content. These applications offer no method through which users can assess or test their knowledge, acting more as a ‘digital textbook’ than an interactive learning tool. A small number of applications (i.e., 6) crashed at least one time during the review process, earning them the label of unstable. However, this does not mean the remainder of the sample is without technical issues. For example, 37 applications in the sample exhibited significant malfunctions during use. Malfunctions may be minor as with Whack a Note [220], which occasionally does not register user input; they may also be major, as with Guitar for Kids Level 1 [221], which does not allow users to unlock progress beyond the initial set of activities. By a large margin, the most common achievement style is to provide users with a score indicating their performance on an activity. Applications which do not use this method tend to have no achievement indicators. A small number (i.e., 6 applications) use a star rating system instead. Very few applications follow a social sharing style, and only one follows the encouraged style. Of the 8 applications which do link to social platforms, there is an even split between the broadcast and direct methods. The large majority of sampled applications do not allow users to skip questions or have the answer(s) revealed. In cases where these actions are possible, it is rarely without consequence. Consequences typically come in the form of a reduction in the user’s score or in the application recording the question as having been answered incorrectly.

120 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART 31 (~18%) 6 (~3%) 14 (8%) 2 (~1%) - - 21 (12%) 6 (~3%) 12 (~7%) - - 11 (~6%) 3 (~2%) 13 (~7%) 24 (~14%) 9 (~5%) 8 (~5%) 26 (~15%) 29 (~17%) 48 (~27%) Number of Applications Supporting Outcome Not Supporting Outcome 169 (~97%) 173 (~99%) 175 (100%) 175 (100%) 154 (88%) 169 (~97%) 163 (~93%) 175 (100%) 164 (~94%) 172 (~98%) 162 (~93%) 151 (~86%) 166 (~95%) 167 (~95%) 149 (~85%) 146 (~83%) 127 (~73%) 144 (~82%) Common characteristics found within the sample of 175 iOS applications able 5.7: T Applications ...... do not support the transfer of... progress do to not another support device. switching from landscape... to are portrait able mode, to or support vice-versa. all functionality... without do an not internet exhibit connection. any bias against... right-handed do users. not exhibit any bias 161 against... (92%) left-handed do users. not use push notifications. ... do not contain bugs which cause them to crash. ... contain no offensive or age-restricted content. ... are not targeted towards any specific... age contain group. only activities which assess user’s... knowledge. do not repeat questions shortly after... asking do them. not allow users to reveal... the do answers not to allow questions. users to skip... questions. do not include links to social... platforms. provide feedback immediately. ... provide a score to indicate the... user’s allow performance users on to an manually activity. adapt their content. ... are available on both the iPad and iPhone. Measured Outcome support Use of devices handles-rotation internet-required rh-friendly lh-friendly push-notifications unstable game-center-integratedachievement-popups ...Content rating do not use game center. Target age group ... thatcontent-only use game center do not notify usersrepeats-questions of achievements they have earned.Answer revealable Question 12 skippable (100%) Social sharing style Feedback Achievement style Progression style Characteristic Device

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5.3.5 Other Application Characteristics

5.3.5.1 Background

Key Outcomes:

• Most applications are in the Music category of the iOS app store • Most applications require an upfront one-off payment, but are relatively low- cost • Once published, applications are not frequently updated • Applications don’t often receive reviews, but when they do they are generally positive The application developers tend to not consider their work to be educational, and rarely provide updates once it is initially published even when new versions of the target device’s operating system are released. This would indicate that developers do not consider their apps to be long-term or particularly lucrative projects, despite asking users to make an upfront payment. Although the application costs are relatively low, given their typically narrow focus users might need to purchase multiple applications to fulﬁll their needs. As such, multiple small purchases can easily stack into a larger investment. The lack of reviews for most of the sampled applications indicates that they do not have many users. This could be due to their narrow focus, lack of depth, infrequent or non-existent updates, or a saturation of the market. Unfortunately, there is no way to verify the number of downloads each application has received.

Application Store Category Figure 5.21 shows the distribution of primary categories developers have nominated for their applications in the iOS app store. Across the entire sample, three primary categories were nominated: ‘Music’, ‘Education’, and ‘Games’. The deﬁnitions of these categories are provided in Table 5.8. ‘Music’ is most commonly nominated, closely followed by ‘Education’; only a small number of developers have chosen to assign their application to the ‘Games’ category. This is broken down further in Appendix B.3, which details all sequences of primary, secondary, tertiary, and quaternary categories across the sample.

Monetisation Models Figure 5.22(a) shows that the large majority of applications in the sample use the Paid monetisation model, requiring some upfront payment from users. However, as can be seen in Figure 5.22(b), these applications fall within a relatively affordable price range with a median cost of $2.49 AUD. The next most popular monetisation model is In-app

Figure 5.20: Distribution of progression styles used by the sampled iOS applications

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Figure 5.21: Primary category nominated by the developers of the sampled applications

Table 5.8: Application store category descriptions provided by Apple Inc. [214]

Genre Description

Music Apps that are for discovering, listening to, recording, performing, or composing music, and that are interactive in nature. For example: music creation, radio, education, sound editing, music discovery, composition, lyric writing, band and recording artists, music videos and concerts, concert ticketing. Education Apps that provide an interactive learning experience on a speciﬁc skill or subject. For example: arithmetic, alphabet, writing, early learning and special education, solar system, vocabulary, col- ors, language learning, standardized test prep, geography, school portals, pet training, astronomy, crafts. Games Apps that provide single or multiplayer interactive activities for entertainment purposes. For example: action, adventure, arcade, board, card, family, music, puzzle, racing, role playing, simulation, sports, strategy.

(a) Distribution of monetisation models used by (b) Distribution of application prices, separated applications in the sample by monetisation model

Figure 5.22: The monetisation strategies used by applications in the sample

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purchases. These applications are also relatively affordable, particularly compared to those following a subscription model, with a median cost of $2.99 AUD. Very few applications are entirely free, receiving no money from users or advertisers. There are some outliers within the distributions. For example, Guitar Lessons - Rock Prodigy [243] is the most expensive application with in-app purchases, with one course costing $49.99 AUD, two courses costing $79.99 AUD, and all four courses costing $99.99 AUD. Piano Dust Buster [229] is also an outlier, offering a $38.99 AUD in-app purchase to unlock additional songs. The most expensive paid applications – Better Ears [215] and Piano Ultimate [258] – are signiﬁcantly cheaper, requiring only a one-off cost of $18.99 AUD each. Additional data was also collected regarding the price changes of applications over time. This is presented in Appendix B.4.

Development Activity Generally, software is updated over time with new features, ﬁxes, or quality improvements. The median number of updates to each of the sampled applications is 5. Figure 5.23 shows that half of the sample have 5 or fewer version changes, and some have never been updated. A small number of applications have greater than 20 updates. Three applications in total – Piano Melody Pro [235], Rhythm Sight Reading Trainer [249], and Piano Maestro [230] – have the highest number of updates seen in the sample, with 40 version changes each. Figure 5.24 shows the number of updates made across the sample of applications over time, in context with the release of major iOS versions. The timing of updates does not appear to coincide with any major updates to the iOS operating system. Prior to 2011, few updates were made. This is due to many of the applications in the sample simply not existing at this time. After this point updates are more frequent, particularly from 2013 to late 2015. More recently, the number of updates has dropped off.

Application Reviews All applications on the iTunes store are open to receiving publicly published written reviews, each of which is accompanied by a whole-number score from 1 to 5. Once 5 reviews have been submitted for an application the associated scores are combined into an aggregate. Figure 5.25 shows the distribution of aggregate scores for the sampled applications. None have received the maximum aggregate score of 5. However, the next highest aggregate rating (i.e., 4) is the most common, indicating that many of the sampled applications have been positively received. A small number have lower aggregate ratings, but most of the remaining apps simply have not received enough reviews to calculate an aggregate score. The number of applications which do not have enough reviews to receive an aggregate score is not surprising when examining the distribution of review counts across the sample. This is shown in Figure 5.26. As can be seen, most applications have received very few reviews. Most applications have received fewer than 10 reviews, and the median number of reviews is 4. Only a small number of applications have received more than 20 reviews, and even fewer still cross the line into triple digit counts. This can be examined further in Figure 5.27 which shows the same distribution with outliers removed. Piano Maestro [230] has, by far, the largest number of reviews, with 725 at the time of writing. Piano Dust Buster [229] is a distant second, with 291 reviews. Both of these applications have received mostly positive reviews, with aggregate ratings of 4 stars. They also both utilise the In-app purchases monetisation model. Three other applications – Glow Piano Lessons

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Figure 5.23: Distribution of number of releases for applications in the sample

[227], Piano Tutor for iPad [252], and Music Theory and Practice by Musicopoulos [253] – have also received over 100 reviews each. These are all published by different developers, and all follow the Paid monetisation model. These three apps have also received aggregate ratings of 4 stars.

5.3.5.2 Audience

Key Outcomes:

• Applications typically track performance data for just one user • Many applications do not have an instrument-based form of input • Applications that do have an instrument-based form of input tend to use either a digital replica or a real instrument – not both The application developers rarely implement user proﬁles in their work. This may be because they do not consider supporting multiple users to be a prior- ity, or simply because doing so adds undesired development time and complexity. As many devices have multiple users (e.g., a school classroom which shares a small number of iPads), this severely limits the utility of the applications, particularly in allowing users to see how they are progressing over time. Although the applications often use a digital replica of a piano for users to input note-based answers, this can not be considered a form of instructing users to play the instrument. That is, it can not be considered instrument-speciﬁc instruction. Rather, this is simply a popular approach for avoiding a complex and potentially confusing alternate user interface for selecting notes.

125 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART iOS 10.0 iOS 9.0 iOS 8.0 iOS 7.0 iOS 6.0 iOS 5.0 iOS 4.0 iOS 3.0 iOS 2.0 Frequency and timing of updates to applications in the sample, and major updates to the iOS operating system. Version updates do not appear to igure 5.24: F correlate with iOS releases.

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Figure 5.25: Distribution of aggregate review scores for the applications in the sample; a score of -1 indicates that an application had an insufﬁcient number of reviews to calculate an aggregate.

Figure 5.26: Distribution of the number of reviews for the latest version of each application in the sample

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Figure 5.27: Distribution of the number of reviews for the latest version of each application in the sample, with outliers removed

Use of Profiles Figure 5.28 shows the distribution of approaches taken by the sampled applications for user profiles. The most common approach – used by 128 of the applications – is to implement a Single profile, where the application supports data management for only one user on one device. Local profiles, used by 23 applications, are the next most frequently used approach. Applications supporting Local profiles allow users to identify themselves when the application starts (e.g., by logging in), and then stores progress and performance data for each unique user. Approximately 20 applications use no profiles. These are almost all apps which do not keep any progress or performance records, but some are apps which offer no activities for users to complete. A small number of applications use online profiles.

Figure 5.28: Distribution of approaches to proﬁles by the applications in the sample

Use of Instruments A signiﬁcant proportion of the applications have no obvious need for an instrument-based method of interacting with users. This is shown in Figure 5.29, which shows that 70 applications in the sample provide no such functionality. However, the remainder do support this interaction mode in some form. The most common approach is for the application to provide a digital replica of an instrument. This typically manifests as a piano keyboard being displayed on the screen, as shown in Figure 5.30, which users can tap to indicate the note(s) which form their answer. A smaller number of applications support physical instruments, often receiving input through the device’s internal microphone. An even smaller number allow users

Figure 5.29: Distribution of approaches to using instruments as input devices across the sampled applications

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to choose whether they would prefer using a digital replica or a physical instrument as the input device.

5.3.5.3 Feedback Model

Key Outcomes:

• Nearly all applications provide users with some kind of feedback • Visual feedback is used significantly more often than auditory feedback • If an application uses auditory feedback, it is most likely to use it consistently if it also uses visual feedback consistently • Most applications immediately tell users if their answer is correct or incorrect • Most applications do not compare a user’s performance to their own past performances or any other user’s performances Whilst applications typically provide users with feedback on their answers, this feedback is simple and rarely goes beyond simply telling the user whether they were correct or incorrect. Feedback does not extend to showing users how they are performing over time, or how their performance compares to other users. Users are rarely given any indication on how they could improve their skills, or details on where and how their answer was wrong. At most they are invited to continue answering until they are correct. Although limited feedback can be a mechanism for encouraging students to find answers on their own, in this case it is more likely to be evidence that developers are selecting the most simple option. More sophisticated methods of feedback would require gaining a perspective of how and where a user went wrong, what gap in the user’s mental model this reveals, and how to effectively address that gap. This is difficult and time-consuming to implement. Simple visual cues are often used to indicate the correctness of a user’s answer, but they are not always shown when expected. Visual feedback is most likely popular as it does not rely on the device’s sound being on. It can also be shown fairly simply and does not require the developer to design a suitable auditory cue.

Feedback Style and Type As discussed in Section 5.3.4, a common characteristic of the applications is that they provide feedback immediately. By combining this information with that in Figure 5.31(a), which shows that the large majority of applications utilise the Veriﬁcation feedback style, it can be said that most applications immediately indicate to users whether their answer is correct or incorrect but provide no additional guidance. This is further supported by Figure 5.31(b). The most common feedback types seen in the applications are Knowledge-of- response, Knowledge-of-correct-response, and Answer-until-correct. These are all similar, in that they’re centered on notifying users whether they are correct or incorrect, and differ only in whether they stop at that point (i.e., with Knowledge-of-response), provide the user with the correct answer (i.e., with Knowledge-of-correct-response), or require the user to keep trying until

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Figure 5.30: An onscreen piano keyboard used by Auralia Chord Recognition [244]. This is an example of on-screen use of instruments.

(a) Styles of feedback used by the sampled applications

(b) Types of feedback used by the sampled applications

Figure 5.31: Distributions of the styles and types of feedback used across the sample of applications

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they discover the correct answer for themselves (i.e., with Answer-until-correct). None of these feedback types offer additional guidance such as materials to help users understand why their answer was incorrect, or to assist them in finding the correct answer. Applications which do offer this extra information represent a small minority of the sample. A total of 9 applications offer no feedback. This is for one of two reasons. Firstly, the application may offer only informational content and no activities, in which case it has no need for a feedback mechanism. The other case involves applications made by Brainscape [218] which, as discussed in Section 5.2.4.2, require users to provide their own form of verification. Five of the feedback types identified by Mason and Bruning [123] and Shute [182] were not found in the sample at all. These are:

• Error-ﬂagging, • Hints-cues-prompts, • Bug-related, • Attribute-isolation, and • Informative-tutoring.

Use of Auditory and Visual Feedback Two possible indicators – visual and auditory – are used by the applications when providing feedback to users. However, these indicators are not utilised to the same degree. Visual feedback is by far more often employed, as shown by Figure 5.32 – a total of 129 applications use visual feedback compared to only 43 applications which use auditory feedback. Both types of feedback are used inconsistently. An inconsistent use of visual feedback might present as an application displaying a ‘success’ image on the screen when the user provides a correct answer, but neglecting to display any indication when the user’s answer is incorrect. For example, Jellybean Tunes [225] inconsistently uses both auditory and visual feedback. When the user correctly taps a note the correct pitch is sounded and the note fades from the screen. However, nothing occurs when the user taps an incorrect note. Visual and auditory feedback are not exclusive – one or both could be used in a single application. Table 5.9 shows how the uses of auditory and visual feedback co-occur within the sample. It can be seen that very few applications use neither type of feedback, and a very small minority use auditory feedback exclusively. A similarly small subset combine auditory feedback with inconsistent visual feedback. This data indicates that when visual feedback is used consistently, any auditory feedback is also likely to be consistent. However, when visual feedback is inconsistent, it is likely that any accompanying auditory feedback would also be consistent. The data makes clear the strong tendency towards using visual feedback, most frequently without any auditory components. This means that applications which use auditory feedback are likely to also use visual feedback, but not vice versa.

Comparison Style When providing feedback, most applications – as shown in Figure 5.33 – employ no (i.e., None) comparison style. Some applications, however, will provide a comparison to a user’s past performances. This may take several forms. For example, Better Ears [234] allows users to see how their scores and response speed has changed over time, using

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Figure 5.32: Use of auditory and visual feedback across the sample of applications

Table 5.9: Co-occurrence of uses of auditory and visual feedback within the sampled applications

Visual Feedback No Yes Inconsistent Auditory Feedback No 10 76 15 Yes 4 35 4 Inconsistent - 18 13

Figure 5.33: Comparison styles used across the sampled applications

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Figure 5.34: Evolution of user’s performance as shown in Better Ears [234]

graphs such as those shown in Figure 5.34. Bass Guitar Trainer [217] takes a more overt approach, displaying a notiﬁcation – shown in Figure 5.35 – that must be dismissed when the user achieves a new high score. Very few applications compare performances between local or global users. However, this is a side-effect of the Use of Proﬁles characteristic, which revealed that few applications support multiple users on the same device or offer online functionality.

5.3.5.4 Incentive and Achievement Model

Key Outcomes:

• Most applications only allow users to wipe all progress records If applications offer any mechanism for managing progress records, it tends to be only in the form of deleting all records. This could be because the developers do not consider a more granular process to be desirable, or because they do not want to spend the time implementing such a feature.

Score Management When offering users the ability to manage their score history, Figure 5.36 shows that if any score management method is implemented it is likely to be Reset-all, which allows users to wipe all score data. A small number of applications allow users to reset scores on an activity-by-activity basis, and an even smaller number offer both methods. If no method is offered, the only way for users to reset the application is to uninstall and reinstall it.

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Figure 5.35: New high score notiﬁcation used by Bass Guitar Trainer [217]

Figure 5.36: Score management strategies offered by applications in the sample

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5.3.5.5 Progression Model

Key Outcomes:

• Most applications support uni-structural learning outcomes As the applications tend to only cover one aspect of musical knowledge to a low depth, they naturally result in low-level learning outcomes for users. Few applications reach a multi-structural level, where users understand multiple aspects of a topic. These levels of learning outcomes are a natural side effect of the applications covering content to a low depth and providing limited types of feedback.

Learning Outcome Figure 5.37 shows that the large majority of applications operate at a low level of learning outcome. A total of 132 applications operate at the Uni-structural level, meaning that they assist users in achieving a basic understanding of one aspect of a topic. A small number of applications operate at a Multi-structural level, and the remainder of the sample operate at a Pre-structural level. The Relational and Extended abstract learning outcomes are not seen in any of the sampled applications.

5.3.6 Characteristic Tags

Key Outcomes:

• Most applications have the same set of characteristic tags • Co-occurrence amongst the characteristic tags is high Most applications are assigned a similar set of characteristic tags, meaning they tend to be similar in functionality and educational features regardless of the musical knowledge they focus on. This also means that the tags naturally have a high co-occurrence. Most of the tags are present in only a small subset of the sample, indicating that developers err on the side of choosing to not implement features or add complexity to their work.

5.3.6.1 Tag Presence

Table 5.10 shows the number of applications with each of the characteristic tags deﬁned in Section 5.2.4.5. Throughout the sample the tags are rarely divisive – applications all tend to have the same set of tags.

Figure 5.37: Learning outcomes of the sampled applications

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Table 5.10: Presence of characteristic tags across the sample

Tag Number of Apps Yes No

rh-friendly 175 - lh-friendly 175 - content-only 3 172 push-notiﬁcations 21 154 game-center-integrated 12 163 internet-required 2 173 unstable 6 169 handles-rotation 14 161 repeats-questions 13 162 saves-scores 122 53 ipad-support 160 15 iphone-support 159 16

5.3.6.2 Tag Co-occurrence

Figure 5.38 shows the co-occurrence of characteristic tags amongst the sample. The lh-friendly and rh-friendly tags have been omitted as they apply to all of the sampled applications. It can be seen that the most commonly seen tags – iphone-support, ipad-support, and saves-scores – are strongly connected with one another due to their prevalence amongst the sample. The remainder of the tags are not as strongly connected, simply as a result of their lack of prevalence amongst the sample. No tags were found in isolation.

5.4 Discussion

Overall, iOS applications for teaching and practicing musical skills tend to be narrow in focus, shallow in depth, simple in design, and poorly supported by their developers. As a result of this, the applications do not appear to have many users, as suggested by their generally small number of reviews. In every aspect of the results, developers seem to have trended towards making choices that simplify and reduce development time and complexity. This has led to a lack of depth in covering musical knowledge, low-level learning outcomes, and lack of sophisticated feedback across the sample. It also means that there are no applications which tailor their feedback or content to the user. Instead, they rely on basic score mechanisms and allowing users to manually set the parameters of the content they will see. Despite all of this, the developers still generally charge an up-front fee for their work. Together, these results combine to reveal a large number of gaps in the field. Few of the applications provide much instructional content, and what is provided could benefit from expert guidance in designing educational material. Many of the applications would also benefit from a more consistent use of feedback and more sophisticated feedback types. For example, if a user is asked to identify the B major key signature from a list of four options and selects the wrong answer, instead of simply telling the user they are wrong the application could show them how to determine the number of sharps or flats in any key signature. Progression models across the sample are limited, with the most sophisticated offerings being those where users can set the parameters of the content. Unfortunately, this is a task users may not be suited to

136 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART Co-occurrence of characteristic tags amongst the sample of applications. The size of each bubble indicates the number of apps with a tag; the igure 5.38: F width of the edges represents the number of apps the connected tags appear on together.

137 CHAPTER 5. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART

given that they are still learning the content. Adaptive progression models present a significant improvement over this, as content would be automatically tailored to the user’s individual misunderstandings. Many of these gaps could be solved algorithmically to great effect, but this has not yet been done. Whilst notation reading skills are heavily covered, many other aspects of musical knowledge are ignored. For example, identifying chord progressions within existing music is rarely covered, nor is creating aesthetically pleasing progressions from scratch. No application covers the principles of melody writing, or instrumentation and orchestration. Instrument-specific instruction rarely goes beyond identifying single notes on an instrument or providing fingering charts for specific notes or chords. One aspect of instrument-specific instruction that is not covered at all is the skill of musical sight reading. As discussed in Chapter 1, this is an important skill and one that suffers from a lack of practice material. This presents a gap that is highly suitable for an algorithmic solution, the development of which is a major goal of this thesis. Such a solution would require a set of parameters to guide the generation of sight reading exercises. The selection of these parameters presents a significant opportunity for an adaptive progression model. Neither of these capabilities have yet been seen in the field.

5.5 Summary

This chapter has shown that there are a number of significant gaps in applications for teaching and practicing musical skills, specifically on the iOS platform. The applications tend to be narrow in focus and shallow in depth, as well as resulting in low-level learning outcomes. There are few places where technology is used to its full potential, despite there being many opportunities for doing so. For example, adaptive progression models, which would automatically cater content to user’s needs, are not seen. Similarly, there are many cases where activities could be algorithmically generated, resulting in a greater variety of content. However, this idea is rarely seen applied. One of the gaps identified was the practice of musical sight reading. Multiple opportunities for improvement exist in this space, including creating an algorithm for generating activities. There is also the potential for applying a completely adaptive progression model to select the parameters for this algorithm. The next chapters will describe the requirements, design, and development of a system capable of closing these gaps, as an example of how technology can be used more effectively in the deliberate practice of musical skills.

138 6 An Algorithm for Generating Musical Sight Reading Exercises

6.1 Overview

In the previous chapter a number of significant gaps were identified in mobile applications for teaching and practicing musical skills. One gap was particularly prominent: the ability to learn and practice music sight reading. As discussed in Chapter 1, there is a significant resource constraint in this area. Given that deliberate practice is key to gaining competence in sight reading, this resource constraint is a large barrier for musicians seeking to develop this skill. This chapter describes an algorithm for generating musical sight reading exercises for monophonic instruments. Polyphonic instruments are considered to be out of scope in order to reduce the complexity of the solution space. However, the potential to extend this solution to polyphonic instruments was considered during its development. The overall goal of the algorithm is to generate new sight reading exercises that are of a specific difficulty level and which contain certain technical characteristics, whilst remaining both playable by a human and aesthetically pleasing. This goal differs from examples of melody generation in the literature, which typically focus only on the aesthetics of the output. To achieve this goal, evolutionary algorithms (EAs) will be applied. There are three primary reasons for this choice. First, Biles [22] notes that evolutionary approaches have been applied to melody generation problems more often than any other technique, and with more success. Secondly, the solution space when generating a melody is large, and evolutionary algorithms are well suited to navigating that space [81]. Lastly, evolutionary algorithms allow for specific goals to be set for a solution whilst still providing space for random elements and emergent behaviours to appear. This means that the solutions found by the algorithm are likely to maintain a higher level of variability compared to other methods, even when using identical configurations. Section 6.2 provides an overview of the general process followed by evolutionary algorithms. In order to apply the algorithm to the generation of sight reading exercises, a novel method of representing melodies was required. This is because existing solutions within the literature do not support critical functionality required for this task. A proposed novel representation method is described in Section 6.3. Sections 6.4 to 6.9 then detail how the general

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evolutionary algorithm was implemented for the speciﬁc application of generating musical sight reading exercises for monophonic instruments.

6.2 Evolutionary Algorithms

6.2.1 Introduction

Evolutionary algorithms (EAs) are analogous to the natural evolutionary process, in that a population is improved over time through the application of natural selection and reproduction [171]. Russell and Norvig [171] describe EAs as being similar to a stochastic beam search, as both are hill climbing techniques combined with elements of random exploration1.

6.2.2 The Evolutionary Process

Figure 6.1 shows the general process followed by evolutionary algorithms. An EA begins with a randomly generated set of candidate solutions, referred to as a ‘population’, then follows an iterative process until some termination criteria is met. This iterative process involves generating a series of new candidate populations, each of which is based on the previous. The aim is that over time the populations will contain incrementally superior solutions to those in previous populations. First, all candidates are measured for their suitability as a solution and assigned a corresponding numerical value (i.e., fitness value). The top n best or ‘elite’ candidates (where n can be 0) are then directly copied into the next population without any alterations. The remainder of the new population is formed through the application of the genetic operators crossover and mutation, described further in Section 6.2.3. Once the new population has reached its target size, the termination criteria are checked. If they have been met, the candidate with the highest fitness over all iterations is returned as the solution. If not, the process is repeated. The algorithm requires a number of aspects be defined:

Population size The number of candidate solutions in a population. If this value is too small the algorithm may converge on a suboptimal solution due to lack of diversity. However, if this value is too large the algorithm may take an excessive amount of time to ﬁnish.

Termination criteria When the algorithm should stop. It is typically a target fitness value, a specific number of iterations, a number of iterations without improvement, or a combination of the three. For example, target a fitness of 0.95, but if it hasn’t been reached within 1000 iterations terminate the algorithm anyway.

Fitness function A numerical measure for quantifying the suitability of a candidate solution. This dictates the likelihood that a candidate will be selected to be part of the next population.

1This comparison is only valid if the evolutionary algorithm uses elitism. Without this mechanism it can not be described as a hill climber.

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Generate new Start population

Create random Measure ﬁtness initial population

Copy elites to new population Is the termination Yes criteria satisﬁed?

Is the new Yes No population big enough?

Generate new Save best population candidate No

Select two candidates from previous population

Finish Apply crossover to generate 2 children

Should mutation be Yes Apply mutation to applied to the the 1st child 1st child?

Should mutation be Yes Apply mutation to applied to the the 2nd child 2nd child?

Copy children into new population

Finish

Figure 6.1: The general process followed by an evolutionary algorithm. Recreated from [233]. Note that the number of parent candidates selected and the number of children generated depends on the operator. This example shows two parents generating two offspring. 141 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Number of elites The number of top candidates from the previous population that will be directly copied to the new population without any adjustments.

Selection method The method for selecting candidates for the crossover operator. Typically a function of each candidate’s ﬁtness value.

Probability of mutation How likely it is that candidates resulting from the crossover operator will be mutated.

Candidate representation How each candidate is encoded.

The speciﬁc values and techniques used for these items with the goal of generating musical sight reading exercises for the ﬂute are described in Chapter 7.

6.2.3 Genetic Operators

6.2.3.1 Overview

Genetic operators are used to create new populations. Whilst their general structure is similar across problem domains, their speciﬁc implementations are based on the representation method of the candidates. In this implementation two genetic operators, crossover and mutation, are used. Crossover is a reproduction method used to create candidates by combining elements from two ‘parents’ from the previous population. The mutation operator applies small random changes to a candidate in order to introduce diversity into the population. Crossover and mutation operators are generally applied based on a probability of occurrence. The probability of applying mutation is typically low (e.g., 1 in 1000) to avoid introducing a detrimental level of randomness into the solution space. Sections 6.2.3.2 and 6.2.3.3 describe the general structure of the crossover and mutation operators, respectively. Their speciﬁc implementations for the application of generating musical sight reading exercises are provided in Sections 6.4.1 and 6.4.2.

crossover point

parent a a` a`` parent b b` b``

child a`b`` a` b`` child b`a`` b` a``

Figure 6.2: A crossover operation between two candidates. This implementation does not preserve length.

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crossover point

parent a a` a`` parent b b` b``

child a`b`` a` b`` child b`a`` b` a``

Figure 6.3: A crossover operation between two candidates where crossover points have been selected such that the results are of the same length as each other and their parents. In this case the crossover point selected is in the middle. However, other points could be selected as long as the resulting children are of the same length as the parents.

6.2.3.2 Crossover

Two candidates, a and b, are selected. A crossover point is randomly chosen in each such that they are both split into two, not necessarily equal, halves. Two new candidates are then created: one using the first part of a and the second part of b, and the second using the second part of a and first part of b. This process is shown in Figure 6.2. Depending on the structure of the candidates and the goals of the algorithm, it may be necessary to select crossover points such that the parts of a and b, when combined, create new candidates of the same length or size as their parents. This is shown in Figure 6.3. The implementation of crossover depends on the structure of the candidates. The structure used in this work is described in Section 6.3 and the specific implementation of crossover is defined in Section 6.4.1. It is important to note that this is just one example of a crossover operator – other implementations are possible.

6.2.3.3 Mutation

Mutation applies a small random change to the structure or internal values of a candidate. The possible changes are typically speciﬁc to the problem domain, thus in this case are based on musical parameters. The mutations used in this work are described in Section 6.4.2.

6.3 Melody Representation

6.3.1 Overview

Many published works in the ﬁeld of melody generation are not clear on how melodies are represented. However, two primary themes emerge: tree-based and sequential structures [22]. This is true for works which both do and do not utilise evolutionary algorithms. Sequential structures, such as that used by Acevedo [1], represent melodies as ordered lists of musical elements. These musical elements are typically individual notes and rests, with each having a length and (where appropriate) a pitch. Pitches can be represented absolutely (e.g., C4), or as an offset from some epoch. Length can also be represented absolutely (e.g., crotchet), or as a time offset from the start of the melody. In some cases, elements may also

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contain a record of ornamental information such as dynamic or articulation markings. Melodies represented this way are read by examining the sequence of musical elements in order. Regardless of the specific encoding scheme, sequential structures are not an ideal choice for an evolutionary algorithm. This is particularly true in this work, where the desired result is a melody of an explicit, fixed length. The practical reason for this lies in the crossover operator. As described in Section 6.2.3.2, the crossover operator swaps sections of two parents to create two new candidates. When using a sequential structure, it is easy for the newly created candidates to have different lengths, simply by choosing asymmetrical crossover points. It is also easy for crossover to create candidates whose note and rest sequences do not fit neatly into entire bar lengths. For example, if two 4-bar parents were selected, while asymmetrical crossover could result in two children with 4-bar lengths it is much more likely to create two children with different lengths and partially complete bars (e.g., 3.4 bars and 4.6 bars). Symmetrical crossover would eliminate this problem. However, it would also severely reduce the variety of new candidates that could be created, as the crossover points in each parent would always need to be symmetrical. Whilst not without fault, tree-based structures avoid this problem entirely. As such, they are used in this work. Section 6.3.2 will describe the functionality already supported by published tree-based structures. The limits of these structures are then described in Section 6.3.3, and a new novel structure which overcomes these limitations is provided in Section 6.3.4.

6.3.2 Melody Trees in the Literature

In the literature, tree-based solutions for melody representation typically follow a binary structure where each node represents a musical element with half the duration of its parent node. This means that the structure of a melody tree adheres to the duration hierarchy shown in Fig- ure 6.4, where the length of a note is entirely dependent on its depth within the tree. Generally the root of the tree represents the entire melody, with nodes in the ﬁrst layer representing individual bars. From this point onwards each additional layer of depth splits node durations in 4 two. For example, in a 4 melody nodes with a depth of 1 would represent semibreves, nodes with a depth of 2 would represent minims, nodes with a depth of 3 would represent crotchets, and so on. Within this structure only leaf nodes represent concrete musical elements (either notes or rests) that would be directly represented on a score. Internal nodes, at a minimum, serve to maintain the duration hierarchy. However, some implementations of melody trees also assign some or all internal nodes special meaning in order to support additional functionality. When interpreting a melody tree, leaf nodes on the left are typically played before leaf nodes on the right. Rizo et al. [168] deﬁned a simple tree representation for melodies which adheres strongly to this binary structure. The work was originally created with the goal of enabling faster comparison of melodic lines. However, the proposed tree structure can be used independently, and has been successfully applied by Rowe [170] in the creation of BlueJam, a system for evolving solo melodies in the blues scale. It has also been applied by Esp´ı et al. [56] for evolving melodies based on a set of training data. Figure 6.5 shows how this tree structure would be 4 used to represent a simple, one-bar melody in 4 time. Each leaf node in the tree represents a single note or rest in the melody. The depth of each leaf node determines the length of its

144 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Figure 6.4: The duration hierarchy typically used by tree structures which are designed to represent melodies in common time. The bottom row of semiquavers has been truncated for space, and the right-hand side of the tree is not shown to completion as it is identical to the left.

musical element, and leaves are annotated to indicate the pitch of the note (e.g., ‘D’, ‘E’, ‘F’), or whether the note is a rest (i.e., ‘r’). Reading the leaf nodes from left to right reveals the intended sequence of notes: a quaver rest, a quaver D, a crotchet E, and a minim F. Representing dotted notes according to this solution requires multiple leaf nodes to be combined. This is achieved with a simple annotation on the ﬁrst node in the combination, as shown in Figure 6.6. The annotation is represented by the ‘+’ character, indicating the two connected nodes should be combined in value when interpreting the tree. Again, the leaf nodes are read from left to right, resulting in a sequence of quaver rest, quaver D, crotchet E, dotted crotchet F (from combining a crotchet and quaver), and quaver E. Only nodes one layer of depth apart and originating from the same subtree can be connected (i.e., combined). For example, the F and D can not be combined as they do not share the same parent minim node. Dahlstedt [47] later proposed a more complex and free-form melody tree structure which supports recursive elements. It was originally designed for an interactive musical installation capable of generating an endless stream of 60 to 90 second musical pieces from scratch, based on its own previous output, or based on some human input. As with the tree proposed by Rizo et al. [168], this tree can be used independently. The tree follows a binary structure where only leaf nodes directly map to elements on the score. However, this tree differs from that proposed by Rizo et al. [168] in that all internal nodes are operators which determine how their subtrees are to be interpreted. The tree also differs in that the length of the musical elements represented by leaf nodes are not dictated directly by their depth within the tree. Instead, each leaf is assigned an explicit duration. This means that sibling nodes do not necessarily have the same length. All internal nodes represent either a splice (S) or union (U) operator. The splice operator indicates that musical elements in a node’s subtree should be concatenated – in other words, played in sequence. In comparison to this, the union operator indicates that the musical ele-

145 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Figure 6.5: A simple melody and its corresponding tree using the melody tree proposed by Rizo et al. [168]

Figure 6.6: A melody with a dotted note and its corresponding tree using the melody tree proposed by Rizo et al. [168]. The ‘+’ symbol indicates the origin node of the combine operator.

146 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

ments in a node’s subtree should be merged – that is, they should be played together. These two operators can be combined to represent reasonably complex polyphonic melodies.

Figure 6.7 shows an example of a melody tree using the structure proposed by Dahlst- edt [47]. As mentioned earlier, one major difference between this tree and that proposed by Rizo et al. [168] is that node durations are defined on a per-node basis, independently of one another. That is, node durations can be of any value, and the duration of one node can not influence the duration of any other node. This means that the resulting melody can be of any arbitrary length, and may not fit neatly into a standard time signature. This is not shown in the example in Figure 6.7, as the melody has deliberately been constructed to fit into a single bar 4 of 4 time. The melody tree proposed by Dahlstedt [47] also allows for recursive elements. This means that the structure explicitly supports the representation of self-similar elements within a melody. Internal nodes in this style of tree can, in addition to being a splice or union operator, optionally be a repeat operator. This operator identifies the subtree that is to be repeated, as well as denoting the number of times the repetition should take place.

Figure 6.8 provides a simple example of a recursive tree and how the recursive elements would be expanded. The repeat operator indicates the subtree to repeat and where the repeat should be placed. In effect, this means an entire subtree is copied and inserted back into the tree at the speciﬁed location. For example, in Figure 6.8(a), the entire subtree of the melody is to be repeated (i.e., copied), and inserted at the position of the node representing the pitch ‘G’. The repeat annotation is moved to the new subtree, and the number of repetitions is reduced by one, resulting in the tree shown in Figure 6.8(b). The process is then repeated until there are no repeats left.

Dahlstedt [47] also describes a number of modiﬁcations that can accompany the repeat operator. For example, it might also include instructions to transpose the pitches in the subtree when it is copied to its new location. Other possible modiﬁcations include altering the durations or volume of notes, or adding articulation markings.

Work by de Leon´ et al. [50] represents a mid-point between the melody tree structures proposed by Rizo et al. [168] and Dahlstedt [47]. It makes use of operators on internal nodes, but also follows the duration hierarchy in Figure 6.4.

Two operators are deﬁned, split (S) and continuation (–). The split operator is the same as the splice operator used by Dahlstedt [47], in that it indicates that musical elements in the node’s subtree should be concatenated (i.e., played in sequence). The continuation operator indicates that the previous note should be extended in length according to the value represented by the connected node. This enables representation of both dotted and tied notes.

Figure 6.9 shows an example of how a melody would be represented using the tree proposed by de Leon´ et al. [50]. Examples of dotted and tied notes are shown, both of which require use of the the continuation operator (i.e., ‘–’). Note durations are dictated by the node’s depth within the tree, and the split (i.e., ‘S’) operator is used to indicate that the subtree’s notes should be played in sequence. It can be seen that elements from the two previously discussed trees are present: the duration hierarchy used by Rizo et al. [168] and the idea of internal node operators used by Dahlstedt [47].

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Figure 6.7: A simple polyphonic melody and its corresponding tree using the melody tree proposed by Dahlstedt [47]. ‘S’ represents the splice operator, and ‘U’ represents the union operator.

6.3.3 The Case for a Novel Melody Tree

Table 6.1 shows a comparison of the characteristics of the melody trees in the literature. All of the trees are able to represent monophonic melodies and dotted notes. Additionally, all three representations allow for subtrees from two different melodies to be swapped at any point, regardless of their original depth, without breaking the tree structure. As described in Section 6.3.1, this is an important characteristic for implementing the crossover operator. The trees proposed by Rizo et al. [168] and de Leon´ et al. [50] both support simple time 4 2 signatures – that is, time signatures such as 4 and 4 where measures can recursively be divided into equal halves without the need for dotted notes. However, neither of these trees support 3 6 9 compound time signatures such as 4, 8, and 8, where measures do not neatly ﬁt into a binary structure. Dahlstedt’s tree is noted as supporting neither simple nor compound time. This is due to the fact that the tree does not structure its nodes according to a duration hierarchy. Instead, it assigns the duration of nodes individually and independently of one another. A time signature

Table 6.1: A comparison of the features of the melody trees proposed in the literature

Feature Rizo et al. [168] Dahlstedt [47] de Leon´ et al. [50] Monophony Polyphony Dotted notes Tied notes Irregular divisions Simple time Compound time Maintain musical grammar Crossover anywhere

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(b) After expanding the ﬁrst recursive (a) Initial recursive melody tree layer

Figure 6.8: Expanding a recursive melody tree using the structure proposed by Dahlstedt [47]

149 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES ´ on et al. [50] A simple melody and its corresponding tree using the melody tree proposed by de Le igure 6.9: F

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is applied to the melody when translating it to a score rather than within the tree itself, and the melody has no guarantee of ﬁtting within the chosen time signature. This means that Dahlstedt’s tree, unlike the trees of Rizo et al. [168] and de Leon´ et al. [50], also does not maintain a musical grammar. That is to say, it can not guarantee that the melody represented will ﬁt neatly into any particular time signature. None of the melody tree structures discussed support irregular divisions such as triplets or tuplets. This severely limits their ability to represent melodies. Rizo’s tree has an additional problem, in that it does not offer a mechanism for representing tied notes. For representing sight reading exercises a melody tree would, at a minimum, need to support:

• monophonic melodies, • dotted notes, • tied notes, • triplets, • simple time signatures, • compound time signatures, • enforceable musical grammar, and • swapping of subtrees at any point.

Additional features that would be useful for representing melodies include support for

• polyphonic melodies • multiple time signatures in one melody, • ornamental and stylistic markings (e.g., mordents, trills), and • additional irregular divisions (e.g., duplets, any variation of the ‘x in the time of y’ pattern).

These additional features are not necessary for the task of generating sight reading melodies for the ﬂute, as is the goal of this thesis, and thus are left as future work. None of the trees in the literature surveyed supported the necessary combination of minimally viable features. As such, a novel melody tree was created that would meet this criteria. This novel tree is described in Section 6.3.4.

6.3.4 Designing a Novel Melody Tree

Several of the minimally viable features for a melody tree identiﬁed in Section 6.3.3 are already supported in existing trees. This is capitalised upon by taking elements from existing trees where possible then adding the additional, missing functionality necessary for representing musical sight reading exercises. Of the trees in the literature, that proposed by Rizo et al. [168] offered the most desired features2, thus will act as a starting point for a novel tree. The features covered by this tree include support for:

2Table 6.1 shows that Rizo and Dahlstedt’s trees have the same number of features. However Rizo’s tree supports simple time and the maintenance of musical grammar. These are desired features which Dahlstedt’s tree does not offer, making Rizo’s tree a more suitable starting point.

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• monophonic melodies, • dotted notes, • tied notes, • simple time signatures, • enforceable musical grammar, and • swapping subtrees at any point.

This leaves two key features absent:

1. Support for compound time signatures 2. Support for triplets

The implementation of these two features is discussed in Sections 6.3.4.1 and 6.3.4.2, respectively.

6.3.4.1 Supporting Compound Time Signatures

The ability to swap subtrees at any point whilst enforcing musical grammar is entirely due to a tree following a duration hierarchy as described in Section 6.3.2. Unfortunately, this encourages a binary structure, which is not ideal for representing compound time signatures. For example, 3 to represent a melody in 4 time, splitting bars equally would result in the ﬁrst layer of nodes representing dotted crotchets. Continuing this pattern, the following layer would contain nodes representing half that value again – a dotted quaver. The next layer would represent dotted semiquavers, then dotted demisemiquavers, and so on. This pattern, shown in Figure 6.10, results in a structure where node lengths are unnecessarily complex, and individual nodes do not represent lengths commonly found in melodies (i.e., non-dotted lengths). An alternative strategy might be to split any compound-lengthed node into two non- 3 equal but more typical lengths. Returning to the example of a melody in 4 time, this would result in the ﬁrst layer being a combination of a minim and crotchet node. The next layer would then comprise two crotchet nodes (from splitting the minim) and two quaver nodes (from splitting the crotchet) as shown in Figure 6.11. This approach presents two problems. Firstly, it breaks the duration hierarchy which requires that all nodes at the same depth have the same length. This complicates the continuation operator as no assumptions can be made regarding a node’s length with respect to its depth. Additionally, it adds more complexity when swapping subtrees in ensuring nodes are reassigned the correct length given their new depths. Secondly, it introduces a decision regarding which node should be left-most in the tree 3 – the longer or shorter of the split? For example, when splitting a 4 bar should the minim or crotchet node be left-most? This choice informs how elegantly a melody can be represented and how often continuation operators need to be used to form longer note lengths. n The solution to these problems is for bars of a time signature m be split into n nodes of m length, where m indicates the number of that length note required to equal the length of a semibreve. So, m = 1 indicates a semibreve, m = 2 indicates a minim, m = 4 indicates a crotchet, and so on.

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Melody

etc.

Figure 6.10: A potential duration hierarchy for ﬁtting a compound time signature in an un- modiﬁed binary tree

Melody

etc.

Figure 6.11: An alternative approach to ﬁtting a compound time signature into an unmodiﬁed binary tree

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This strategy means that the second layer of a melody tree is non-binary, but the remainder is. Unfortunately, this gives rise to one problem. In order to successfully implement the crossover operator, it must be possible to swap any subtree from one melody with any subtree from another. This is an issue when the second layer of the tree is non-binary, as the parent node of a non-binary layer (i.e., the node representing a single bar) may be swapped with the parent node of a binary layer. As shown in Figure 6.12, this is difficult to resolve even in simple cases. The solution to this problem is to remove the layer of ‘bar’ nodes entirely, meaning that the tree starts with a layer containing n ∗ number of bars nodes of m length. This means that the first layer of the tree may contain many nodes, but every one of those nodes is binary with child nodes that have lengths exactly half of their parent. Additionally, because the value of ‘m’ is taken from the time signature, it is guaranteed to be a length which can be recursively split into two equal, non-compound halves. Within the crossover operator, swaps only occur between subtrees. Therefore the root node is never touched, meaning swaps are only made between nodes of the first layer and below. By removing the layer of bars, only binary nodes will ever be selected to trade places. This means the duration hierarchy can easily be maintained whilst still enforcing musical grammar. Additionally, notes longer than m can still be represented through the use of one or several linked continuation operators.

6.3.4.2 Supporting Triplets

Triplets are implemented with an internal node operator similar to the split and continuation operators used by Dahlstedt [47]. As shown in Figure 6.13, the triplet operator is placed on the ﬁrst direct parent of the triplet leaf nodes. If all leaves within the triplet are of the same length, the triplet operator is placed one layer above. However, if the leaves within the triplet are of different lengths, the triplet operator is placed on the ﬁrst common parent. The triplet operator does not break the duration hierarchy, nor does it restrict the swapping of subtrees. If the triplet operator itself is selected to be swapped, the entire triplet is moved. If a subtree within the triplet is selected to swap, notes within that subtree will – as- suming they are swapped to a non-triplet parent node – be interpreted as having a standard, non-triplet length. Conversely, the subtree swapped into its place will then be interpreted as part of the triplet. This is shown in Figure 6.14.

6.4 Genetic Operators for Evolving Sight Reading Exercises

6.4.1 Crossover

The implementation of crossover is reasonably straightforward. First, two parent candidates are selected using the method described in Section 6.5. Then, a node from the melody tree of each candidate is randomly picked. The subtrees starting from these nodes are taken from each parent and their positions are swapped. An example of this is shown in Figure 6.15. Once the subtrees are swapped, the durations of their nodes are altered with respect to their overall depth within their new tree. For example, the subtree from the ﬁrst parent melody in Figure 6.15 is placed one layer higher, so its durations are doubled. Similarly, the

154 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Crossover point = Melody

D D C cont. C

C D r E

(a) The ﬁrst parent melody tree with crossover point highlighted

Crossover point = Melody

C D E D C

D E

(b) The second parent melody tree with crossover point highlighted

Melody

D E D C C ? ? cont.

(c) The result of placing the subtree from the second melody at the crossover point in the ﬁrst melody. The root node is reassigned to a dotted minim length, but it is not clear what length its children should be given.

155 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Melody

C D E D C

D ? ? ?

C D r E ? ? ? ?

(d) The result of placing the subtree from the ﬁrst melody at the crossover point in the second melody. The root node is reassigned to a crotchet minim length, but it is not clear what lengths its children and grandchildren should be given.

Figure 6.12: Attempting to apply the crossover operator between binary and ternary points in two parent melody trees

Melody

t F F combine

r D E

Figure 6.13: A melody tree containing a triplet

156 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Crossover point =

Melody

t F

C D E

(a) The ﬁrst parent melody tree

Crossover point =

Melody

C D E F

(b) The second parent melody tree

157 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Melody

t F

C D

E F

(c) The result of placing the subtree from the second melody at the crossover point in the ﬁrst melody. Note that the subtree is now part of the triplet.

Melody

C D

(d) The result of placing the subtree from the ﬁrst melody at the crossover point in the second melody. Note that the subtree is no longer interpreted as part of a triplet.

Figure 6.14: Applying the crossover operator where one crossover point is part of a triplet and the other crossover point is not

158 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Crossover point = Melody

F G F

A G

(a) The ﬁrst parent melody tree

Crossover point = Melody

F F cont.

F A G A

(b) The second parent melody tree

159 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Melody

F G F

G A

(c) The result of placing the subtree from the second melody at the crossover point in the ﬁrst melody. Note that the subtree is now placed one layer lower, so the duration of each node has been halved.

Melody

A F F cont.

F A

(d) The result of placing the subtree from the ﬁrst melody at the crossover point in the second melody. Note that the subtree is now placed one layer higher, so the duration of the node has been doubled.

Figure 6.15: Applying the crossover operator

160 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

subtree from the second parent melody is placed one layer lower, so its durations are halved. No additional alterations are made. This simple implementation is possible because the melody tree representation ensures that no matter which subtrees are swapped the resulting melody trees will still be grammati- cally correct. Additionally, the length of the melodies remains ﬁxed as the node durations are adjusted according to their new depths.

6.4.2 Mutation

The purpose of a mutation operator is to make a small change to a candidate. As the candidates in this work are melodies, the potential mutations are musical in nature and speciﬁc to the domain. One alteration type is randomly selected from the following:

Change note type Randomly select a leaf node. If the node represents a note, change it to a rest. If the node represents a rest, change it to a note with a random pitch.

Split node Randomly select a leaf node. Change that node into an internal node with two randomly initialised children. The children nodes should be given duration values half that of their parent. An example of this is shown in Figure 6.16.

Reduce node Randomly select a leaf node. Remove that node and its siblings and randomly reinitialise their parent. The parent node should have a duration value twice that of its children. An example of this is shown in Figure 6.17.

Reinitialise note Randomly select a node representing a note (not a rest). Reinitialise the node with a random pitch value.

Add triplet Randomly select any node within the tree. If the node is a leaf, change it to an internal node, add the triplet operator, and randomly initialise and add three children to it. If the node already has children, add the triplet operator and randomly initialise and add a third child to it. Examples of these two variations are shown in Figures 6.18 and 6.19.

Remove triplet Randomly select any node within the tree that has a triplet operator attached. Remove the triplet operator then randomly select one of the node’s children and remove the subtree from that point.

Add continuation Randomly select any leaf node within the tree that does not already have a continuation operator attached. Add a continuation operator to the node. Then, if the next leaf node in the tree is not the same type, change it so that it is. For example, if the randomly selected node is a note and the next leaf node is a rest, change the rest to a note with the same pitch as the randomly selected node. An example of this is shown in Figure 6.20.

Remove continuation Randomly select any node within the tree that has a continuation operator attached. Remove the operator.

161 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Node to split = Melody

C D E F

(a) The original melody tree, with the node to split marked

Melody

D E F

C E

(b) The melody tree after applying the split mutation. New pitches for the children nodes were randomly selected.

Figure 6.16: An example of the split mutation

Melody Node to reduce =

C C cont.

C E G E

(a) The original melody tree, with the node to reduce marked

Melody

F C C cont.

C E

(b) The melody tree after applying the reduce mutation. A new pitch for the parent node was randomly selected.

Figure 6.17: An example of the reduce mutation

162 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Node selected = Melody

C D

(a) The original melody tree, with the node to add the triplet to marked

Melody

C D E D C

(b) The melody tree after applying the add triplet mutation. New pitches were randomly selected.

Figure 6.18: Adding a triplet to a node without any children

Node selected = Melody

C D

(a) The original melody tree, with the node to change to a triplet marked

Melody

t E

C D C

(b) The melody tree after applying the add triplet mutation. The pitch for the new child node was randomly selected.

Figure 6.19: Adding a triplet to a node with existing children

163 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Node selected = Melody

E F

(a) The original melody tree, with the node to add a continuation to marked

Melody

cont. C F

(b) The melody tree after applying the ‘add continuation’ mutation. The pitch connected to the selected node has been altered to match.

Figure 6.20: Applying the add continuation mutation

Any change that is not possible is not considered when randomly selecting an alteration. For example, if a melody does not contain any triplets then ‘Remove triplet’ will not be selected. The algorithm conﬁguration also allows for individual mutation operators to be disabled regardless of whether they are possible or not for any given candidate. Additionally, the random elements of mutation (e.g., giving a note a new randomly selected pitch) are constrained with respect to a target range and key signature. This is discussed further in Sections 6.8 and 6.9.

6.5 Parent Selection

As discussed in Section 6.2.2, selection methods define the probability that each candidate in a population will be chosen for reproduction operations. In this work, Pareto selection is used. Instead of considering a candidate’s overall fitness value, Pareto selection examines fitness in terms of individual characteristics. This is useful for situations where a single fitness value does not make sense [59, 165]. For example, consider the task of evolving a box with an appropriate width, depth, height, strength, and weight. Here, an overall or combined fitness value will not work, as per- fection in one aspect of the box does not offset weakness in another aspect. That is, better fitness in height does not compensate for poor fitness in depth. Similarly, good fitness in width does not make up for poor fitness in strength. Pareto selection deals with this issue by considering the individual aspects of fitness. The probability that a candidate will be selected is based on the number of other candidates in the same population that it is superior to in every aspect. Using the box example, a candidate is only better than another candidate if it has a superior

164 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

width, depth, height, strength, and weight. Once this value is known, Equation 6.5.1 can be used to determine the selection probability for a candidate.

(1 + Wi) probability of selectioni = Pn j=1 Wj § ¤ th ¦6.5.1 ¥ Wi : the number of candidates the i candidate in a population is superior to in every aspect n : the total number of candidates in the population

The task of evolving musical sight reading exercises benefits from the use of Pareto selection. An exercise needs to meet multiple criteria, both technical and aesthetic. For example, an exercise at the Grade 1 level might need to use only crotchet lengths and have only one or two rests. Additionally, the melody might also need to meet aesthetic criteria such as beginning and ending on the tonic note. As with the box problem, an overall fitness value does not work for these types of requirements. A good selection of note lengths does not make up for a lack of aesthetic qualities. Similarly, a melody sounding good does not make up for an absence of appropriate technical characteristics given the target difficulty. As such, Pareto selection is an ideal solution.

6.6 Fitness

The fitness measures are designed to guide the evolutionary process towards creating a melody with a specific set of characteristics. For this work six measures are used, each of which has an associated target value. A melody is assigned a score in the range [0, 1.0] for each measure based on how close it is to the target value. The score is calculated using Equation 6.6.1 as the difference between the candidate’s actual and target value for a fitness measure.

fitnessfi = 1.0 − abs(tf − afi) § ¤ ¦6.6.1 ¥ tf : the target value for ﬁtness measure f

afi : the actual value for ﬁtness measure f for candidate i

To illustrate this idea, return to the example of evolving a box. A target height for the box may be set as 10 cm. If a candidate box had a height of 10 cm it would receive a score of 1.0 for the ‘height’ measure. However, it the box had a height of 5 cm it would receive a score of 0.5. Similarly, if the box overshot the target with a height of 15 cm it would also receive a score of 0.5. Each of the six ﬁtness measures used in this work is based on counting a speciﬁc element within the melody. These counts are described as being either time or count based. A count- based measure takes the count as a raw value. For example, 6 of the notes in the melody are crotchets. Alternatively, time-based measures take the raw count value and interpret it

165 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

4 as a proportion of melody time. For example, in a 4-bar long melody in 4 time a count of 8 crotchets would be interpreted as 50% of the melody being crotchets, because the melody could potentially fit a total of 16 crotchets. Table 6.2 lists the type of each of the six fitness measures used. These fitness measures are:

Target note lengths The proportion of melody time to be taken by each note length. For example, 50% of the melody time should be ﬁlled by crotchets; 25% of the melody time should be ﬁlled by quavers.

Target rest lengths The proportion of melody time to be taken by each rest length. For example, 25% of the melody time should be ﬁlled by crotchet rests.

Allowable lengths The acceptable lengths for notes and rests in the melody. For example, only use notes and rests with crotchet or quaver lengths.

Target intervals The proportion of each size of interval to include. Size is represented in scale degrees. For example, 50% of intervals should be 1 scale degree in size; 50% of intervals should be 2 scale degrees in size.

Allowable intervals The acceptable interval sizes to use in the melody. Size is represented in scale degrees. For example, only use intervals with sizes of 1 or 2 scale degrees.

Melody shape The number of segments in the melody containing three contiguous notes where the pitches move consistently up or down. For example, 80% of the melody segments should be shapely.

The target note proportions and target rest proportions should sum to represent exactly 100% of the melody time. Similarly, the target interval proportions should sum to represent 100% of the intervals. The allowable lengths and allowable intervals are derived automatically from the target note, rest, and interval proportions. For example, if target proportions are set for crotchet and quaver notes, and a target proportion is set for crotchet rests, the allowable lengths overall are crotchets and quavers. Similarly, if target proportions are set for intervals of size 1, 2, and 3, the allowable intervals are 1, 2, and 3. The ‘melody shape’ measure is illustrated further in Figure 6.21. In this example, the melody contains a total of ten segments. Note that segments containing rests or fewer than three notes are not counted. Of these ten segments, only four contain notes which move con- 4 sistently up or down in pitch. Therefore, in this case the melody shape is 10 , or 0.4.

Table 6.2: Categorisations of each ﬁtness measure as time or count based

Fitness Measure Type

Target note proportions Time-based Target rest proportions Time-based Allowable Lengths Count-based Target interval proportions Count-based Allowable Intervals Count-based Melody shape Count-based

166 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Segment 3 Segment 8

Segment 2 Segment 5 Segment 7 Segment 10

Segment 1 Segment 4 Segment 6 Segment 9

Segment 1 Segment 6

Segment 2 Segment 7

Segment 3 Segment 8

Segment 4 Segment 9

Segment 5 Segment 10

Figure 6.21: Calculating the shape of a melody. Tick marks indicate the segments which are counted as having shape, as the pitches within the segment move consistently up or down.

Table 6.3: Calculating the fitness of the melody in Figure 6.22 against an arbitrarily selected set of targets. The finally fitness value for each measure is in bold.

Fitness Measure Target Actual Fitness

13 13 Target note proportions 0.75 crotchets 16 crotchets 1 − abs(0.75 − 16 ) = 0.9375 2 2 Target rest proportions 0.25 crotchets 16 crotchets 1 − abs(0.25 − 16 ) = 0.875 15 15 Allowable lengths Crotchets 17 allowable lengths 17 ≈ 0.8824 0 Target interval proportions 0.3 size 0 13 intervals of size 0 1 − abs(0.3 − 0) = 0.7 9 9 0.5 size 1 13 intervals of size 1 1 − abs(0.5 − 13 ) ≈ 0.8077 3 3 0.2 size 2 13 intervals of size 2 1 − abs(0.2 − 13 ) ≈ 0.9692 (0.7 + 0.8077 + 0.9692) ÷ 3 ≈ 0.8256 12 12 Allowable intervals 0, 1, and 2 13 allowable intervals 13 ≈ 0.9231 6 6 Melody shape 0.3 11 shapely segments 1 − abs(0.3 − 11 ) ≈ 0.7545

Figure 6.22: An example melody

167 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Consider the example target values for a melody set out in Table 6.3. These targets indicate that the evolutionary algorithm should attempt to create a melody made entirely of crotchets, most of which are notes (as opposed to rests). They specify a large target proportion for intervals with a size of 1, but also requests that some intervals of 0 and 2 scale degrees be used. The melody shape target is set to 0.3, meaning that 30% of the segments in the melody should have notes which move consistently up or down in pitch. Now consider the melody shown in Figure 6.22. To calculate the fitness value for each measure we must calculate the actual proportions and numbers of notes, rests, and intervals, and compare them to the targets. For measures such as ‘target note/rest proportions’, ‘target interval proportions’, and ‘melody shape’, the fitness value is calculated according to Equa- tion 6.6.1. The remaining fitness measures are calculated as raw counts, as their target is for 100% of the melody to fit within the assigned parameters. For example, the fitness for ‘allowable intervals’ is calculated as the number of intervals of an allowable size divided by the total number of intervals in the melody. Table 6.3 shows how each fitness measure would be calculated for this melody, given an arbitrarily selected set of targets. The process by which appropriate targets are set for each fitness measure is discussed in Section 6.9.

6.7 Population Diversity

A population diversity measure provides an indication of how a population is evolving over time. Low diversity means that many candidates are genetically similar, and so there is not much variation within the population. This could lead to premature termination and a poor final solution. A high diversity indicates greater variation, but too high a value could result in significantly longer running times as the algorithm must navigate a larger search space. Typically, diversity will fall over time as the population converges on a solution. The diversity measure used in this work is a melody specific approach used by Aloupis et al. [6], Lin and Wu [111], and Lin et al. [112]. It involves calculating the distance between two melodies by comparing their geometric shapes. Each melody is converted into a shape similar to a bar chart where the length and position of line segments are based on the length and pitch of the notes in the melody. The distance between the two shapes is then calculated. Figures 6.23 and 6.24 show how two different melodies can be converted into geometric shapes. These shapes can then be placed on the same axis and the difference between them calculated, as shown in Figure 6.25. To calculate the diversity of a population, the sum of the differences between every pair of candidates is calculated in this manner. When running the evolutionary algorithm, diversity is calculated for each population so that its change over time can be observed. In order to enable the comparison of diversity results between different executions of the algorithm, each collection of diversity values is normalised to the range [0, 1.0].

6.8 Initialisation

The ﬁrst step in an evolutionary algorithm is to create an initial population. To avoid introducing bias, this population is often generated randomly. In the domain of music, this means

168 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

70 MIDI Number

1 2 3 4 5 6 7 8 Time (crotchets)

Figure 6.23: An example melody and its related geometric shape

70 MIDI Number

1 2 3 4 5 6 7 8 Time (crotchets)

Figure 6.24: A second example melody and its related geometric shape

169 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES 8 7 2 x (72 - 72) = 0 Melody A Melody B Di ﬀ erence 6 1 x (71 - 67) = 4 5 4 0.5 x (71 - 69) = 1 Time (crotchets) 0.5 x (71 - 67) = 2 1 x (69 - 67) = 2 3 2 erence(melody A, melody B) = 0 + 3 1 2 4 13 Di ﬀ erence(melody Calculating the difference between the melodies in Figures 6.23 and 6.24 1 x (74 - 71) = 3 0.5 x (69 - 67) = 1 1 igure 6.25: F 1 x (72 - 72) = 0 70 60 75 65 MIDI Number

170 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

creating random sequences of notes and rests. Both the notes and rests could have a randomly selected length, and notes would also have a randomly selected pitch. The large number of potential lengths (e.g., semibreve, minim, crotchet, quaver, semiquaver, dotted variants etc.) and pitches (128 possible pitches according to the MIDI specification) means that, if left unre- stricted, the initial population should be diverse. Given that the goal of this work is to create musical sight reading exercises, some reasonable limitations can be placed on initialisation. As will be discussed in Section 6.9, several parameters are set for the evolutionary algorithm. Some of these parameters are used by the fitness measures described in Section 6.6. However, others represent non-negotiable or fixed characteristics. These characteristics are:

• Length (number of bars), • Time signature, • Key signature, and • Range.

When generating an exercise of a particular difficulty for a particular instrument, these characteristics are known. As discussed in Section 6.3.4, both the length and time signature are required to form the structure of the melody tree used to represent candidate solutions. As they both remain static throughout a single execution of the algorithm, these characteristics can safely be fixed or hard-coded into the solution space. The key signature and range are also known characteristics. As such, they can be used to restrict the random generation of pitches both during initialisation and by mutation operators. In other words, pitches will be randomly selected from those in the target key and within the target range. Given that pitches outside the target range and key signature add no value to a candidate solution, this approach serves only to reduce the search space – it is highly unlikely to reduce the quality of the final solution, only the time needed to find it.

6.9 Algorithm Conﬁguration

A configuration file is often used to provide all details required to run an evolutionary algorithm. In this case it is a JSON formatted file that describes:

Fitness parameters Described in Section 6.6.

Fixed characteristics Described in Section 6.8.

Population size The number of candidates to consider during each iteration of the algorithm.

Number of elites The number of best candidates from the previous population to be directly copied into the new population without any adjustments.

Probability of mutation The chance that each result of the crossover operator will be mutated.

171 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

Probability of generating a rest In initialisation, determines how likely a rest will be generated as opposed to a note; if set to 0, mutation operations related to rests will not be used.

Probability of generating a continuation In initialisation, determines how likely a rest or note will be assigned the continuation operator; if set to 0, mutation operations related to continuations will not be used.

Random method The method to use when selecting a random pitch; can be Gaussian or uniform.

Random seed Required for repeatability.

The ‘probability of generating a rest’ and ‘probability of generating a continuation’ values can both be set to 0, in which case the algorithm will avoid creating rests or continuations both during initialisation and mutation. This allows the search space to be restricted where appropriate. For example, if rests are not desired in the final solution, rests should not be introduced into the solution space at any point. The same is true for continuations. The logic behind this is similar to the logic for restricting random pitch selection with respect to the target range and key. That is, if rests or continuations are not desired in the final solution, there is no value in allowing them during the evolutionary process as it is extremely unlikely that they will contribute positively to the fitness of a candidate.

Listing 6.1: An example conﬁguration ﬁle for the evolutionary algorithm

1 "global":{

2 "random_seed": 1

3 },

4 "melody":{

5 "key": "C",

6 "tonality": "major",

7 "number_bars": 8,

8 "time_numerator": 2,

9 "time_denominator": 4,

10 "lowest_note": "G4",

11 "highest_note": "C5"

12 },

13 "experiment":{

14 "population_size": 50,

15 "num_elites": 1,

16 "mutation_chance": 0.01,

17 },

18 "melody_tree":{

19 "random_note_method": "gauss",

20 "chance_for_rest": 0.1,

21 "chance_for_cont": 0.0,

22 "chance_for_triplet": 0.0

23 },

24 "fitness":{

25 "note_proportions":{

26 "included": true,

27 "target_proportions":{

172 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

28 "4":{

29 "target_proportion": 0.875,

30 }

31 }

32 },

33 "rest_proportions":{

34 "included": true,

35 "target_proportions":{

36 "4":{

37 "target_proportion": 0.125,

38 }

39 }

40 },

41 "interval_proportions":{

42 "included": true,

43 "target_proportions":{

44 "0":{

45 "target_proportion": 0.5,

46 },

47 "1":{

48 "target_proportion": 0.1667,

49 },

50 "2":{

51 "target_proportion": 0.3333,

52 }

53 }

54 },

55 "melody_shape":{

56 "target_shape": 0.4

57 },

58 }

Listing 6.1 shows an example conﬁguration for the algorithm. In this case, the algorithm 2 is directed to create an 8 bar exercise in C major using 4 time. Continuations and triplets are not allowed, but rests can be used. The algorithm should restrict pitches to the range of G4 to C5, and random pitch selection should follow a Gaussian distribution. A population size of 50 candidates should be used, and the chance of mutating the results of the crossover operator should be set to 1%. In terms of notes and rests, only crotchets are desired. The algorithm should attempt to create an exercise where 87.5% of the time is ﬁlled by crotchet notes, and the remaining 12.5% of time by crotchet rests. Only intervals of size 0, 1, or 2 are wanted. Half of the intervals should be unison (i.e., have a size of 0), one third should have a size of 2, and the remainder should have a size of 1. The melody should be reasonably shapely, ideally with 40% of segments having pitches which move consistently up or down.

6.10 Summary

In this chapter the general evolutionary algorithm was presented as well as a speciﬁc implementation for generating monophonic sight reading exercises. To support this implementation

173 CHAPTER 6. AN ALGORITHMFOR GENERATING MUSICAL SIGHT READING EXERCISES

a novel representation method for musical melodies was developed. The design and justification for this novel method was provided. When describing the execution of the algorithm, the example configuration listed in Section 6.9 was created for validation purposes only. In application, the fixed characteristics and fitness targets are derived from existing published sight reading exercises. This and other aspects of the experimental design are the focus of the next chapter.

174 7 Experimental Design

7.1 Overview

In the previous chapter an evolutionary algorithm for generating musical sight reading exercises for monophonic instruments was presented. This chapter describes a structured experimental process for testing the algorithm, as well as a method for evaluating the quality and ‘ﬁtness for purpose’ of the algorithm’s output. Sections 7.2 and 7.3 discuss the process of selecting parameters for the algorithm. The method used to evaluate the output is then described in Sections 7.5 and 7.6. Chapter 8 presents the results of executing this experimental design.

7.2 A Method for Designing Algorithm Conﬁgurations

One aspect of the algorithm highlighted in Chapter 6, specifically Section 6.9, is the set of parameters used to influence the evolutionary process. Selecting suitable values for each parameter is a key component of the experimental design. Before potential values can be considered, a target monophonic instrument needs to be selected. Sight reading exercises are rarely generic. Rather, they are typically written for a specific instrument. This is because each instrument, even those within the same family (e.g., violin and viola), typically have unique technical requirements. Instruments can vary in note range, fingering patterns, and key, all of which affect the technical difficulty of playing specific pitches, key signatures, intervals, and rhythms. For example, the C major scale is easy to play on a flute; on a clarinet, however, the C major scale is much harder and F major is often introduced first [13]. The design of the algorithm allows for any monophonic instrument to be targeted. How- ever, for consistency and comparability between results only a single instrument – the flute – is used in this experimental design. The flute was chosen as it is both monophonic and non- transposing. It is also a relatively popular instrument, meaning there are a large number of sight reading exercise books published for it. This is important as parameter sets for the algorithm were derived from the characteristics of existing, published, sight reading exercises. This ensures that the targets set for the algorithm are both realistic and grounded in accepted, widely-used, professionally written examples. Section 7.3 describes the set of published exercises used as target models for the algo-

175 CHAPTER 7. EXPERIMENTAL DESIGN

rithm. These are referred to as the ‘source exercises’, as they are the basis of the values used for the algorithm’s conﬁguration. Each source exercise was converted into a single algorithm conﬁguration, a process which is in detail in Section 7.4.

7.3 Source Exercises

7.3.1 Overview

As noted in Section 7.2, parameters for the evolutionary algorithm were selected according to target models based on existing, published, professionally written sight reading exercises. These ‘source exercises’ are taken from four books, which together represent the Australian Music Examinations Board (AMEB), Associated Board of the Royal Schools of Music (ABRSM), and Trinity College curriculums. The four books were selected due to their alignment with these curriculums. This means that exercises of the same difficulty level across the different books should be comparable in technical difficulty, as the curricula are similar in their sight reading requirements. Each book is also authored by a single composer, meaning exercises within each book are likely to be of a consistent style. Table 7.1 shows the total number of exercises in each book, and how many of those exercises are used as target models for the algorithm. Grades 1 and 2 were chosen as the primary difficulty levels with which to validate the algorithm’s capabilities. That is, the experimental design focuses on testing the algorithm’s ability to generate exercises of Grade 1 and Grade 2 difficulty. Grade 3 exercises were also modelled in order to explore the limits of the algorithm in generating more technically and musically complex material. The reason for selecting these earlier grades as test cases lies in the utility of the exercises. Formal exams at the Grade 1 level are a student’s first exposure to musical sight reading, so naturally students at this level find large quantities of practice material useful. A wide variety of practice exercises is also useful at other early grade levels as students come to grips with sight reading techniques. Students studying later Grade levels – typically Grade 5 and above – often require fewer sight reading exercises. There are likely two reasons for this. Firstly, students at this level should already have a solid foundation of sight reading skills, and thus require less practice material. Secondly, at these levels students can use entire pieces from lower grades as sight reading exercises, reducing the need for purpose written material. Sections 7.3.2, 7.3.3, and 7.3.4 describe the characteristics of the source exercises at the Grade 1, 2, and 3 difficulty levels, respectively. These provide an idea of the general characteristics of exercises at each level – that is, what the proposed algorithm is attempting to emulate. They also provide support for the rules listed in Section 7.6, which are used to rate the quality of the algorithm’s output with respect to each grade level. Each individual characteristic is discussed more deeply with respect to the Grade 1, 2, and 3 sources exercises in Sections 7.3.5 to 7.3.12.

7.3.2 Characteristics of the Grade 1 Source Exercises

Grade 1 is one of the ﬁrst formal difﬁculty levels most students face, regardless of their chosen instrument. As Grade 1 tasks students with learning the fundamental skills for their chosen in-

176 CHAPTER 7. EXPERIMENTAL DESIGN

Table 7.1: Summary of source exercises extracted from published books

Book Total No. Grade 1 Grade 2 Grade 3 Unused (Grade 4+) Exercises

Improve Your Sight-Reading! [69] 79 25 16 38 - Flute Sight-Reading [181] 96 12 12 12 60 Sound at Sight - Sight Reading Pieces 80 20 20 20 20 for Flute; Book 1 [162] Flute Specimen Sight Reading [10] 71 15 16 12 28

Total: 72 64 82 108

strument, the different curriculum bodies (i.e., AMEB, ABRDM) often have similar requirements at this level. Table 7.2 provides an overview of the typical characteristics of the Grade 1 source exercises for the ﬂute. The most common key signatures are C and F major, likely due to their small 4 number of sharps and ﬂats. The most frequent time signature used is 4, which matches well with the most commonly used note and rest length of crotchet. At this level exercises tend to cover only a small range of notes, and the intervals between those notes are typically small. Whilst these characteristics represent the typical values at the Grade 1 level, others can be seen. For example, the G major and A minor key signatures are also used by some Grade 1 source exercises.

7.3.3 Characteristics of the Grade 2 Source Exercises

The typical characteristics of the Grade 2 source exercises overlap in some parts with those of the Grade 1 source exercises. However, there are some differences. For example, many Grade 2 source exercises are also written in the key of F major, but the Grade 2 exercises also feature 4 an increased usage of G major and A minor. The Grade 2 source exercises make heavy use of 4 3 timing, but almost as frequently employ 4. Table 7.3 shows a complete accounting of the typical characteristics of the Grade 2 source exercises. Differences from Grade 1 represent an expected increase in technical difﬁculty. For example, although the Grade 1 and 2 exercises mostly used crotchet length notes with some quavers, the Grade 2 exercises increased the use of minims. Similarly, whilst the Grade 1 exercises mostly used intervals with a size of 1, the Grade 2 exercises show an increased use of intervals with a size of 2.

7.3.4 Characteristics of the Grade 3 Source Exercises

The Grade 3 source exercises again represent an increase in technical difﬁculty from the previous grade. However, the characteristics still exhibit crossover with those of the Grade 1 and 2 exercises. Table 7.4 shows the typical characteristics of the Grade 3 source exercises. F major is no longer a commonly used key signature, replaced instead by G major and A minor. The typical range of pitches still spans one octave, but the most common highest pitch is higher than in the Grade 1 and 2 exercises, indicating that the exercises use higher (i.e., typically harder to play) pitches overall. The most common note and rest lengths have not changed from Grade 2, nor have the most commonly used intervals. This does not mean, however, that the difﬁ-

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Table 7.2: Characteristics of the sample of published Grade 1 sight reading exercises for the ﬂute. Ratios and proportions are represented in terms of time.

Characteristic Typical Value(s) for Grade 1 Flute Exercises

Key Signature F major, C major 4 Time Signature 4 Exercise Length 8 bars Range 12 semitones (one octave) F4 → G5 Note lengths 90 – 100% crotchets 0 – 10% quavers 0 – 5% minims, dotted minims, semiquavers Rest Lengths 95 – 100% crotchets 0 – 5% quavers, semiquavers Ratio of Notes to Rests 90% notes : 10% rests Intervals (as scale degrees) 95 – 100% gaps of 1 scale degree 0 – 5% gaps of 0 or 2 – 7 scale degrees

Table 7.3: Characteristics of the sample of published Grade 2 sight reading exercises for the ﬂute. Ratios and proportions are represented in terms of time.

Characteristic Typical Value(s) for Grade 2 Flute Exercises

Key Signature G major, A minor, F major 4 3 Time Signature 4, 4 Exercise Length 8 bars Range 12 semitones (one octave) G4 → A5 Note lengths 80 – 90% crotchets 0 – 10% quavers 0 – 10% minims 0 – 5% dotted minims, semiquavers, dotted crotchets, dotted quavers, semibreves Rest Lengths 95 – 100% crotchets 0 – 5% quavers, semiquavers, minims Ratio of Notes to Rests 95% notes : 5% rests Intervals (as scale degrees) 85 – 95% gaps of 1 scale degree 0 – 10% gaps of 0 or 2 scale degrees 0 – 5% gaps of 2 – 7 scale degrees

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culty has not been increased in these areas. As discussed in Sections 7.3.5 to 7.3.12, many of the characteristics exhibit wider ranges of values than the previous difﬁculty levels, even if the typically chosen values have not altered.

7.3.5 Use of Key Signatures

The key signatures used in the Grade 1 exercises, presented in Figure 7.1, are most commonly those with zero or one sharp or flat. As such, C, F, and G major are common, as are A, D, and E minor. Occasionally an exercise is written in B[ major, which has two flats. The Grade 2 source exercise are typically written in G major, A minor, or F major. If you consider the raised seventh of A minor, these are all key signatures with one sharp or flat. This indicates an increase in complexity from Grade 1, where a greater number of exercises are written in key signatures with no sharps or flats. The Grade 3 source exercises are written in one of ten key signatures. The most commonly used of those ten are G major and A minor. However, several other key signatures such as D major and E minor are used with only slightly less frequency. Overall, the use of key signatures at this difficulty level is much more varied than in Grade 1 and 2. Figure 7.2(a) shows more clearly the number of sharps and flats in each of the key signatures used by the Grade 1 source exercises. As expected, most of the exercises are major, and use key signatures with zero or one sharp or flat. The increase in complexity from Grade 1 to Grade 2 is further illustrated in Figure 7.2(b), which shows that fewer exercises are written in key signatures with no sharps or flats. Additionally, when a key signature with no sharps or flats is used, it tends to be minor rather than major. Figure 7.2(c) shows how the complexity increases again with the Grade 3 source exercises. An increased use of minor key signatures can be seen, as well as a tendency towards key signatures with a larger number of sharps and flats. Appendices C.1, D.1, and E.1 provide complete listings of the key signatures used by each individual source exercise.

7.3.6 Use of Time Signatures

Figure 7.3 shows the distribution of time signatures used by the Grade 1, 2, and 3 source 4 exercises. The most common by far at the Grade 1 level is 4, likely because it is one of the first 2 that beginning musicians are exposed to. 4 time is also used, probably because it is similar in 4 3 structure to 4. The only compound time signature used at this level is 4 which, whilst generally 4 2 considered as more complex than 4 and 4, still offers the familiar presence of crotchet notes. 4 Whilst the Grade 2 source exercises share a frequent use of 4 with Grade 1, they also 3 3 significantly increase the usage of 4 time. Being a compound time signature, 4 is slightly more 4 3 complex than 4 for new players, as it splits bars into an odd number of beats. However, 4 still uses crotchets as the primary beat marker, making it a less dramatic increase in complexity from 6 Grade 1 than other compound time signatures such as 8. 4 As with Grade 1 and 2, 4 time is still heavily used by the Grade 3 source exercises. 3 3 However, 4 and 8 also have a greater presence at this difficulty level. Being a compound time 3 signature that splits bars into quaver beats instead of crotchets, 8 represents a jump in difficulty 4 over the previous grade levels. The Grade 3 source exercises also contain the first use of 8. Again, this is a more complex time signature as it is unusual to split a bar into four quaver

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Table 7.4: Characteristics of the sample of published Grade 3 sight reading exercises for the ﬂute. Pitches are represented as MIDI numbers, and ratios are represented in terms of time.

Characteristic Typical Value(s) for Grade 3 Flute Exercises

Key Signature G major, A minor 4 3 Time Signature 4, 4 Exercise Length 8 bars Range 12 semitones (one octave) G4 → D6 Note lengths 80 – 90% crotchets, minims 0 – 10% quavers 0 – 10% dotted minims, semiquavers, dotted crotchets, dotted quavers, semibreves Rest Lengths 95 – 100% crotchets 0 – 5% quavers, minims Ratio of Notes to Rests 95% notes : 5% rests Intervals (as scale degrees) 85 – 95% gaps of 1 scale degree 0 – 10% gaps of 2 scale degrees 0 – 5% gaps of 0 or 3 – 7, or 14 scale degrees

Figure 7.1: The key signatures used by the Grade 1, 2, and 3 source exercises. Unless followed by an ‘m’ indicating a minor key, the key signatures are major.

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(a) Grade 1 source exercises

(b) Grade 2 source exercises

Figure 7.2: The number of sharps and ﬂats in the key signatures used by each of the Grade 1, 2, and 3 source exercises

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Figure 7.3: The time signatures used by the Grade 1, 2, and 3 source exercises

4 2 beats. However, the similarity of 8 to 4 – which contains the same number of quavers per bar but structures them differently – means that it is a reasonable increase in complexity from the Grade 2 exercises. Appendices C.1, D.1, and E.1 list the time signatures used in each individual Grade 1, 2, and 3 source exercise.

7.3.7 Length

Figure 7.4 shows that each Grade 1 source exercise is typically 8 or 16 bars long, regardless of its time signature. A small number of exercises have 4, 12 or 14 bars, but no exercise uses an anacrusis, where the length of a single bar is split into two shorter bars which are placed at the beginning and end of the melody respectively. The consistent use of even numbers of bars is most likely because an exercise typically comprises one or two phrases. An odd number of bars would prevent the phrases from being the same length, which significantly reduces musical aesthetics. The Grade 2 source exercises are typically 8 bars long. Exercise lengths at this difficulty level range from 4 bars to 24 bars, meaning that overall the Grade 2 source exercise lengths are more variable than the Grade 1 source exercises. The Grade 3 source exercises, as with the Grade 2 source exercises, are typically 8 bars long, but range between 4 and 22 bars. None of the source exercises at these difficulty levels contain repeats. A full list of the number of bars in each Grade 1, 2, and 3 source exercise can be found in Appendices C.1, D.1, and E.1.

7.3.8 Pitch Range

As can be seen in Figure 7.5, the Grade 1 source exercises have a relatively small range, most being spread over roughly an octave (12 semitones). Figure 7.6(a) shows which exact pitches are covered by each Grade 1 source exercise, as well as each exercise’s most commonly used pitch or pitches. Almost all of the Grade 1 source exercises cover the pitches from MIDI 67 (G4) to 72 (C5). This is a relatively easy range of notes to play on the ﬂute, and matches well

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Figure 7.4: Number of bars in each of the Grade 1, 2, and 3 source exercises. Lengths marked with ‘+’ contain an anacrusis.

Figure 7.5: Pitch range of each Grade 1, 2, and 3 source exercise in semitones

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(a) Grade 1 source exercises

(b) Grade 2 source exercises

Figure 7.6: Range spread and pitch mode for each of the Grade 1, 2, and 3 source exercise

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with the favoured key signatures identified in Section 7.3.5. The most common pitch for each exercise is typically in the middle of the range. The Grade 2 source exercises also tend to range over a single octave. However, the spread of values is quite different from Grade 1. For example, the Grade 2 exercises have ranges between 8 and 19 semitones, whereas the ranges of Grade 1 exercises fall between 5 and 16 semitones. Additionally, the most common lowest and highest notes for Grade 2 are a full tone higher than for Grade 1, indicating that overall the exercises use higher, and typically more difficult to play, pitches. The pitches covered by each Grade 2 source exercise, shown in Figure 7.6(b), are typically higher than those covered by the Grade 1 exercises, further supporting the notion that the Grade 2 exercises contain overall higher pitches. The Grade 2 exercises also have a much wider variety of most common pitches. This is likely a side effect of the greater variation in key signature, as the most common pitches in a melody are expected to relate to a melody’s key signature. The range of the Grade 3 source exercises is also often 12 semitones. However, a much larger proportion of exercises have larger ranges, up to 24 semitones (two octaves). Few exercises at the Grade 3 level have ranges smaller than one octave. This indicates that, on average, the Grade 3 exercises typically cover a larger range of notes than the Grade 1 and 2 exercises. The pitches covered by each Grade 3 source exercise, shown in Figure 7.6(c) tend towards higher (i.e., more difficult) pitches than the Grade 1 and 2 exercises. The most commonly used lowest pitch – G4 – is the same at Grade 2 and 3. However, the Grade 3 source exercises increase the most common highest pitch to D6, a full fourth higher than in the Grade 2 source exercises. The most frequent note(s) within each exercise are highly variable, implying that the exercises are not all centered around the same pitch(es). This indicates greater variation in the musical material. The ranges for each individual Grade 1, 2, and 3 source exercise can be found in Appen- dices C.1, D.1, and E.1.

7.3.9 Proportion of Notes vs. Rests

Figure 7.7(a) shows that the Grade 1 source exercises typically contain significantly more notes than rests, frequently using notes exclusively. Most Grade 1 source exercises have over 80% of their time made up by notes, with only two exercises having fewer than 70%. The Grade 2 exercises continue the trend, again filling significantly more time with notes compared to rests. Figure 7.7(b) shows that, as in Grade 1, there are also several cases where notes are used exclusively. On average, the Grade 2 source exercises have around 95% of their time taken by notes, with only 5% taken by rests. Grade 3 shifts the trend, Figure 7.7(c) showing that almost all of the exercises at this difficulty level contain both notes and rests. However, the amount of time taken by rests is typically small. On average, the Grade 3 source exercises have around 95% of their time taken by notes, with only 5% taken by rests. Appendices C.2, D.2, and E.2 provide a full accounting of the time taken by notes and rests in each Grade 3 source exercise.

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(a) Grade 1

(b) Grade 2

Figure 7.7: Percentage of time in each of the Grade 1, 2, and 3 source exercises ﬁlled by notes and rests

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(a) Grade 1

(b) Grade 2

Figure 7.8: Amount of note time taken by each unique note length, as a percentage of time taken by all notes in the Grade 1, 2, and 3 source exercises. Rests are not included. Bubble diameter represents the number of exercises containing that proportion.

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7.3.10 Note Lengths

Figure 7.8(a) shows that the majority of melody time in the Grade 1 source exercises is filled by crotchets. Quavers are the next most frequently used note length. Semiquavers are occasionally used, as are minims and dotted minims. Although not represented in the figure, when notes longer than crotchets (i.e., minims and dotted minims) are used at this level, they are typically placed at the end of a phrase. The majority of melody time in the Grade 2 source exercises, as with Grade 1, is filled with crotchet length notes. However, Figure 7.8(b) shows that at this difficulty level there are no exercises which use crotchets exclusively. Quavers also feature more in the Grade 2 source exercises than in the Grade 1 source exercises, as do minims. Occasionally semiquavers will be used, as are dotted quavers and crotchets. Figure 7.8(c) shows that whilst the Grade 3 source exercises still comprise a large proportion of crotchets, they are not as dominant as they are in Grades 1 and 2. At this difficulty level the use of both minims and quavers are also increased. Other note lengths that are used include semibreves, dotted quavers, dotted crotchets, dotted minims, and semiquavers. However, these lengths are used more sparingly. The exact counts and time percentages of each note length in the Grade 1, 2, and 3 source exercises are tabulated in Appendices C.3, D.3, and E.3.

7.3.11 Rest Lengths

The Grade 1 source exercises tend to use a single rest length or have no rests, as can be seen in Figure 7.9(a). This limited palate is likely due to the fact that only a small percentage of each exercise is comprised of rests. When rests are present, they are typically of a crotchet length. Only rarely are quaver and semiquaver length rests utilised. Figure 7.9(b) shows that the Grade 2 source exercises also tend to use just a single rest length. Typically the length used is a crotchet, though in two cases only minim length rests are used. A small number of exercises use some quaver and semiquaver length rests in addition to those with crotchet lengths. The Grade 3 source exercises typically use one rest length exclusively or have no rests at all. As seen in Figure 7.9(c), crotchet length rests are the most common, but a small number of exercises use minim or quaver rests. Occasionally exercises use minim or quaver rests exclusively, but they are most commonly seen in combination with crotchet rests. The exact counts and time percentages of each rest length in the Grade 1, 2, and 3 source exercises are tabulated in Appendices C.4, D.4, and E.4.

7.3.12 Intervals

The gaps between adjacent notes in the Grade 1 source exercises are typically small. This is shown in Figure 7.10(a), which reveals that the vast majority of gaps over all Grade 1 source exercises are one scale degree in size. That is, adjacent notes are typically only one scale step away from each other in terms of the exercise’s key signature. The next most commonly used gaps are 0 and 2, where adjacent notes are either of the same pitch or two steps apart, respectively. Larger interval sizes are rarely used, and when they are, they are applied sparingly.

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(a) Grade 1

(b) Grade 1

Figure 7.9: Amount of rest time taken by each unique rest length, as a percentage of cumulative time taken by all rests in each Grade 1, 2, and 3 source exercise. Notes are not included. Bubble diameter represents the number of exercises containing that proportion.

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(a) Grade 1

(b) Grade 2

Figure 7.10: The percentage of intervals of each size used in the Grade 1, 2, and 3 source exercises. Intervals are represented as the distance between two adjacent notes in scale degrees. Bubble diameter represents the number of exercises containing that proportion.

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The gaps between adjacent notes in the Grade 2 source exercises are also typically small, the most common gap being one scale degree. Gaps of two and three scale degrees are the next most common, but gap sizes between zero and seven scale degrees are also used. The distributions of each interval size in each Grade 2 source exercise, shown in Figure 7.10(b), are similar to those for the Grade 1 source exercises. A strong majority of intervals have a size of one, and several have a size of two. Compared to Grade 1, the Grade 2 source exercises feature more intervals with a size of three. As with the Grade 1 and 2 source exercises, the Grade 3 source exercises again mostly utilise intervals with a size of 1. The next most common gap between adjacent notes is 2, followed by 3, 0, 4, and 5. Gaps as large as 14 can be found, but only rarely. Figure 7.10(c) shows that the use of relatively small intervals is consistent across all of the Grade 3 source exercises. It also shows the increased use of other larger interval sizes compared to the previous grades, a characteristic indicating an increase in difﬁculty. Appendices C.5, D.5, and E.5 provide the exact number of each sized interval used in each of the Grade 1, 2, and 3 source exercises.

7.4 The Algorithm Conﬁgurations

As discussed in Section 7.2, each source exercise can be converted into a set of parameters for the algorithm (i.e., an algorithm configuration). Each configuration represents a particular target model, the characteristics of which the algorithm is tasked with emulating. To create the algorithm configurations, each source exercise is analysed and the characteristics relevant to the algorithm’s fitness measures (defined in Section 6.6) and initialisation (defined in Section 6.8) are extracted. This includes the key signature, time signature, and length of each exercise, as well as each exercise’s proportion of notes, rests, and intervals. The melody shape of each exercise is also calculated. From these values the allowable intervals, note lengths, and rest lengths can be inferred. It may seem that this process is unnecessary given that the typical characteristics of the Grade 1, 2, and 3 exercises have already been identified. Why model source exercises individually when you could use the typical or average values for the algorithm parameters? The reason for this is twofold. Firstly, targeting the typical characteristics ignores the variety present in exercises at even the lowest level of difficulty. This severely limits the variety of solutions the algorithm can generate, as it will be constrained by a single parameter set for each difficulty level. The second reason relates to the purpose of the experiment design in exploring the capabilities of the algorithm. If the algorithm is tasked only with generating ‘typical’ sight reading exercises, the results only indicate how it performs generating typical sight reading exercises. To gain a wider understanding of the algorithm’s performance, it should be tested on a broader range of input. Using each source exercise as a template allows this to be done. Two additional characteristics also need to be extracted: whether each exercise contains rests and ties. This information is used to set the probability of generating a rest and the probability of generating a continuation when the algorithm randomly generates the initial population. As discussed in Section 6.9, the algorithm can be restricted from introducing rests and continuations into the solution space. If the source exercise being modelled does not

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contain a rest or continuation, the relevant probability is set to 0. Otherwise, the probability is arbitrarily set to 0.1. In addition to the fitness measures and initialisation, there is a final set of values that need to be provided which can not be extracted from the source exercises. These values all relate directly to configuring evolution, and are set as follows in every configuration:

Population size: 50 Number of elites: 1 Probability of mutation: 0.01 (i.e., 1%) Random method: Gaussian Selection method: Pareto Termination criteria: 100 generations with no improvement

Each configuration is also assigned a fixed random number generator seed, so that its output can be reproduced. The algorithm configurations as described are intended to be specific enough to guide the evolutionary process, but still broad enough that there are many acceptable solutions for a given target model. To show this, three configurations are created for each source exercise, each of which differ only in their random number generator seed. This means that after being executed with every configuration the algorithm will have generated three different sight reading exercises for each target model. Comparing these results will indicate how consistent the algorithm is in finding acceptable solutions, and the similarities between solutions generated using the same set of targets. Appendices F, G, and H provide a complete listing of the configurations used to test the algorithm in generating Grade 1, 2, and 3 exercises, respectively. The resulting exercises generated were manually analysed using the method described in Sections 7.5 and 7.6. These results are presented in Chapter 8.

7.5 Forming A Method for Evaluating the Algorithm Output

7.5.1 Overview

In order to evaluate the algorithm there needs to be a method for formally and consistently rating the quality of its output. Such a method does not currently appear to exist. It may seem that the fitness measures present a fitting solution to this problem. However, as will be discussed next in Section 7.5.2, there are several reasons why they are not suited to the task. The ideal method must consider both the general aesthetics of the generated melodies and aspects specific to sight reading. Both factors are critical – a melody which sounds good but is not appropriate for sight reading is not fit for purpose, nor is a melody which is technically appropriate but aesthetically weak. Section 7.5.3 discusses how the creation of a method for evaluating the algorithm’s output was approached. Section 7.5.4 describes some of the related literature, from which a ruleset for grading the aesthetics and technical appropriateness of a generated sight reading exercise can be formed. This ruleset is presented in Section 7.6.

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7.5.2 Using the Fitness Measures

Fitness alone can not be relied upon as a measure of quality for the solutions generated by the algorithm. Whilst they are indicative of the value of a solution, the fitness measures are not necessarily a complete descriptor of a good sight reading exercise and to use them in isolation could incorrectly suggest that they are. It is also risky to use the same measures for both guiding evolution and evaluating the results of the evolutionary search. This is because it should not be assumed that the fitness measures are either appropriate or comprehensive. Assessing the output of an evolutionary algorithm can be seen as an exercise in validating the fitness measures, given that they are the driving force in creating the output. In light of this, it would not be reasonable to use the fitness measures as the sole criteria by which the algorithm output is judged.

Another factor to consider is that the fitness measures were designed to evolve sight reading exercises which emulate the characteristics of existing and accepted exercises. For example, the Allowable lengths measure scores a generated solution based on how many of its notes and rests have lengths which are considered appropriate for the target difficulty level. As discussed in Section 7.4, the lengths classified as ‘appropriate’ are derived from a particular source exercise, as are the targets for all of the fitness measures. Although this helps to guide the evolution towards creating melodies which emulate the characteristics of an exercise that is known to be fit for purpose, it does not necessarily mean that other note lengths are inappropriate.

For example, a Grade 1 source exercise may comprise only crotchet length notes and rests. This means that an exercise generated by the algorithm with only crotchet length notes and rests would achieve a perfect score for this measure with respect to that particular source exercise. However, it does not mean that a generated exercise is guaranteed to be unﬁt for purpose should it contain notes or rests of other lengths. Many Grade 1 source exercises feature notes and rests with lengths other than a crotchet, meaning these other lengths must also be appropriate for the difﬁculty level.

It is also important to note that the actual appropriateness of any particular note or rest length lies not only in the raw length value (e.g., demisemi quavers are not seen at the Grade 1 level), but also the context in which the note is placed. For example, whilst quaver and crotchet lengths are both suitable for Grade 1 exercises, a single quaver note followed by a crotchet note creates a syncopated rhythmic pattern which is too technically challenging for the Grade 1 level and would not be used. This particular nuance is not captured by any of the ﬁtness measures.

Similar arguments can be made for all of the fitness measures, in that a generated exercise is not necessarily of poor quality simply because it does not meet the target(s) extracted from a source exercise. For this and the other reasons discussed, the fitness measures can not be used as the primary method by which the algorithm output is judged. This does not mean that the measures are poorly devised, only that they are not a complete representation of a good solution. Additional fitness measures could be added, but doing so would risk unnecessarily restricting the solution space to the point where the algorithm’s output exhibits little to no variance.

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7.5.3 Elements of a Good Musical Sight Reading Exercise

Describing exactly what makes a musical sight reading exercise fit for purpose requires quantifying both the aesthetics of the melody as well as its technical appropriateness with respect to a specific difficulty level and instrument. Either one of these tasks is uniquely challenging on its own. Some guidance can be found by examining existing published exercises. These mostly reveal the technical properties which are appropriate for each difficulty level, such as the acceptable note lengths, interval sizes, and use of syncopation. Additional guidelines can be inferred. For example, some sequences of notes are clearly unplayable. Other components, such as repeated large gaps between notes, are widely accepted as being difficult to play [174]. Other factors to consider relate to the aesthetics of the melodies. Musical aesthetics are notoriously difficult to quantify and remain the subject of much debate and ongoing research within the scholarly community. One reason for this is that musical rules tend to be derived empirically, in that they emerge by examining trends in common practice rather than being determined a priori. Another reason is that they are largely contextual, and depend on the culture, genre, age, and purpose of the music in question. This means that not only are they open for discussion and interpretation, but they also evolve over time. Fortunately, the application domain of the algorithm presented in this work naturally restricts the scope of the musical rules that need to be considered. The purpose of the proposed algorithm is to generate sight reading exercises which would be suitable for students preparing for formal musical examinations such as those facilitated by the Australian Music Examinations Board (AMEB) and the UK’s Associated Board of the Royal Schools of Music (ABRSM). The curricula developed by these organisations strictly fall within Western Classical Music from the Common Practice period. This is a relatively well-documented period with a number of widely accepted musical guidelines for aesthetically pleasing melodic and harmonic structures. As the algorithm proposed in this work focuses on monophonic melodies, only the guidelines relating to melodic structures need to be considered. Additionally, sight reading exercises are uniformly short in length, meaning that complex concepts of musical form, which describe formal structures for musical pieces to follow, do not apply as it is not required. A goal of the experimental design presented in this chapter was to devise a set of rules which define an aesthetically pleasing melody for the common practice period of Western classical music. To be included in the set, a rule needs to be both well supported in the literature and fit with the source exercises described in Section 7.3. Additional rules relating to the technical appropriateness of a melody are extracted from the source exercises. The ruleset can be used to assign the algorithm output quality ratings indicating each generated exercise’s fitness for purpose independently of the evolutionary algorithm’s fitness measures.

7.5.4 Extracting Rules from the Literature

Given that the evolutionary algorithm is intended to generate musical sight reading exercises appropriate for practical music examinations such as those by the AMEB and ABRSM, the curricula set by these respective examination bodies represent a natural starting point. Both curricula include music theory components which task students with writing melodies from scratch. The speciﬁcations for these melodies consistently align with the style, length, and difﬁculty of sight reading exercises. This means that the criteria by which student’s melodies are judged could

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also be used for evaluating algorithmically generated sight reading exercises. Unfortunately, there are no clear marking or assessment schemes, rubrics, or requirements provided by the governing bodies of these or other similar curricula. The AMEB syllabus [13] notes that students answering creative melody writing questions should attempt to write a “balanced melody”. It does not, however, define what a balanced melody is. The AMEB also provide a video series “Ask Andrew” [12], which walks viewers through the process of answering a melody writing question. Again, no specific criteria are presented, only general advice such as to create an “arched” shape and that the use of repeated patterns is viewed favourably. The ABRSM syllabus uses marking bands for creative questions. Guidelines for each band are publicly available but specific criteria, if there are any, is not listed. For example, answers assigned the highest band are described as needing to have “musical interest”, “style”, and a “good sense of shape and direction”, all whilst being “musically convincing” [11]. Given the lack of more specific criteria, it appears that the interpretation of the guidelines is left to individual assessors, who may or may not moderate one another’s marking. Additional guidance on what makes a pleasing or technically valid melody can be found in the field of music theory. One application of this knowledge is in the placement of intervals within a melody. Although the algorithm’s fitness measures define the allowable intervals and target interval proportions, they do not specify any particular pitches that should make up those intervals. This means that although acceptably sized intervals may be placed throughout a solution, the resulting melody could still sound poor. Music theory provides several reasons for this poor outcome. One is the inherent dissonance of individual intervals. It is widely accepted that some intervals are more aesthetically pleasing than others. For example, Hindemith [76] was an early proponent in the theory of dissonance, presenting his own rankings of the least to most dissonance intervals as being:

1. C → C (unison) 2. C → G (perfect 5th) 3. C → F (perfect 4th) 4. C → A (major 6th) 5. C → E (major 3rd) 6. C → E[ (minor 3rd) 7. C → A[ (minor 6th) 8. C → D (major 2nd) 9. C → B[ (minor 7th) 10. C → D[ (minor 2nd) 11. C → B (major 7th) 12. C → F] (tritone)

These rankings are largely supported by another more widely supported ordering system based on the theory of just intonation [30, 210], a tuning method where instruments are tuned according to set frequency ratios between pitches. This method gave rise to a theory of dissonance where more complex ratios are ranked as more dissonant. Although modern West- ern instruments are tuned using twelve-tone equal temperament, resulting in slightly different ratios, the ordering is the same [35, 36, 164]. According to this theory, the intervals ranked from least to most dissonant are:

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1. 1:1 (unison) 2. 2:1 (octave) 3. 3:2 (perfect 5th) 4. 4:3 (perfect 4th) 5. 5:3 (major 6th) 6. 5:4 (major 3rd) 7. 6:5 (minor 3rd) 8. 8:5 (minor 6th) 9. 9:8 (major 2nd) 10. 9:5 (minor 7th) 11. 15:8 (major 7th) 12. 16:15 (minor 2nd) 13. 45:32 (tritone)

A major difference between the two sets of rankings is the positions of major 7th and minor 2nd, which are swapped. The rankings presented by Hindemith [76] also forgo including the octave interval, which is ranked as the second most aesthetically pleasing by later scholars. Both theories describe intervals exclusively using the tonic as the lower note. As such, they do not perfectly align with the task of evaluating a melody, where the lower note could have any pitch. However, some guidelines for aesthetically pleasing melodies can be extracted. These are presented in Section 7.6. These rankings are not presented to suggest that dissonance should be avoided. In fact, some dissonance adds musical interest to a melody. The difﬁculty in applying dissonance lies in how often it should be used and the contexts in which the dissonant intervals are placed. Indeed, the contexts of both consonant and dissonant intervals – where context refers to the preceding and following intervals as well as the melody’s key signature – are crucial to the aesthetics of a melody. One widely accepted concept in Western music theory is the notion of resolving intervals. Dissonant intervals are often described as being ‘unstable’, and common advice is that their instability should be resolved or stabilised, typically with a pitch considered strong given the key signature [204]. For example, Goetschius [65] suggests the following resolutions, written in terms of scale degrees:

• VII should resolve to I, • VI should resolve to V, • IV should resolve to III, and • II should resolve to I or III.

These resolutions are designed to manage dissonance and emphasise the key signature of a melody, both of which reduce harmonic stress. Other suggestions in the literature are also related to the context of intervals, but not speciﬁcally resolving dissonance. For example, many scholars strongly advise that a melody should change direction after an interval of a fourth or more [5, 65, 101, 154, 174]. They also encourage that no more than two intervals of a fourth or more be placed contiguously, and that if there are two large intervals in sequence that the ﬁrst should be larger than the second.

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Other scholars make more general suggestions for melodic aesthetics. For example, Miller [130] notes that a variety of small and large intervals should be intermixed, and that only pitches from the target key signature should be selected. Similarly, much of the literature highlights the effectiveness of self-similar structures within a melody. These and additional guidelines can be translated into a ruleset for evaluating the aesthetics of a sight reading exercise. Some of these rules require manual (i.e., human) assessment due to subjective qualities. Section 7.6 describes the complete ruleset, which addresses both the melodic aesthetics and technical appropriateness of a generated sight reading exercise. The section will also detail the process of applying the ruleset to a collection of algorithmically generated sight reading exercises in order to determine overall quality ratings regarding their ﬁtness for purpose.

7.6 A Method for Evaluating the Quality of Algorithmically Generated Musical Sight Reading Exercises

7.6.1 General Approach

Section 7.5.2 discussed why the ﬁtness measures used to drive the evolutionary algorithm are not ideal for capturing the overall quality of the algorithm’s output. However, to determine the validity of the evolutionary algorithm its output does need to be evaluated. As discussed in Section 7.5.3, there are two facets to a good sight reading exercise: its musical aesthetics and its technical appropriateness. Rules for both facets can be extracted from existing sight reading exercises (i.e., the source exercises), and literature published by music scholars. Relevant literature and the source exercises were examined, resulting in a collection of 29 individual rules. Each rule relates to the technical appropriateness of an exercise, the melodic aesthetics of an exercise, or both, and can be further categorised as relating to one of four facets:

• Note/Rest selection Rules relating to the length, pitch, and location selected for each note and rest in the melody. • Intervals Rules relating to the size and placement of intervals. • Melodic structure Rules relating to the shape and form of the melody. • Rhythmic structure Rules relating to the sequences of note and rest lengths in the melody.

Of the 29 total rules, 9 relate only to the technical appropriateness of an exercise, 12 relate only to the melodic aesthetics of an exercise, and 8 relate to both. The number of rules relating to each individual facet can be seen in Figure 7.11. Many of the rules refer to the ‘strong’ beats of a melody. Beats which are seen as ‘strong’ depend on the time signature. In time signatures where bars can be divided into two equal

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4 parts, the first beat and the beat half-way through are strong (e.g., beats 1 and 3 in 4 bars are strong). In all other time signatures the first beat of the bar is strong. Some rules also refer to scale degrees. In this case, the scale degrees are with respect to the target key signature of the generated exercise. Each algorithmically generated exercise will be examined with respect to the ruleset, and a rating selected from a five-point Likert scale [110]: Very bad, Bad, Average, Good, or Very good. A major distinction between the five ratings is that some represent exercises that are fit for purpose (i.e., Average, Good, Very good), and the rest represent those which are not (i.e., Very bad, Bad). Table 7.5 shows the criteria for assigning each Likert rating. First, an exercise is examined for unreasonable or unplayable elements. An exercise containing these elements is assigned the ‘Very bad’ rating, reserved for such special cases. For example, if an exercise contained long strings of dotted semiquavers with demi-semiquaver rests, and every third note was tied to the next, it would be unreasonable at any difficulty level. In this case, the exercise is assigned a ‘Very bad’ rating. If this is not the case, a number can be calculated representing how much of an exercise is in violation of the rules. This percentage translates directly to one of the other four ratings (i.e., Very good, Good, Average, Bad). Each source exercise was written for a specific difficulty level. As such, each exercise generated by the proposed algorithm will be evaluated with respect to the difficulty level of the source exercise used as the target model. The exercises will also be evaluated against the criteria for the other two grade levels considered in this design. That is, every generated exercise is evaluated against the criteria for Grade 1, 2, and 3. This is done to capture cases where an exercise is fit for purpose, just not for the intended difficulty level. For example, an exercise intended to be appropriate for Grade 2 students might not be sufficiently complex, yet be appropriate for the Grade 1 level. Similarly, an exercise targeted at Grade 1 might be overly complex, but be suitable for Grade 2. Each exercise is also given a rating based on whether it can be improved or upgraded with a small number of alterations. Figure 7.12 shows the difference between the two. An exercise is said to be ‘improved’ if it was already fit for purpose and becomes more so as a result of the changes. Alternatively, an exercise is said to be ‘upgraded’ if the changes move it from being unfit to being fit for purpose. Currently, changes are made manually when assessing each

12 Melodic Aesthetics (M) Technical Appropriateness (T) 9 8

5 Note/Rest Selection Note/Rest Selection 4 3

Intervals 2 4 Intervals 2

3 Melodic Structure Melodic Structure 1 2

Rhythmic Structure 1 Rhythmic Structure 2

Figure 7.11: The number of rules for evaluating the technical appropriateness and melodic aesthetic of a sight reading exercise, and the number of those rules relating to each of the four facets.

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Table 7.5: Criteria for assigning each Likert rating to an algorithmically generated sight reading exercise

Rating Fit for purpose? Percentage of melody Textual description violating ruleset

Very good Yes - ‘No’ problems Good Yes ≤ 10% ‘A few’ problems Average Yes ≤ 25% ‘Some’ problems Bad No > 25% ‘Several’ problems Very bad No - Unreasonable or unplayable elements

improve

Very bad - Bad - Average - Good - Very good

upgrade

Figure 7.12: The Likert rating for an exercise can be upgraded from ‘unfit’ to ‘fit for purpose’, or be improved in its fitness for purpose after a small number of repairs.

Table 7.6: Summary of rules in the ruleset for evaluating algorithmically generated sight reading exercises. Numbers refer to the rule numbers in Table 7.7.

Technical Appropriateness Melodic Aesthetics Both

Note/Rest selection 1 - 4 10 - 14 22 - 24 Intervals 5 - 6 15 - 18 25 - 26 Melodic structure 7 19 - 21 27 - 28 Rhythmic structure 8 - 9 - 29

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exercise. When determining potential changes, at most 5% of the melody can be altered. Ac- ceptable alterations include changes to note pitches, note and rest lengths, and note and rest placements. Only changes which could be represented algorithmically should be used, as it is intended that these changes could be incorporated into the algorithm in the future. Once a small set of changes is made, an exercise is evaluated again with respect to the ruleset and a new Likert rating is assigned. The post-alteration ratings serve a dual purpose. They show the potential of the algorithm to be improved, and serve to highlight the biggest problems currently preventing the generated exercises from being more ﬁt for purpose. This information could be used to drive future work.

Table 7.7: The origin of each rule in the ruleset for evaluating algorithmically generated sight reading exercises

Rules for evaluating... Rules relating to... Rule Origin

Technical Appropriateness Note/Rest selection 1. Rest proportions Source exercises 2. Note lengths Source exercises 3. Rest lengths Source exercises 4. Tied notes Source exercises Intervals 5. Interval sizes Source exercises 6. Interval proportions Source exercises Miller [130] Melodic Structure 7. Key signature Source exercises Rhythmic Structure 8. Time signature Source exercises 9. Playability Source exercises Melodic Aesthetics Note/Rest selection 10. Note placement Perricone [154] 11. Tonic repetition Laitz [101] Perricone [154] 12. Opening note Laitz [101] Perricone [154] Associated Board of the Royal Schools of Music [12] 13. Phrase endings Source exercises Goetschius [65] 14. Peak note Associated Board of the Royal Schools of Music [12] Intervals 15. Tritones Source exercises Perricone [154] Goetschius [65] Aldwell and Cadwal- lader [5] Schoenberg [174] 16. Augmented and di- Source exercises minished intervals

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Perricone [154] Goetschius [65] Aldwell and Cadwal- lader [5] Schoenberg [174] 17. Closing intervals Source exercises Laitz [101] 18. Interval resolutions Goetschius [65] Melodic structure 19. Melodic direction Goetschius [65] 20. Contextualising Goetschius [65] leaps Perricone [154] Aldwell and Cadwal- lader [5] Schoenberg [174] 21. Peak placement Associated Board of the Royal Schools of Music [12] Rhythmic structure - - Technical Appropriateness Note/Rest selection 22. Placement of long Source exercises and Melodic Aesthetics notes Goetschius [65] 23. Placement of rests Source exercises Goetschius [65] 24. Target key signature Source exercises Miller [130] Intervals 25. Gap placement Source exercises Laitz [101] Miller [130] 26. Leaps Laitz [101] Melodic structure 27. Repetition Source exercises Associated Board of the Royal Schools of Music [12] Miller [130] 28. Length Source exercises Goetschius [65] Rhythmic structure 29. Syncopation Source exercises Miller [130]

Sections 7.6.2 and 7.6.3 details the portions of the ruleset relating to the technical appropriateness and melodic aesthetics of a generated exercise, respectively. Section 7.6.4 covers the subset of rules relating to both technical appropriateness and melodic aesthetics. Table 7.6 shows which rules relate to which categories, and the source(s) from which each rule originates are provided in Table 7.7.

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7.6.2 Rules for Technical Appropriateness

The following rules relate to the technical appropriateness of an exercise. That is, whether it is suitable with respect to a particular difﬁculty level.

Rules Relating to Note/Rest Selection

1. Rest proportions No more than 10% of the melody should be made up of rests, unless a larger proportion is present in the target source exercise.

2. Note lengths An exercise should only use note lengths seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only use minim, crotchet, quaver, semiquaver, and semibreve length notes.

3. Rest lengths An exercise should only use rest lengths seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only use crotchet, quaver, and semiquaver length rests.

4. Tied notes Grade 1 exercises for the flute should not contain any tied notes. Grade 2 exercises for the flute should contain at most 5% tied notes. Grade 3 exercises for the flute should contain at most 10% tied notes. If the target source exercise contains a larger proportion of tied notes than those listed here, the maximum percentage of tied notes an exercise can contain is that of the target source exercise.

Rules Relating to Intervals

5. Interval sizes An exercise should only use intervals seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only use intervals up to a size of 7.

6. Interval proportions At least 90% of the intervals should be between 0 and 3 in size, inclusive (i.e., between a unison and a fourth). At least 50% of the intervals should be between notes only one scale degree apart (i.e., a second).

Rules Relating to Melodic Structure

7. Key signature An exercise should only be written in a key signature seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only be written in the keys of C, F, G, and B[ major, or A, D, and E minor.

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Rules Relating to Rhythmic Structure

8. Time signature An exercise should only be written in a time signature seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only be 4 2 3 written in 4, 4, or 4.

9. Playability Each bar of the melody should only contain sequences of note lengths seen in source exercises of the same difficulty level. For example, a bar in a Grade 1 exercise for the 4 flute in 4 time can contain two minims in a row, but would not be filled with a string of semiquavers.

7.6.3 Rules for Melodic Aesthetics

The following rules relate to the melodic aesthetics of an exercise. That is, whether it is pleasing to listen to.

Rules Relating to Note/Rest Selection

10. Note placement Strong notes from the target key (i.e., I, III, V) should be placed on at least 50% of the strong beats in the melody.

11. Tonic repetition At least 10% of the strong beats in the melody should be ﬁlled with a tonic note.

12. Opening note The opening pitch of an exercise should be I, III, or V.

13. Phrase endings The note before a rest should be at least crotchet length.

14. Peak note The highest note in the melody should be used no more than 3 times.

Rules Relating to Intervals

15. Tritones Tritones should never be used.

16. Augmented and diminished intervals Augmented and diminished intervals should never be used.

17. Closing interval The melody should end with II → I, VII → I, IV → I, or V → I.

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18. Interval resolutions After a jump (i.e., an interval greater than a fourth), instability should always be resolved. IV should resolve to III. II should resolve to I or III. VI should resolve to V. VII should resolve to I.

Rules Relating to Melodic Structure

19. Melodic direction If the melody is moving up in pitch, it should not change direction on VII. If the melody is moving down in pitch, it should not change direction on IV or VI.

20. Contextualising leaps The melody should switch direction after a leap (i.e., an interval greater than a fourth). If there are two leaps in a row, the ﬁrst should be larger.

21. Peak placement The peak should fall within the middle 50% of the melody.

Rules Relating to Rhythmic Structure There are no rules relating to rhythmic structure that are solely relevant to melodic aesthetics. In the proposed ruleset, rules relating to rhythmic structure are either purely technical in nature (i.e., rules 8 and 9), or are pertinent to both the technical appropriateness and melodic aesthetics of an exercise (i.e., rule 29).

7.6.4 Rules Relating to Both Technical Appropriateness and Melodic Aes- thetics

The following rules relate to both the technical appropriateness and the melodic aesthetics of an exercise. That is, they evaluate whether it is suitable with respect to a speciﬁc difﬁculty level and also pleasing to listen to.

Rules Relating to Note/Rest Selection

22. Placement of long notes 80% of notes longer than a crotchet should be placed on strong beats of the bar.

23. Placement of rests 80% of rests should be placed on weak beats of the bar.

24. Target key signature All notes should have pitches from the target key signature.

Rules Relating to Intervals

25. Gap placement There should be no more than 3 intervals of a third or more in sequence, unless the sequence forms an arpeggio.

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26. Leaps There should be no more than two intervals of a fourth or more in a row.

Rules Relating to Melodic Structure

27. Repetition A self-similar structure should not be repeated exactly more than twice in a row. If the structure is transposed when repeated, it is not considered to be repeated exactly.

28. Length An exercise should be of a length, in bars, seen in source exercises of the same difﬁculty level. For example, Grade 1 exercises for the ﬂute are expected to only be 4, 8, 12, 14, or 16 bars long.

Rules Relating to Rhythmic Structure

29. Syncopation Grade 1 exercises for the flute should contain no syncopation. Grade 2 exercises for the flute can contain up to 10% syncopation. Grade 3 exercises for the flute can contain up to 20% syncopation.

7.6.5 Recording Broken Rules

As each exercise is examined with respect to the ruleset, the overall category of any rules that are broken is recorded. When considering the results, this data will provide a perspective on potential areas for future work in improving the algorithm. Broken rules are only recorded with respect to the generated exercises’ intended difﬁ- culty level. For example, if a generated exercise is supposed to be of Grade 1 difﬁculty, only the rules it breaks with respect to Grade 1 are recorded – not those for Grade 2 or 3. The severity of the rule violations are not measured.

7.7 Summary

This chapter described an experimental design intended to test the capabilities of the evolutionary algorithm presented in Chapter 6. The experiment required the extraction of a set of source exercises from published books of sight reading material and the use of these source exercises as target models for the algorithm. A method for evaluating the algorithm’s output was described, which requires examining each generated exercise in terms of its adherence to a ruleset which evaluates the technical appropriateness and the melodic aesthetics of a solution. This ruleset is separate to the fitness measures, meaning that while the fitness measures influence the evolutionary process, they are not used to evaluate the output of the algorithm. The percentage of an exercise which is in violation of the ruleset is translated to a rating on a five- point Likert scale categorising the overall quality and fitness for purpose of that solution. The specific rules broken by each generated exercise are recorded to gain insight into gaps within the algorithm. Chapter 8 presents the results of executing this experimental design.

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8 Evaluating the Evolutionary Algorithm

8.1 Overview

In the previous chapter an experimental design was presented for assessing the quality and fitness for purpose of the output of the evolutionary algorithm described in Chapter 6. This chapter details the results of executing that experimental design. This chapter will begin with a discussion of whether the generated exercises were able to emulate the characteristics of the source exercises. This is done in terms of the characteristics used to describe the source material in Chapter 7, specifically Section 7.3, and ranges from examining the most typical characteristics of the exercises, as in Section 8.2, to a more detailed view, as in Sections 8.3 and 8.4. The fitness values and diversity achieved by the generated exercises will be explored in Section 8.5. These results should provide a good indication of the fitness for purpose of the generated exercises. They do not, however, provide a complete view. To do this, the Likert ratings of the generated exercises will be discussed in Section 8.6. These ratings evaluate the fitness for purpose of each exercise in terms of their technical appropriateness and musical aesthetics independently of these characteristics and the evolutionary parameters. The rules violated by the generated exercises are presented in Section 8.7. This is accompanied by a discussion in Section 8.8 of the algorithm’s ability to consistently generate reasonably similar results when using the same parameter sets but different random number generator seeds. For reference, the parameters of the evolutionary algorithm were set as follows:

Number of Grade 1 exercises generated: 216 (from 72 source exercises) Number of Grade 2 exercises generated: 192 (from 64 source exercises) Number of Grade 3 exercises generated: 246 (from 82 source exercises) Population size: 50 Number of elites: 1 Probability of mutation: 0.01 (i.e., 1%) Random method: Gaussian Termination criteria: 100 generations with no improvement

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8.2 General Characteristics of the Generated Exercises

8.2.1 Overview

A preliminary examination of the generated exercises can be done by comparing the most typical values for a set of measured characteristics between the source and generated exercise. These results, presented in Sections 8.2.2 to 8.2.4, show how closely, in general, the generated exercises were able to match the characteristics of the source exercises. Overall, the generated exercises were able to closely match the most typical characteristics of the source exercises. This is a good indication of the fitness for purpose of the results, which will be discussed further in later sections. As the grade level increases the typical characteristics of the generated and source exercises diverge more. This is an expected consequence of the increased complexity of the source exercises, which naturally results in an increased difficulty in emulating their structure with the simplified fitness measures used in this work.

8.2.2 Grade 1

The Grade 1 generated exercises almost exactly match the most typical characteristics of the Grade 1 source exercises, as seen in Table 8.1. Compared to the source exercises, the generated exercises often exhibit a slightly smaller range, the most common highest note falling one full tone from G5 to F5. The generated exercises also include some semibreves, which were not seen in the source exercises. They also exhibit slightly fewer crotchet rests and slightly increased proportions of quaver and semiquaver rests.

8.2.3 Grade 2

Table 8.2 shows that, compared to the source exercises, the Grade 2 generated exercises exhibit only slight differences in their most typical characteristics. As with the Grade 1 exercises, the most common highest note drops a full tone, this time from A5 to G5. The typical proportions of crotchet note lengths increase in range from 80 – 90% to 75 – 90%. This is compensated for by increases in other note lengths, but not enough to alter the most typical proportions. The typical proportions of rest lengths also change. Crotchets are used less frequently, a drop which is compensated for by an increased use of quavers, semiquavers, and minims.

8.2.4 Grade 3

At the Grade 3 level, the most typical range of the generated exercises, shown in Table 8.3, is signiﬁcantly different from the most typical range of the source exercises. The most common lowest note increases a tone from G4 to A4, while the most common highest note drops almost half an octave from D6 to A5. This change is accompanied by an increase in the use of note lengths least frequently seen in the source exercises – dotted minims, semiquavers, dotted crotchets, dotted quavers, and semibreves. The Grade 3 generated exercises also show an overall decrease in the use of crotchet rests, due to the existence of semiquaver rests which were not seen in the source exercises.

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Table 8.1: Typical characteristics of published and generated Grade 1 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are ﬁxed and not expected to change.

Characteristic Typical Value(s) Source Exercises Generated Exercises

Key Signature* F major, C major F major, C major 4 4 Time Signature* 4 4 Exercise Length* 8 bars 8 bars Range 12 semitones (one octave) 12 semitones (one octave) F4 → G5 F4 → F5 Note lengths 90 – 100% crotchets 90 – 100% crotchets 0 – 10% quavers 0 – 10% quavers 0 – 5% minims, dotted minims, semiquavers 0 – 5% minims, dotted minims, semiquavers, semibreves Rest Lengths 95 – 100% crotchets 90 – 100% crotchets 0 – 5% quavers, semiquavers 0 – 10% quavers, semiquavers Ratio of Notes to Rests 90% notes : 10% rests 90% notes : 10% rests Intervals 95 – 100% gaps of 1 scale degree 95 – 100% gaps of 1 scale degree 0 – 5% gaps of 0 or 2 – 7 scale degrees 0 – 5% gaps of 0 or 2 – 7 scale degrees

Table 8.2: Typical characteristics of published and generated Grade 2 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are ﬁxed and not expected to change.

Characteristic Typical Value(s) Source Exercises Generated Exercises

Key Signature* G major, A minor, F major G major, A minor, F major 4 3 4 3 Time Signature* 4, 4 4, 4 Exercise Length* 8 bars 8 bars Range 12 semitones (one octave) 12 semitones (one octave) G4 → A5 G4 → G5 Note lengths 80 – 90% crotchets 75 – 90% crotchets 0 – 10% quavers 0 – 10% quavers 0 – 10% minims 0 – 10% minims 0 – 5% dotted minims, semiquavers, dotted 0 – 5% dotted minims, semiquavers, dotted crotchets, dotted quavers, semibreves crotchets, dotted quavers, semibreves Rest Lengths 95 – 100% crotchets 85 – 100% crotchets 0 – 5% quavers, semiquavers, minims 0 – 15% quavers, semiquavers, minims Ratio of Notes to Rests 95% notes : 5% rests 95% notes : 5% rests Intervals (as scale degrees) 85 – 95% gaps of 1 scale degree 85 – 95% gaps of 1 scale degree 0 – 10% gaps of 0 or 2 scale degrees 0 – 10% gaps of 0 or 2 scale degrees 0 – 5% gaps of 2 – 7 scale degrees 0 – 5% gaps of 2 – 7 scale degrees

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Table 8.3: Typical characteristics of published and generated Grade 3 sight reading exercises. Ratios and proportions are represented in terms of time. Differences between the source and generated exercises are highlighted in bold. Characteristics marked with ‘*’ are ﬁxed and not expected to change.

Characteristic Typical Value(s) Source Exercises Generated Exercises

Key Signature* G major, A minor G major, A minor 4 3 4 3 Time Signature* 4, 4 4, 4 Exercise Length* 8 bars 8 bars Range 12 semitones (one octave) 12 semitones (one octave) G4 → D6 A4 → A5 Note lengths 80 – 90% crotchets, minims 75 – 90% crotchets, minims 0 – 10% quavers 0 – 10% quavers 0 – 10% dotted minims, semiquavers, 0 – 15% dotted minims, semiquavers, dotted crotchets, dotted quavers, dotted crotchets, dotted quavers, semibreves semibreves Rest Lengths 95 – 100% crotchets 90 – 100% crotchets 0 – 5% quavers, minims 0 – 5% quavers, minims 0 – 5% semiquavers Ratio of Notes to Rests 95% notes : 5% rests 95% notes : 5% rest Intervals (as scale degrees) 85 – 95% gaps of 1 scale degree 85 – 95% gaps of 1 scale degree 0 – 10% gaps of 2 scale degrees 0 – 10% gaps of 2 scale degrees 0 – 5% gaps of 0 or 3 – 7, 0 – 5% gaps of 0 or 3 – 7, or 14 scale degrees or 14 scale degrees

8.3 Fixed Characteristics

8.3.1 Use of Key Signatures

As the key signature in each algorithm conﬁguration is hard-coded to match the key signature of the related source exercise, the distribution of key signatures used by the generated exercises is exactly the same as the distribution of key signatures used by the source exercises. For convenience, this distribution has been validated in Figure 8.1.

8.3.2 Use of Time Signatures

As with the key signatures, the time signature in each algorithm conﬁguration was hard-coded to match the time signature of the related source exercise. Given this, the distribution of time signatures used by the generated exercises again exactly matches the distribution of time signatures used by the source exercises. This distribution has been validated in Figure 8.2.

8.3.3 Length

The lengths of the generated exercises, shown in Figure 8.3, are almost identical to those of the source exercises. As with the key and time signatures, each algorithm configuration contained a hard-coded length in terms of the number of bars. However, the algorithm does not currently support anacruses, which are sometimes present in the source exercises. In cases where a source exercise contained an anacrusis, the target length specified in the related algorithm configuration was set to the total number of bars in the source exercise ignoring the anacrusis.

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Figure 8.1: The key signatures used by the generated exercises. Unless followed by an ‘m’ indicating a minor key, the key signatures are major.

Figure 8.2: The time signatures used by the generated exercises

Figure 8.3: The number of bars in each of the generated exercises

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That is, if the source exercise contained 16 bars with an anacrusis, the algorithm conﬁguration would contain a ﬁxed target length of 16 bars.

8.3.4 Pitch Range

The distributions of pitch ranges between the generated and source exercises, shown in Fig- ures 8.4(a) and 8.4(b) respectively, are similar. All three distributions peak at 12 semitones and drop significantly in their use of other range sizes. Compared to the source exercises, the generated exercises exhibit a greater variety of ranges and an increased use of smaller ranges (i.e., ranges less than 12 semitones in size). Although the range for each exercise was fixed with respect to a particular source exercise, the algorithm does not enforce that the specified range be used to its limits, only that all pitches selected must fall within that range. So as not to overly restrict the solution space, the algorithm also does not currently allow a desired most common pitch to be specified for an exercise. It is for these reasons that the range sizes, range spreads, and most common pitches at every grade level differ between the three sets of results and the source exercises, despite the exercises in each set all being generated using the same configuration values at each grade level. Compared to the source exercises, the generated exercises show a less consistent use of range and a larger variation in the most frequently used pitches. This is expected given that full use of the range is not enforced, and that the most frequent pitch of a generated exercise is not specifically influenced by the algorithm. Figures 8.6(a), 8.6(b), and 8.6(c) show the range spread and most common pitches of each generated Grade 1 exercise for the three unique random number generator seeds. Fig- ures 8.8(a), 8.8(b), and 8.8(c) provide the range spread and most common pitches of the generated Grade 2 exercises. Finally, Figures 8.10(a), 8.10(b), and 8.10(c) show the range spread and most common pitches of the generated Grade 3 exercises. For reference, the range spreads and most common pitches of the source exercises are given in Figures 8.5, 8.7, and 8.9 for Grades 1, 2, and 3, respectively.

8.4 Target Characteristics

8.4.1 Proportion of Notes vs. Rests

The amount of time in each exercise that should be filled by notes and rests is not specified exactly in the source exercises, but can be inferred from the target proportions of specific note and rest lengths. That is, if the target proportion for crotchet notes is 0.5, the target proportion of quaver notes is 0.25, and target proportion of crotchet rests is 0.25, it can be inferred that the target proportion of notes is 0.75. In the generated exercises there were no cases where an exercise contained rests if its corresponding source exercise contained no rests. This is because rests were not generated at any stage of the algorithm’s execution when a source exercise did not contain any rests. For cases where both note and rest target proportions were provided, the resulting exercises regularly matched those target proportions exactly. As the complexity of the solution space increased (i.e., as the target grade level increased), the target note and rest

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(a) Generated exercises

(b) Source exercises

Figure 8.4: Pitch ranges of the Grade 1, 2, and 3 source and generated exercises in semitones

Figure 8.5: Range spread and most common pitch for each Grade 1 source exercise

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(a) First set of Grade 1 generated exercises

(b) Second set of Grade 1 generated exercises

Figure 8.6: Range spread and most common pitch for the three sets of Grade 1 generated exercises 214 CHAPTER 8. EVALUATING THE EVOLUTIONARY ALGORITHM

Figure 8.7: Range spread and most common pitch for each Grade 2 source exercise

proportions were still frequently achieved, but less so. This is likely due to the larger number of allowable note and rest lengths at higher difﬁculty levels. In these cases the algorithm simply has more opportunity to select notes and rests with lengths that do not comply with the target proportions.

Figures 8.12(a), 8.12(b), and 8.12(c) show the proportions of notes and rests for each of the three Grade 1 result sets. Figures 8.14(a), 8.14(b), and 8.14(c) show the proportions for the Grade 2 generated exercises, and Figures 8.16(a), 8.16(b), and 8.16(c) provide the proportions for Grade 3. The proportions of notes and rests in the source exercises for Grades 1, 2, and 3 are provided for reference in Figures 8.11, 8.13, and 8.15, respectively.

8.4.2 Note Lengths

The generated exercises closely emulate the target note lengths extracted from the source exercises. This is shown in Figures 8.17(a) and 8.17(b) for Grade 1, Figures 8.18(a) and 8.18(b) for Grade 2, and Figures 8.19(a) and 8.19(b) for Grade 3.

At each difficulty level there were note lengths in some exercises that were not present in any of the source exercises. For Grade 1 the only unallowable note length used was a semibreve. This is not of significant concern given that semibreves are valid note lengths, and not unheard of at a Grade 1 level even though they are not present in the sample of Grade 1 source exercises used in this work. The unallowable note lengths at the Grade 2 and 3 levels, however, represent more of an issue. These notes, grouped together in the ‘Other’ category, represent lengths such as doubly dotted quavers and hemidemisemiquavers, which are rarely if ever seen at even the highest difficulty levels. However, exercises containing notes with a length of ‘Other’ are few in number and the generated exercises at every difficulty level most typically contain only notes with allowable lengths. It is likely that the exercises with ‘Other’ note lengths are rated as ‘Very Bad’ on the Likert scale, due to the excessive difficulty of playing the unallowable lengths.

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(a) First set of Grade 2 generated exercises

(b) Second set of Grade 2 generated exercises

Figure 8.8: Range spread and most common pitch for the three sets of Grade 2 generated exercises 216 CHAPTER 8. EVALUATING THE EVOLUTIONARY ALGORITHM

Figure 8.9: Range spread and most common pitch for each Grade 3 source exercise

8.4.3 Rest Lengths

As with the note lengths, the proportions of rest lengths in the generated exercises are reasonably close to the proportions of rest lengths in the source exercises. This can be seen in Figures 8.20(a) and 8.20(b) for Grade 1, Figures 8.21(a) and 8.21(b) for Grade 2, and Fig- ures 8.22(a) and 8.22(b) for Grade 3. At each difficulty level the generated exercises exhibited some rest lengths that were not present in the source exercises. For example, the Grade 1 generated exercises had some minim rests, and the Grade 3 generated exercises had several semiquaver rests. The generated exercises at all three difficulty levels also contained rests with lengths classified as ‘Other’, a category denoting lengths not seen in any of the source exercises. The use of ‘Other’ rest lengths in the generated exercises increases with the target difficulty level. However, many of these lengths are dotted crotchets and semibreves, rather than more unplayable lengths such as doubly dotted semiquavers. This means that, unlike exercises with ‘Other’ note lengths, exercises with ‘Other’ rest lengths are not necessarily unplayable or assigned the ‘Very Bad’ Likert rating. Additionally, although the Grade 3 source exercises do not contain any semiquaver rests, it is not unheard of for exercises at this level to contain such rest lengths. This means that exercises containing these rest lengths are not necessarily unfit for purpose. Overall, the proportions of rest lengths are more variable in the generated exercises compared to the source exercises. This indicates that the generated exercises were not always able to match the target rest proportions exactly. They were, however, able to come close. Additionally, the spread of proportional values in the generated exercises is close to those of the source exercises. The generated exercises do not match the target rest proportions as closely as they do the target note proportions. It is important to note that this is most likely a side effect of the exercises containing significantly fewer rests than notes. A low number of rests within each exercise means that discrepancies between the actual and target rest proportions are amplified simply because each individual rest represents a relatively large proportion of the overall rest time. This results in cases where a single rest length being of an ‘unallowable’ length can have

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(a) First set of Grade 3 generated exercises

(b) Second set of Grade 3 generated exercises

Figure 8.10: Range spread and most common pitch for the three sets of Grade 3 generated exercises 218 CHAPTER 8. EVALUATING THE EVOLUTIONARY ALGORITHM

Figure 8.11: Percentage of time ﬁlled by notes and rests in each Grade 1 source exercise

a large effect on the overall rest proportions. For example, if an exercise was given a target of containing 4 crotchet rests, having one of those rests generated as two quaver rests means that 25% of the rest time is filled by an ‘unallowable’ length, and the target rest proportion was only 75% met. This situation is much less likely to happen with note proportions, simply because significantly more time within each exercise is filled by notes.

8.4.4 Intervals

At each of the three difﬁculty levels, the proportions of intervals exhibited in the generated exercises closely match the target proportions set by the source exercises. This can be seen in Figures 8.23(a) and 8.23(b) for Grade 1, Figures 8.24(a) and 8.24(b) for Grade 2, and Figures 8.25(a) and 8.25(b) for Grade 3.

Across each grade level the use of intervals with a size of 0 is higher in the generated exercises than in the source exercises. However, as this increase in use is only slight it is not overly concerning. The Grade 3 generated exercises also show an increased use of intervals with the sizes 1, 2, and 3, but again the difference is not signiﬁcant. Compared to the source exercises, the Grade 1, 2, and 3 generated exercises exhibit greater variation in interval proportions. As with the rest length proportions, this is most likely an indication that the generated exercises were not always able to exactly match the target proportions. They were, however, able to come close.

The Grade 3 generated exercises contain a small number of intervals with sizes deﬁned as ‘unallowable’. That is, sizes which are not seen in the source exercises. There are also no Grade 3 generated exercises with size 14 intervals. These were seen in the source material, although rarely. It is likely that these two outcomes are linked. That is, that those intervals generated with the unallowable sizes of 8, 9, and 12 were created as a side effect of the algorithm attempting to produce intervals with an allowable target size of 14.

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(a) First set of Grade 1 generated exercises

(b) Second set of Grade 1 generated exercises

Figure 8.12: Percentage of time ﬁlled by notes and rests for the three sets of Grade 1 generated exercises

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Figure 8.13: Percentage of time ﬁlled by notes and rests in each Grade 2 source exercise

8.5 Fitness

8.5.1 Validating the Implementation of the Fitness Measures

In order to validate the construction of the chosen fitness measures, the algorithm was executed 6 separate times, each with only one of the fitness measures turned on, and the mutation operator disabled. If a fitness measure has been both validly conceived and implemented correctly, its value should generally improve over time before reaching a plateau. Fitness measures exhibiting this pattern can be seen as an effective influence on the evolutionary process, thus a potentially valuable addition to the algorithm. Each fitness measure was evaluated individually to avoid any cases where different measures interfere with one another. Mutation was disabled as it introduces new musical information into the population. This would dilute the results, as it would not be clear if fitness had improved due to the measure being tested, or due to a lucky mutation. Figures 8.27 through 8.31 show the fitness values achieved when running the algorithm with each individual fitness measure and no mutation. In every case the overall fitness increases over time before reaching a stable state. As such, the fitness measures can be considered to have been validated.

8.5.2 Fitness of the Generated Exercises

The generated exercises across every grade level consistently achieved high fitness values on every fitness measure. This can be seen in Figures 8.32, 8.33, and 8.34 for Grades 1, 2, and 3, respectively. In terms of the spread of values for each fitness measure there is not a notable difference as the difficulty (i.e., grade level) of the generated exercises increases. Table 8.4 shows this more clearly, providing the minimum and maximum values for each fitness measure at each grade level, as well as the average and standard deviation of the fitness values. At each grade level there was at least one exercise that achieved a perfect score on each of the fitness measures. The average fitness value for each measure was consistently high, ranging between 0.95

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(a) First set of Grade 2 generated exercises

(b) Second set of Grade 2 generated exercises

Figure 8.14: Percentage of time ﬁlled by notes and rests for the three sets of Grade 2 generated exercises

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Figure 8.15: Percentage of time ﬁlled by notes and rests in each Grade 3 source exercise

Table 8.4: Summary of fitness values for each grade level of generated exercises. Shows that at least one exercise reached the maximum value for each fitness measure (i.e., 1.0), and that the average fitness values for each measure were high at every difficulty level.

Fitness Measure Grade Minimum Maximum Average Standard Deviation

Target note lengths 1 ~0.53 1.0 ~0.95 ~0.11 2 ~0.66 1.0 ~0.96 ~0.08 3 ~0.73 1.0 ~0.95 ~0.06 Target rest lengths 1 ~0.96 1.0 ~0.95 ~0.01 2 ~0.94 1.0 ~0.99 ~0.01 3 ~0.92 1.0 ~0.99 ~0.01 Allowable lengths 1 0.65 1.0 ~0.99 ~0.04 2 ~0.95 1.0 ~0.99 ~0.01 3 0.72 1.0 ~0.99 ~0.03 Target intervals 1 ~0.82 1.0 ~0.95 ~0.05 2 ~0.92 1.0 ~0.97 ~0.03 3 ~0.83 1.0 ~0.96 ~0.04 Allowable intervals 1 ~0.94 1.0 ~0.99 ~0.01 2 0.96 1.0 ~0.99 ~0.01 3 ~0.94 1.0 ~0.99 ~0.01 Melody shape 1 0.8 1.0 ~0.99 ~0.02 2 ~0.88 1.0 ~0.99 ~0.01 3 0.9 1.0 ~0.99 ~0.01

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(a) First set of Grade 3 generated exercises

(b) Second set of Grade 3 generated exercises

Figure 8.16: Percentage of time ﬁlled by notes and rests for the three sets of Grade 3 generated exercises

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(a) Grade 1 generated exercises

(b) Grade 1 source exercises

Figure 8.17: Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 2 generated exercises

(b) Grade 2 source exercises

Figure 8.18: Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 3 generated exercises

(b) Grade 3 source exercises

Figure 8.19: Amount of note time taken by each unique note length as a percentage of time taken by all notes in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 1 generated exercises

(b) Grade 1 source exercises

Figure 8.20: Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 2 generated exercises

(b) Grade 2 source exercises

Figure 8.21: Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 3 generated exercises

(b) Grade 3 source exercises

Figure 8.22: Amount of rest time taken by each unique rest length as a percentage of time taken by all rests in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 1 generated exercises

(b) Grade 1 source exercises

Figure 8.23: The percentage of intervals of each size used in the Grade 1 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 2 generated exercises

(b) Grade 2 source exercises

Figure 8.24: The percentage of intervals of each size used in the Grade 2 generated and source exercises. Bubble size indicates the number of exercises.

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(a) Grade 3 generated exercises

(b) Grade 3 source exercises

Figure 8.25: The percentage of intervals of each size used in the Grade 3 generated and source exercises. Bubble size indicates the number of exercises.

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Figure 8.26: The ‘Target note lengths’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

Figure 8.27: The ‘Target rest lengths’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

Figure 8.28: The ‘Allowable lengths’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

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Figure 8.29: The ‘Target intervals’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

Figure 8.30: The ‘Allowable intervals’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

Figure 8.31: The ‘Melody shape’ ﬁtness over a run of the algorithm where it is the only ﬁtness measure used and mutation is turned off

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Figure 8.32: The ﬁtness of the generated Grade 1 exercises over each ﬁtness measure. Bubble diameter is relative to the number of exercises.

Figure 8.33: The ﬁtness of the generated Grade 2 exercises over each ﬁtness measure. Bubble diameter is relative to the number of exercises.

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Figure 8.34: The ﬁtness of the generated Grade 3 exercises over each ﬁtness measure. Bubble diameter is relative to the number of exercises.

and 0.99 inclusive. Similarly, the standard deviations of the fitness values were consistently low, indicating that little variance was exhibited across the fitness values for each measure. The minimum values are more variable, both across fitness measures and within the same fitness measure across different grade levels. They can also be relatively low, in some cases more than 0.3 below the average. However, given the high average fitness and low standard deviations, such minimum values represent outliers rather than trends.

Overall, there are no fitness measures on which the generated exercises scored consistently better or worse. This is true both when comparing different fitness measures within a grade level, and when comparing fitness values on the same measures across different grade levels.

Given the application domain, it is likely that some of the fitness measures may have conflicting goals. That is, an increase in one fitness value may be directly related to a decrease in another. For example, consider an exercise which meets its target proportion of notes and rests, but contains two unallowable rest lengths (e.g., two quaver rests instead of a single crotchet rest). If one or both of those unallowable rests were changed to notes, the ‘Allowable lengths’ fitness of that exercise would improve. However, the extra notes would mean that the exercise no longer meets the target note and rest proportions, thus decreasing its fitness in the ‘Target note lengths’ and ‘Target rest lengths’ fitness measures. The results presented in this chapter indicate that the fitness measures do not influence one another, given that the generated exercises achieved consistently high fitness scores. As such, potentially conflicting goals amongst the fitness measures can be considered not an issue.

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8.5.3 Diversity of the Evolved Populations

The diversity of the evolved populations was recorded for each algorithm run using the method described in Section 6.7. The purpose of the diversity calculation is to determine whether the population is potentially converging too soon, an issue that would be suggested by low diversity values. Conversely, too high a diversity could indicate that the evolutionary drivers are not strong enough to guide the population towards overall improvement, or that the problem is not suitable. Figure 8.35 shows a typical progression of a population’s diversity over a single run of the algorithm. The diversity starts high and drops relatively quickly as the evolutionary pressure is applied. This coincides with a rapid increase in fitness. After these most dramatic improvements in fitness have been achieved the algorithm progresses more slowly. Fitness still improves over time but soon reaches a plateau. Diversity, however, continues to fluctuate. This is mostly due to the mutation operator introducing new, random musical elements into the population. These new elements add diversity, but in this case rarely improve the fitness of the best candidate. Results such as these validate that the populations are not prematurely converging, nor are the evolutionary drivers weak. Diversity does typically drop quickly, but it continues to spike throughout the algorithm’s execution and rarely drops below 0.2. These factors, combined with the positive results discussed in Section 8.6, suggest that the algorithm is functioning as intended.

8.6 Likert Quality Ratings

8.6.1 Grade 1

The majority of the Grade 1 generated exercises are ‘fit for purpose’, as seen in Figure 8.36(a), with over 60% being assigned a ‘Very good’, ‘Good’, or ‘Average’ rating. This proportion increases to almost 80% when small repairs are made to some exercises, as show in Figure 8.36(b). Figures 8.37(a) and 8.37(b) show these ratings in more detail. It can be seen that the proportion of Grade 1 generated exercises rated as ‘Very good’ dramatically increases after small repairs are made. Additionally, approximately 10% of the exercise deemed ‘unfit for purpose’ (i.e., rated ‘Bad’) are upgraded to a ‘fit for purpose’ rating. The decrease in the number of exercises rated ‘Average’ and ‘Good’ after repairs are due to many of these exercises being improved to a ‘Very good’ standard. Table 8.5 shows how the Likert ratings of the Grade 1 generated exercises changed after being repaired. It shows that, as expected, no exercise is rated worse after being repaired. Additionally, most exercises only increase their rating one level, for example from ‘Average’ to ‘Good’. Many of the exercises rated as ‘Bad’ could not be repaired, but the large majority of exercises rated ‘Average’ or ‘Good’ were able to be improved. Figures 8.38(a) through 8.38(d) provide examples of generated Grade 1 exercises assigned each of the Likert ratings. None of the exercises at this difficulty level were assigned a ‘Very bad’ rating, so no example has been given. Reasons are provided for each example’s rating. Further discussion of the Likert ratings as they relate to the ruleset for evaluating algorithmically generated musical sight reading exercises is provided in Section 8.7.

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Figure 8.35: A typical progression of diversity values over a single run of the algorithm. The ﬁtness line tracks the average value of the six ﬁtness measures for the best candidate in each generation’s population to provide a general indication of the population’s overall improvement.

(a) Before repair (b) After repair

Figure 8.36: Fitness for purpose of the Grade 1 generated exercises before and after repair

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When evaluating the Grade 1 generated exercises against the criteria for Grade 2 and Grade 3 exercises, the Likert ratings were predictably poor. Figure 8.39 shows that some of the Grade 1 generated exercises are ‘fit for purpose’ as Grade 2 exercises. These are not necessarily exercises that were ‘unfit for purpose’ as Grade 1 material, as there is some overlap between the two sets of criteria. They do not, however, reach the standards of a ‘Very good’ Grade 2 exercise. When examined with respect to the criteria for Grade 3 exercises, the Grade 1 generated exercises invariably receive ‘Bad’ ratings, indicating that they are not fit for purpose. This is because the Grade 1 generated exercises lack the complexity required at the Grade 3 difficulty level.

8.6.2 Grade 2

Figure 8.41(a) shows that approximately half of the Grade 2 generated exercises are fit for purpose. This is roughly 15% less than the Grade 1 generated exercises. The proportion of Grade 2 exercises rated as ‘fit for purpose’ increases once small repairs are made, reaching approximately the same percentage as the Grade 1 generated exercises before repairs. This drop in the number of ‘fit for purpose’ exercises is an expected result due to the increased complexity of the Grade 2 exercises compared to Grade 1. Figures 8.42(a) and 8.42(b) show the distributions of Likert ratings for the Grade 2 generated exercises in more detail, both before and after repairs are made. Before repairs, approximately 10% more exercises are rated as ‘Bad’ compared to Grade 1. After repairs, this drops to less than 5%, indicating that several exercises were able to be upgraded in fitness for purpose. Table 8.6 shows exactly how the ratings of the Grade 2 exercises changed after being repaired. As with the Grade 1 generated exercises, all of the Grade 2 exercises either stayed at the same rating, or improved their rating with repairs. Additionally, most of the Grade 2 generated exercises, if improved by repairs, improved their rating by just one level (e.g., ‘Bad’ to ‘Average’). The major difference between the Grade 1 and 2 distributions is the presence of ‘Very bad’ exercises. These account for around 10% of the Grade 2 generated exercises, a proportion which does not change after repairs are made. This indicates that the ‘Very bad’ exercises can not be upgraded in fitness for purpose, or even improved to a ‘Bad’ rating. Given that the criteria for a ‘Very bad’ rating is unplayable elements within an exercise, it is not surprising that a small number of changes could not resolve these issues. For reference, examples of generated Grade 2 exercises assigned each Likert rating are provided in Figures 8.43(a) through 8.43(e). When evaluated with respect to the criteria for Grade 1 exercises, Figure 8.44 shows

Table 8.5: Likert ratings of the Grade 1 generated exercises before and after repair

Post-repair Rating Very bad Bad Average Good Very good

Very bad - -- -- Bad - 53 18 1 1 Pre-repair Rating Average - - 3 38 1 Good - -- - 66 Very good - -- - 41

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(a) Before repair

(b) After repair

Figure 8.37: Likert ratings of the Grade 1 generated exercises before and after repair

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(a) An example of a Grade 1 generated exercise with a ‘Very good’ rating

(b) An example of a Grade 1 generated exercise with a ‘Good’ rating. This exercise received a ‘Good’ rating due to repeated pitches and minor syncopation.

(c) An example of a Grade 1 generated exercise with an ‘Average’ rating. This exercise received an ‘Average’ rating due to minor syncopation and poor rest placement.

(d) An example of a Grade 1 generated exercise with a ‘Bad’ rating. This exercise received a ‘Bad’ rating due to syncopation, some poor rest placement, unallowable intervals, and repeated pitches.

Figure 8.38: Examples of Grade 1 generated exercises assigned each of the Likert quality ratings. An example of an exercise rated as ‘Very bad’ is not provided as none of the Grade 1 exercises were assigned this rating.

Figure 8.39: Likert ratings of the Grade 1 generated exercise when viewed as Grade 2 exercises

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Figure 8.40: Likert ratings of the Grade 1 generated exercise when viewed as Grade 3 exercises

(a) Before repair (b) After repair

Figure 8.41: Fitness for purpose of the Grade 2 generated exercises before and after repair

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that the Grade 2 generated exercises are rarely fit for purpose. Most exercises reaching the ‘fit for purpose’ criteria are rated as ‘Average’, with just a single exercise placed in each of the ‘Good’ and ‘Very good’ categories. The same proportion of exercises are rated as ‘Very bad’, as the criteria for this category is similar across the difficulty levels. The remaining exercises – approximately 80% – fall into the ‘Bad’ category. Similar results are found when rating the Grade 2 generated exercises against the Grade 3 criteria. Again, the same exercises are rated as ‘Very bad’. However, a larger number of exercises reach the criteria for the ‘Average’ and ‘Good’ ratings, leading to more exercises overall being fit for purpose.

8.6.3 Grade 3

As discussed in Chapter 7, the expectations of consistent quality in the algorithm’s output at the Grade 3 level were low given the increased complexity of the Grade 3 source exercises. With this prediction in mind, the results were as expected. Figure 8.46(a) shows that just under 40% of the Grade 3 generated exercises are fit for purpose. This proportion increases to just over 40% in Figure 8.46(b) after repairs are made, leaving the majority of the generated exercises still unfit for purpose. Figures 8.47(a) and 8.47(b) show the distributions of ratings in more detail. Both before and after repairs the largest number of exercises are rated as ‘Bad’, with around 50% of the Grade 3 generated exercises falling into this category in both cases. As with the Grade 2 generated exercises, the same exercises are rated as ‘Very bad’ before and after repairs, indicating that these exercises can not be improved with only a small number of alterations. The largest improvement gained by the repairs is to the ‘Very good’ category, which increases from approximately 5% to almost 20%. Given the relatively low drop in the proportion of ‘Bad’ exercises, this increase is largely due to ‘Average’ and ‘Good’ exercises being upgraded in fitness for purpose. Table 8.7 shows how the ratings change in the Grade 3 generated exercises before and after repairs. Examples of Grade 3 generated exercises assigned each of the five Likert ratings can be seen in Figures 8.48(a) to 8.48(e). The ‘Very bad’ example is particularly notable, showing a larger proportion of unplayable elements than Figure 8.43(e), the ‘Very bad’ example from the Grade 2 generated exercises. This increase in proportion of unplayable elements is typical for the ‘Very bad’ Grade 3 generated exercises. As expected, Figure 8.49 shows that the Grade 3 generated exercises invariably fail to meet the standards of a Grade 1 exercise. This is most typically due to the Grade 3 exercises

Table 8.6: Likert ratings of the Grade 2 generated exercises before and after repair

Post-repair Rating Very bad Bad Average Good Very good

Very bad 19 - 1 -- Bad - 52 23 3 - Pre-repair Rating Average - - 5 24 1 Good - -- - 38 Very good - -- - 26

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(a) Before repair

(b) After repair

Figure 8.42: Likert ratings of the Grade 2 generated exercises before and after repair

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(a) An example of a Grade 2 generated exercise with a ‘Very good’ rating

(b) An example of a Grade 2 generated exercise with a ‘Good’ rating. This exercise received a ‘Good’ rating due to repeated pitches.

(c) An example of a Grade 2 generated exercise with an ‘Average’ rating. This exercise received an ‘Average’ rating due to poor placement of larger intervals.

(d) An example of a Grade 2 generated exercise with a ‘Bad’ rating. This exercise received a ‘Bad’ rating due to excessively long tied notes.

(e) An example of a Grade 2 generated exercise with a ‘Very bad’ rating. This exercise received a ‘Very bad’ rating due to the unplayable sequence in bar 6.

Figure 8.43: Examples of Grade 2 generated exercises assigned each of the Likert quality ratings

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Figure 8.44: Likert ratings of the Grade 2 generated exercise when viewed as Grade 1 exercises

Figure 8.45: Likert ratings of the Grade 2 generated exercise when viewed as Grade 3 exercises

(a) Before repair (b) After repair

Figure 8.46: Fitness for purpose of the Grade 3 generated exercises before and after repair

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being too complex. Almost the same can be said when evaluating the Grade 3 generated exercises against the criteria for Grade 2 exercises. However, instead of all the exercises being unﬁt for purpose, in this case a small number are rated as ‘Average’. This can be seen in Figure 8.50.

8.7 Rule Violations

The categories of rules broken by the Grade 1, 2, and 3 generated exercises are summarised in Figures 8.51(a), 8.51(b), and 8.51(c), respectively. At all three grade levels, the most commonly broken rules relate to the melodic aesthetics of an exercise. This means that whilst the exercises might be technically appropriate, they contain elements which are not pleasing to the ear. Few exercises exclusively violate rules relating to technical appropriateness. There are two reasons for this. Firstly, many of the rules relating exclusively to technical appropriateness relate to an exercise achieving some target proportion of rests, notes, and intervals. As shown in previous sections, the algorithm has been quite successful at this task. Secondly, as discussed when describing the ruleset in Chapter 7, factors relating to the technical appropriateness often also relate to the melodic aesthetics of an exercise, as elements of an exercise which are technically inappropriate (e.g., placement of long notes) typically also sound poor. This means that violations of technical appropriateness often fall into the ‘Both’ category, as these rules typically also relate to melodic aesthetics.

8.8 Repeatability in the Quality of Output

8.8.1 Fixed Characteristics

Section 8.3 provided a discussion on how the three different result sets for the three grade levels meet the fixed characteristics (i.e., time signature, key signature, length). As these characteristics are fixed, they are the same between different executions of the algorithm regardless of the random number generator seed used. The only difference is in the range. Whilst the range is fixed in each algorithm configuration, the exercises generated do not necessarily use their assigned range to its limits. This means that the exact range of each generated exercise differs between the three result sets. Similarly, the most frequently used pitch in each exercise is not directly influenced, and thus can differ when using the same algorithm configurations with different random number generator seeds. However, despite this, Figures 8.6, 8.8, and 8.10 showed that the three sets of results are similar in their use of range and most common pitches.

Table 8.7: Likert ratings of the Grade 3 generated exercises before and after repair

Post-repair Rating Very bad Bad Average Good Very good

Very bad 26 -- -- Bad - 111 18 1 - Pre-repair Rating Average - - 17 26 2 Good - -- 5 29 Very good - -- - 11

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(a) Before repair

(b) After repair

Figure 8.47: Likert ratings of the Grade 3 generated exercises before and after repair

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(a) An example of a Grade 3 generated exercise with a ‘Very good’ rating

(b) An example of a Grade 3 generated exercise with a ‘Good’ rating. This exercise received a ‘Good’ rating due to poorly placed rests and large intervals.

(c) An example of a Grade 3 generated exercise with an ‘Average’ rating. This exercise received an ‘Average’ rating due to poor placement of rests and poor interval selection.

(d) An example of a Grade 3 generated exercise with a ‘Bad’ rating. This exercise received a ‘Bad’ rating due to poor rest placement and interval selection.

(e) An example of a Grade 3 generated exercise with a ‘Very bad’ rating. This exercise received a ‘Very bad’ rating due to the unplayable sequences in bars 6, 7, and 12.

Figure 8.48: Examples of Grade 3 generated exercises assigned each of the Likert quality ratings

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Figure 8.49: Likert ratings of the Grade 3 generated exercise when viewed as Grade 1 exercises

Figure 8.50: Likert ratings of the Grade 3 generated exercise when viewed as Grade 2 exercises

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(a) Grade 1

(b) Grade 2

Figure 8.51: The categories of rules broken by the Grade 1, 2, and 3 generated exercises

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8.8.2 Proportion of Notes vs. Rests

Section 8.4 showed some of the consistency between the three sets of results on meeting the target characteristics. Speciﬁcally, Figures 8.12, 8.14, and 8.16 show the proportions of notes and rests between the three sets of algorithm runs for Grade 1, 2, and 3, respectively. Similar to the results for range spread and most commonly used pitches, the proportions of notes and rests are almost identical between the three sets of results.

8.8.3 Note Lengths

Figures 8.52, 8.53, and 8.54 show the proportions of note time taken by each unique note length for each of the three sets of results for Grade 1, 2, and 3, respectively. In all cases, the three sets of results for each grade level match closely with one another. For example, the proportions of note lengths in the Grade 1 generated exercises feature large numbers of crotchets, slightly fewer quavers, and relatively small numbers of minims, dotted minims, and semiquavers. Similarly, every result set for the Grade 2 level shows large proportions of crotchet length notes, mid-sized proportions of minims and quavers, and small proportions of the remaining lengths. The spread of proportion values are similar, and all three result sets exhibit note lengths with ‘Other’ lengths. The same can be said when comparing the three result sets at the Grade 3 level. Combined, these results indicate that the algorithm is able to consistently produce exercises with similar proportions of note lengths when using the same parameter sets. That is, exercises generated with the same conﬁgurations but using different random number generator seeds can be expected to exhibit similar if not identical proportions of note lengths.

8.8.4 Rest Lengths

The proportions of rest lengths seen in the Grade 1, 2, and 3 exercises across the three sets of results are shown in Figures 8.55, 8.56, and 8.57, respectively. At each grade level, the proportions are notably close between the result sets The similarities extend to both the spread of proportion values and number of exercises with each proportion of a rest length. As with the proportions of note lengths described in 8.8.3, these results indicate that the algorithm is consistent in its ability to generate the desired target proportions of rests.

8.8.5 Intervals

Figures 8.58, 8.59, and 8.60 show the use of intervals over the three result sets for Grades 1, 2, and 3, respectively. At every grade level the three distributions closely match, both in the spread and size of the proportions. There are some minor differences between the proportions of infrequently seen interval sizes. For example, the second set of Grade 1 generated exercises contain no intervals with a size of 7. Similarly, the ﬁrst set of results for Grade 3 contain the only exercises with intervals with a size of 12. However, these differences are relatively minor, and represent only one or two exercises. These results indicate that the algorithm is capable of consistently meeting target interval proportions.

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(a) Run 1

(b) Run 2

Figure 8.52: Amount of note time taken by each unique note length in the Grade 1 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.53: Amount of note time taken by each unique note length in the Grade 2 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.54: Amount of note time taken by each unique note length in the Grade 3 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.55: Amount of rest time taken by each unique rest length in the Grade 1 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.56: Amount of rest time taken by each unique rest length in the Grade 2 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.57: Amount of rest time taken by each unique rest length in the Grade 3 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.58: The percentage of intervals of each size used in the Grade 1 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.59: The percentage of intervals of each size used in the Grade 2 generated exercises over each result set

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(a) Run 1

(b) Run 2

Figure 8.60: The percentage of intervals of each size used in the Grade 3 generated exercises over each result set

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8.8.6 Likert Quality Ratings

Figures 8.61, 8.62, and 8.63 show the distributions of Likert ratings over the three result sets for Grade 1, 2, and 3, respectively. The results for each grade level are extremely consistent in their proportions of ‘Very bad’ and ‘Bad’ ratings, meaning that each set of exercises generated with the same target grade level contain similar proportions of ‘fit for purpose’ and ‘unfit for purpose’ exercises. Ratings within the ‘fit for purpose’ range, however, are not as consistent. For example, the first and third result sets for Grade 1 contain approximate 15% ‘Very good’ ratings. On the other hand, the second result set for Grade 1 contains just over 30% ‘Very good’ ratings. Similar characteristics are present, if less pronounced, at the Grade 2 and 3 levels. One important facet to note is that many of the exercises generated with the same configurations received the same rating. This is particularly true of the generated exercises which are not fit for purpose. That is, if an exercise resulting from a particular configuration received a ‘Very bad’ or ‘Bad’ rating in the first result set, the corresponding exercises in the second and third result sets are very likely to have also received the same rating. Exercises generated with the same configurations that were assigned ‘fit for purpose’ ratings are less likely to be given the same rating across different result sets. However, there are very few cases where two exercises generated with the same configuration are not at least assigned adjacent ratings. For example, it is rare that an exercise that was rated as ‘Average’ in one result set would have a corresponding rating in another result set of ‘Very good’. These results indicate that the algorithm is capable of consistently producing ‘fit’ or ‘unfit for purpose’ results with a given set of configurations. They also suggest that repeated use of a ‘fit for purpose’ configuration may not result in consistently high or low quality results.

8.9 Summary

This chapter presented the results of executing the experimental design detailed in Chapter 7. Overall the results were supportive of the algorithm design, particularly at the Grade 1 and 2 difficulty levels. They showed that the algorithm was not only capable of emulating the characteristics of the source exercises, but able to do so in a way that was generally fit for the purpose of musical sight reading. At the Grade 3 level the algorithm was less consistently able to produce quality sight reading exercises. This was an expected outcome due to the increased complexity represented by this difficulty level. However, the results show the potential of the algorithm to manage this increased complexity. This is an avenue for future work and will be discussed further in Chapter 9. When repeatedly executing the algorithm using the same set of configurations but different random number generator seeds the algorithm was relatively consistent in its output on all measures, including general characteristics their fitness for purpose. When a generated exercise was not ‘fit for purpose’ the reason was recorded, revealing potential avenues for future improvement. These avenues, as well as a deeper discussion of the issues raised in this chapter and the work presented in this thesis as a whole are discussed in the next chapter.

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(a) Run 1

(b) Run 2

Figure 8.61: The Likert ratings over each result set of the Grade 1 generated exercises

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(a) Run 1

(b) Run 2

Figure 8.62: The Likert ratings over each result set of the Grade 2 generated exercises

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(a) Run 1

(b) Run 2

Figure 8.63: The Likert ratings over each result set of the Grade 3 generated exercises

266 9 Discussion and Future Work

9.1 Overview

The previous chapter presented the results of executing the experimental design outlined in Chapter 7. This experimental design defined a process for measuring the quality of output of the evolutionary algorithm for generating musical sight reading exercises described in Chap- ter 6. This chapter will discuss the implications of these results, including possible future work. Also discussed is the significance of the results overall, and other avenues for technological development within the field of music practice and education. First, Section 9.2 revisits the research questions defined in Chapter 1, and describes how they have been addressed through the work presented in this thesis. Section 9.3 then describes how the taxonomy presented in Chapter 3 could be applied to other domains, and ways in which it could be further developed. Section 9.4 returns to the general question of how software could be better utilised in music education. Specifically, it focuses on the opportunity to develop intelligent tutoring systems which are able to adapt their content to the user’s specific needs. The current capabilities of the evolutionary algorithm are examined in Section 9.5. This is followed by a discussion in Section 9.6 on how the algorithm could be further developed, and the relative costs and benefits of the potential directions for future work. The impact of expert models is discussed in Section 9.7, including what more sophisticated models of expert-written musical sight reading exercises may contain, and how that might affect the algorithm currently and in the future. Lastly, Section 9.8 shows how the algorithm can be applied to generate sight reading exercises for instruments other than the flute.

9.2 Research Questions in Review

In Chapter 1, four research questions were proposed. The work presented in this thesis has addressed these questions as follows:

1. How is technology currently being used in music education? This question has been addressed in two ways. First, on a broad level through an examination of the history of music education in Chapter 2. Then, a more directed approach was taken, focusing on the use of applications on the iOS platform.

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This platform was chosen due to its popularity and large quantity of applications targeted to music education. By applying the taxonomy presented in Chapter 3, the content and activities within the applications could be both described and compared. This revealed which areas of musical knowledge the applications focused on, the depth to which this was done, and how users were tasked with demonstrating their knowledge and skills. Additionally, the applications were reviewed in terms of their general design with respect to established principles of best practice within the literature. Also identiﬁed were the methods of progression within the applications, how feedback mechanisms were applied, and their educational outcomes.

2. What are the opportunities for increased or more effective use of technology in musical sight reading education? The data gathered through the process of addressing the ﬁrst research question allowed for the identiﬁcation of several areas of opportunity to better utilise the capabilities of technology in music education. For example, it was found that most applications on the iOS platform use ‘drill-and-practice’ style activities. These types of activities are effective for rote learning, but typically result in low-level learning outcomes as they do not encourage the acquisition of deep knowledge. One opportunity – the algorithmic generation of musical sight reading exercises – was chosen as the focus for this work. Section 9.4 will discuss other opportunities and how they might be addressed in the future.

3. What algorithmic techniques are appropriate for generating music that is aesthetically pleasing, playable by a human, and appropriate for the development of musical sight reading skills? In addition to discussing the historical context of modern techniques, Chapter 2 identi- ﬁed key algorithms used to generate music. The relative beneﬁts of each approach were discussed, with accompanying examples showing how the techniques have been used in the past. This discussion led to the selection of evolutionary algorithms as the focus of this work. Given this, a more in-depth discussion of their use within the literature was provided.

4. How can algorithmically generated musical sight reading exercises be measured for fitness of purpose? To determine the effectiveness of any solution designed to generate musical sight reading exercises, a method for evaluating generated solutions is required. Such a method was not available within the literature. Addressing this question resulted in a ruleset and framework being developed, defined in Chapter 7. Comprising 29 individual rules based on literature in music theory and an analysis of expert-written examples, the ruleset considers both the general aesthetics and technical appropriateness of a musical sight reading exercise. The framework describes how the ruleset should be applied, and how the rules broken by an exercise can be translated into an overall quality rating on a five-point Likert scale. The evaluation framework is intentionally agnostic of the algorithm used to generate the exercises. This means it can be applied to future work which may take a different

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approach.

9.3 Expanding the Taxonomy

The taxonomy presented in Chapter 3 is not a static tool – it is intended that it will evolve and grow with the field. Its use in this work raises some points to consider for its future development. The first point is that of broad areas. Most portions of the taxonomy are relatively specific and targeted in their definition. For example, the ‘Reading’ category covers the aspects of musical knowledge needed to understand what pitch to play and its intended length relative to other pitches. This is a well-defined scope, and it is clear which areas of musical knowledge should be included. The same can not be said of the ‘Instrument-specific Instruction’ and ‘Historical or Gen- eral Knowledge’ content categories. Whilst it is clear which aspects of musical knowledge should fall under each of these categories, the content they describe is broad and diverse. Fur- ther development to these categories could sub-divide the relevant content so that it could be more accurately described. For example, one of the areas covered by the ‘Historical or Gen- eral Knowledge’ category is ‘Well-known works’. This area could be further categorised by genre, time period, composer, instrument, or some combination of these descriptors. Similarly, ‘Instrument-specific Instruction’ could categorise content based on the class of instrument and the type of instruction (e.g., beginning or advanced). Given the broad nature of these content categories, an argument could be made for developing complete individual taxonomies for each. This would be a significant undertaking, and require a thorough examination of relevant literature, educational materials, and possibly consultation with subject matter experts. When defining the activity types in the taxonomy, the goal was to describe the structure of each activity only. For example, the activities are largely defined by how a question is presented (e.g., through auditory or visual means) and how students are asked to respond (e.g., recognition or description). In the future, it may be valuable to incorporate more information. One area which could be included is the complexity of the activity. This is not the same as difficulty, but the two areas may overlap. Complexity should consider the intended skill level of the student, the cognitive load they are placed under, and the number of steps required for successful completion of the activity. For example, identifying the ‘crotchet’ from four pictures of different note types is less complex than notating a perfect fifth interval in the key of A major.

9.4 Opportunities for Software in Music Education

One outcome of the state of the art analysis of iOS applications presented in Chapter 5 was the identiﬁcation of several areas of opportunity for better utilisation of technology. Only one of these areas was selected as the focus for this work, meaning many areas remain for potential future development. One key area is the development of personalised content. Often described as Intelligent Tutoring Systems or Computer Aided Instruction [91, 197, 198], these are systems which follow a loop of:

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1. Present the user with a task 2. Assess the user’s response and provide them with feedback 3. Use knowledge of the user’s errors to select future tasks which address their weaknesses

Typically, a user’s errors are classiﬁed, then an appropriate follow-up activity addressing that type of error is selected from a library of tasks. One way technology can be better utilised in this process is by generating tasks algorithmically. This would remove the need to curate an extensive library of activities which address all potential user errors. Some applications already do this. However, they exclusively do so for content and activity types where the generation of appropriate tasks is trivial. For example, if a user is consistently poor at identifying crotchet and semibreve symbols, they are more frequently asked to identify those symbols. Or, if the user is being tasked with notating certain intervals and they consistently fail to accurately write a minor third, they are more frequently asked to write a minor third interval. Given that adaptive approaches have been shown to enhance and speed student learning [44, 198], it would be wise to expand this approach to more complex tasks and areas of knowledge. The work in this thesis has focused largely on iOS applications. However, the software evaluation framework described in Chapter 5 can be applied to applications on other platforms. In the future it would be valuable to perform similarly structured reviews of applications developed for the Android, Windows, OSX, and web-based platforms. This would provide a detailed view of the capabilities of the applications supported by other devices, and may reveal further opportunities for development. Additionally, the outcomes between the platforms could be compared, resulting in an overall state of the art of the ﬁeld. It is also likely that some opportunities for development would be common between the platforms. This means that the overall utility and potential use of any work undertaken to address these opportunities would increase. Structured reviews could also be undertaken for traditional music education materials. As with the software applications, this would reveal what musical content is covered, and how students are tasked with practicing and demonstrating their knowledge and skills. One outcome of such a review would be the ability to compare and align the capabilities of traditional educational materials with software-based materials. Additionally, it may reveal areas and tasks which are covered by traditional materials but not yet in software. This would raise the question of whether these areas and tasks could be covered by software, why or why not, and how software coverage might be achieved.

9.5 Current Capabilities of the Evolutionary Algorithm

The results presented in Chapter 8 show that the evolutionary algorithm for generating musical sight reading exercises, as described in Chapter 6, is capable of producing fit for purpose results. Moreover, the majority the output was fit for purpose. This is particularly true at the Grade 1 and 2 difficulty levels. Although the output at the Grade 3 level is not as robust, it demonstrates the algorithm’s potential to apply to more complex difficulty levels. These results are particularly promising given the relatively simplistic and general nature of the fitness

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measures. The key question surrounding the algorithm is whether it generates appropriate solutions for musical sight reading. This is partially addressed by the structure of the algorithm itself, in that it is designed around the notion of emulating models of expert-written examples. It was shown to successfully do this, as the generated exercises exhibited similar if not identical characteristics to the expert-written source exercises. The capabilities of the algorithm to produce appropriate, fit for purpose output is additionally supported by the Likert quality ratings, which show that the generated exercises also conform to the expectations of musical aesthetics and technical appropriateness defined by the field of music theory. The repeatability of the results also indicate that the quality of the algorithm’s output is a result of its design, rather than random factors. The results in Chapter 8 indicate that the quality of many of the solutions can be improved or even upgraded with minor adjustments. Many of these adjustments can be implemented algorithmically, and represent a valuable path for future work. When examining the Likert quality ratings of an exercise with respect to its characteristics there appear to be no links. That is, the quality of an exercise is not related to its key signature, time signature, length, note proportions, or interval proportions. This indicates that the inability of the algorithm to consistently produce quality output at the Grade 3 level is a result of an increase in overall complexity rather than any other factors. Higher quality results should be possible were this complexity to be better modelled and incorporated into the evolutionary process. For example, the presence of rests in an exercise affects its overall structure. If not placed carefully within a sequence of notes, rests can cause unintended syncopation or awkward breaks in phrasing. The existence of a rest also affects the measurement of intervals within an exercise, as two notes separated by a rest are not considered to be part of an interval during fitness calculations. Given that rests become more frequent in number and length at later difficulties, these issues become more prominent and affect the overall solution quality. The pitch range of exercises also grows with the difficulty level. That is, exercises at the Grade 3 level cover a greater range of pitches than exercises at the Grade 1 level. An increase in pitch range increases the solution space. This is because there are simply more potential pitches to select, thus more potential for an algorithm to select pitch sequences which are aesthetically or technically inappropriate. Naturally, this increase in the size of the solution space also causes an increase in the difficulty of generating a quality solution. This problem is com- pounded when considering other musical artefacts, as the size of the solution space similarly increases with additions to the sets of allowable note lengths and intervals. The interaction of these elements also needs to be considered. For example, increasing the allowable intervals in an exercise where only crotchet note lengths are allowed would increase the overall solution space. If additional note lengths were also to be allowed, the solution space would increase exponentially, not linearly. This is because some interval sequences, which would have been appropriate between crotchets, would not be appropriate with shorter note lengths. These issues were expected, particularly given the general approach taken to measuring fitness. Further work in modelling the requirements of higher difficulty exercises and incorporating those models into the algorithm would help to manage the expanding size of the solution space, thus the algorithm’s capacity to generate more complex exercises.

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One potential drawback of the Likert ratings currently presented in the results is that they were all measured using a single rater. To check for consistency more robustly it would be ideal to have the same exercises rated using the same framework by multiple experts.

9.6 Future Directions for Algorithmic Development

When developing an algorithm for generating musical sight reading exercises, there are trade- offs to be made. One key decision is whether the algorithm will be specific or general. For example, a specific algorithm might only generate Grade 2 exercises focusing on breath control for the clarinet. Alternatively, a general algorithm might aim to generate an exercise for any wind instrument at any difficulty level. There are benefits and drawbacks to each approach. The more specific the target, the more focused the algorithm can be. This means more domain knowledge can be incorporated and more restrictive parameters can be set. It is likely that a specific approach would enable the quality of output to be improved. However, a specific approach would, by definition, also be limited in its utility. A general approach would need to consider many more factors. For example, for an algorithm to target multiple instruments it would need to model the differences between the technical requirements for those instruments. A more general algorithm is likely to have an increased utility. However, it also takes on the risk of attempting to cover too much scope, which would limit its ability to generate quality output. The approach taken in this work is somewhere in between. It is not so general as to target many difficulty levels, but it also isn’t restricted to a single type of exercise. Although the application of the algorithm presented in this work was generating musical sight reading exercises for the flute, its parameters are purely data driven – they are not instrument-specific. Instead, appropriate values can be extracted from models of expert-written examples, which may relate to any chosen monophonic instrument. This is discussed further in Section 9.8. Some avenues for future development can be found in the ruleset used to evaluate the quality of solutions. For example, the rule for ‘Note placement’ states that Strong notes from the target key (i.e., I, III, V) should be placed on at least 50% of the strong beats in the melody. This indicates that music sounds better when strong notes from the target key are placed on strong beats of the bar. Such note placements could be encouraged by the evolutionary algorithm. Doing so might reduce or even remove the need for this evaluation rule, but should also increase the aesthetics of results by reinforcing the key signature. A similar approach could be taken to reinforce the time signature of an exercise. This relates to the ‘Placement of long notes’ rule, which states that 80% of notes longer than a crotchet should be placed on strong beats of the bar, and the ‘Placement of rests’ rule, which states that 80% of rests should be placed on weak beats of the bar. By encouraging these optimal note and rest placements the music should ‘feel’ like it is written in the target time signature. This would increase the overall aesthetics of generated melodies and avoid some situations where phrases seem to end abruptly. Currently, the algorithm is hard-coded to ensure the first and last notes of an exercise are assigned the tonic pitch of the target key signature. This helps to resolve the melody harmonically. However, in the source exercises there are many cases where the first and last pitches are not the tonic. As this is not currently supported by the algorithm, future work could seek to implement such functionality. This might require additions to the evaluation ruleset to

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handle the special case of making sure the start and end pitches of a melody suitably relate to the target key signature. As an addition to modelling expert-written examples, the algorithm could incorporate alternative models of musical complexity. These models would be relative to a specific instrument. One possible model is the musiplectics system [77]. In this work, Holder et al. [77] defines a method for computationally measuring the complexity of a musical score for any instrument. Measuring the complexity of a score first requires the definition of several parameters for the chosen instrument. Currently, only the parameters for a B[ clarinet are provided. Imple- menting support for more instruments represents a non-trivial quantity of work, most of which requires input from an expert in the instrument in question. However, doing so might result in a valuable addition to the capabilities of the evolutionary algorithm. Another area of improvement for the algorithm would be to use key progressions. Cur- rently, the algorithm generates exercises within a particular key signature. It does not, however, create melodies which follow key progressions. For example, a common four-bar key progression is I, IV , V , I. If the exercise was in C major, this would mean that the four bars would be written in C major, F major, G major, and C major, in that order. Chord progressions give a melody a sense of movement and interest. Although not considered in this work, the source exercises do use chord progressions. As such, it would make sense for the algorithm to do so as well. One way chord progressions could be implemented would be to use the progression map proposed by Stephen Mugglin [189] and shown in Figure 9.1. This map defines transitions between chords which will sound aesthetically pleasing. As a starting point, just the core transitions could be implemented (i.e., the central blue boxes in Figure 9.1), followed by the more abstract transitions (i.e., the outer green boxes in Figure 9.1) at a later time. This implementation would not require any changes to be made to the tree structure used to represent melodies. Although each bar would focus on a different key, the melody overall would still be in the one key signature. That is, even if the second bar in a C major melody might be written in F major, it would still only use pitches from the C major scale. The ruleset for evaluating exercises, however, would need to be updated. This is because some of the rules explicitly reference the target key. For example, the ‘Note placement’ rule states that Strong notes from the target key (i.e., I, III, V) should be placed on at least 50% of the strong beats in the melody. If the generated melodies were to follow chord progressions, the ‘target key’ part of this rule would need to be interpreted as referring to the key of the bar, not of the overall melody. Some of the source exercises also change key completely as they progress, or contain accidentals outside of the key signature. Neither of these features is currently supported by the algorithm. Allowing additional accidentals is non-trivial, as it would simply require removing the restriction within the algorithm which prevents it from choosing pitches outside the target key. However, this implementation would introduce significant complexity to the system, as the potential for selecting poor sounding pitch sequences would dramatically increase. A better implementation would allow non-key pitches to be selected, but restrict when that could occur. Allowing for complete key changes is a more difficult task. Currently, the melody tree structure does not record the key signature of the melody it describes. As such, it also does not support the ability to record a change in key signature. This is not necessarily an issue,

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A Progression Map for Major Keys

#Idim7 IIIm7b5

VI #IVm7b5 7,9,b9 iim VIm7b5 m7,m9 b3

#IIdim7 II #IVm7b5 V 7,9,b9 7,9,11,13,sus

VII #Vdim7 7,9,b9 iiim VIIm7b5 m7

IIIm7b5 III Vm vim 7,9,b9 7 m7,m9

I I/3 #Idim7 7,9,b9 IV IIIm7b5 6,M7,m,m6

#IVm7b5 VI Im6 iim 7,9,b9 II m7,m9 Idim/b3 7,9,b9 V IVm7 bVI7 7,9,11,13,sus V/2 bII7 bVI I/5 bVII9 #IVm7b5 bVII 9

I IV/1 Chords in italics have been respelled: 2,6,M7,M9,sus V/1 bVI7 = bVI(aug6)

Suggestions for Use 1 - Begin with the blue boxes. Start at I. Jump to another blue area. Follow the arrows back toward I. (Example: I-IV-V-I) 2 - Start with any blue box. Create a 3 or 4-chord progression by following the arrows. (Examples: ii-V-I or vi-IV-ii-V) 3 - You may jump to a green location at any time. When you do, there is a tendency to follow the arrows back toward the blue locations. 4 - If two locations have the same name, you may switch from one to the other. This gives more options for choosing the next chord. 5 - The arrows indicate strong, natural-sounding progressions. For interest, sometimes go opposite the direction of the arrows.

The expression X/Y indicates chord X with scale note Y in the bass. Copyright 1995, 2001, 2004, 2017 Stephen Mugglin Permission is given to make not-for-profit copies. - More information at Chordmaps.com.

Figure 9.1: A transition network for key signatures by Stephen Mugglin [189]

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as information relating to the key signatures can be recorded elsewhere. The true difficulty lies in determining when a key change is appropriate, what the new key should be, and how to smoothly transition between the old and new keys. Such functionality would require significant changes to the algorithm. It would also require the key change to be noted in the output so that the melody can be interpreted correctly when applying the evaluation ruleset. Another feature of the source exercises not currently shown in the generated exercises is anacruses. An anacrusis is where a single bar is split into two parts which are placed at the beginning and end of a melody. This type of structure is not supported by the melody tree or the algorithm, and adding support would require significant work. However, it is necessary for complete recreations of realistic musical sight reading exercises. In Section 9.4 the opportunity for technology to personalise learning was discussed. The same feedback loop of presenting the user with a task, assessing their response, then generating follow up tasks addressing their errors could be applied to musical sight reading. The work presented in this thesis addresses only one aspect of a full intelligent tutoring system: the algorithmic generation of exercises. Significant additional work is required to close the gaps from this point to a complete intelligent tutoring system. For example, a method would be needed to measure a user’s performance and classify their mistakes. Another method would then be needed to translate these classifications into an appropriate set of parameters for the evolutionary algorithm, which could then generate the next exercise. It is entirely possible that the currently available parameters for the algorithm are not expressive enough for this task, meaning that the algorithm would also need to be restructured of significantly modified.

9.7 Building Better Models of Expert Knowledge

Given that the algorithm is designed to emulate expert models of musical sight reading exercises, it stands to reason that developing better expert models would improve the quality of its output. Currently, the expert models are a combination of simple characteristics (i.e., key signature, time signature) and statistical measures (i.e., note/rest/interval proportions). As such, there is significant scope for further development in this area. One area for potential development relates to the analysis of co-occurring features. Cur- rently, the note, rest, and interval proportions are treated separately. However, it is possible that there are some dependencies between these features that are not currently being captured. For example, it might be that larger intervals are more likely to be placed on longer notes, and smaller intervals on shorter notes. Finding these types of co-occurrences should be a relatively simple task. More difficult would be determining which co-occurring features are important to emulate, and how they should be implemented. A similar area is that of sequence or pattern identification. The source exercises, and music in general, exhibit many clear patterns. For example, often a dotted quaver will be followed by a semiquaver, or four semiquavers will be used in sequence. These types of patterns generally serve to reinforce the beats within the music and create a sense of rhythmic stabil- ity. Identifying the use of these patterns within the source exercises, and incorporating them into the algorithm would serve to both better emulate the characteristics of the expert-written examples, and create more generally aesthetically pleasing results. A complex area that hasn’t yet been addressed either through the analysis of source

275 CHAPTER 9. DISCUSSIONAND FUTURE WORK

exercises or in the algorithm development is that many musical sight reading exercises are targeted to developing a specific skill. For example, some exercises for the flute contain a large proportion of long notes to encourage the development of breath control. Others might specifically use a series of arpeggios to reinforce scale structures. Incorporating this type of information into the algorithm would be a significant undertaking. It would require extensive expert knowledge to identify the purposes of different musical sight reading exercises and describe how they have been written to address these purposes. Developing the ability to algorithmically generate similarly targeted exercises would be as, if not more, difficult. However, doing so would greatly increase the utility of the generated exercises, as they would be able to more specifically target the needs of different users. This would be particularly true if incorporated into an adaptive intelligent tutoring system, where purposeful exercises could be autonomously chosen based on a user’s past performances. The ruleset used to evaluate algorithmically generated musical sight reading exercises is based on a combination of music theory literature and analysis of expert-written examples. If better expert models were to be developed, it may also become necessary or valuable to modify this ruleset. For example, if an exercise were generated with a specific purpose (e.g., to develop breath control), one or more rules might be included to measure whether that goal has successfully been met.

9.8 Applying the Algorithm to Other Instruments

As discussed in Section 9.6, although the use of the algorithm presented in this work was to generate musical sight reading exercises for the ﬂute, the parameters are purely data driven. That is, they are instrument-agnostic. Given this, the algorithm can be applied to generate exercises for any monophonic instrument. This would involve curating a set of expert-written examples, and using those examples to determine appropriate parameters. Additional work would be required to support polyphonic instruments, particularly in the development of the tree structure used to represent melodies. To validate the algorithm’s abilities in generating exercises for other instruments, the evaluation ruleset would need to be revisited. Whilst the rules themselves are instrument- agnostic, their exact interpretation is sometimes relative to the analysis of expert-written examples. For example, the ‘Tied notes’ rule states that:

Grade 1 exercises for the flute should not contain any tied notes. Grade 2 exercises for the flute should contain at most 5% tied notes. Grade 3 exercises for the flute should contain at most 10% tied notes. If the target source exercise contains a larger proportion of tied notes than those listed here, the maximum percentage of tied notes an exercise can contain is that of the target source exercise.

These proportions of 0, 5, and 10% were selected based on an examination of the source exercises. As these exercises are speciﬁc to the ﬂute, the proportions may not be appropriate for other instruments. If the algorithm were applied to another instrument and formal measurement of the results was desired, rules such as these would need to be revised with respect to a new set of expert-written examples.

276 CHAPTER 9. DISCUSSIONAND FUTURE WORK

9.9 Summary

This chapter has provided a discussion of the work presented in this thesis as a whole. The implications and potential future directions of the work were identiﬁed and described, particularly avenues for continuing development of the algorithm for generating musical sight reading exercises. The research questions deﬁned in Chapter 1 were revisited, and it was shown how these research questions have been addressed. The next chapter will summarise the work presented in this thesis.

277

10 Thesis Summary

10.1 Research Questions

The work in this thesis was developed around four research questions, ﬁrst deﬁned in Chapter 1:

1. How is technology currently being used in music education?

2. What are the opportunities for increased or more effective use of technology in musical sight reading education?

3. What algorithmic techniques are appropriate for generating music that is aesthetically pleasing, playable by a human, and appropriate for the development of musical sight reading skills?

4. How can algorithmically generated musical sight reading exercises be measured for ﬁtness of purpose?

Through the presented work, all four of these questions have been addressed. First, Chapter 2 provided a historical context for music education and how technology has been used. This was followed in Chapter 5 by an analysis of the state of the art of music teaching applications on the iOS platform. These both served to clearly show how technology has been and is currently being used in music education. Several opportunities for better utilisation of technology were identified. Many of these resulted from the analysis of the state of the art of iOS music teaching applications, but additional opportunities were identified through discussions of the needs of music teachers and students. One opportunity – the algorithmic generation of musical sight reading exercises – was chosen as the focus for this work. This choice necessitated the third question, so that a valid approach could be taken to developing a system for generating these exercises. Chapter 2 addressed this question. In this chapter, key algorithms used to generate music were identified and discussed with reference to examples from the literature. The chosen approach – evolutionary algorithms – was discussed in particular depth. The final question was raised due to the lack of methods within the literature to measure the quality of algorithmically generated musical sight reading exercises. It has been addressed

279 CHAPTER 10. THESIS SUMMARY

through the development of a ruleset and framework, deﬁned in Chapter 7, for measuring the general aesthetics and technical appropriateness of exercises.

10.2 Key Contributions

The process of addressing the key questions of this research has resulted in the following novel contributions being presented in this thesis:

1. A formal taxonomy for describing musical content and activities

2. A framework for completing structured reviews of educational applications

3. An analysis of the state of the art of iOS applications for teaching and practicing musical skills

4. A novel tree structure for representing musical melodies

5. An evolutionary algorithm for generating monophonic sight reading exercises

6. A ruleset and framework for measuring the quality and ﬁtness for purpose of algorithmically generated musical sight reading exercises

The implications of these contributions have been discussed, as well as their applications and uses in other areas. It has also been shown that in addition to these being valuable contributions to the ﬁeld in their current state, their utility can be further developed and reﬁned in the future.

280 References

[1] Andres Acevedo. Fugue composition with counterpoint melody generation using genetic algorithms. In International Symposium on Computer Music Modeling and Retrieval, pages 96–106. Springer, 2004.

[2] Margareta Ackerman and David Loker. Algorithmic songwriting with alysia. arXiv preprint arXiv:1612.01058, 2016.

[3] Kamil Adiloglu and Ferda Alpaslan. A machine learning approach to two-voice counterpoint composition. Knowledge-Based Systems, 20(3):300–309, 2007.

[4] David Daniel Albarrac´ın-Molina, Juan C Moya, and Francisco J Vico. An evo-devo system for algorithmic composition that actually works. In Proceedings of the 2016 on Genetic and Evolutionary Computation Conference Companion, pages 37–38. ACM, 2016.

[5] Edward Aldwell and Allen Cadwallader. Harmony and voice leading. Cengage Learning, 2018.

[6] Greg Aloupis, Thomas Fevens, Stefan Langerman, Tomomi Matsui, Antonio Mesa, Yurai Nunez, David Rappaport, and Godfried Toussaint. Computing a geometric measure of the similarity between two melodies. In Proceedings of the 15th Canadian Conference on Computational Geometry, pages 81–84, 2003.

[7] Charles Ames. Automated composition in retrospect: 1956-1986. Leonardo, pages 169– 185, 1987.

[8] Lorin Anderson, David Krathwohl, and Benjamin Bloom. A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Allyn & Bacon, 2001.

[9] Arved Ashby. Schoenberg, boulez, and twelve-tone composition as “ideal type”. Journal of the American Musicological Society, 54(3):585–625, 2001.

[10] Associated Board of the Royal Schools of Music. Flute Specimen Sight Reading. Associated Board of the Royal Schools of Music, 1995.

[11] Associated Board of the Royal Schools of Music. Music Theory marking criteria. https://us.abrsm.org/en/our-exams/information-and-regulations/ music-theory-marking-criteria-grades-6-8/, September 2018.

[12] Associated Board of the Royal Schools of Music. AMEB Ask Andrew: Introduction to Melody Writing. https://www.youtube.com/watch?v=dHSsD2GqDQM, September 2018.

[13] Australian Music Examinations Board. 2018 Manual of Syllabuses. Australian Music Examinations Board, 2018.

[14] Carl Philipp Emanuel Bach. Einfall: einen doppelten Kontrapunkt in der Oktave von sechs Takten zu machen, ohne die Regeln davon zu wissen. 1757.

[15] Robert Baker. Musicomp: MUsic Simulator-Interpreter for COMpositional Procedures for the IBM 7090. Experimental Music Studio, 1963.

281 REFERENCES

[16] Louise Banton. The role of visual and auditory feedback during the sight-reading of music. Psychology of music, 23(1):3–16, 1995.

[17] James Bastien. Sight Reading Level 2. National Braille Association, 1983.

[18] Rick Bidlack. Chaotic systems as simple (but complex) compositional algorithms. Com- puter Music Journal, 16(3):33–47, 1992.

[19] John Biggs and Kevin Collis. Evaluating the quality of learning: the SOLO taxonomy (structure of the observed learning outcome). Academic Press, 1982.

[20] John Biles. GenJam: A genetic algorithm for generating jazz solos. In Proceedings of the International Computer Music Conference, page 131. International Computer Music Accociation, 1994.

[21] John Biles. Autonomous genjam: eliminating the ﬁtness bottleneck by eliminating ﬁt- ness. In Proceedings of the 2001 Genetic and Evolutionary Computation Conference Work- shop Program, San Francisco, 2001.

[22] John Biles. Evolutionary computation for musical tasks. In Evolutionary Computer Music, pages 28–51. 2007.

[23] Heather Birch and Earl Woodruff. Technical exercise practice: Can piano students be motivated through gamiﬁcation? Journal of Music, Technology & Education, 10(1):31– 50, 2017.

[24] Benjamin Bloom, Lauren Sosniak, and Others. Developing talent in young people. Ballan- tine Books, 1985.

[25] Bloom’s Taxonomy Made Easy. Bloom’s taxonomy of educational objectives. Longman, 1965.

[26] Georg Boenn, Martin Brain, Marina De Vos, and Others. Automatic composition of melodic and harmonic music by answer set programming. In International Conference on Logic Programming, pages 160–174. Springer, 2008.

[27] Arielle Bonneville-Roussy and Th´er`ese Bouffard. When quantity is not enough: Dis- entangling the roles of practice time, self-regulation and deliberate practice in musical achievement. Psychology of Music, 43(5):686–704, 2015.

[28] William Lowe Bryan and Noble Harter. Studies in the physiology and psychology of the telegraphic language. Psychological Review, 4(1):27, 1897.

[29] Jim Bumgardner and Others. Kircher’s mechanical composer: A software implementation. In Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture, pages 21–28. Tarquin Publications, 2009.

[30] Murray Campbell, Clive Greated, and Eric Arnold. The musician’s guide to acoustics, 1990.

[31] Michael Chan. Automated Composer of Style Sensitive Music. In Proceedings of the Second Australian Undergraduate Students’ Computing Conference, page 40, 2004.

282 REFERENCES

[32] Todd Cherner, Judy Dix, and Corey Lee. Cleaning up that mess: A framework for classifying educational apps. Contemporary Issues in Technology and Teacher Education, 14(2): 158–193, 2014.

[33] Marcus Childress and Guang-Lea Lee. Reviewing software as a means of enhancing instruction. Information Technology in Childhood Education, 255:261, 1999.

[34] Cynthia Chiong and Carly Shuler. Learning: Is there an app for that. In Investigations of young children’s usage and learning with mobile devices and apps. New York: The Joan Ganz Cooney Center at Sesame Workshop, pages 13–20, 2010.

[35] Gene Cho. The discovery of musical equal temperament in China and Europe in the six- teenth century, volume 93. Edwin Mellen Press, 2003.

[36] Gene Cho. The signiﬁcance of the discovery of the musical equal temperament in the cultural history. Journal of Xinghai Conservatory of Music, 2:002, 2010.

[37] John Clinton. The Quadrille Melodist, consisting of an almost endless variety of new quadrilles. E. Butler & Co, 1865.

[38] Trinity College. Musical Knowledge (Initial – Grade 5). Supporting tests, 2016.

[39] David Cope. Experiments in musical intelligence. In Proceedings of the International Computer Music Conference. San Francisco, 1987.

[40] David Cope. Experiments in musical intelligence (emi): Non-linear linguistic-based composition. Journal of New Music Research, 18(1-2):117–139, 1989.

[41] David Cope. Facing the music: Perspectives on machine-composed music. Leonardo Music Journal, pages 79–87, 1999.

[42] David Cope and Melanie Mayer. Experiments in musical intelligence, volume 12. AR editions Madison, 1996.

[43] Albert Corbett and John Anderson. Locus of feedback control in computer-based tutoring: Impact on learning rate, achievement and attitudes. In Proceedings of the SIGCHI conference on Human factors in computing systems, pages 245–252. ACM, 2001.

[44] Albert Corbett and Holly Trask. Instructional interventions in computer-based tutoring: differential impact on learning time and accuracy. In Proceedings of the SIGCHI conference on Human Factors in Computing Systems, pages 97–104. ACM, 2000.

[45] Alexa Ray Corriea. Rocksmith 2014 is coming to PS4, Xbox One in Novem- ber. Polygon, 2014. URL https://www.polygon.com/2014/9/23/6834315/ rocksmith-2014-is-coming-to-ps4-xbox-one-in-november.

[46] Richard Crozier. The Music Teacher’s Companion: A Practical Guide. Associated Board of the Royal Schools of Music, 2000.

[47] Palle Dahlstedt. Autonomous evolution of complete piano pieces and performances. 2007.

283 REFERENCES

[48] Abu Dalhoum, Abdel Latif, Manuel Alfonseca, Manuel Cebrian´ Ramos, Rafael Sanchez-´ Alfonso, and Alfonso Ortega. Computer-generated music using grammatical evolution. 2008.

[49] Fabio De Felice, Fabio Abbattista, and Francesco Scagliola. Genorchestra: An interactive evolutionary agent for musical composition. In Proceedings of the 5th International Conference GA2002, Politecnico di Milano University, Italy, 2002.

[50] Pedro de Leon,´ Jos´e Inesta,˜ Jorge Calvo-Zaragoza, and David Rizo. Data-based melody generation through multi-objective evolutionary computation. Journal of Mathematics and Music, 10(2):173–192, 2016.

[51] Frank Drewes and Johanna Hogberg.¨ An algebra for tree-based music generation. In Algebraic Informatics, pages 172–188. Springer, 2007.

[52] Kemal Ebcioglu.˘ An expert system for harmonizing four-part chorales. Computer Music Journal, 12(3):43–51, 1988.

[53] Michael Edwards. Algorithmic composition: computational thinking in music. Commu- nications of the ACM, 54(7):58–67, 2011.

[54] Arne Eigenfeldt. Kinetic engine: toward an intelligent improvising instrument. In Pro- ceedings of the Sound and Music Computing Conference, pages 97–100, 2006.

[55] K Ericsson, Ralf Krampe, and Clemens Tesch-Romer.¨ The role of deliberate practice in the acquisition of expert performance. Psychological review, 100(3):363, 1993.

[56] David Esp´ı, Pedro J de Leon,´ Carlos P´erez-Sancho, David Rizo, Jos´e Inesta,˜ Francisco Moreno-Seco, and Antonio Pertusa. A cooperative approach to style-oriented music composition. 2007.

[57] Mary Farbood and Bernd Schoner.¨ Analysis and synthesis of palestrina-style counterpoint using markov chains. In ICMC, 2001.

[58] Jose D Fernandez´ and Francisco Vico. Ai methods in algorithmic composition: A comprehensive survey. Journal of Artiﬁcial Intelligence Research, 48:513–582, 2013.

[59] Carlos Fonseca and Peter Fleming. Multiobjective genetic algorithms made easy: selection sharing and mating restriction. 1995.

[60] Johann Joseph Fux. Gradus ad parnassum. 1725.

[61] Philip Galanter. Computational aesthetic evaluation: past and future. In Computers and Creativity, pages 255–293. Springer, 2012.

[62] S Daniel Galyen. Sight-reading ability in wind and percussion students: A review of recent literature. Update: Applications of Research in Music Education, 24(1):57–70, 2005.

[63] Howard Gardner. Frames of mind: The theory of multiple intelligences. Basic books, 2011.

284 REFERENCES

[64] Stanley Gill. A technique for the composition of music in a computer. The Computer Journal, 6(2):129–133, 1963.

[65] Percy Goetschius. Exercises in Melody-writing. BiblioBazaar, LLC, 2009.

[66] Morag Grant. Serial music, serial aesthetics: compositional theory in post-war Europe, volume 16. Cambridge University Press, 2005.

[67] Thomas B Gregory. The effect of rhythmic notation variables on sight-reading errors. Journal of Research in Music Education, 20(4):462–468, 1972.

[68] Wendell Hanna. The new Bloom’s Taxonomy: Implications for music education. Arts Education Policy Review, 108(4):7–16, 2007.

[69] Paul Harris. Improve Your Sight-reading!: Flute. Faber Music, 1994.

[70] Goffredo Haus and Alberto Sametti. Scoresynth: A system for the synthesis of music scores based on petri nets and a music algebra. Computer, 24(7):56–60, 1991.

[71] Stephen Hedges. Dice music in the eighteenth century. Music & Letters, 59(2):180–187, 1978.

[72] Jay Hennig, Akash Umakantha, and Ryan Williamson. A classifying variational autoen- coder with application to polyphonic music generation. arXiv preprint arXiv:1711.07050, 2017.

[73] Dorien Herremans, Ching-Hua Chuan, and Elaine Chew. A functional taxonomy of music generation systems. ACM Computing Surveys (CSUR), 50(5):69, 2017.

[74] Hermann Hild, Johannes Feulner, and Wolfram Menzel. Harmonet: A neural net for harmonizing chorales in the style of js bach. In Advances in neural information processing systems, pages 267–274, 1992.

[75] Lejaren Hiller Jr and Leonard Isaacson. Musical composition with a high speed digital computer. In Audio Engineering Society Convention. Audio Engineering Society, 1957.

[76] Paul Hindemith. The Craft of Musical Composition: Theoretical Part, volume 1. Schott & Co Ltd, 1970.

[77] Ethan Holder, Eli Tilevich, and Amy Gillick. Musiplectics: computational assessment of the complexity of music scores. In 2015 ACM International Symposium on New Ideas, New Paradigms, and Reﬂections on Programming and Software (Onward!), pages 107– 120. ACM, 2015.

[78] Bruce Jacob. Composing with genetic algorithms. 1995.

[79] Jen Jenson, Suzanne De Castell, Rachel Muehrer, and Milena Droumeva. So you think you can play: An exploratory study of music video games. Journal of Music, Technology & Education, 9(3):273–288, 2016.

[80] Wei Ji. Effectiveness of Targeted Feedback towards Rhythm Sightreading in University/College-Level Music Education Contexts. PhD thesis, Education: Faculty of Ed- ucation, 2017.

285 REFERENCES

[81] Matt Johnson, Daniel Tauritz, and R Wilkerson. Evolutionary computation applied to melody generation. In Proceedings of the ANNIE, 2004.

[82] Maximos A Kaliakatsos-Papakostas, Andreas Floros, Nikolaos Kanellopoulos, and Michael N Vrahatis. Genetic evolution of l and ﬂ-systems for the production of rhythmic sequences. In Proceedings of the 14th annual conference companion on Genetic and evolutionary computation, pages 461–468. ACM, 2012.

[83] Maximos A Kaliakatsos-Papakostas, Andreas Floros, and Michael N Vrahatis. Intelligent generation of rhythmic sequences using ﬁnite l-systems. In 2012 Eighth International Conference on Intelligent Information Hiding and Multimedia Signal Processing, pages 424–427. IEEE, 2012.

[84] Kristo Kao˜ and Margus Niitsoo. Matchmysound: Introducing feedback to online music education. In International Conference on Web-Based Learning, pages 217–225. Springer, 2014.

[85] Kai Karma. The Ability to Structure Acoustic Material as a Measure of Musical Aptitude: I. Background Theory and Pilot Studies. ERIC, 1973.

[86] Robert Keller and David Morrison. A grammatical approach to automatic improvisation. In Proceedings of the Fourth Sound and Music Conference, 2007.

[87] Yaser Khalifa, Badar Khan, Jasmin Begovic, Airrion Wisdom, and Andrew Wheeler. Evo- lutionary music composer integrating formal grammar. In Proceedings of the 9th annual conference companion on Genetic and evolutionary computation, pages 2519–2526. ACM, 2007.

[88] Athanasius Kircher. Arca Musarithmica. 1650.

[89] Johann Philipp Kirnberger. Der allezeit fertige menuetten-und polonoisenkomponist. Berlin: Germany Winter (1757), 1757.

[90] Roman Klinger and Gunter¨ Rudolph. Evolutionary composition of music with learned melody evaluation. In Proceedings of the Int. Conference on Computational Intelligence, Man-machine Systems and Cybernetics (CIMMACS’06), 2006.

[91] Mladen Konecki. Learning to play musical instruments through dynamically generated lessons in real-time based on adaptive learning system. Central European Conference on Information and Intelligent Systems, 2014.

[92] Mladen Konecki. Learning to play musical instruments through dynamically generated lessons in real-time based on adaptive learning system. In Proceedings of the 25th Central European Conference on Information and Intelligent Systems, pages 124–129, 2014.

[93] Mladen Konecki. Self-paced computer aided learning of music instruments. In Informa- tion and Communication Technology, Electronics and Microelectronics (MIPRO), 2015 38th International Convention on, pages 809–813. IEEE, 2015.

[94] Reinhard Kopiez and Ji In Lee. Towards a general model of skills involved in sight reading music. Music education research, 10(1):41–62, 2008.

286 REFERENCES

[95] Ladonna Kornicke. An exploratory study of individual difference variables in piano sight- reading achievement. UMI/Bell & Howell, 1992.

[96] David Krathwohl. A revision of bloom’s taxonomy: An overview. Theory into practice, 41 (4):212–218, 2002.

[97] Raymond Kulhavy and William Stock. Feedback in written instruction: The place of response certitude. Educational Psychology Review, 1(4):279–308, 1989.

[98] Jacob Kwalwasser. Victor Talking Machine Co., Camden, NJ, 1926.

[99] Jacob Kwalwasser. Tests and measurements in music. Birchard, 1927.

[100] Jacob Kwalwasser. Exploring the musical mind. Coleman-Ross Co., 1955.

[101] Steven Geoffrey Laitz. The complete musician: An integrated approach to tonal theory, analysis, and listening, volume 1. Oxford University Press, USA, 2008.

[102] Mikael Laurson and Mika Kuuskankare. Towards idiomatic instrumental writing: A constraint based approach. In Proceedings of the 2nd Annual Symposium on Systems Research in the Arts, 2000.

[103] Lily Law. Assessing and Understanding Individual Differences in Music Perception Abilities. PhD thesis, The University of York, 2012.

[104] Sylvain Le Groux and Paul Verschure. Towards adaptive music generation by reinforcement learning of musical tension. In Proceedings of the 6th Sound and Music Conference, Barcelona, Spain, volume 134, 2010.

[105] Cheng-Yuan Lee and Todd Cherner. A comprehensive evaluation rubric for assessing instructional apps. Journal of Information Technology Education: Research, 14:21–53, 2015.

[106] Paul Leedy and Jeanne Ormrod. Practical research: Planning and design. Pearson, 2013.

[107] Andreas C Lehmann and Victoria McArthur. Sight-reading. The science and psychology of music performance, pages 135–150, 2002.

[108] Tao Li and Mitsunori Ogihara. Music genre classiﬁcation with taxonomy. Acoustics, Speech, and Signal Processing, pages 197–200, 2005.

[109] Feynman Liang. Bachbot: Automatic composition in the style of bach chorales. PhD thesis, Masters thesis, University of Cambridge, 2016.

[110] Rensis Likert. A technique for the measurement of attitudes. Archives of psychology, 1932.

[111] Hwei-Jen Lin and Hung-Hsuan Wu. Efﬁcient geometric measure of music similarity. Information Processing Letters, 109(2):116–120, 2008.

[112] Hwei-Jen Lin, Hung-Hsuan Wu, and Yang-Ta Kao. Geometric measures of distance between two pitch contour sequences. Journal of Computers, 19(2):44–66, 2008.

287 REFERENCES

[113] Aristid Lindenmayer. Mathematical models for cellular interactions in development i. ﬁlaments with one-sided inputs. Journal of theoretical biology, 18(3):280–299, 1968.

[114] Man Yat Lo. Evolving cellular automata for music composition with trainable ﬁtness functions. PhD thesis, University of Essex, 2012.

[115] ManYat Lo and Simon Lucas. Evolving musical sequences with n-gram based trainable ﬁtness functions. In 2006 IEEE International Conference on Evolutionary Computation, pages 601–608. IEEE, 2006.

[116] Roisın´ Loughran and Michael O’Neill. Grammatical Evolution for the Composition of Piano Melodies. 2015.

[117] Roisın´ Loughran and Michael O’Neill. The popular critic: Evolving melodies with popularity driven ﬁtness. In Proceedings of the 4 th international workshop on musical metacre- ation. Paris, 2016.

[118] Ada Lovelace. ‘notes on l. menabrea’s ‘sketch of the analytical engine invented by charles babbage, esq.”’. Taylor’s Scientiﬁc Memoirs, 3:1843, 1843.

[119] T Maddox and J Otten. Using an evolutionary algorithm to generatefour-part 18th century harmony. 2000.

[120] Claudia Maina. Athanasius Kircher. Arca Musarithmica and Many Sound Devices. Digicult, 2010. URL http://digicult.it/digimag/issue-055/ athanasius-kircher-arca-musarithmica-and-many-sound-devices/.

[121] Bill Manaris, Dallas Vaughan, Christopher Wagner, Juan Romero, and Robert B Davis. Evolutionary music and the zipf-mandelbrot law: Developing ﬁtness functions for pleasant music. In Workshops on Applications of Evolutionary Computation, pages 522–534. Springer, 2003.

[122] Bill Manaris, Penousal Machado, Clayton McCauley, Juan Romero, and Dwight Krehbiel. Developing ﬁtness functions for pleasant music: Zipf’s law and interactive evolution systems. In Workshops on Applications of Evolutionary Computation, pages 498–507. Springer, 2005.

[123] B Mason and Roger Bruning. Providing feedback in computer-based instruction: What the research tells us. Center for Instructional Innovation, 15:2007, 2001.

[124] Jon McCormack and Mark d’Inverno. Computers and creativity, 2011.

[125] Gary McPherson. Giftedness and talent. SAGE Publications, Incorporated, 2014.

[126] Gary McPherson and Alf Gabrielsson. From sound to sign. The science and psychology of music performance: Creative strategies for teaching and learning, pages 99–116, 2002.

[127] Gary McPherson and James Renwick. A longitudinal study of self-regulation in children’s musical practice. Music Education Research, 3(2):169–186, 2001.

[128] Leonard Meyer. Explaining music: Essays and explorations. Univ of California Press, 1973.

288 REFERENCES

[129] Ben Miller. Music learning through video games and apps: Guitar hero, rock band, am- plitude, frequency, and rocksmith, and bandfuse, and bit. trip complete, and audiosurf, and beat hazard, and biophilia. American Music, 31(4):511–514, 2013.

[130] Michael Miller. The complete idiot’s guide to music theory. Penguin, 2005.

[131] Ministry of Education (Schools Division) Victoria. Designing an Instrumental Music Pro- gram: An Overview of Areas of Learning and Skill Development. National Library of Australia Cataloguing, pages 1–32, 1988.

[132] Eduardo Miranda. Cellular automata music: from sound synthesis to musical forms. In Evolutionary computer music, pages 170–193. Springer, 2007.

[133] Eduardo Miranda and John Biles. Evolutionary computer music. Springer, 2007.

[134] Artemis Moroni, Jonatasˆ Manzolli, Fernando Von Zuben, and Ricardo Gudwin. Vox populi: Evolutionary computation for music evolution. In Creative evolutionary systems, pages 205–221. Elsevier, 2002.

[135] Michael Mozer. Neural network music composition by prediction: Exploring the beneﬁts of psychoacoustic constraints and multi-scale processing. Connection Science, 6(2-3): 247–280, 1994.

[136] Enrique Munoz,˜ Jose Cadenas, Yew Ong, and Giovanni Acampora. Memetic music composition. IEEE Transactions on Evolutionary Computation, 20(1):1–15, 2016.

[137] My Music Theory. 10. Tones & Semitones. https://www.mymusictheory. com/learn-music-theory/for-students/grade-1/grade-1-course/ 111-10-tones-a-semitones, July 2010.

[138] Frieder Nake. Construction and intuition: Creativity in early computer art. In Computers and creativity, pages 61–94. Springer, 2012.

[139] Eugene Narmour. Explorations in music, the arts, and ideas: Essays in honor of Leonard B. Meyer. Pendragon Press, 1988.

[140] Mar´ıa Navarro, Marcelo Caetano, Gilberto Bernardes, Leandro de Castro, and Juan Cor- chado. Automatic generation of chord progressions with an artiﬁcial immune system. In International Conference on Evolutionary and Biologically Inspired Music and Art, pages 175–186. Springer, 2015.

[141] Maria Navarro, Juan Manuel Corchado, and Yves Demazeau. Music-mas: Modeling a harmonic composition system with virtual organizations to assist novice composers. Expert Systems with Applications, 57:345–355, 2016.

[142] Nicholas Tollervey. Music Theory 101. http://ntoll.org/article/ music-theory-101, October 2009.

[143] Gerhard Nierhaus. Algorithmic composition: paradigms of automated music generation. Springer Science & Business Media, 2009.

289 REFERENCES

[144] Gerhard Nierhaus. Historical development of algorithmic procedures. Algorithmic Com- position: Paradigms of Automated Music Generation, pages 7–66, 2009.

[145] Tomasz Oliwa and Markus Wagner. Composing music with neural networks and probabilistic ﬁnite-state machines. In Workshops on Applications of Evolutionary Computation, pages 503–508. Springer, 2008.

[146] Harry Ferdinand Olson. Music, physics and engineering, volume 1769. Courier Corpora- tion, 1967.

[147] Paul Owens and John Sweller. Cognitive load theory and music instruction. Educational Psychology, 28(1):29–45, 2008.

[148] Ender Ozcan¨ and Turker¨ Erçal. A genetic algorithm for generating improvised music. In International Conference on Artificial Evolution (Evolution Artificielle), pages 266–277. Springer, 2007.

[149] Franc¸ois Pachet. Musical virtuosity and creativity. In Computers and creativity, pages 115–146. Springer, 2012.

[150] Franc¸ois Pachet and Daniel Cazaly. A taxonomy of musical genres. Content-Based Multimedia Information Access Conference (RIAO), Paris, April 2000, April 2000. URL http://www.csl.sony.fr/downloads/papers/2000/pachet-riao2000.pdf.

[151] Francois Pachet and Pierre Roy. Musical harmonization with constraints: A survey. Con- straints, 6(1):7–19, 2001.

[152] George Papadopoulos and Geraint Wiggins. A genetic algorithm for the generation of jazz melodies. Proceedings of STEP, 98, 1998.

[153] George Papadopoulos and Geraint Wiggins. Ai methods for algorithmic composition: A survey, a critical view and future prospects. In AISB Symposium on Musical Creativity, volume 124, pages 110–117. Edinburgh, UK, 1999.

[154] Jack Perricone. Melody in songwriting: tools and techniques for writing hit songs. Hal Leonard Corporation, 2000.

[155] Richard Pinkerton. Information theory and melody. Scientiﬁc American, 194(2):77–87, 1956.

[156] Stephen Pope. A taxonomy of computer music. Contemporary Music Review, 13(2): 137–145, 1996.

[157] Praxis Educational Testing Service. Music: Content Knowledge. The Praxis Study Com- panion, 2016.

[158] Przemyslaw Prusinkiewicz. Score generation with l-systems. In ICMC, 1986.

[159] Donya Quick. Kulitta: a framework for automated music composition. PhD thesis, 2014.

[160] Donya Quick and Paul Hudak. Grammar-based automated music composition in haskell. In Proceedings of the ﬁrst ACM SIGPLAN workshop on Functional art, music, modeling & design, pages 59–70. ACM, 2013.

290 REFERENCES

[161] Gary Rader. A method for composing simple traditional music by computer. Communi- cations of the ACM, 17(11):631–638, 1974.

[162] James Rae. Sound at Sight - Sight Reading Pieces for Flute; Book 1. Trinity College London, 2007.

[163] Yves Raimond, Samer Abdallah, Mark Sandler, and Frederick Giasson. The Music On- tology. ISMIR 2007: 8th International Conference on Music Information Retrieval, 8:417– 422, 2007.

[164] Rudolf Rasch. Tuning and temperament. The Cambridge history of Western music theory, pages 193–222, 2002.

[165] Je rey Horn, Nicholas Nafpliotis, and David Goldberg. A niched pareto genetic algorithm for multiobjective optimization. In Proceedings of the ﬁrst IEEE conference on evolutionary computation, IEEE world congress on computational intelligence, volume 1, pages 82–87. Citeseer, 1994.

[166] Paulo Ribeiro, Francisco C Pereira, Miguel Ferrand, Am´ılcar Cardoso, and Pinhal de Mar- rocos. Case-based melody generation with muzacazuza. In Proceedings of the AISB’01 Symposium on Artiﬁcial Intelligence and Creativity in Arts and Science, pages 67–74, 2001.

[167] Deborah Rifkin and Philip Stoecker. A revised taxonomy for music learning. Journal of Music Theory Pedagogy, 25:155–89, 2011.

[168] David Rizo, Jos´e Inesta, and Francisco Moreno-Seco. Tree-structured representation of musical information. In Iberian Conference on Pattern Recognition and Image Analysis, pages 838–846. Springer, 2003.

[169] Curtis Roads and John Strawn. The computer music tutorial. MIT press, 1996.

[170] Ciaran´ Rowe. BlueJam: A heuristic-based approach to evolutionary music generation. Technical report, 2008.

[171] Stuart Russell and Peter Norvig. Artiﬁcial intelligence: a modern approach. Malaysia; Pearson Education Limited,, 2016.

[172] O Sandred, Mikael Laurson, and Mika Kuuskankare. Revisiting the illiac suite – a rule- based approach to stochastic processes. Sonic Ideas/Ideas Sonicas, 2:42–46, 2009.

[173] Antonino Santos, Bernardino Arcay, Julian Dorado, Juan Romero, and Jose Rodriguez. Evolutionary computation systems for musical composition. In International Conference on Acoustics and Music: Theory and Applications (AMTA 2000), volume 1, pages 97–102, 2000.

[174] Arnold Schoenberg. Fundamentals of music composition. St. Martin’s Press, 1967.

[175] Gaspar Schott. Organum mathematicum. 1668.

[176] Drew Schulz. Pianote: A sight-reading program that algorithmically generates music based on human performance. 2016.

291 REFERENCES

[177] Stephan Schwanauer and David Levitt. Machine models of music. MIT Press, 1993.

[178] Marco Scirea, Julian Togelius, Peter Eklund, and Sebastian Risi. Metacompose: A compositional evolutionary music composer. In International Conference on Evolutionary and Biologically Inspired Music and Art, pages 202–217. Springer, 2016.

[179] Mathieu Barthet Sefki Kolozali, George Fazekas. The Musical Instrument Taxonomy A. Technical report, Centre for Digital Music, Queen Mary, University of London, 2011.

[180] Mathieu Barthet Sefki Kolozali, George Fazekas. The Musical Instrument Taxonomy B. Technical report, Centre for Digital Music, Queen Mary, University of London, 2011.

[181] Johanna Selleck. Flute Sight-Reading (Series 3). Australian Music Examinations Board (AMEB), 2012.

[182] Valerie Shute. Focus on Formative Feedback. Review of Educational Research, (1):153– 189, 2008.

[183] Valerie Shute. Focus on formative feedback. Review of educational research, 78(1):153– 189, 2008.

[184] John Sloboda, Jane Davidson, Michael Howe, and Derek Moore. The role of practice in the development of performing musicians. British journal of psychology, 87(2):287–309, 1996.

[185] J Sowa. A machine to compose music: Instruction manual for geniac. New Haven: Oliver Garfeld Co, 1956.

[186] Robert Spillman. Sightreading at the Keyboard. Schirmer Books, 1990.

[187] Maximilian Stadler. Table pour composer des minuets et des trios a` la inﬁnie, avec deux dez a` jouer. Wenck Paris, 1780.

[188] Mark Steedman. A generative grammar for jazz chord sequences. Music Perception: An Interdisciplinary Journal, 2(1):52–77, 1984.

[189] Stephen Mugglin. A Progression Map for Major Keys. http://mugglinworks.com/ chordmaps/chartmaps.htm, 2017.

[190] Johan Sundberg and Bjorn¨ Lindblom. Generative theories in language and music descriptions. Cognition, 4(1):99–122, 1976.

[191] The Associated Board of the Royal Schools of Music. ABRSM Syllabus. The Associated Board of the Royal Schools of Music, 2018.

[192] Belinda Thom. Bob: an interactive improvisational music companion. In Proceedings of the fourth international conference on Autonomous agents, pages 309–316. ACM, 2000.

[193] Peter Todd. A connectionist approach to algorithmic composition. Computer Music Jour- nal, 13(4):27–43, 1989.

292 REFERENCES

[194] Nao Tokui, Hitoshi Iba, and Others. Music composition with interactive evolutionary computation. In Proceedings of the 3rd international conference on generative art, volume 17, pages 215–226, 2000.

[195] Michael Towsey, Andrew Brown, Susan Wright, and Joachim Diederich. Towards melodic extension using genetic algorithms. Educational Technology & Society, 4(2):54–65, 2001.

[196] Victoria Tsangari. An interactive software program to develop pianists’ sight-reading ability. 2010.

[197] Herre van Oostendorp, Erik van der Spek, and Jeroen Linssen. Adapting the Complexity Level of a Serious Game to the Proﬁciency of Players. 2014.

[198] Kurt VanLehn. The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 46, 2011.

[199] Walter Vispoel. Recent Research in Computerized Adaptive Testing of Musical Aptitude. Update: Applications of Research in Music Education, 11(2):39–42, 1993.

[200] Walter Vispoel and Don Coffman. Computerized-Adaptive and Self-Adapted Mu- sic Listening Tests: Psychometric Features and Motivational Beneﬁts. Applied Mea- surement in Education, 1994. URL http://www.tandfonline.com/doi/abs/10.1207/ s15324818ame0701{_}4.

[201] Rodney Waschka. Composing with genetic algorithms: Gendash. In Evolutionary Com- puter Music, pages 117–136. Springer, 2007.

[202] Peter Webster. Key research in music technology and music teaching and learning. Jour- nal of Music, Technology & Education, 4(2-3):115–130, 2012.

[203] John White. The analysis of music. Metuchen, NJ: Scarecrow Press, 1984.

[204] C Wiffen and J Burrows. Eyewitness companions: classical music, 2005.

[205] Geraint Wiggins, George Papadopoulos, Somnuk Phon-Amnuaisuk, and Andrew Tuson. Evolutionary methods for musical composition. Dai Research Paper, 1998.

[206] Lowe Bryan William and Noble Harter. Studies on the telegraphic language: The acquisition of a hierarchy of habits. Psychological review, 6(4):345, 1899.

[207] Todd C Wilson. An implementation of a drill and practice system to assist in the teaching of basic music theory. 2004.

[208] Thomas Wolf. A cognitive model of musical sight-reading. Journal of Psycholinguistic Research, 5(2):143–171, 1976.

[209] Peter Worth and Susan Stepney. Growing music: musical interpretations of l-systems. In Workshops on Applications of Evolutionary Computation, pages 545–550. Springer, 2005.

[210] David Wright. Mathematics and music, volume 28. American Mathematical Society, 2009.

[211] Liangrong Yi and Judy Goldsmith. Automatic generation of four-part harmony. BMA, 268, 2007.

293

Software References

[212] 262Hz. Interval Ear Training. https://itunes.apple.com/au/app/ interval-ear-training/id361125793, July 2015. Version 3.0.

[213] All Forces. Nota. https://itunes.apple.com/au/app/nota/id333179169, October 2012. Version 1.30.

[214] Apple Inc. Choosing a category, 2017. URL https://developer.apple.com/ app-store/categories/.

[215] appsolute GmbH. Better Ears - Music and Ear Training. https://itunes.apple. com/au/app/better-ears-music-ear-training/id284444548, October 2015. Version 3.0.1.

[216] LLC Apricot Digital Publishing. Music Reading Essentials. https://itunes.apple.com/ au/app/music-reading-essentials/id501483486, April 2015. Version 3.0.

[217] BidBox LLC. Bass Guitar Trainer. https://itunes.apple.com/au/app/ bass-guitar-trainer/id437855764, October 2011. Version 1.5.4.

[218] Brainscape. Ultimate Music Theory - Smart Audio Flashcards. https://itunes.apple. com/au/app/learn-music-theory-basic-rudiments/id724841765, May 2016. Ver- sion 3.20160423.

[219] James Buchanan. Note Brainer Pro. https://itunes.apple.com/us/app/ note-brainer-pro/id391291323, February 2017. Version 3.0.

[220] Christian Liang. Whack A Note (Music Reading Game). https://itunes.apple.com/ au/app/whack-a-note-music-reading-game/id820665068, March 2014. Version 1.0.

[221] Cindy Barba. Guitar For Kids Level 1. https://itunes.apple.com/ca/app/ guitar-for-kids-level-1/id695297753, September 2013. Version 1.0.

[222] Azati Corporation. NoteWorks. https://itunes.apple.com/au/app/noteworks/ id546003758, March 2016. Version 1.3.1.

[223] Coursera. Fundamentals of Music Theory. https://www.coursera.org/course/ musictheory, 2016.

[224] Easy Ear Training. Chordelia Triad Tutor - learn to hear Major, Minor, Augmented and Diminished chords - for the beginner and advanced musician who plays Guitar, Ukulele, Sax and more. https://itunes.apple.com/us/app/chordelia-triad-tutor-learn/ id426201096, September 2014. Version 1.10.9.

[225] Gary Froehlich. Jellybean Tunes - An Introduction to Reading and Composing Mu- sic for Kids. https://itunes.apple.com/au/app/jellybean-tunes-introduction/ id448230539, January 2015. Version 1.4.2.

[226] Gracenotes, LLC. Sight reading factory. https://www.sightreadingfactory.com/, 2019.

295 SOFTWARE REFERENCES

[227] Apps For Hunger Inc. Glow Piano Lessons. https://itunes.apple.com/au/app/ glow-piano-lessons/id441970188, September 2011. Version 1.3.1.

[228] Cape Cod Music Apps Inc. SightReadPlus. https://itunes.apple.com/us/app/ sightreadplus/id635326147, Janruary 2016. Version 1.4.1.

[229] JoyTunes. Piano Dust Buster by JoyTunes. https://itunes.apple.com/au/app/ piano-dust-buster-by-joytunes/id502356539, September 2015. Version 3.0.2.

[230] JoyTunes. Piano Maestro by JoyTunes - Piano practice. https://itunes.apple.com/ au/app/piano-maestro-by-joytunes-piano-practice/id604699751, October 2016. Version 4.1.1.

[231] Khan Academy. Music. https://www.khanacademy.org/humanities/music/, 2016.

[232] Kobus Botha. Etude sight reader. http://www.etudesoftware.com/, 2019.

[233] John R. Koza. Genetic programming. http://geneticprogramming.com/Tutorial/, 2018.

[234] Leading Tone Media. ClefTutor - Music Notes Game. https://itunes.apple.com/au/ app/cleftutor-music-notes-game/id539358800, June 2013. Version 2.0.4.

[235] Learn To Master Ltd. Piano Melody Pro - Learn Songs and Play by Ear. https: //itunes.apple.com/us/app/piano-melody-pro-learn-songs-and-play-by-ear/ id437498350, May 2017. Version 11.20.

[236] Christian Liang. Glossary of Music Quiz (The A-Z Reference to Music Termi- nology). https://itunes.apple.com/us/app/glossary-music-quiz-z-reference/ id844155730, March 2014. Version 1.0.

[237] LMuse Limited. Rhythm Cat Pro. https://itunes.apple.com/au/app/ rhythm-cat-pro-learn-to-read/id502479679, November 2015. Version 1.4.

[238] Marek Ledvina. Music Intervals. https://itunes.apple.com/us/app/ music-intervals/id464007843, June 2012. Version 1.1.

[239] Music Theory Online. Music Theory. http://www.simplifyingtheory.com/, 2016.

[240] Musicroom.com. Music Theory for Beginners. https://itunes.apple.com/au/app/ music-theory-for-beginners/id435161137, March 2015. Version 2.4.

[241] musictheory.net. Theory Lessons. https://itunes.apple.com/us/app/ theory-lessons/id493157418, September 2015. Version 2.4.

[242] NoteTutor. Note Tutor. https://itunes.apple.com/us/app/note-tutor/ id315099430, December 2014. Version 1.3.1.

[243] The Way of H. Guitar Lessons: Rock Prodigy. https://itunes.apple.com/au/app/ guitar-lessons-rock-prodigy/id407303228, March 2015. Version 2.2.1.

[244] Rising Software. Auralia Chord Recognition. https://itunes.apple.com/us/app/ auralia-chord-recognition/id979462049, November 2015. Version 1.3.

296 SOFTWARE REFERENCES

[245] Rising Software. Auralia Scales. https://itunes.apple.com/au/app/ auralia-scales/id978248581, November 2015. Version 1.3.

[246] Rising Software. Musition Note Reading. https://itunes.apple.com/au/ app/music-theory-for-beginners/id43516113://itunes.apple.com/us/app/ musition-note-reading/id828140891?mt=8, November 2015. Version 1.3.

[247] Rising Software. Musition Rhythm Notation. https://itunes.apple.com/us/app/ musition-rhythm-notation/id979462026, November 2015. Version 1.3.

[248] Rising Software. Musition Symbols. https://itunes.apple.com/us/app/ musition-symbols/id848703822, November 2015. Version 1.3.

[249] Rolfs Apps. Rhythm Sight Reading Trainer. https://itunes.apple.com/au/app/ rhythm-sight-reading-trainer/id396302174, December 2016. Version 8.7.0.

[250] SkyLeap Music. The Fundamentals of Music. http://www.fundamentalsofmusic.com/, 2013.

[251] SmileyApps. Music Theory Tutor. https://itunes.apple.com/us/app/ music-theory-tutor/id882116619, September 2015. Version 1.1.

[252] LLC SmileyApps. Piano Tutor for iPad. https://itunes.apple.com/au/app/ piano-tutor-for-ipad/id364898961, September 2015. Version 7.2.

[253] SpartanApps. Music Theory and Practice by Musicopoulos. https://itunes. apple.com/us/app/music-theory-practice-by-musicopoulos/id319290362, Octo- ber 2013. Version 2.6.1.

[254] Synaptic Stuff, LLC. Piano Genius - Free Piano Game with Classical and Pop Songs. https://itunes.apple.com/us/app/ piano-genius-free-piano-game-with-classical-and-pop-songs/id577684319, January 2016. Version 1.4.1.

[255] Ubisoft Entertainment. Rocksmith. https://rocksmith.ubisoft.com/rocksmith/ en-us/home/, 2013.

[256] Unknown. Sheet music generator. http://randomsheetmusic.com.

[257] Westover. Rhythm In Reach. https://itunes.apple.com/us/app/rhythm-in-reach/ id308463505, September 2011. Version 1.5.2.

[258] By Better Day Wireless. Piano: Ultimate. https://itunes.apple.com/us/app/ piano-ultimate/id530911981, March 2015. Version 1.1.

[259] Raja Mohammad Zishanullah. Learn Guitar Theory. https://itunes.apple.com/au/ app/learn-guitar-theory/id470514399, November 2015. Version 5.0.

297

A Musical Glossary

A.1 Deﬁnitions

Note a pitch with a length.

Pitch the lowness or highness of a tone. Deﬁned by a pitch class and an octave.

Pitch class the category of pitch. Classes are C, D, E, F, G, A, and B.

Octave the distance between two pitches of the same class on a musical keyboard.

Semitone the distance between two directly adjacent notes on a musical keyboard. Also referred to as a ‘half tone’.

Tone two semitones. Also referred to as a ‘whole tone’.

Accidental a marker which raises or lowers a pitch one semitone.

Bar a.k.a., ‘measure’; a division of a musical score. All bars in a score with the same time signature have the same duration.

Time signature deﬁnes the duration of a single bar.

Key signature indicates which pitch classes should always be modiﬁed with an accidental, regardless of whether one is explicitly written.

Scale a speciﬁc pattern of notes. Deﬁned by a scale type and a key.

Scale degree where in a scale sequence a particular pitch class is placed, where the starting pitch is 1.

Interval describes the distance between two notes. Deﬁned by a numerical size and a type.

299 APPENDIX A.MUSICAL GLOSSARY

A.2 Basic Concepts

A.2.1 Pitch

Pitch refers to the lowness or highness of a tone. Pitches can be measured and defined precisely according to their frequency (e.g., 440Hz). There are seven pitch classes, labelled in ascending order: C, D, E, F, G, A, and B. Each pitch class occurs multiple times on a musical keyboard, with each instance having a different frequency. The exact frequency of a pitch is determined by a combination of its pitch class and octave. A pitch in octave 2 is exactly double the frequency of the same pitch in octave 1. Similarly, a pitch in octave 3 is exactly half the frequency of the same pitch in octave 4. The number of octaves is theoretically infinite, but typicaly ranges from [−1, 8]. Pitches can be represented in multiple ways. One popular method is simply a combination of the pitch class and octave, for example ‘C4’. Another common method is MIDI (Musical Instrument Digital Interface) format. Using MIDI, pitches are represented by whole integers in the range [0, 127], where 0 is equivalent to C-1, and 127 maps to G9. The gaps between adjacent pitches are referred to as tones and semitones. A semitone is the smallest gap possible on a piano keybaord, and a tone is two semitones. Examples of each are shown in Figure A.1. Each pitch class can be modified with one of two accidentals: a sharp (]) or flat ([). These accidentals raise or lower the pitch one semitone, respectively. Figure A.2 shows how this works.

A.2.2 Rhythm

There are several common note lengths. These are shown in Figure A.3. Smaller note and rest lengths are created by adding additional tails to the symbols. To enhance the readability of a musical score, the notes are presented in a series of bars (a.k.a. measures). Each bar is separated by a single vertical line, and the length of a single bar is defined by a time signature. A time signature is two numbers placed on top of each other. The top note refers to the number of lengths that fit in the bar, and the bottom number refers to the duration of those lengths. The duration (i.e., bottom) number is written in terms of how 4 many of that length fits in a semibreve. For example, 4 indicates that each bar should contain 6 the duration of four crtochet notes. Alternatively, 8 indicates that each bar should contain the duration of six quaver notes. Notes lengths can be modified by placing a dot next to the symbol. This indicates that the length is equal to the standard duration multiplied by 1.5. For example, a dotted minim is equal to the length of 1.5 minim notes.

A.2.3 Key Signatures and Scales

The key signature of a piece indicates which pitch classes should always be modiﬁed with an accidental. For example, if the key signature indicates that notes with a pitch class of ‘C’ should always be played with a sharp, every ‘C’ should be played with a sharp regardless of whether the sharp symbol is explicitly written next to the note. Each key signature is referred to by a

300 APPENDIX A.MUSICAL GLOSSARY

Figure A.1: A piano keyboard with examples of an octave, tones, and semitones labelled. Taken from [142].

Figure A.2: A piano keyboard with one octave of pitch classes labelled. Taken from [137].

Figure A.3: Common musical lengths and their symbols. ‘Value’ indicates the duration of each length type in reference to a semibreve. Adapted from [137].

301 APPENDIX A.MUSICAL GLOSSARY

pitch class (e.g., ‘G’, ‘B[’) and a type. The most common types are ‘major’ and ‘minor’ (e.g., ‘D major’). The key signature of a piece also indicates the scale. A scale is a speciﬁc pattern of notes. As with the key signature, a scale is deﬁned by a scale type (i.e., ‘major’ or ‘minor’) and a pitch class. The pitch class represents the starting note for the scale, and the scale type indicates which pattern to use. For example, the ‘major’ pattern is: tone, tone, semitone, tone, tone, tone, semitone. This means that starting from a ‘C’, the major scale is C, D, E, F, G, A, B, C. Scales always start and end on the same pitch note, one octave apart. Each pitch in a scale can be referred to by its scale degree. This refers to where in the sequence that pitch class is placed, where the starting pitch is 1. For example, in the example of C major provided above, the pitch class ‘D’ is at scale degree 2. Similarly, the pitch class ‘A’ is at scale degree 6.

A.2.4 Intervals

An interval describes the distance between two notes. It is deﬁned by a numerical size and a type. The size is in reference to how many pitch classes apart the two notes are, including themselves. For example, an interval between C and E has a size of 3. Similarly, an interval between D and A has a size of 5. The type of the interval further reﬁnes the distance, and can be described in terms of a number of semitones. A major interval is the same number of semitones as there are between the starting note of a scale and the note at scale degree x, where x is the size of the interval. It does not matter which scale you use, as they are all composed using the same pattern. For example, the number of semitones in a major 3rd interval is the same as the number of semitones between a ‘C’ and a ‘E’, as ‘E’ is the note at the third scale degree of the ‘C major’ scale. This number is 4. The same process can be followed for a ‘minor’ interval. For example, the number of semitones in a minor 3rd interval is the same as the number of semitones between a ‘C’ and a ‘E[’, as ‘E[’ is the note at the third scale degree of the ‘C minor’ scale. This number is 3. There are four cases where intervals can not be of a ‘major’ or ‘minor’ type: when the size is 1, 4, 5, or 8. The reason for this is that the notes at these scale degrees are the same whether the scale type is major or minor. Intervals of these sizes are instead referred to as ‘perfect’.

302 B iOS Music Teaching Applications: State of the Art Extras

B.1 Depth and Focus of Content and Activities

B.1.1 Depth and Focus Ratings

B.1.1.1 Auditory Recognition Activities

Table B.1 shows the breakdown of depth and focus ratings for auditory recognition activities. It can be seen that the most popular content area to test with this activity is Elements of Harmony, which is the only content area to receive a ‘Very High’ focus rating. Over all the content areas, Auditory Recognition activities tend to be rated at around a ‘Medium’ depth. Neither Reading nor Historical and General Knowledge content is assessed with an Auditory Recognition activity by any application in the sample.

B.1.1.2 Visual Recognition Activities

Visual Recognition activities most commonly assess Reading content, as shown by Table B.2. A total of 35 applications are rated as having a ‘Very High’ focus on Visual Recognition activities of Reading content, and over 10 applications have ratings of ‘Medium’ or ‘High’ in the same category. However, as seen with other activities, these focus ratings are paired with relatively low depth ratings, which tend to be around the ‘Low’ or ‘Medium’ levels. The same pattern can be seen for other content areas. No applications have Visual Recognition activities for either the Harmonic Structures or Historical and General Knowledge content areas.

B.1.1.3 Auditory Description Activities

As can be seen in Table B.3, very few applications use Auditory Description activities. Those that do tend to give the activity a low focus, with little exception. Generally, the focus ratings are approximately the same, or slightly higher than the companion depth ratings for each content area.

303 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS -- 4 2 -- 6 - 1------12 Depth Ratings 4 9 -- 1 2 ----- 2 -- 1 - - 1 - 1 1 - 10 --1 - 27 ------Focus Ratings --2 - 45 4 6 3--1 - -- - Depth and focus ratings for auditory recognition activities able B.1: T Very Low- Low1 Medium High Very High Very Low Low Medium High Very High - - - 1 - eading Content Auditory recognition of ... Rhythm Content Category R Scales Content Elements of Harmony Content Harmonic Structures Content Style Content Instrument-Speciﬁc Content Historical and General Knowledge Content -

304 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS 6 ------1---- 1 1 -- 8 Depth Ratings 29 22 499 2 -- 3 1 6 - 1 -- 9 3 3 5 - 4 2 - 35 7 10 4 - 11 - -- 1 11 - -- 11 Focus Ratings 3 13 374 4 -- 5 2- 1 1 -- Depth and focus ratings for visual recognition activities able B.2: T Very Low Low Medium High Very High Very Low Low Medium High Very High 5 1 3 1 - 2 1 eading Content Visual recognition of ... Category R Rhythm Content Scales Content Elements of Harmony Content Harmonic Structures Content Style Content Instrument-Speciﬁc Content Historical and General Knowledge Content -

305 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS ------1 -- Depth Ratings 11-- 2 2 - ---- 1 ------1 - - 2 - 1 -----1 1 ------1 - Focus Ratings 111 1 1 - -- - 1 1 ---- - Depth and focus ratings for auditory description activities able B.3: T Very Low- Low- - Medium1 High- 1 Very High- Very Low Low Medium High Very High eading Content Auditory description of ... Rhythm Content Scales Content Elements of Harmony Content Harmonic Structures Content Style Content Instrument-Speciﬁc Content Historical and General Knowledge Content - Category R

306 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS ------Depth Ratings 122 3 3 1 1 2 2 1 -- - 1 1 1 - 3 2 1 - 1 - - -1--- 1 - --1-- 1 1 - - Focus Ratings 132 2 1 1 2 1 -- - 1 - - 1 2 Depth and focus ratings for visual description activities able B.4: T Very Low Low2 2 Medium1 High- 1 Very High- Very Low Low Medium High Very High - eading Content Visual description of ... Rhythm Content Scales Content Elements of Harmony Content Harmonic Structures Content Style Content Instrument-Speciﬁc Content Historical and General Knowledge Content - Category R

307 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

B.1.1.4 Visual Description Activities

Across the sample of applications Visual Description activities were used with all content areas except for Instrument-Speciﬁc. However, they were used infrequently, and usually at a ‘Low’ or ‘Medium’ focus. Figure B.4 shows that, again, depth ratings tend to be lower than the focus ratings. However, this pattern is not as pronounced as with other activity types.

B.1.1.5 Visual Playback Activities

Table B.5 shows that Visual Playback activities in the sample of applications most often ask users to interpret Rhythm and pitch information. It also shows that applications which assess Rhythm and pitch tend to give the activity a ‘Very high’ focus. However, as with other activity types, this high focus rating is not accompanied by a high depth rating. Instead, Visual Playback activities of Rhythm and pitch are most commonly rated at a ‘Medium’ depth. Pitch only and Rhythm only variants of the activity are used less frequently, but again they tend have lower depth ratings than focus ratings.

B.1.1.6 Memory Playback Activities

Memory playback activities were used sparsely in the sample of applications, as seen in Ta- ble B.6. The most common variation of the activity is to ask users to interpret only melodic information (i.e., Pitch only). Again, the depth ratings for each variation of the activity are invariably accompanied by lower depth ratings.

B.1.1.7 Notation Activities

Table B.7 shows the ratings for each variation of Notation activity. Pitch only, Scales content, and Elements of harmony content were the most common Notation activities used by applications in the sample. Whilst focus ratings are most commonly between ‘Low’ and ‘High’, depth ratings center around the ‘Very Low’ to ‘Medium’ levels. This mirrors the pattern of higher focus ratings accompanied by lower depth ratings seen in the results for other activity types.

B.2 Application Structures

By interpreting the application structures as graphs, we can ﬁnd the breadth and depth of each application’s menu hierarchy. This indicates how the applications organise their content, and how users would need to navigate that content. Figures B.1 and B.4 show the distribution of the sampled application’s structural breadths and depths, respectively. These reveal that the applications consistently exhibit menu structures between 1 and 5 layers deep, but have highly variable breadths. Figure B.3 compares the structural breadths and depths for the applications. It shows that although the distribution for breadth is wide, most applications have a relatively small breadth (i.e., less than 40), accompanied by a relatively low depth (i.e., 2 or less). This data can also be used to determine whether applications tend to focus on presenting content, providing activities, or offering a variety. Figure B.4 shows the distribution of activities and content areas used by all parts of all applications. Many applications exclusively provide

308 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS 412 2 - 1 29 Depth Ratings 2 43 1 4 3 2 - 34 3 23 2 4 Depth and focus ratings for visual playback activities Focus Ratings able B.5: 1 2 2- 2 1 T - - Very Low Low Medium High Very High Very Low Low Medium High Very High and pitch - Visual playback of ... Category Rhythm Pitch only Rhythm only

309 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS -- 1 ------5 Depth Ratings -- - 1 --2 -- 1 1 ------3 -- - 1 --1 --- 1 Focus Ratings Depth and focus ratings for memory playback activities ------1---- 3 able B.6: T - - 1 - Very Low Low Medium High Very High Very Low Low Medium High Very High and pitch Harmonic structures content - Pitch only Rhythm only Scales content Elements of harmony content - Category Rhythm Memory playback of ...

310 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS ------1 ------1 1 Depth Ratings 1 - ---- 2 2 223 - 3 - - 3 1 1 - 2 - 5 - 1 ------3 - --213 1 1 - Depth and focus ratings for notation activities Focus Ratings able B.7: 1 1 ---- - 3 13-- - 2 2 4 T - 1 - 1 - Very Low Low Medium High Very High Very Low Low Medium High Very High and pitch Style content Instrument-speciﬁc content - Harmonic structures content 1 Pitch only Rhythm only Scales content Elements of harmony content 1 Category Rhythm Notation of ...

311 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

one (i.e., only content, or only activities), and a large proportion split their parts approximately evenly between the two. The remainder tend to have more parts providing activities than presenting content. Figure B.5 expands on this, by showing how the number of application parts presenting content compares to the number of application parts providing activities across the sample of applications. The number of parts presenting content remains consistently low, with many applications having no parts which do so. However, the number of parts providing activities is often above zero, generally falling in the range of [1, 20]. This supports the notion that whilst many applications offer both, they tend to place more emphasis on providing activities for users to complete than they do presenting content.

B.3 Application Store Category

An application’s primary genre represents a top-level categorisation. This can be further spec- iﬁed with secondary, tertiary, and quaternary genres. For example, Note Tutor [242] has a primary genre of ‘Music’, secondary genre of ‘Family’, tertiary genre of ‘Educational’, and ﬁnally a quaternary genre of ‘Games’. Not all applications have four levels of categorisation, but all have nominated at least a secondary genre. Figures B.6, B.7, and B.8 show the genre trees for each of the primary genres (i.e., ‘Mu- sic’, ‘Education’, and ‘Games’) nominated by the application developers. These trees show that a core set of genres – ‘Music’, ‘Games’, ‘Education’, and ‘Educational’ – are repeated consistently at all levels of categorisation. Other genres such as ‘Reference’, ‘Entertainment’, and ‘Family’ also appear, but less frequently. Most genre sequences contain only a small number of applications. However, both the ‘Music → Education’ and ‘Education → Music’ sequences describe a large portion of the sample, containing 63 and 48 applications respectively. The genre of an application determined where it is contained the app store, the charts it appears in, and its prominence in search results [214]. Apple recommends that developers consider an application’s purpose, where users may look for that type of applications, and where similar applications are placed in the store before selecting genres for their work. It also describes each of the primary categories of genre developers can choose. Table 5.8 provides the descriptions for the three primary genres nominated by this sample of developers.

B.4 Application Monetisation

Figure B.9 shows how the prices of applications in the sample have changed over time. It can be seen that aside from a small number of outliers, most of the applications set their prices within a low range. This range can be further examined in Figure B.10, which shows the price changes made by applications in the sample up to and including $20AUD. Interestingly, the prices selected by developers have formed a grid, indicating that a small number of common price points are favoured. Across the entire sample, in the sub-$20.00AUD price range only 14 prices are ever selected: $0.99 to $9.99 in $1 increments, then $11.99, $13.99, $14.99, and $19.99. Within these options, prices less than $5AUD are particularly popular. Figure B.11 shows the distribution of the number of price changes for applications in the sample. The majority of applications tend to alter their prices fewer than 5 times, and very few

312 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

Figure B.1: Distribution of the structural breadths of the sampled applications

Figure B.2: Distribution of the structural depths of the sampled applications

313 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

Figure B.3: Structural breadth compared to structural depth across all sampled applications

applications have over 10 changes. Glow Piano Lessons [227] most frequently adjusts its cost, having done so on 37 occassions at the time of writing.

314 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

Figure B.4: Percentage of application parts which present content and which provide activities. Each horizontal bar represents one application from the sample.

315 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

Figure B.5: Number of application parts covering content compared to number of parts presenting activities across all sampled applications

316 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS [1 app] Games (6014) Educational (7008) Music (7011) [1 app] [2 apps] Games (6014) Educational (7008) [1 app] Family (7009) Family Games (6014) Educational (7008) [2 apps] Music (7011) Games (6014) Educational (7008) [1 app] Books (6018) Music (6011) [63 apps] Education (6017) [1 app] Genre tree for applications with a primary genre of ‘Music’; brackets contain the iTunes genre identiﬁers. Entertainment (6016) igure B.6: F [1 app] [2 apps] Music (7011) Games (6014) Educational (7008) [10 apps] Reference (6006) Reference

317 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS [2 apps] Music (7011) Games (6014) Educational (7008) [2 apps] Entertainment (6016) [2 apps] Educational (7008) [2 apps] Education (6017) Games (6014) Educational (7008) [3 apps] Music (7011) [48 apps] Music (6011) [1 app] Reference (6006) Reference Genre tree for applications with a primary genre of ‘Education’; brackets contain the iTunes genre identiﬁers. igure B.7: F

318 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS [1 app] Music (7011) Reference (6006) Reference Educational (7008) [1 app] Music (7011) Education (6017) Educational (7008) [2 apps] Music (7011) Games (6014) Education (6017) [1 app] Music (7011) Education (6017) Educational (7008) [2 apps] Music (6011) Music (7011) Educational (7008) Genre tree for applications with a primary genre of ‘Games’; brackets contain the iTunes genre identiﬁers. igure B.8: F

319 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS Price changes made to the sample of applications over time. The bubble sizes indicate the number of applications at each price point, with the igure B.9: smallest bubble representing 1. F

320 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS Price changes made to the sample of applications costing less than $20AUD over time. Each bubble represents one price change. igure B.10: F

321 APPENDIX B. IOSMUSIC TEACHING APPLICATIONS:STATE OF THE ART EXTRAS

Figure B.11: Distribution of number of price changes for applications in the sample

322 C Characteristics of Published Sight Reading Exercises: Grade 1 Details

C.1 Metadata: Key and Time Signatures, Lengths, Ranges

Table C.1: Metadata for all grace 1 source exercises

Exercise Key Signature Time Signature Length Range Lowest Note Highest Note (bars) (semitones)

2 ex1 F major 4 8 5 67 (G4) 72 (C5) 2 ex2 C major 4 8 8 64 (E4) 72 (C5) 2 ex3 C major 4 8 8 64 (E4) 72 (C5) 2 ex4 A minor 4 8 7 67 (G4) 74 (D5) 2 ex5 G major 4 8 8 64 (E4) 72 (C5) 2 ex6 F major 4 16 8 64 (E4) 72 (C5) 2 ex7 C major 4 16 8 64 (E4) 72 (C5) 2 ex8 F major 4 16 8 64 (E4) 72 (C5) 2 ex9 C major 4 16 8 64 (E4) 72 (C5) 4 ex10 A minor 4 8 8 71 (B4) 77 (F5) 4 ex11 C major 4 8 14 67 (G4) 81 (A5) 4 ex12 C major 4 8 12 67 (G4) 79 (G5) 4 ex13 C major 4 12 12 67 (G4) 79 (G5) 4 ex14 C major 4 12 10 71 (B4) 81 (A5) 4 ex15 C major 4 14 14 67 (G4) 81 (A5) 4 ex16 C major 4 12 14 67 (G4) 81 (A5) 3 ex17 B[ major 4 8 14 65 (F4) 79 (G5) 3 ex18 F major 4 8 12 65 (F4) 77 (F5) 3 ex19 F major 4 8 14 65 (F4) 79 (G5) 3 ex20 F major 4 8 14 65 (F4) 79 (G5) 3 ex21 F major 4 8 12 65 (F4) 77 (F5) 3 ex22 F major 4 16 12 65 (F4) 77 (F5) 3 ex23 F major 4 16 14 67 (G4) 81 (A5)

323 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

3 ex24 F major 4 16 16 65 (F4) 81 (A5) 3 ex25 B[ major 4 16 13 69 (A4) 82 (B[5) 4 ex26 F major 4 4 8 64 (E4) 72 (C5) 4 ex27 C major 4 4 8 64 (E4) 72 (C5) 4 ex28 G major 4 4 7 65 (F4) 72 (C5) 4 ex29 C major 4 4 10 62 (D4) 72 (C5) 4 ex30 C major 4 4 8 64 (E4) 72 (C5) 4 ex31 C major 4 4 8 64 (E4) 72 (C5) 4 ex32 F major 4 8 8 64 (E4) 72 (C5) 4 ex33 C major 4 8 10 62 (D4) 72 (C5) 4 ex34 C major 4 8 10 62 (D4) 72 (C5) 4 ex35 C major 4 8 10 62 (D4) 72 (C5) 4 ex36 D minor 4 8 10 62 (D4) 72 (C5) 4 ex37 C major 4 8 10 62 (D4) 72 (C5) 4 ex38 F major 4 8 12 65 (F4) 77 (F5) 4 ex39 F major 4 8 12 65 (F4) 77 (F5) 4 ex40 F major 4 8 7 65 (F4) 72 (C5) 2 ex41 G major 4 8 12 67 (G4) 79 (G5) 2 ex42 F major 4 8 12 65 (F4) 77 (F5) 2 ex43 F major 4 8 12 65 (F4) 77 (F5) 4 ex44 F major 4 8 12 65 (F4) 77 (F5) 4 ex45 F major 4 8 12 65 (F4) 77 (F5) 4 ex46 G major 4 8 12 67 (G4) 79 (G5) 4 ex47 F major 4 8 12 65 (F4) 77 (F5) 4 ex48 F major 4 8 12 65 (F4) 77 (F5) 2 ex49 C major 4 8 10 69 (A4) 79 (G5) 2 ex50 F major 4 8 12 65 (F4) 77 (F5) 2 ex51 F major 4 8 12 65 (F4) 77 (F5) 4 ex52 F major 4 8 12 65 (F4) 77 (F5) 4 ex53 G major 4 8 12 67 (G4) 79 (G5) 4 ex54 B[ major 4 8 8 69 (A4) 77 (F5) 4 ex55 F major 4 8 12 65 (F4) 77 (F5) 4 ex56 B[ major 4 8 12 65 (F4) 77 (F5) 4 ex57 G major 4 8 12 67 (G4) 79 (G5) 4 ex58 F major 4 16 12 65 (F4) 77 (F5) 2 ex59 C major 4 16 9 72 (C4) 81 (A5) 3 ex60 G major 4 16 15 64 (E4) 79 (G5) 4 ex61 F major 4 16 14 65 (F4) 79 (G5) 3 ex62 A minor 4 16 15 64 (E4) 79 (G5) 4 ex63 F major 4 16 14 65 (F4) 79 (G5) 4 ex64 G major 4 16 13 66 (F]4) 79 (G5) 4 ex65 E minor 4 16 15 64 (E4) 79 (G5) 3 ex66 F major 4 16 14 65 (F4) 79 (G5) 4 ex67 G major 4 16 12 67 (G4) 79 (G5) 2 ex68 C major 4 16 15 64 (E4) 79 (G5) 3 ex69 F major 4 16 12 65 (F4) 77 (F5)

324 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

4 ex70 G major 4 16 12 67 (G4) 79 (G5) 4 ex71 C major 4 16 15 64 (E4) 79 (G5) 3 ex72 E minor 4 16 15 64 (E4) 79 (G5)

C.2 Percentage of Notes and Rests

Table C.2: Counts and percentages of notes and rests in each grade 1 source exercise

Exercise No. Crotchets (%) No. Rests (%)

ex1 14 (87.5) 2 (12.5) ex2 13 (81.25) 3 (18.75) ex3 14 (87.5) 2 (12.5) ex4 13 (81.25) 3 (18.75) ex5 14 (87.5) 2 (12.5) ex6 26 (81.25) 6 (18.75) ex7 25 (~78.13) 7 (~21.88) ex8 22 (68.75) 10 (31.25) ex9 28 (87.5) 4 (12.5) ex10 29 (100) - ex11 28 (100) - ex12 18 (75) 6 (25) ex13 41 (~97.62) 1 (~2.38) ex14 43 (100) - ex15 45 (~84.91) 8 (~15.09) ex16 31 (~86.11) 5 (~13.89) ex17 16 (~88.89) 2 (~11.11) ex18 18 (~94.74) 1 (~5.26) ex19 18 (~94.74) 1 (~5.26) ex20 16 (80) 4 (20) ex21 14 (~73.68) 5 (~26.32) ex22 32 (~88.89) 4 (~11.11) ex23 40 (~85.11) 7 (~14.89) ex24 34 (100) - ex25 31 (~6.11) 5 (~13.89) ex26 12 (~92.31) 1 (~7.69) ex27 12 (100) - ex28 11 (~91.67) 1 (~8.33) ex29 12 (100) - ex30 13 (100) - ex31 11 (~91.67) 1 (~8.33) ex32 28 (100) - ex33 24 (100) - ex34 23 (~95.83) 1 (~4.17) ex35 26 (100) - ex36 21 (~95.45) 1 (~4.55)

325 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

ex37 25 (100) - ex38 22 (100) - ex39 20 (100) - ex40 21 (100) - ex41 13 (100) - ex42 13 (100) - ex43 14 (100) - ex44 22 (100) - ex45 24 (100) - ex46 22 (100) - ex47 23 (100) - ex48 21 (100) - ex49 14 (100) - ex50 12 (100) - ex51 13 (100) - ex52 24 (100) - ex53 24 (100) - ex54 21 (~95.45) 1 (~4.55) ex55 22 (100) - ex56 20 (~90.91) 2 (~9.09) ex57 23 (100) - ex58 42 (~80.77) 10 (~19.23) ex59 34 (~94.44) 2 (~5.56) ex60 36 (90) 4 (10) ex61 47 (~88.68) 6 (~11.32) ex62 39 (~86.67) 6 (~13.33) ex63 43 (~81.13) 10 (~18.87) ex64 48 (~85.71) 8 (~14.29) ex65 51 (~92.73) 4 (~7.27) ex66 43 (~95.56) 2 (~4.44) ex67 40 (80) 10 (20) ex68 25 (~69.44) 11 (~30.56) ex69 41 (~87.23) 6 (~12.77) ex70 37 (~84.09) 7 (~15.91) ex71 44 (~84.62) 8 (~15.38) ex72 35 (87.5) 5 (12.5)

C.3 Note Lengths in Detail

326 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS (~13.04) (15) (~13.64) (37.5) ------1 1 2 6 2 (26.09) 1 (~15.79) ------(~48.78) (18.75) (~43.48) (~20.83) (~26.09) (20) (~36.36) (~8.33) - - - - 3 5 5 10 3 2 8 2 1 (~8.70) 3 (~31.58) 1 (~4.88) 7 (~46.67) - - - - - 4 (25) 5 (~21.74) 2 (~8.51) 6 (~54.55) Raw count and percentage of melody time ﬁlled by each note length for all grade 1 source exercises able C.3: T (100) (100) (100) (100) (81.25) (~56.52) (~79.17) (~51.22) (~60.87) (65) (50) (~54.17) 13 13 26 22 26 13 38 21 14 13 22 26 14 (100) 14 (100) 14 (100) 25 (100) 28 (100) 24 (75) 36 (~78.26) 43 (~91.49) 10 (~45.45) ercise No. Crotchets (% of time) No. Quavers (% of time) No. Semiquavers (% of time) No. Minims (% of time) No. Dotted Minims (% of time) ex19ex21 15 (~65.22) ex23 10 (~52.63) ex25 39 (~95.12) 16 (~53.33) Ex ex1 ex2 ex4 ex6 ex8 ex10 ex12 ex14 ex16 ex18 ex20 ex22 ex24 ex3 ex5 ex7 ex9 ex11 ex13 ex15 ex17

327 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS ------(25) (25) (25) (25) (25) (25) (~28.57) ------2 2 - 2 2 2 - 2 2 ------2 (25) - - 2 (25) 2 (25) - - 2 (25) (~28.57) (~42.86) (37.5) (25) (~46.67) (60) (25) (31.25) (37.5) (25) (25) (31.25) (50) (12.5) (~7.14) 2 3 3 4 7 9 4 5 3 4 4 5 4 2 1 4 (50) 4 (50) 3 (~42.86) 8 (50) 6 (37.5) 7 (43.75) 6 (37.5) 3 (37.5) 2 (25) 2 (12.5) 3 (18.75) 2 (25) 3 (37.5) 2 (12.5) (~71.43) (62.5) (75) (~53.33) (40) (50) (43.75) (62.5) (50) (50) (43.75) (62.5) (~64.29) (~57.14) (50) 10 8 10 24 16 12 16 14 10 16 16 14 8 20 18 8 (50) 8 (50) 8 (~57.14) 16 (50) 20 (62.5) 18 (56.25) 12 (37.5) 10 (62.5) 12 (75) 20 (62.5) 18 (56.25) 49 (75) 10 (62.5) 20 (62.5) ex26 ex28 ex30 ex32 ex34 ex36 ex38 ex40 ex42 ex44 ex46 ex48 ex50 ex52 ex54 ex27 ex29 ex31 ex33 ex35 ex37 ex39 ex41 ex43 ex45 ex47 ex49 ex51 ex53

328 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS (~11.11) (5.36) (~6.52) (~5.36) - 2 - - 1 1 - 1 - - - 2 (~11.11) 1 (5.36) - - 2 (10.34) - 1 (~7.14) (~10.87) (~19.05) - - - - - 10 8 - - 12 (20.69) ------12 (14.29) (~16.67) 1 ------2 (25) 2 (25) - - - (60.71) (~8.33) (~29.63) (~36.36) (14.29) (~21.43) (~26.09) (~37.21) 1 8 8 3 6 6 - 17 8 1 (~6.90) 8 (~27.12) 10 (~37.04) 10 (~35.71) 4 (25) 3 (18.75) 7 (~24.14) 9 (~34.62) 5 (~23.81) (75) (~59.26) (~63.64) (~85.71) (~73.21) (~56.52) (~80.95) (~33.93) (~62.79) 18 32 28 36 41 26 17 19 27 16 (50) 18 (56.25) 38 (~65.52) 34 (~65.38) 23 (~54.76) ex59 21 (~72.41) ex65ex67 43 (72.89) 28 (~51.85) ex71 33 (~58.93) ex55 ex56 ex58 ex60 ex62 ex64 ex66 ex68 ex70 ex72 ex57 ex61 ex63 ex69

329 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

C.4 Rest Lengths in Detail

Table C.4: Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 1 source exercises

Exercise No. Crotchets (% of time) No. Quavers (% of time) No. Semiquavers (% of time)

ex1 2 (100) - - ex2 3 (100) - - ex3 2 (100) - - ex4 3 (100) - - ex5 2 (100) - - ex6 6 (100) - - ex7 7 (100) - - ex8 10 (100) - - ex9 4 (100) - - ex10 - - - ex11 - - - ex12 3 (~33.33) 3 (~66.67) - ex13 - 1 (100) - ex14 - - - ex15 7 (~77.78) 1 (~22.22) - ex16 3 (~42.86) 2 (~57.14) - ex17 2 (100) - - ex18 1 (100) - - ex19 1 (100) - - ex20 4 (100) - - ex21 5 (100) - - ex22 4 (100) - - ex23 7 (100) - - ex24 - - - ex25 5 (100) - - ex26 - 1 (100) - ex27 - - - ex28 - 1 (100) - ex29 - - - ex30 - - - ex31 - 1 (100) - ex32 - - - ex33 - - - ex34 - 1 (100) - ex35 - - - ex36 - 1 (100) - ex37 - - - ex38 - - - ex39 - - -

330 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

ex40 - - - ex41 - - - ex42 - - - ex43 - - - ex44 - - - ex45 - - - ex46 - - - ex47 - - - ex48 - - - ex49 - - - ex50 - - - ex51 - - - ex52 - - - ex53 - - - ex54 - - 1 (100) ex55 - - - ex56 - - 2 (100) ex57 - - - ex58 10 (100) - - ex59 1 (~33.33) 1 (~66.67) - ex60 4 (100) - - ex61 6 (100) - - ex62 6 (100) - - ex63 8 (~66.67) 2 (33.33) - ex64 8 (100) - - ex65 3 (60) 1 (40) - ex66 2 (100) - - ex67 10 (100) - - ex68 11 (100) - - ex69 6 (100) - - ex70 6 (75) 1 (25) - ex71 8 (100) - - ex72 5 (100) - -

C.5 Intervals in Detail

Table C.5: Number and percentage of intervals of each size for all grade 1 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes.

Exercise Number of Scale Degrees (%) 0 1 2 3 4 5 6 7

ex1 4 (57.1) 2 (28.6) - 1 (14.3) - - - - ex2 7 (70) 3 (30) ------ex3 4 (33.3) 8 (66.7) ------ex4 1 (1) 8 (80) 1 (10) - - - - -

331 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

ex5 1 (10) 6 (60) 2 (20) 1 (10) - - - - ex6 4 (36.4) 7 (63.6) ------ex7 1 (5.6) 14 (77.8) 2 (11.1) 1 (5.6) - - - - ex8 - 7 (87.5) 1 (12.5) - - - - - ex9 5 (20.8) 7 (29.2) 5 (20.8) 7 (29.2) - - - - ex10 - 26 (92.9) 2 (7.1) - - - - - ex11 - 17 (63) 8 (29.6) 2 (7.4) - - - - ex12 - 5 (55.6) 2 (22.2) 1 (11.1) 1 (11.1) - - - ex13 2 (5.7) 18 (51.4) 8 (22.9) 6 (17.1) 1 (2.9) - - - ex14 13 (31) 19 (45.2) 7 (16.7) 3 (7.1) - - - - ex15 - 18 (48.6) 13 (35.1) 2 (5.4) 2 (5.4) 1 (2.7) 1 (2.7) - ex16 - 13 (54.2) 7 (29.2) 1 (4.2) 2 (8.3) 1 (4.2) - - ex17 - 7 (58.3) 2 (16.7) 1 (8.3) 2 (16.7) - - - ex18 1 (6.2) 4 (25) 9 (56.2) 1 (6.2) 1 (6.2) - - - ex19 - 9 (56.2) 3 (18.8) 3 (18.8) 1 (6.2) - - - ex20 - 8 (72.7) 2 (18.2) 1 (9.1) - - - - ex21 3 (33.3) 2 (22.2) 4 (44.4) - - - - - ex22 - 22 (78.6) 3 (10.7) 1 (3.6) 1 (3.6) 1 (3.6) - - ex23 - 23 (76.7) 4 (13.3) 3 (10) - - - - ex24 - 26 (83.9) 3 (9.7) 1 (3.2) - 1 (3.2) - - ex25 - 13 (65) 3 (15) 3 (15) - 1 (5) - - ex26 - 6 (85.7) 1 (14.3) - - - - - ex27 1 (9.1) 9 (81.8) 1 (9.1) - - - - - ex28 1 (12.5) 7 (87.5) ------ex29 1 (9.1) 9 (81.8) 1 (9.1) - - - - - ex30 4 (33.3) 7 (58.3) 1 (8.3) - - - - - ex31 - 7 (70) 3 (30) - - - - - ex32 5 (27.8) 12 (66.7) 1 (5.6) - - - - - ex33 1 (4.3) 22 (95.7) ------ex34 - 16 (72.7) 5 (22.7) 1 (4.5) - - - - ex35 3 (12) 18 (72) 2 (8) 2 (8) - - - - ex36 1 (6.7) 10 (66.7) 3 (20) 1 (6.7) - - - - ex37 3 (12.5) 18 (75) 2 (8.3) 1 (4.2) - - - - ex38 38 (23.8) 11 (52.4) 4 (19) 1 (4.8) - - - - ex39 - 16 (84.2) 3 (15.8) - - - - - ex40 2 (10) 13 (65) 3 (15) 1 (5) 1 (5) - - - ex41 1 (8.3) 8 (66.7) - 2 (16.7) 1 (8.3) - - - ex42 - 5 (41.7) 4 (33.3) 3 (25) - - - - ex43 - 10 (76.9) 2 (15.4) 1 (7.7) - - - - ex44 - 8 (38.1) 11 (52.4) 1 (4.8) - 1 (4.8) - - ex45 - 18 (78.3) 3 (13) 2 (8.7) - - - - ex46 - 16 (76.2) 4 (19) 1 (4.8) - - - - ex47 - 16 (72.7) 4 (18.2) 1 (4.5) 1 (4.5) - - - ex48 1 (5) 14 (70) 3 (15) 2 (10) - - - - ex49 1 (11.1) 3 (33.3) 4 (44.4) 1 (11.1) - - - - ex50 - 7 (63.6) 2 (18.2) 2 (18.2) - - - -

332 APPENDIX C.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 1 DETAILS

ex51 2 (16.7) 5 (41.7) 4 (44.4) 1 (8.3) - - - - ex52 3 (13) 16 (69.6) 2 (8.7) 2 (8.7) - - - - ex53 - 10 (43.5) 9 (39.1) 3 (13) - 1 (4.3) - - ex54 3 (15.8) 9 (47.4) 4 (21.1) 2 (10.5) - 1 (5.3) - - ex55 4 (19) 5 (23.8) 11 (52.4) 1 (4.8) - - - - ex56 6 (35.3) 3 (17.6) 7 (41.2) 1 (5.9) - - - - ex57 - 13 (59.1) 6 (27.3) - 2 (9.1) 1 (4.5) - - ex58 16 (50) 14 (43.8) 2 (6.2) - - - - - ex59 6 (19.4) 25 (80.6) ------ex60 - 16 (50) 10 (31.2) 4 (12.5) - 1 (3.1) 1 (3.1) - ex61 1 (2.6) 11 (28.2) 15 (38.5) 11 (28.2) - 1 (2.6) - - ex62 - 17 (51.5) 8 (24.2) - 8 (24.2) - - - ex63 8 (24.2) 11 (33.3) 6 (18.2) 5 (15.2) 2 (6.1) 1 (3) - - ex64 5 (12.5) 27 (67.5) 5 (12.5) 2 (5) - - - 1 (2.5) ex65 4 (8.5) 25 (53.2) 6 (12.8) 6 (12.8) 3 (6.4) 3 (6.4) - - ex66 7 (17.5) 16 (40) 10 (25) 5 (12.5) 2 (5) - - - ex67 6 (20) 20 (66.7) 4 (13.3) - - - - - ex68 - 14 (100) ------ex69 - 17 (56.7) 3 (10) 7 (23.3) 2 (6.7) 1 (3.3) - - ex70 1 (3.3) 13 (43.3) 12 (40) 1 (3.3) 1 (3.3) 2 (6.7) - - ex71 10 (27.8) 19 (52.8) 5 (13.9) 1 (2.8) - 1 (2.8) - - ex72 4 (13.3) 15 (50) 6 (20) 4 (13.3) 1 (3.3) - - -

333

D Characteristics of Published Sight Reading Exercises: Grade 2 Details

D.1 Metadata: Key and Time Signatures, Lengths, Ranges

Table D.1: Metadata for all grace 2 source exercises

Exercise Key Signature Time Signature Length Range Lowest Note Highest Note (bars) (semitones)

4 ex1 G major 4 8 12 67 (G4) 79 (G5) 3 ex2 G major 4 8 12 67 (G4) 79 (G5) 4 ex3 G major 4 8 13 66 (F]4) 79 (G5) 4 ex4 E minor 4 10 13 66 (F]4) 79 (G5) 3 ex5 G major 4 16 14 67 (G4) 81 (A5) 4 ex6 G major 4 16 8 67 (G4) 81 (A5) 3 ex7 G major 4 18 12 67 (G4) 79 (G5) 3 ex8 G major 4 15 16 67 (G4) 83 (B5) 4 ex9 C major 4 4 12 67 (G4) 79 (G5) 3 ex10 D minor 4 8 10 72 (C5) 82 (B[5) 2 ex11 G major 4 8 16 67 (G4) 83 (B5) 3 ex12 C major 4 8 10 71 (B4) 81 (A5) 4 ex13 C major 4 12 14 67 (G4) 81 (A5) 3 ex14 G major 4 16 12 67 (G4) 79 (G5) 3 ex15 C major 4 16 14 67 (G4) 81 (A5) 4 ex16 C major 4 12 17 64 (E4) 81 (A5) 3 ex17 F major 4 8 12 65 (F4) 77 (F5) 3 ex18 F major 4 8 13 64 (E4) 77 (F5) 3 ex19 F major 4 8 10 62 (D4) 72 (C5) 3 ex20 F major 4 8 12 65 (F4) 77 (F5) 4 ex21 F major 4 8 13 64 (E4) 77 (F5) 4 ex22 F major 4 8 12 65 (F4) 77 (F5) 3 ex23 D minor 4 8 15 62 (D4) 77 (F5)

335 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

3 ex24 D minor 4 8 12 62 (D4) 74 (D5) 4 ex25 D minor 4 8 14 62 (D4) 76 (E5) 3 ex26 A minor 4 8 11 65 (F4) 76 (E5) 3 ex27 C major 4 8 12 64 (E4) 76 (E5) 4 ex28 C major 4 8 13 64 (E4) 77 (F5) 4 ex29 F major 4 8 12 65 (F4) 77 (F5) 3 ex30 F major 4 8 9 65 (F4) 74 (D5) 3 ex31 A minor 4 8 9 68 (G]4) 77 (F5) 2 ex32 G major 4 8 12 67 (G4) 79 (G5) 2 ex33 A minor 4 8 12 64 (E4) 76 (E5) 4 ex34 A minor 4 8 12 69 (A4) 81 (A5) 4 ex35 C major 4 8 12 67 (G4) 79 (G5) 4 ex36 F major 4 8 10 67 (G4) 77 (F5) 4 ex37 A minor 4 8 12 69 (A4) 81 (A5) 3 ex38 A minor 4 8 12 69 (A4) 81 (A5) 3 ex39 G major 4 8 12 71 (B4) 83 (B5) 2 ex40 B[ major 4 8 8 69 (A4) 77 (F5) 2 ex41 A minor 4 8 12 69 (A4) 81 (A5) 4 ex42 G major 4 8 12 67 (G4) 79 (G5) 4 ex43 A minor 4 8 12 69 (A4) 81 (A5) 4 ex44 A minor 4 8 12 69 (A4) 81 (A5) 4 ex45 D minor 4 8 12 69 (A4) 81 (A5) 3 ex46 A minor 4 8 9 67 (G4) 76 (E5) 4 ex47 G major 4 8 12 67 (G4) 79 (G5) 4 ex48 B[ major 4 8 12 65 (F4) 77 (F5) 3 ex49 G major 4 17 17 62 (D4) 79 (G5) 4 ex50 D major 4 16 15 66 (F]4) 81 (A5) 4 ex51 A minor 4 16 17 64 (E4) 81 (A5) 3 ex52 E minor 4 16 17 64 (E4) 81 (A5) 2 ex53 C major 4 16 9 72 (G4) 81 (A5) 3 ex54 B minor 8 16 19 62 (D4) 81 (A5) 4 ex55 F major 4 12 17 64 (E4) 81 (A5) 4 ex56 E minor 4 16 17 64 (E4) 81 (A5) 4 ex57 G major 4 17 15 64 (E4) 79 (G5) 2 ex58 F major 4 24 19 62 (D4) 81 (A5) 4 ex59 A minor 4 15 17 62 (D4) 79 (G5) 3 ex60 A minor 4 16 17 64 (E4) 81 (A5) 4 ex61 E minor 4 16 19 62 (D4) 81 (A5) 3 ex62 A minor 4 20 14 67 (G4) 81 (A5) 4 ex63 E minor 4 16 15 64 (E4) 79 (G5) 4 ex64 D major 4 16 19 62 (D4) 81 (A5)

D.2 Percentage of Notes and Rests

336 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

Table D.2: Counts and percentages of notes and rests in each grade 2 source exercise

Exercise No. Crotchets (%) No. Rests (%)

ex1 21 (~95.45) 1 (~4.55) ex2 16 (~76.19) 5 (~23.81) ex3 30 (~96.77) 1 (~3.23) ex4 33 (100) - ex5 33 (~94.29) 2 (~5.71) ex6 40 (~86.96) 6 (~13.04) ex7 44 (~91.67) 4 (~8.33) ex8 36 (~94.74) 2 (~5.26) ex9 19 (95) 1 (5) ex10 32 (100) - ex11 24 (96) 1 (4) ex12 25 (~86.21) 4 (~13.79) ex13 47 (~97.92) 1 (~2.08) ex14 51 (~94.44) 3 (~5.56) ex15 60 (~98.36) 1 (~1.64) ex16 47 (94) 3 (6) ex17 22 (~91.67) 2 (~8.33) ex18 19 (~86.36) 3 (~13.64) ex19 21 (100) - ex20 19 (~90.48) 2 (~9.52) ex21 29 (~96.67) 1 (~3.33) ex22 17 (85) 3 (15) ex23 27 (~96.43) 1 (~3.57) ex24 21 (~91.30) 2 (~8.70) ex25 25 (~92.59) 2 (~7.41) ex26 22 (~92.67) 2 (~8.33) ex27 21 (~77.78) 6 (22.22) ex28 20 (~90.91) 2 (~9.09) ex29 25 (100) - ex30 18 (100) - ex31 20 (100) - ex32 13 (100) - ex33 15 (100) - ex34 28 (100) - ex35 25 (100) - ex36 24 (100) - ex37 25 (100) - ex38 18 (100) - ex39 20 (100) - ex40 14 (100) - ex41 15 (100) - ex42 26 (100) -

337 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

ex43 25 (100) - ex44 23 (100) - ex45 24 (100) - ex46 18 (100) - ex47 19 (100) - ex48 22 (100) - ex49 34 (~94.44) 2 (~5.56) ex50 40 (~76.92) 12 (~23.08) ex51 45 (90) 5 (10) ex52 39 (90) 4 (10) ex53 44 (~91.67) 4 (~8.33) ex54 32 (~91.43) 3 (~8.57) ex55 59 (~98.33) 1 (~1.67) ex56 46 (~79.31) 12 (~20.69) ex57 68 (100) - ex58 66 (~94.28) 4 (~5.71) ex59 68 (~94.44) 4 (~5.56) ex60 38 (~88.37) 5 (~11.63) ex61 53 (~92.98) 4 (~7.02) ex62 40 (~88.89) 5 (~11.11) ex63 62 (~91.18) 6 (~8.82) ex64 58 (~89.23) 7 (~10.77)

D.3 Note Lengths in Detail

338 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS (~15.52) (~6.98) (12.5) (~6.67) (~13.29) (~13.64) (~11.54) (~13.64) No. Dotted Minims (% of time) - - 3 1 1 - 1 - 1 1 1 1 - - - 1 (~6.38) 1 (12.5) 1 (~9.68) - 2 (~19.35) - 2 (~13.04) - 1 (~13.64) ------No. Dotted Crotchets (% of time) ------No. Dotted Quavers (% of time) (~15.38) - - - - - 1 (~12.90) ------1 - No. Semiquavers (% of time) ------No. Semibreves (% of time) - - - - (~41.67) (30) (~24.44) (~18.60) (~22.73) (~9.52) (~9.09) (~3.85) No. Minims (% of time) - - - - 20 12 22 16 4 4 2 10 - 17 (~54.84) - 4 (~8.33) - Raw count and percentage of melody time ﬁlled by each note length for all grade 2 source exercises (~41.38) (~31.58) (35) (~23.26) (10) (~13.33) (~18.60) (~19.05) (~27.27) (~38.46) (~36.36) able D.3: No. Quavers (% of time) 3 7 12 5 - 1 3 4 2 3 5 4 6 (24) T (~68.42) (65) (~43.10) (~69.77) (~45.83) (60) (~55.56) (~62.79) (~57.14) (50) (~30.77) (~27.27) (% of time) 13 26 25 30 11 12 25 27 12 11 8 6 13 (~41.94)29 6 (~93.55) (~38.71)22 1 (~47.83) - (~6.45) 9 (~39.13) - - 29 (~71.70) 6 (~25.53)14 (~63.64) 12 (~12.77) - 1 (~9.09) 6 (~13.64) - ercise No. Crotchets ex3 ex5 ex7ex9 38 (76) ex11 8 (~53.33) 7 (~45.16)ex13 1 (~13.33)ex15 - 10 (~33.33) 26 (~55.32)ex17 - 1ex19 (~4.23) 13 (~54.17)ex21 32 (~34.04) 12 3 - (~38.71)ex23 (25) 10 3 (~43.48) (~19.35) 3 12 (~26.09) (~19.35) - 14 (~30.43) - Ex ex1 ex2 ex4 ex6 ex8 ex10 ex12 ex14 ex16 ex18 ex20 ex22 ex24

339 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS (~27.27) (30) (25) (37.5) (25) (~13.64) 2 3 2 - - - 3 - - - 2 - - 2 1 (10) 2 (25) ------2 (~13.04) 1 (~5.17) - - - 1 (12.5) (~10.47) (~3.41) ------4 (~13.04) 2 (~5.17) - 1 (~5.36) ------3 1 ------3 (~8.04) ------(~13.33) (25) (12.5) (12.5) (25) 1 (~13.33) - 1 (12.5) 1 (12.5) - 1 (12.5) 1 (12.5) - - - 2 (25) - - - - - 1 - - - 2 - - 1 1 - 2 ------(~18.18) (~6.67) (~3.49) (~1.14) 8 4 ------3 1 6 (10) - - - - - 27 (~48.21) 3 (~2.68) (20) (~16.67) (37.5) (25) (12.5) (25) (18.75) (37.5) (~16.67) (25) (~13.95) (~18.18) - 3 2 3 4 2 - 2 3 6 2 4 3 4 - 4 (25) (~54.54) (~58.33) (62.5) (75) (62.5) (62.5) (75) (68.75) (50) (58.33) (50) (~72.09) (~63.64) (30) 12 9 14 10 24 20 15 12 22 16 14 16 31 28 14 (~46.67) 3 (20) 14 (87.5)20 (62.5) 1 (12.5)20 (62.5) 4 (25) - 4 (25) 14 (87.5)20 (62.5) 1 (12.5)18 (56.25) 4 (25) - 5 (31.25)16 (~34.78) - 20 8 (~34.48) (~34.78) 14 4 (~48.28) (~4.35) 8 (~6.90) - - ex33 ex35 ex37 ex41 ex43 ex45 ex49 ex51 ex25 ex26 ex28 ex30 ex32 ex34 ex36 ex38 ex40 ex42 ex44 ex46 ex48 ex50 ex52 ex27 12 (~66.67)ex29 18 1 (56.25)ex31 (~11.11) 18 (75) 8 (~22.22) 7 (43.75) - - ex39 17 (~70.83) 2 (~16.67) - ex47 16 (50) ex53 10 (~35.71) -

340 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS (~10.91) - - - - 2 ------(~6.67) (18) (~13.95) (~10.91) 10 (~25.86) - 1 (~2.34) - 7 (~17.80) 1 6 - 4 4 ------(~44.44) (~56.82) (~20.83) (6) (~4.65) (~3.64) 20 6 50 4 4 20 18 (~15.52) - (40) (16) (~13.64) (~23.26) - 4 3 5 11 - (~48.89) (60) (~29.55) (~58.14) (~34.55) (~79.17) 11 30 13 25 19 38 20 (~42.55)46 5 (~71.86) (~21.28)29 4 (~54.72) 34 (12.5) (~36.17) - 27 3 (~45.76) (~11.32) 17 (~13.28) 8 36 (~27.12) (~33.96) - - 11 (~9.32) - ex55 ex57 ex59 ex61 ex63 34 (~58.62) - ex54 ex56 ex58 ex60 ex62 ex64

341 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

D.4 Rest Lengths in Detail

Table D.4: Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 2 source exercises

Exercise No. Crotchets No. Quavers No. Semiquavers No. Minims (% of time) (% of time) (% of time) (% of time)

ex1 1 (100) - - - ex2 5 (100) - - - ex3 1 (100) - - - ex4 - - - - ex5 2 (100) - - - ex6 6 (100) - - - ex7 4 (100) - - - ex8 2 (100) - - - ex9 1 (100) - - - ex10 - - - - ex11 - - - 1 (100) ex12 4 (100) - - - ex13 1 (100) - - - ex14 3 (100) - - - ex15 1 (100) - - - ex16 1 (20) 2 (80) - - ex17 2 (100) - - - ex18 3 (100) - - - ex19 - - - - ex20 2 (100) - - - ex21 1 (100) - - - ex22 - 3 (100) - - ex23 1 (100) - - - ex24 2 (100) - - - ex25 2 (100) - - - ex26 2 (100) - - - ex27 6 (100) - - - ex28 2 (100) - - - ex29 - - - - ex30 - - - - ex31 - - - - ex32 - - - - ex33 - - - - ex34 - - - - ex35 - - - - ex36 - - - - ex37 - - - - ex38 - - - -

342 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

ex39 - - - - ex40 - - - - ex41 - - - - ex42 - - - - ex43 - - - - ex44 - - - - ex45 - - - - ex46 - - - - ex47 - - - - ex48 - - - - ex49 2 (100) - - - ex50 3 (~14.29) 9 (~85.71) - - ex51 4 (~66.67) 1 (~33.33) - - ex52 4 (100) - - - ex53 2 (100) - - - ex54 - - - 3 (100) ex55 1 (100) - - - ex56 10 (~71.43) 2 (~28.57) - - ex57 - - - - ex58 4 (100) - - - ex59 3 (~42.86) - 1 (~57.14) - ex60 5 (100) - - - ex61 3 (60) 1 (40) - - ex62 5 (100) - - - ex63 6 (100) - - - ex64 6 (75) 1 (25) - -

D.5 Intervals in Detail

Table D.5: Number and percentage of intervals of each size for all grade 2 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes.

Exercise Number of Scale Degrees (%) 0 1 2 3 4 5 6 7

ex1 12 (60) 4 (20) 2 (10) 2 (10) - - - - ex2 7 (58.3) 2 (16.7) 2 (16.7) - 1 (8.3) - - - ex3 - 24 (85.7) 4 (14.3) - - - - - ex4 2 (6.2) 25 (78.1) 3 (9.4) 1 (3.1) - 1 (3.1) - - ex5 - 20 (71.4) 3 (10.7) 3 (10.7) - 2 (7.1) - - ex6 - 29 (85.3) 4 (11.8) 1 (2.9) - - - - ex7 13 (32.5) 15 (37.5) 10 (25) 2 (5) - - - - ex8 - 24 (72.7) 8 (24.2) 1 (3) - - - - ex9 10 (58.8) 2 (11.8) 4 (23.5) 1 (5.9) - - - - ex10 3 (9.7) 20 (64.5) 5 (16.1) 2 (6.5) 1 (3.2) - - - ex11 1 (5) 15 (75) 4 (20) - - - - -

343 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

ex12 8 (38.1) 6 (28.6) 7 (33.3) - - - - - ex13 - 21 (51.2) 12 (29.3) 3 (7.3) 1 (2.4) 2 (4.9) 1 (2.4) 1 (2.4) ex14 4 (8.3) 26 (54.2) 10 (20.8) 6 (12.5) 1 (2.1) - 1 (2.1) - ex15 7 (12.7) 36 (65.5) 6 (10.9) 3 (5.5) 3 (5.5) - - - ex16 - 21 (52.5) 15 (37.5) 3 (7.5) 1 (2.5) - - - ex17 1 (5.3) 11 (57.9) 5 (26.3) 2 (10.5) - - - - ex18 3 (18.8) 8 (50) 4 (25) 1 (6.2) - - - - ex19 1 (5) 15 (75) 3 (15) 1 (5) - - - - ex20 - 12 (75) 2 (12.5) 2 (12.5) - - - - ex21 - 24 (88.9) 1 (3.7) 2 (7.4) - - - - ex22 - 7 (53.8) 2 (15.4) 2 (15.4) 2 (15.4) - - - ex23 - 15 (60) 6 (24) 4 (16) - - - - ex24 - 12 (80) 1 (6.7) 2 (13.3) - - - - ex25 3 (15) 14 (50) 2 (10) 1 (5) - - - ex26 - 10 (52.6) 9 (47.4) - - - - - ex27 - 15 (93.8) 1 (6.2) - - - - - ex28 - 8 (47.1) 5 (29.4) 3 (17.6) 1 (5.9) - - - ex29 3 (12.5) 15 (62.5) 4 (16.7) 1 (4.2) 1(4.2) - - - ex30 - 14 (82.4) 2 (11.8) - 1 (5.9) - - - ex31 1 (5.9) 12 (70.6) 4 (23.5) - - - - - ex32 1 (8.3) 3 (25) 7 (58.3) 1 (8.3) - - - - ex33 2 (20) 2 (20) 3 (30) 1 (10) 1 (10) 1 (10) - - ex34 1 (4) 11 (44) 7 (28) 3 (12) 3 (12) - - - ex35 1 (5) 11 (55) 5 (25) 2 (10) 1 (5) - - - ex36 7 (30.4) 12 (52.2) 2 (8.7) 2 (8.7) - - - - ex37 1 (5.3) 15 (78.9) 1 (5.3) 2 (10.5) - - - - ex38 - 4 (30.8) 7 (53.8) 2 (15.4) - - - - ex39 - 12 (63.2) - 3 (15.8) 3 (15.8) 1 (5.3) - - ex40 4 (44.4) 3 (33.3) - - 2 (22.2) - - - ex41 1 (8.3) 2 (16.7) 2 (16.7) 7 (58.3) - - - - ex42 - 11 (44) 9 (36) 4 (16) 1 (4) - - - ex43 2 (9.1) 11 (50) 5 (22.7) 4 (18.2) - - - - ex44 2 (9.1) 8 (36.4) 8 (36.4) 3 (13.6) 1 (4.5) - - - ex45 4 (17.4) 7 (30.4) 8 (34.8) 4 (17.4) - - - - ex46 - 9 (52.9) 4 (23.5) 3 (17.6) 1 (5.9) - - - ex47 - 12 (66.7) 4 (22.2) 2 (11.1) - - - - ex48 4 (21.1) 8 (42.1) 3 (15.8) 4 (21.1) - - - - ex49 2 (6.2) 15 (46.9) 10 (31.2) 3 (9.4) - - 1 (3.1) 1 (3.1) ex50 - 12 (42.9) 5 (17.9) 3 (10.7) 4 (14.3) 4 (14.3) - - ex51 1 (2.5) 27 (67.5) 4 (10) 2 (5) 3 (7.5) - - 3 (7.5) ex52 5 (15.2) 22 (66.7) 3 (9.1) 1 (3) 1 (3) - - 1 (3) ex53 10 (31.2) 15 (46.9) 5 (15.6) 2 (6.2) - - - - ex54 1 (3.4) 19 (65.5) 6 (20.7) 2 (6.9) 1 (3.4) - - - ex55 - 26 (45.6) 20 (35.1) 6 (10.5) 4 (7) 1 (1.8) - - ex56 4 (11.8) 19 (55.9) 7 (20.6) 2 (5.9) 2 (5.9) - - - ex57 - 48 (71.6) 11 (16.4) 5 (7.5) 2 (3) 1 (1.5) - -

344 APPENDIX D.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 2 DETAILS

ex58 9 (14.5) 34 (54.8) 11 (17.7) 5 (8.1) 3 (4.8) - - - ex59 1 (2.3) 38 (86.4) 4 (9.1) - - 1 (2.3) - - ex60 - 20 (87) 1 (4.3) 1 (4.3) - 1 (4.3) - - ex61 - 29 (60.4) 7 (14.6) 8 (16.7) 2 (4.2) 2 (4.2) - - ex62 - 26 (76.5) 3 (8.8) 5 (14.7) - - - - ex63 - 38 (67.9) 9 (16.1) 3 (5.4) 3 (5.4) 3 (5.4) - - ex64 6 (12.2) 34 (69.4) 4 (8.2) 3 (6.1) 1 (2) 1 (2) - -

345

E Characteristics of Published Sight Reading Exercises: Grade 3 Details

E.1 Metadata: Key and Time Signatures, Lengths, Ranges

Table E.1: Metadata for all grace 3 source exercises

Exercise Key Signature Time Signature Length Range Lowest Note Highest Note (bars) (semitones)

4 ex1 C major 4 8 12 67 (G4) 79 (G5) 4 ex2 A minor 4 8 12 69 (A4) 81 (A5) 3 ex3 A minor 4 8 12 69 (A4) 81 (A5) 3 ex4 A minor 4 8 8 69 (A4) 77 (F5) 4 ex5 A minor 4 12 12 69 (A4) 81 (A5) 4 ex6 F major 4 16 17 65 (F4) 82 (B[5) 3 ex7 A minor 4 20 20 64 (E4) 84 (C6) 3 ex8 A minor 4 16 12 69 (A4) 81 (A5) 4 ex9 C major 4 8 17 67 (G4) 84 (C6) 3 ex10 C major 4 8 9 72 (C5) 81 (A5) 4 ex11 D major 4 7 10 73 (C]5) 83 (B5) 3 ex12 B minor 4 8 10 69 (A4) 79 (G5) 4 ex13 D major 4 12 12 69 (A4) 81 (A5) 3 ex14 G major 4 15 19 64 (E4) 83 (B5) 4 ex15 G major 4 12 17 66 (F]4) 83 (B5) 4 ex16 D major 4 16 14 69 (A4) 83 (B5) 3 ex17 A minor 8 8 14 69 (A4) 83 (B5) 3 ex18 B[ major 8 8 19 65 (F4) 84 (C6) 3 ex19 G major 8 8 14 67 (G4) 81 (A5) 4 ex20 B[ major 8 12 13 69 (A4) 82 (B[5) 3 ex21 B[ major 8 20 14 70 (B[4) 84 (C6) 3 ex22 A minor 8 16 12 69 (A4) 81 (A5) 3 ex23 F major 8 20 14 65 (F4) 79 (G5)

347 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

4 ex24 B[ major 8 23 14 65 (F4) 79 (G5) 2 ex25 C major 4 12 17 67 (G4) 84 (C6) 3 ex26 D minor 4 4 8 74 (D5) 82 (B[5) 4 ex27 D minor 4 9 13 69 (A4) 82 (B[5) 4 ex28 D minor 4 11 17 65 (F4) 82 (B[5) 3 ex29 D minor 4 16 15 71 (B4) 86 (D6) 4 ex30 G major 4 12 19 67 (G4) 86 (D6) 3 ex31 D minor 4 16 8 73 (C]5) 81 (A5) 3 ex32 A minor 4 8 14 67 (G4) 81 (A5) 3 ex33 G minor 4 8 12 67 (G4) 79 (G5) 4 ex34 F major 4 4 16 65 (F4) 81 (A5) 4 ex35 G major 4 11 12 67 (G4) 79 (G5) 3 ex36 G minor 4 14 19 67 (G4) 86 (D6) 3 ex37 G major 8 22 20 66 (F]4) 86 (D6) 4 ex38 C major 4 12 19 67 (G4) 88 (D6) 2 ex39 G major 4 8 19 67 (G4) 86 (D6) 2 ex40 E minor 4 8 14 67 (G4) 81 (A5) 2 ex41 E minor 4 8 19 64 (E4) 83 (B5) 3 ex42 G major 4 8 21 62 (D4) 83 (B5) 4 ex43 G major 4 8 19 67 (G4) 86 (D6) 2 ex44 D major 4 8 19 62 (D4) 81 (A5) 2 ex45 D major 4 8 17 69 (A4) 86 (D6) 3 ex46 D major 4 8 20 61 (C]4) 81 (A5) 2 ex47 F major 4 8 19 65 (F4) 84 (C6) 3 ex48 F major 4 8 21 60 (C4) 81 (A5) 2 ex49 C major 4 8 17 67 (G4) 84 (C6) 2 ex50 D minor 4 8 24 62 (D4) 86 (D6) 4 ex51 F major 4 8 13 64 (E4) 77 (F5) 4 ex52 G major 4 8 16 67 (G4) 83 (B5) 4 ex53 E minor 4 8 19 64 (E4) 83 (B5) 4 ex54 A minor 4 8 17 64 (E4) 81 (A5) 2 ex55 D major 4 8 12 74 (D5) 86 (D6) 2 ex56 D major 4 8 14 64 (E4) 78 (F]5) 2 ex57 F major 4 8 10 72 (C5) 82 (B[5) 2 ex58 E minor 4 8 15 64 (E4) 79 (G5) 3 ex59 G major 4 8 12 67 (G4) 79 (G5) 3 ex60 G major 4 8 14 62 (D4) 76 (E5) 3 ex61 A minor 4 8 15 69 (A4) 84 (C6) 4 ex62 A minor 4 8 15 69 (A4) 84 (C6) 4 ex63 E minor 4 8 14 67 (G4) 81 (A5) 4 ex64 E minor 4 8 12 71 (B4) 83 (B5) 4 ex65 D major 4 8 15 64 (E4) 79 (G5) 4 ex66 G major 4 8 16 62 (D4) 78 (F]5) 4 ex67 C major 4 8 15 64 (E4) 79 (G5) 3 ex68 A minor 4 8 20 64 (E4) 84 (C6) 3 ex69 E minor 4 8 16 67 (G4) 83 (B5)

348 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

4 ex70 E minor 4 8 16 67 (G4) 83 (B5) 2 ex71 B[ major 4 14 21 65 (F4) 86 (D6) 4 ex72 E minor 4 13 21 63 (E[4) 84 (C6) 3 ex73 D major 4 16 24 62 (D4) 86 (D6) 4 ex74 G minor 4 12 24 62 (D4) 86 (D6) 3 ex75 C major 4 16 18 66 (F]4) 84 (C6) 4 ex76 G major 4 12 21 62 (D4) 83 (B5) 4 ex77 D minor 4 12 24 62 (D4) 86 (D6) 2 ex78 D major 4 12 24 62 (D4) 86 (D6) 3 ex79 F major 4 16 17 65 (F4) 82 (B[5) 4 ex80 A minor 4 17 22 64 (E4) 86 (D6) 4 ex81 D minor 4 12 24 62 (D4) 86 (D6) 4 ex82 B[ major 4 12 24 62 (D4) 86 (D6)

E.2 Percentage of Notes and Rests

Table E.2: Counts and percentages of notes and rests in each grade 3 source exercise

Exercise No. Crotchets (%) No. Rests (%)

ex1 23 (~95.83) 1 (~4.17) ex2 26 (~92.86) 2 (~7.14) ex3 24 (96) 1 (4) ex4 25 (~96.15) 1 (~3.85) ex5 42 (87.5) 6 (12.5) ex6 48 (~94.12) 3 (~5.88) ex7 49 (~94.23) 3 (~5.77) ex8 52 (~92.86) 4 (~7.14) ex9 42 (~95.45) 2 (~4.55) ex10 24 (100) - ex11 33 (~91.67) 3 (~8.33) ex12 26 (~92.86) 2 (~7.14) ex13 50 (~87.72) 7 (~12.28) ex14 40 (100) - ex15 59 (~96.72) 2 (~3.28) ex16 39 (~92.86) 3 (~7.14) ex17 16 (~94.12) 1 (~5.88) ex18 17 (~70.83) 7 (~29.17) ex19 20 (~90.91) 2 (~9.09) ex20 27 (~79.41) 7 (~20.59) ex21 39 (~86.67) 6 (~13.33) ex22 34 (100) - ex23 47 (100) - ex24 53 (100) - ex25 38 (100) - ex26 16 (~94.12) 1 (~5.88)

349 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

ex27 25 (~89.29) 3 (~10.71) ex28 51 (~94.44) 3 (~5.56) ex29 47 (100) - ex30 55 (~98.21) 1 (~1.79) ex31 31 (~75.61) 10 (~24.39) ex32 32 (100) - ex33 26 (~86.67) 4 (~13.33) ex34 21 (100) - ex35 47 (~90.38) 5 (~9.62) ex36 59 (100) - ex37 37 (92) 4 (8) ex38 42 (~91.30) 4 (~8.70) ex39 20 (100) - ex40 23 (~95.83) 1 (~4.17) ex41 22 (100) - ex42 21 (~95.45) 1 (~4.55) ex43 26 (~89.66) 3 (~10.34) ex44 21 (~95.45) 1 (~4.55) ex45 20 (100) - ex46 20 (~90.91) 2 (~9.09) ex47 26 (100) - ex48 29 (100) - ex49 26 (100) - ex50 23 (~95.83) 1 (~4.17) ex51 36 (100) - ex52 41 (~95.35) 2 (~4.65) ex53 36 (~97.30) 1 (~2.70) ex54 38 (100) - ex55 23 (~95.83) 1 (~4.17) ex56 25 (100) - ex57 18 (90) 2 (10) ex58 21 (~91.30) 2 (~8.70) ex59 26 (~92.86) 2 (~7.14) ex60 22 (~91.67) 2 (~8.33) ex61 22 (100) - ex62 36 (~87.80) 5 (~12.20) ex63 29 (~80.56) 7 (~19.44) ex64 32 (~91.43) 3 (~8.57) ex65 34 (~97.14) 1 (~2.86) ex66 43 (100) - ex67 40 (100) - ex68 30 (~96.77) 1 (~3.23) ex69 25 (100) - ex70 33 (~92.67) 3 (~8.33) ex71 50 (~90.91) 5 (~9.09) ex72 54 (~94.74) 3 (~5.26)

350 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

ex73 55 (~96.49) 2 (~3.51) ex74 55 (~94.83) 3 (~5.17) ex75 52 (~86.67) 8 (~13.33) ex76 67 (~98.53) 1 (~1.47) ex77 59 (~92.19) 5 (~7.81) ex78 51 (~91.07) 5 (~8.93) ex79 56 (~90.32) 6 (~9.68) ex80 61 (~83.56) 12 (~16.44) ex81 63 (~85.14) 11 (~14.86) ex82 63 (~85.14) 11 (~14.86)

E.3 Note Lengths in Detail

351 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS (~10.34) (5) (~13.95) (25) (~26.67) (~14.75) No. Dotted Minims (% of time) 1 - 1 2 2 - 4 3 - - - - - 1 (~7.69) - - - - - 2 (~10.53) - - - - (~20.69) (~26.09) (22.5) (~29.27) (37.5) 4 (20) 3 (~11.54) - - 4 (~22.2) 4 (20) 3 (~19.57) 6 (~15.79) - - - 1 (~13.04) 4 4 9 ------4 6 - No. Dotted Crotchets (% of time) ------No. Dotted Quavers (% of time) ------No. Semiquavers (% of time) No. Semibreves (% of time) ------(~21.74) (~30.23) (~27.23) (~13.33) (100) (~41.46) (~54.17) (~21.74) (~6.90) (7.5) (~16.67) No. Minims (% of time) 4 10 9 26 8 12 12 - 17 17 26 20 18 (~81.82) - 28 (~51.85) - 38 (~63.33) - 24 (30) - 24 (40) - 10 (~43.48) - Raw count and percentage of melody time ﬁlled by each note length for all grade 3 source exercises (~33.33) (~52.46) (~6.90) (~8.70) (~18.18) (~13.33) (~13.04) able E.3: No. Quavers (% of time) 1 1 10 - - 2 3 16 - - - 3 2 (10) - T (~55.17) (~43.48) (~31.67) (~55.81) (~58.33) (~54.55) (~46.67) (~32.79) (~65.22) (~29.27) (~8.33) (% of time) 16 10 19 24 14 12 14 20 - 6 2 30 8 (~26.67) 7 (~46.67)16 (~41.03) 4 (~6.67) 3 (~15.28) - 19 (~24.36) - 24 (60) 2 (~18.18)7 (~25.93) - 5 (~16.67) - - ercise No. Crotchets ex5 ex13 ex19 ex21 ex23 Ex ex1 ex2 ex4 ex6 ex8 ex10 ex12 ex14 ex16 ex18 ex20 ex22 ex24 ex3 7 (~30.43)ex7 3 (~26.09)ex9 31 (~54.39) 11 (~23.91)ex11 18 4 - (60) (~14.04) 10 (~38.46) 6 (12.2) 3ex15 (~23.08) - 24 (~52.17) 20ex17 (~38.46) - 5 3 (~43.48) (~13.04) 32 (~34.78) - -

352 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS (~6.38) (12.5) (~13.04) (~13.64) (12.5) - - 1 1 - - - - 1 - 1 1 - - - - 2 (~21.43) - - - - 2 (12.5) - - - - - 1 (~9.38) - (~3.66) (~9.57) (~6.52) (10) (~13.64) (~18.75) (10) 5 (~19.74) 1 (3.8) 1 (~5.36) - 1 (~9.38) - - 5 (~15.63) - 1 (~4.84) 2 (18.75) 2 (18.75) 3 (~28.13) - - - 1 3 - - - - - 1 1 2 3 1 - (12.5) (32.81) (~7.14) (~10.11) - 3 (11.25) ------4 7 8 (~15.38) 4 - 6 ------1 (~14.29) ------(~27.27) (~12.20) (~8.51) (~4.17) (10.94) (~2.38) (~3.37) 12 20 16 4 7 4 6 ------8 (~5.13) (25) (~33.33) (60) (50) (~39.58) (~63.33) (40) (~8.54) (~7.45) (~1.12) (~19.57) (~13.64) - 7 7 12 - 28 1 18 9 15 6 19 19 24 7 (17.5) 3 (3.75) 20 (62.5)21 (~65.63) - - - 31 (50) - 20 (31.25) - 14 (43.75) - (~72.73) (~39.02) (~17.02) (25) (~4.76) (~40.45) (~13.33) (~34.78) (~13.33) (~18.18) (~8.33) (~13.33) (~6.67) 4 8 4 - 2 1 9 1 4 1 2 1 1 1 - - - - (~36.59) (~51.06) (~45.83) (~52.38) (~44.94) (~53.33) (31.25) (~26.67) (~26.09) (~26.67) (~40.91) (~20.83) (~13.33) - 15 24 11 5 22 20 4 6 4 9 5 2 16 15 (62.5)9 (~31.03) 1 (~8.33)26 (~54.17) 8 (~55.17) 6 (12.5) 1 (~4.17) 8 (~13.79) 16 (~16.67) - 13 (~13.54)31 - (~79.49) - 14 - (~45.16)5 - (31.25)6 (37.5) 1 (12.5) 12 (37.5)3 (18.75) - 1 (12.5) 13 (~40.63)11 (~34.38) - 14 4 (~45.16) (25) 4 (~25.81) 18 (~29.03) - ex27 ex29 ex31 14 (~36.84)ex33 12 7 (60) ex35 (~36.84) 5ex37 (~6.58)ex39 - ex41 ex43 8 (~28.57)ex45 ex47 1 (~7.14) 6 (37.5) ex49 13 (~23.21) 4 (25) ex51 - ex53 ex25 ex26 ex28 ex30 ex32 ex34 ex36 ex38 ex40 ex42 ex44 ex46 ex48 ex50 ex52

353 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS (~40.91) (~11.11) - - - 3 - 1 ------2 (~27.27) - 1 (~9.38) 1 (12.5) ------(10) (~20.45) (~6.52) (~8.65) ------4 (~13.04) - 2 (~6.98) 4 (~14.29) ------3 6 2 - 3 (~3.57) ------8 (~13.04) - - - - 7 (~13.13) ------1 - - - - 1 (12.5) ------(~8.89) (~34.52) ------16 - - 29 - (~45.38) (62.5) (~57.14) (~31.82) (~40.74) (~33.33) (~21.88) (~30.43) (25) (~16.67) (~40.91) (~54.35) (~38.10) (~27.88) 22 20 16 14 22 18 14 14 14 15 36 50 16 29 16 (~36.36) - 26 (~40.63) - 18 (~36.73) 22 (~22.45) - 32 (~38.10) - 10 (20) - 14 (17.5) 7 (~4.38) (31.25) (12.5) (~14.29) (~9.09) (~14.81) (~14.81) (31.25) (~14.29) (40) (~18.18) (~13.04) (~15.38) 5 1 1 1 2 2 5 - 2 9 4 3 - 4 1 (~14.29) 10 (~35.71) - 1 (8) 2 (~16.67) 10 (~20.83) - 2 (~8.70)2 (10) 10 (~10.87) 8 (~4.35) (~34.38) (~44.44) (~40.74) (~46.88) (~69.57) (~60.71) (~24.44) (~26.09) (~48.08) (16) (~28.57) (~18.18) (~20.45) (~23.81) 11 4 4 4 12 11 15 16 17 11 9 12 5 25 4 (~26.67)7 (50) 1 (~13.33)8 (~36.36) 18 (60) - - 18 (72) 12 (37.5)12 (50) - 10 (~40.82)23 - (50) 22 (55) 20 (~46.51)20 1 (~47.62) (~4.65)5 - (~13.51) 36 (~41.86) - 2 (~10.81) 56 (~75.68) - ex55 ex57 ex59 ex63 ex67 ex69 ex71 ex73 ex75 ex77 ex79 ex81 ex54 ex56 ex58 ex60 ex62 ex64 ex66 ex68 ex70 ex72 ex74 ex76 ex78 ex80 ex61 11 (~45.83) 5ex65 (~41.67) 19 (~61.29) 6 (12.5) 3 (~19.35) - 12 (~19.35) -

354 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS - - - - - (~58.02) 47 (~4.94) 1 (~37.04) 15 ex82

355 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

E.4 Rest Lengths in Detail

Table E.4: Raw count and percentage of cumulative rest time ﬁlled by each rest length for all grade 3 source exercises

Exercise No. Crotchets (% of time) No. Quavers (% of time) No. Minims (% of time)

ex1 - 1 (100) - ex2 1 (~33.33) 1 (~66.67) - ex3 1 (100) - - ex4 1 (100) - - ex5 6 (100) - - ex6 2 (50) 1 (50) - ex7 3 (100) - - ex8 3 (60) 1 (40) - ex9 2 (100) - - ex10 - - - ex11 1 (50) - 2 (50) ex12 2 (100) - - ex13 6 (75) 1 (25) - ex14 - - - ex15 2 (100) - - ex16 3 (100) - - ex17 - - 1 (100) ex18 - - 7 (100) ex19 - - 2 (100) ex20 - - 7 (100) ex21 - - 6 (100) ex22 - - - ex23 - - - ex24 - - - ex25 - - - ex26 1 (100) - - ex27 3 (100) - - ex28 3 (100) - - ex29 - - - ex30 1 (100) - - ex31 10 (100) - - ex32 - - - ex33 4 (100) - - ex34 - - - ex35 5 (100) - - ex36 - - - ex37 - - 4 (100) ex38 3 (~85.71) - 1 (~14.29) ex39 - - -

356 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

ex40 1 (100) - - ex41 - - - ex42 1 (100) - - ex43 2 (50) 1 (50) - ex44 1 (100) - - ex45 - - - ex46 2 (100) - - ex47 - - - ex48 - - - ex49 - - - ex50 1 (100) - - ex51 - - - ex52 2 (100) - - ex53 1 (100) - - ex54 - - - ex55 1 (100) - - ex56 - - - ex57 2 (100) - - ex58 2 (100) - - ex59 2 (100) - - ex60 2 (100) - - ex61 - - - ex62 5 (100) - - ex63 7 (100) - - ex64 1 (20) 2 (80) - ex65 1 (100) - - ex66 - - - ex67 - - - ex68 1 (100) - - ex69 - - - ex70 2 (50) 1 (50) - ex71 2 (~57.14) - 3 (~42.86) ex72 2 (50) 1 (50) - ex73 1 (100) - - ex74 2 (50) 1 (50) - ex75 8 (100) - - ex76 - 1 (100) - ex77 5 (100) - - ex78 1 (~33.33) - 4 (~66.67) ex79 6 (100) - - ex80 12 (100) - - ex81 11 (100) - - ex82 4 (~53.33) - 7 (~46.67)

E.5 Intervals in Detail

357 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

Table E.5: Number and percentage of intervals of each size for all grade 3 source exercises. Interval sizes are represented as difference in scale degrees between contiguous notes.

Exercise Number of Scale Degrees (%) 0 1 2 3 4 5 6 7 14

ex1 - 17 (77.3) 4 (18.2) 1 (4.5) - - - - - ex2 - 17 (94.4) - - 1 (5.6) - - - - ex3 - 12 (70.6) - 3 (17.6) 2 (11.8) - - - - ex4 - 22 (91.7) 2 (8.3) ------ex5 - 22 (73.3) 4 (13.3) 2 (6.7) 2 (6.7) - - - - ex6 - 35 (77.8) 4 (8.9) 5 (11.1) 1 (2.2) - - - - ex7 8 (21.1) 23 (60.5) 4 (10.5) 1 (2.6) 1 (2.6) - - 1 (2.6) - ex8 2 (4.2) 39 (81.2) 5 (10.4) 1 (2.1) 1 (2.1) - - - - ex9 5 (12.5) 32 (80) 3 (7.5) ------ex10 2 (18.2) 8 (72.7) 1 (9.1) ------ex11 3 (10.3) 21 (72.4) 4 (13.8) 1 (3.4) - - - - - ex12 2 (8.3) 19 (79.2) 2 (8.3) - 1 (4.2) - - - - ex13 2 (4.7) 25 (58.1) 9 (20.9) 4 (9.3) 3 (7) - - - - ex14 1 (2.6) 21 (53.8) 14 (35.9) 3 (7.7) - - - - - ex15 5 (8.8) 38 (66.7) 10 (17.5) 2 (3.5) 1 (1.8) 1 (1.8) - - - ex16 3 (8.3) 23 (63.9) 4 (11.1) 2 (5.6) 2 (5.6) 1 (2.8) - 1 (2.8) - ex17 - 9 (90) 1 (10) ------ex18 - 6 (50) 1 (8.3) 4 (33.3) 1 (8.3) - - - - ex19 3 (16.7) 7 (38.9) 5 (27.8) 3 (16.7) - - - - - ex20 1 (4.8) 12 (57.1) 6 (28.6) 1 (4.8) 1 (4.8) - - - - ex21 3 (8.8) 28 (82.4) 2 (5.9) 1 (2.9) - - - - - ex22 - 16 (51.6) 11 (35.5) 3 (9.7) 1 (3.2) - - - - ex23 2 (4.5) 38 (86.4) - 3 (6.8) - 1 (2.3) - - - ex24 1 (2.1) 32 (66.7) 9 (18.8) 2 (4.2) 3 (6.2) 1 (2.1) - - - ex25 - 26 (70.3) 5 (13.5) 3 (8.1) 2 (5.4) 1 (2.7) - - - ex26 2 (13.3) 12 (80) 1 (6.7) ------ex27 4 (21.1) 7 (36.8) 4 (21.1) 2 (10.5) 2 (10.5) - - - - ex28 6 (13.3) 33 (73.3) 1 (2.2) 2 (4.4) 2 (4.4) - - 1 (2.2) - ex29 3 (7.9) 34 (89.5) - 1 (2.6) - - - - - ex30 - 40 (74.1) 9 (16.7) 3 (5.6) - 2 (3.7) - - - ex31 2 (10) 14 (70) 1 (5) 2 (10) 1 (5) - - - - ex32 3 (9.7) 17 (54.8) 8 (25.8) 1 (3.2) - 2 (6.5) - - - ex33 - 10 (58.8) 5 (29.4) 1 (5.9) 1 (5.9) - - - - ex34 4 (20) 5 (25) 6 (30) 3 (15) 2 (10) - - - - ex35 1 (2.8) 18 (50) 8 (22.2) 5 (13.9) 2 (5.6) 2 (5.6) - - - ex36 - 27(57.4) 14 (29.8) 4 (8.5) - - - 2 (4.3) - ex37 2 (4.9) 29 (70.7) 5 (12.2) 2 (4.9) - 2 (4.9) - 1 (2.4) - ex38 - 20 (64.5) 3 (9.7) 3 (9.7) - 3 (9.7) - 2 (6.5) - ex39 - 12 (63.2) 6 (31.6) 1 (5.3) - - - - - ex40 - 10 (47.6) 11 (52.4) ------

358 APPENDIX E.CHARACTERISTICSOF PUBLISHED SIGHT READING EXERCISES:GRADE 3 DETAILS

ex41 - 8 (38.1) 9 (42.9) 4 (19) - - - - - ex42 - 7 (36.8) 9 (47.4) 2 (10.5) 1 (5.3) - - - - ex43 1 (4.5) 17 (77.3) 3 (13.6) 1 (4.5) - - - - - ex44 - 6 (31.6) 11 (57.9) 1 (5.3) 1 (5.3) - - - - ex45 - 11 (57.9) 2 (10.5) 3 (15.8) 2 (10.5) 1 (5.3) - - - ex46 - 7 (41.2) 5 (29.4) 2 (11.8) 3 (17.6) - - - - ex47 1 (4) 7 (28) 12 (48) 2 (8) - 3 (12) - - - ex48 1 (3.6) 11 (39.3) 13 (46.4) 3 (10.7) - - - - - ex49 - 15 (60) 7 (28) 3 (12) - - - - - ex50 - 14 (73.7) 5 (26.3) ------ex51 4 (11.4) 24 (68.6) 4 (11.4) 3 (8.6) - - - - - ex52 2 (5.3) 26 (68.4) 6 (15.8) 4 (10.5) - - - - - ex53 - 16 (55.2) 6 (20.7) 6 (20.7) 1 (3.4) - - - - ex54 - 18 (56.2) 3 (9.4) 7 (21.9) 4 (12.5) - - - - ex55 - 17 (81) 2 (9.5) 2 (9.5) - - - - - ex56 - 12 (50) 6 (25) 5 (20.8) 1 (4.2) - - - - ex57 - 9 (60) 3 (20) 2 (13.3) 1 (6.7) - - - - ex58 1 (6.7) 6 (40) 5 (33.3) 2 (13.3) 1 (6.7) - - - - ex59 1 (4.3) 17 (73.9) 3 (13) 1 (4.3) 1 (4.3) - - - - ex60 - 14 (77.8) 2 (11.1) 1 (5.6) - - - 1 (5.6) - ex61 2 (10.5) 12 (63.2) - 2 (10.5) 2 (10.5) 1 (5.3) - - - ex62 9 (29) 15 (48.4) 3 (9.7) 1 (3.2) 2 (6.5) - - 1 (3.2) - ex63 - 14 (63.6) 4 (18.2) 2 (9.1) 2 (9.1) - - - - ex64 2 (9.1) 13 (59.1) 3 (13.6) 2 (9.1) 2 (9.1) - - - - ex65 3 (9.4) 20 (62.5) 4 (12.5) 2 (6.2) 3 (9.4) - - - - ex66 - 11 (33.3) 14 (42.4) 2 (6.1) 3 (9.1) 3 (9.1) - - - ex67 8 (20.5) 17 (43.6) 13 (33.3) 1 (2.6) - - - - - ex68 4 (13.8) 13 (44.8) 7 (24.1) 2 (6.9) - 1 (3.4) - 2 (6.9) - ex69 - 11 (55) 6 (30) 2 (10) 1 (5) - - - - ex70 4 (13.3) 16 (53.3) 1 (3.3) 3 (10) 4 (13.3) 2 (6.7) - - - ex71 6 (13.3) 27 (60) 8 (17.8) 4 (8.9) - - - - - ex72 - 33 (70.2) 9 (19.1) 4 (8.5) 1 (2.1) - - - - ex73 - 34 (64.2) 8 (15.1) 6 (11.3) 3 (5.7) 2 (3.8) - - - ex74 - 31 (75.6) 3 (7.3) 2 (4.9) 4 (9.8) 1 (2.4) - - - ex75 - 30 (73.2) 4 (9.8) 4 (9.8) 2 (4.9) - - 1 (2.4) - ex76 2 (3.6) 29 (51.8) 14 (25) 6 (10.7) 1 (1.8) 4 (7.1) - - - ex77 2 (4.3) 33 (70.2) 6 (12.8) 4 (8.5) 1 (2.1) 1 (2.1) - - - ex78 7 (15.9) 30 (68.2) 1 (2.3) 3 (6.8) 2 (4.5) 1 (2.3) - - - ex79 - 31 (73.8) 4 (9.5) 2 (4.8) 2 (4.8) 3 (7.1) - - - ex80 - 29 (67.4) 7 (16.3) 5 (11.6) 1 (2.3) - 1 (2.3) - - ex81 2 (4.9) 21 (51.2) 12 (29.3) 5 (12.2) - - - - 1 (2.4) ex82 3 (6.1) 31 (63.3) 7 (14.3) 4 (8.2) 2 (4.1) 2 (4.1) - - -

359

F Algorithm Parameters Used to Generate Grade 1 Exercises

Table F.1: Parameters used to generate Grade 1 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table C.1 when describing the Grade 1 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places.

Source Rests? Ties? Melody Shape Note Proportions Rest Proportions Interval Proportions ex1 - 0 Crotchet: 0.88 Crotchet: 0.12 0: 0.33 1: 0.17 3: 0.08 ex2 - 0.18 Crotchet: 0.81 Crotchet: 0.19 0: 0.7 1: 0.3 ex3 - 0.42 Crotchet: 0.88 Crotchet: 0.12 0: 0.33 1: 0.67 ex4 - 0.18 Crotchet: 0.81 Crotchet: 0.19 0: 0.1 1: 0.8 2: 0.1 ex5 - 0.42 Crotchet: 0.88 Crotchet: 0.12 0: 0.08 1: 0.5 2: 0.17 3: 0.08 ex6 - 0.33 Crotchet: 0.81 Crotchet: 0.19 0: 0.2 1: 0.35 ex7 - - 0.52 Minim: 0.19 - 1: 0.93 Crotchet: 0.81 2: 0.07 ex8 - - 0.42 Minim: 0.25 - 1: 0.63 Crotchet: 0.75 2: 0.3 3: 0.07 ex9 - 0.62 Minim: 0.31 Minim: 0.19 1: 0.42 Crotchet: 0.41 Crotchet: 0.09 2: 0.17 3: 0.08

361 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

4: 0.08 ex10 - 0.46 Minim: 0.21 Minim: 0.04 0: 0.05 Crotchet: 0.75 1: 0.46 2: 0.21 3: 0.15 4: 0.03 ex11 0.43 Minim: 0.5 Crotchet: 0.08 1: 0.5 Crotchet: 0.42 2: 0.14 3: 0.07 4: 0.14 ex12 0.25 Semibreve: 0.12 Crotchet: 0.04 0: 0.06 Minim: 0.25 1: 0.25 Crotchet: 0.58 2: 0.56 3: 0.06 4: 0.06 ex13 0.5 Semibreve: 0.25 Crotchet: 0.04 1: 0.56 Minim: 0.08 2: 0.19 Crotchet: 0.62 3: 0.19 4: 0.06 ex14 0.57 Semibreve: 0.12 Crotchet: 0.17 1: 0.73 Minim: 0.17 2: 0.18 Crotchet: 0.54 3: 0.09 ex15 0.25 Semibreve: 0.12 Crotchet: 0.21 0: 0.33 Minim: 0.25 1: 0.22 Crotchet: 0.42 2: 0.44 ex16 0.47 Semibreve: 0.12 Crotchet: 0.08 1: 0.79 Minim: 0.33 2: 0.11 Crotchet: 0.46 3: 0.04 4: 0.04 5: 0.04 ex17 - 0.3 Crotchet: 0.78 Crotchet: 0.22 0: 0.06 1: 0.78 2: 0.11 3: 0.06 ex18 - 0.6 Crotchet: 0.69 Crotchet: 0.31 1: 0.58 2: 0.08 ex19 - 0.04 Crotchet: 0.88 Crotchet: 0.12 0: 0.21 1: 0.29 2: 0.21 3: 0.29 ex20 - - 0.37 Minim: 0.21 - 0: 0.31 Crotchet: 0.79 1: 0.45 2: 0.17 3: 0.07 ex21 - 0.37 Minim: 0.07 Minim: 0.04 1: 0.47 Crotchet: 0.77 Crotchet: 0.12 2: 0.34

362 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

3: 0.05 4: 0.05 5: 0.03 6: 0.03 ex22 - 0.62 Minim: 0.42 Minim: 0.08 1: 0.5 Crotchet: 0.44 Crotchet: 0.06 2: 0.27 3: 0.04 4: 0.08 5: 0.04 ex23 0.53 Minim: 0.04 Crotchet: 0.15 1: 0.66 Crotchet: 0.81 2: 0.11 3: 0.09 ex24 - 0.59 Semibreve: 0.38 - 1: 0.79 Minim: 0.08 2: 0.09 Crotchet: 0.54 3: 0.03 5: 0.03 ex25 0.24 Semibreve: 0.19 Crotchet: 0.1 1: 0.5 Minim: 0.25 2: 0.12 Crotchet: 0.46 3: 0.12 5: 0.04 ex26 - 0.7 Minim: 0.25 Minim: 0.12 1: 0.55 Crotchet: 0.62 2: 0.09 ex27 - - 0.5 Minim: 0.5 - 0: 0.09 Crotchet: 0.5 1: 0.82 2: 0.09 ex28 - 0.22 Minim: 0.38 Minim: 0.12 0: 0.1 Crotchet: 0.5 1: 0.7 ex29 - - 0.6 Minim: 0.5 - 0: 0.09 Crotchet: 0.5 1: 0.82 2: 0.09 ex30 - - 0.36 Minim: 0.38 - 0: 0.33 Crotchet: 0.62 1: 0.58 2: 0.08 ex31 - 0.56 Minim: 0.38 Minim: 0.12 1: 0.7 Crotchet: 0.5 2: 0.3 ex32 - - 0.42 Minim: 0.25 - 0: 0.19 Crotchet: 0.75 1: 0.44 2: 0.04 ex33 - - 0.5 Minim: 0.5 - 0: 0.04 Crotchet: 0.5 1: 0.96 ex34 - 0.67 Minim: 0.44 Minim: 0.06 1: 0.73 Crotchet: 0.5 2: 0.23 3: 0.05 ex35 - - 0.42 Minim: 0.38 - 0: 0.12 Crotchet: 0.62 1: 0.72 2: 0.08

363 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

3: 0.08 ex36 - 0.42 Minim: 0.56 Minim: 0.06 0: 0.05 Crotchet: 0.38 1: 0.5 2: 0.15 3: 0.05 ex37 - - 0.48 Minim: 0.44 - 0: 0.12 Crotchet: 0.56 1: 0.75 2: 0.08 3: 0.04 ex38 - - 0.35 Semibreve: 0.25 - 0: 0.24 Minim: 0.25 1: 0.52 Crotchet: 0.5 2: 0.19 3: 0.05 ex39 - - 0.61 Semibreve: 0.25 - 1: 0.84 Minim: 0.38 2: 0.16 Crotchet: 0.38 ex40 - - 0.42 Semibreve: 0.25 - 0: 0.1 Minim: 0.31 1: 0.65 Crotchet: 0.44 2: 0.15 3: 0.05 4: 0.05 ex41 - - 0.45 Minim: 0.38 - 0: 0.08 Crotchet: 0.62 1: 0.67 3: 0.17 4: 0.08 ex42 - - 0.55 Minim: 0.38 - 1: 0.42 Crotchet: 0.62 2: 0.33 3: 0.25 ex43 - - 0.5 Minim: 0.25 - 1: 0.77 Crotchet: 0.75 2: 0.15 3: 0.08 ex44 - - 0.35 Semibreve: 0.25 - 1: 0.38 Minim: 0.25 2: 0.52 Crotchet: 0.5 3: 0.05 5: 0.05 ex45 - - 0.5 Semibreve: 0.25 - 1: 0.78 Minim: 0.12 2: 0.13 Crotchet: 0.62 3: 0.09 ex46 - - 0.6 Semibreve: 0.25 - 1: 0.76 Minim: 0.25 2: 0.19 Crotchet: 0.5 3: 0.05 ex47 - - 0.62 Semibreve: 0.25 - 1: 0.73 Minim: 0.19 2: 0.18 Crotchet: 0.56 3: 0.05 4: 0.05 ex48 - - 0.68 Semibreve: 0.25 - 0: 0.05

364 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

Minim: 0.31 1: 0.7 Crotchet: 0.44 2: 0.15 3: 0.1 ex49 - - 0.5 Minim: 0.25 - 0: 0.08 Crotchet: 0.75 1: 0.23 2: 0.31 3: 0.08 ex50 - - 0.5 Minim: 0.5 - 1: 0.64 Crotchet: 0.5 2: 0.18 3: 0.18 ex51 - - 0.55 Minim: 0.38 - 0: 0.17 Crotchet: 0.62 1: 0.42 2: 0.33 3: 0.08 ex52 - - 0.55 Semibreve: 0.25 - 0: 0.13 Minim: 0.12 1: 0.7 Crotchet: 0.62 2: 0.09 3: 0.09 ex53 - - 0.32 Semibreve: 0.25 - 1: 0.43 Minim: 0.12 2: 0.39 Crotchet: 0.62 3: 0.13 5: 0.04 ex54 - 0.21 Semibreve: 0.25 Semibreve: 0.12 0: 0.16 Minim: 0.06 1: 0.47 Crotchet: 0.56 2: 0.21 3: 0.11 5: 0.05 ex55 - - 0.35 Semibreve: 0.25 - 0: 0.19 Minim: 0.25 1: 0.24 Crotchet: 0.5 2: 0.52 3: 0.05 ex56 - 0.28 Semibreve: 0.12 Semibreve: 0.25 0: 0.35 Minim: 0.06 1: 0.18 Crotchet: 0.56 2: 0.41 3: 0.06 ex57 - - 0.57 Semibreve: 0.25 - 1: 0.59 Minim: 0.19 2: 0.27 Crotchet: 0.56 4: 0.09 5: 0.05 ex58 0.28 Semibreve: 0.09 Crotchet: 0.16 0: 0.5 Minim: 0.25 1: 0.44 Crotchet: 0.5 2: 0.06 ex59 - 0.47 Minim: 0.06 Minim: 0.06 0: 0.19 Crotchet: 0.66 Crotchet: 0.03 1: 0.81 Quaver: 0.19 ex60 0.56 Minim: 0.33 Crotchet: 0.08 1: 0.5

365 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

Crotchet: 0.58 2: 0.31 3: 0.12 5: 0.03 6: 0.03 ex61 0.44 Semibreve: 0.09 Crotchet: 0.09 0: 0.02 Minim: 0.22 1: 0.27 Crotchet: 0.59 2: 0.37 3: 0.27 5: 0.02 ex62 - 0.54 Minim: 0.12 Crotchet: 0.12 1: 0.52 Crotchet: 0.75 2: 0.24 4: 0.24 ex63 - 0.15 Minim: 0.28 Minim: 0.06 0: 0.24 Crotchet: 0.53 Crotchet: 0.12 1: 0.33 2: 0.18 3: 0.15 4: 0.06 5: 0.03 ex64 0.33 Semibreve: 0.05 Crotchet: 0.12 0: 0.12 Minim: 0.19 1: 0.68 Crotchet: 0.64 2: 0.12 3: 0.05 7: 0.03 ex65 - 0.51 Minim: 0.25 Minim: 0.03 0: 0.09 Crotchet: 0.67 Crotchet: 0.05 1: 0.53 2: 0.13 3: 0.13 4: 0.06 5: 0.06 ex66 0.39 Semibreve: 0.06 Crotchet: 0.04 0: 0.17 Minim: 0.25 1: 0.4 Crotchet: 0.54 2: 0.25 Quaver: 0.1 3: 0.12 4: 0.05 ex67 0.34 Semibreve: 0.09 Crotchet: 0.16 0: 0.2 Minim: 0.31 1: 0.67 Crotchet: 0.44 2: 0.13 ex68 - 0.48 Crotchet: 0.53 Crotchet: 0.34 1: 1 Quaver: 0.12 ex69 0.31 Semibreve: 0.06 Crotchet: 0.12 1: 0.5 Minim: 0.21 2: 0.09 Crotchet: 0.48 3: 0.21 Quaver: 0.12 4: 0.06 5: 0.03 ex70 0.43 Semibreve: 0.05 Minim: 0.03 0: 0.03 Minim: 0.53 Crotchet: 0.09 1: 0.43

366 APPENDIX F. ALGORITHM PARAMETERS USEDTO GENERATE GRADE 1 EXERCISES

Crotchet: 0.3 2: 0.4 3: 0.03 4: 0.03 5: 0.07 ex71 0.4 Semibreve: 0.05 Crotchet: 0.12 0: 0.28 Minim: 0.31 1: 0.53 Crotchet: 0.52 2: 0.14 3: 0.03 5: 0.03 ex72 0.39 Minim: 0.33 Crotchet: 0.1 0: 0.13 Crotchet: 0.56 1: 0.5 2: 0.2 3: 0.13 4: 0.03

367

G Algorithm Parameters Used to Generate Grade 2 Exercises

Table G.1: Parameters used to generate Grade 2 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table D.1 when describing the Grade 2 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places.

Source Rests? Ties? Melody Shape Note Proportions Rest Proportions Interval Proportions ex1 0.42 Semibreve: 0.19 Crotchet: 0.03 1: 0.6 Minim: 0.38 2: 0.2 Crotchet: 0.41 3: 0.1 4: 0.1 ex2 0.43 Minim: 0.25 Crotchet: 0.21 1: 0.58 Crotchet: 0.54 2: 0.17 3: 0.17 5: 0.08 ex3 - 0.57 Minim: 0.06 Crotchet: 0.03 1: 0.86 Crotchet: 0.91 2: 0.14 ex4 - - 0.65 Minim: 0.35 - 0: 0.06 Crotchet: 0.65 1: 0.78 2: 0.09 3: 0.03 5: 0.03 ex5 0.55 Semibreve: 0.12 Crotchet: 0.04 1: 0.67 Minim: 0.38 2: 0.1 Crotchet: 0.46 3: 0.1 5: 0.07 ex6 - 0 Minim: 0.12 Crotchet: 0.06 0: 0.59 Crotchet: 0.5 1: 0.12 Quaver: 0.31 2: 0.24 3: 0.06 ex7 - - 0.47 Semibreve: 0.12 - 0: 0.1

369 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

Crotchet: 0.46 1: 0.65 Quaver: 0.42 2: 0.16 3: 0.06 4: 0.03 ex8 - 0.36 Crotchet: 0.44 Quaver: 0.03 0: 0.05 Quaver: 0.53 1: 0.68 2: 0.18 ex9 0.13 Minim: 0.08 Crotchet: 0.17 0: 0.38 Crotchet: 0.5 1: 0.29 Quaver: 0.25 2: 0.33 ex10 - 0.49 Minim: 0.25 Crotchet: 0.02 1: 0.47 Crotchet: 0.6 2: 0.27 Quaver: 0.12 3: 0.07 4: 0.02 5: 0.04 6: 0.02 7: 0.02 ex11 0.61 Semibreve: 0.14 Crotchet: 0.09 1: 0.85 Minim: 0.38 2: 0.12 Crotchet: 0.39 3: 0.03 ex12 0.33 Minim: 0.22 Crotchet: 0.07 0: 0.33 Crotchet: 0.7 1: 0.38 2: 0.25 3: 0.05 ex13 0.65 Semibreve: 0.07 Crotchet: 0.04 1: 0.73 Minim: 0.22 2: 0.24 Crotchet: 0.67 3: 0.03 ex14 0.45 Semibreve: 0.06 Crotchet: 0.06 0: 0.08 Minim: 0.12 1: 0.54 Crotchet: 0.52 2: 0.21 Quaver: 0.23 3: 0.12 4: 0.02 6: 0.02 ex15 0.41 Semibreve: 0.06 Crotchet: 0.02 0: 0.12 Minim: 0.04 1: 0.62 Crotchet: 0.54 2: 0.1 Quaver: 0.33 3: 0.05 4: 0.05 ex16 - 0.51 Minim: 0.17 Minim: 0.08 1: 0.48 Crotchet: 0.56 Crotchet: 0.02 2: 0.34 Quaver: 0.17 3: 0.07 4: 0.02 ex17 0.35 Semibreve: 0.12 Crotchet: 0.08 0: 0.05 Minim: 0.08 1: 0.58 Crotchet: 0.58 2: 0.26 Quaver: 0.12 3: 0.11

370 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

ex18 0.35 Semibreve: 0.12 Crotchet: 0.12 0: 0.19 Minim: 0.17 1: 0.5 Crotchet: 0.5 2: 0.25 Quaver: 0.08 3: 0.06 ex19 - 0.47 Semibreve: 0.12 - 0: 0.05 Minim: 0.25 1: 0.75 Crotchet: 0.54 2: 0.15 Quaver: 0.08 3: 0.05 ex20 0.53 Semibreve: 0.12 Crotchet: 0.08 1: 0.75 Minim: 0.25 2: 0.12 Crotchet: 0.46 3: 0.12 Quaver: 0.08 ex21 0.63 Semibreve: 0.12 Crotchet: 0.03 1: 0.89 Minim: 0.19 2: 0.04 Crotchet: 0.38 3: 0.07 Quaver: 0.19 ex22 0.47 Semibreve: 0.12 Minim: 0.19 1: 0.54 Minim: 0.31 2: 0.15 Crotchet: 0.25 3: 0.15 Quaver: 0.03 4: 0.15 ex23 0.48 Minim: 0.25 Crotchet: 0.04 1: 0.6 Crotchet: 0.42 2: 0.24 Quaver: 0.29 3: 0.16 ex24 0.63 Semibreve: 0.12 Crotchet: 0.08 1: 0.67 Minim: 0.33 2: 0.06 Crotchet: 0.25 3: 0.11 Quaver: 0.21 ex25 0.3 Semibreve: 0.12 Crotchet: 0.06 0: 0.14 Minim: 0.19 1: 0.64 Crotchet: 0.44 2: 0.09 Quaver: 0.09 3: 0.05 ex26 0.6 Semibreve: 0.25 Crotchet: 0.08 1: 0.53 Crotchet: 0.5 2: 0.47 Quaver: 0.17 ex27 0.58 Minim: 0.08 Crotchet: 0.25 1: 0.94 Crotchet: 0.5 2: 0.06 Quaver: 0.17 ex28 0.56 Semibreve: 0.12 Crotchet: 0.06 1: 0.47 Minim: 0.19 2: 0.29 Crotchet: 0.28 3: 0.18 Quaver: 0.06 4: 0.06 ex29 - - 0.48 Minim: 0.44 - 0: 0.12 Crotchet: 0.56 1: 0.62 2: 0.17 3: 0.04 4: 0.04

371 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

ex30 - 0.69 Semibreve: 0.25 - 1: 0.82 Minim: 0.17 2: 0.12 Crotchet: 0.58 4: 0.06 ex31 - 0.56 Semibreve: 0.25 - 0: 0.05 Crotchet: 0.75 1: 0.63 2: 0.21 ex32 - - 0.45 Minim: 0.38 - 0: 0.08 Crotchet: 0.62 1: 0.25 2: 0.58 3: 0.08 ex33 - - 0.23 Minim: 0.12 - 0: 0.14 Crotchet: 0.88 1: 0.14 2: 0.21 3: 0.07 4: 0.07 5: 0.07 ex34 - - 0.5 Minim: 0.25 - 0: 0.04 Crotchet: 0.75 1: 0.41 2: 0.26 3: 0.11 4: 0.11 ex35 - - 0.43 Semibreve: 0.12 - 0: 0.04 Minim: 0.25 1: 0.46 Crotchet: 0.62 2: 0.21 3: 0.08 4: 0.04 ex36 - 0.32 Semibreve: 0.25 - 0: 0.3 Minim: 0.12 1: 0.52 Crotchet: 0.62 2: 0.09 3: 0.09 ex37 - - 0.65 Semibreve: 0.12 - 0: 0.04 Minim: 0.25 1: 0.62 Crotchet: 0.62 2: 0.04 3: 0.08 ex38 - 0.5 Semibreve: 0.38 - 1: 0.24 Crotchet: 0.62 2: 0.41 3: 0.12 ex39 - 0.39 Semibreve: 0.12 - 1: 0.63 Minim: 0.17 3: 0.16 Crotchet: 0.71 4: 0.16 5: 0.05 ex40 - 0.17 Minim: 0.25 - 0: 0.31 Crotchet: 0.75 1: 0.23 4: 0.15 ex41 - - 0.15 Minim: 0.12 - 0: 0.07 Crotchet: 0.88 1: 0.14

372 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

2: 0.14 3: 0.5 ex42 - - 0.33 Semibreve: 0.12 - 1: 0.44 Minim: 0.19 2: 0.36 Crotchet: 0.69 3: 0.16 4: 0.04 ex43 - - 0.39 Semibreve: 0.12 - 0: 0.08 Minim: 0.25 1: 0.46 Crotchet: 0.62 2: 0.21 3: 0.17 ex44 - - 0.43 Semibreve: 0.12 - 0: 0.09 Minim: 0.38 1: 0.36 Crotchet: 0.5 2: 0.36 3: 0.14 4: 0.05 ex45 - 0.36 Semibreve: 0.12 - 0: 0.17 Minim: 0.31 1: 0.3 Crotchet: 0.56 2: 0.35 3: 0.17 ex46 - 0.44 Semibreve: 0.25 - 1: 0.53 Minim: 0.17 2: 0.24 Crotchet: 0.58 3: 0.18 4: 0.06 ex47 - 0.35 Semibreve: 0.25 - 1: 0.67 Minim: 0.44 2: 0.22 Crotchet: 0.31 3: 0.11 ex48 - 0.45 Semibreve: 0.25 - 0: 0.19 Minim: 0.25 1: 0.38 Crotchet: 0.5 2: 0.14 3: 0.19 ex49 0.41 Semibreve: 0.12 Crotchet: 0.04 0: 0.06 Minim: 0.12 1: 0.47 Crotchet: 0.33 2: 0.31 Quaver: 0.04 3: 0.09 6: 0.03 7: 0.03 ex50 0.5 Minim: 0.07 Minim: 0.28 1: 0.43 Crotchet: 0.48 Crotchet: 0.05 2: 0.18 Quaver: 0.02 3: 0.11 4: 0.14 5: 0.14 ex51 0.42 Semibreve: 0.05 Minim: 0.03 0: 0.03 Minim: 0.05 Crotchet: 0.06 1: 0.68 Crotchet: 0.31 2: 0.1 Quaver: 0.06 3: 0.05 4: 0.07

373 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

7: 0.07 ex52 0.35 Semibreve: 0.12 Crotchet: 0.08 0: 0.15 Minim: 0.03 1: 0.67 Crotchet: 0.58 2: 0.09 Quaver: 0.01 3: 0.03 4: 0.03 7: 0.03 ex53 0.29 Minim: 0.05 Crotchet: 0.12 0: 0.25 Crotchet: 0.31 1: 0.38 Dotted Quaver: 0.07 2: 0.12 Quaver: 0.42 3: 0.05 Semiquaver: 0.02 ex54 0.43 Minim: 0.06 Quaver: 0.06 0: 0.03 Crotchet: 0.46 1: 0.66 Quaver: 0.42 2: 0.21 3: 0.07 4: 0.03 ex55 - 0.47 Minim: 0.21 Crotchet: 0.02 1: 0.46 Crotchet: 0.42 2: 0.35 Quaver: 0.35 3: 0.11 4: 0.07 5: 0.02 ex56 0.5 Minim: 0.12 Minim: 0.06 0: 0.12 Crotchet: 0.47 Crotchet: 0.16 1: 0.56 Quaver: 0.05 2: 0.21 3: 0.06 4: 0.06 ex57 - 0.47 Minim: 0.02 - 1: 0.72 Crotchet: 0.72 2: 0.16 Quaver: 0.13 3: 0.07 4: 0.03 5: 0.01 ex58 - 0.48 Minim: 0.12 Crotchet: 0.08 0: 0.15 Crotchet: 0.27 1: 0.55 Quaver: 0.52 2: 0.18 3: 0.08 4: 0.05 ex59 - 0.38 Minim: 0.1 Semibreve: 0.07 0: 0.02 Crotchet: 0.48 Crotchet: 0.05 1: 0.59 Quaver: 0.3 2: 0.06 5: 0.02 ex60 0.61 Minim: 0.12 Crotchet: 0.1 1: 0.61 Crotchet: 0.52 2: 0.03 Quaver: 0.04 3: 0.03 5: 0.03 ex61 0.49 Minim: 0.16 Minim: 0.03 1: 0.59

374 APPENDIX G.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 2 EXERCISES

Crotchet: 0.42 Crotchet: 0.05 2: 0.14 Quaver: 0.09 3: 0.16 4: 0.04 5: 0.04 ex62 0.55 Semibreve: 0.1 Crotchet: 0.08 1: 0.76 Minim: 0.1 2: 0.09 Crotchet: 0.32 3: 0.15 Quaver: 0.03 ex63 0.57 Minim: 0.23 Crotchet: 0.09 1: 0.68 Crotchet: 0.53 2: 0.16 Quaver: 0.14 3: 0.05 4: 0.05 5: 0.05 ex64 - 0.52 Crotchet: 0.68 Minim: 0.04 0: 0.12 Quaver: 0.18 Crotchet: 0.11 1: 0.65 2: 0.08 3: 0.06 4: 0.02 5: 0.02

375

H Algorithm Parameters Used to Generate Grade 3 Exercises

Table H.1: Parameters used to generate Grade 3 exercises. Hard-coded characteristics such as key and time signatures are not included as they are listed in the Table E.1 when describing the Grade 3 source exercises. Melody shape, note proportions, rest proportions, and interval proportions are all targets, and have been rounded to two decimal places.

Source Rests? Ties? Melody Shape Note Proportions Rest Proportions Interval Proportions ex1 0.67 Minim: 0.44 Minim: 0.06 1: 0.77 Crotchet: 0.25 2: 0.18 Quaver: 0.06 3: 0.05 ex2 0.71 Semibreve: 0.09 Minim: 0.06 1: 0.71 Minim: 0.06 Crotchet: 0.03 4: 0.04 Crotchet: 0.5 Quaver: 0.06 ex3 0.36 Minim: 0.19 Crotchet: 0.04 1: 0.52 Crotchet: 0.29 3: 0.13 Quaver: 0.23 4: 0.09 ex4 0.52 Minim: 0.08 Crotchet: 0.04 1: 0.92 Crotchet: 0.42 2: 0.08 Quaver: 0.21 ex5 0.6 Semibreve: 0.07 Crotchet: 0.13 1: 0.61 Minim: 0.1 2: 0.11 Crotchet: 0.36 3: 0.06 Quaver: 0.21 4: 0.06 ex6 0.65 Crotchet: 0.56 Crotchet: 0.06 0: 0.12 Quaver: 0.38 1: 0.8 2: 0.07 ex7 - 0.5 Semibreve: 0.25 - 0: 0.09 Crotchet: 0.58 1: 0.35 Quaver: 0.17 2: 0.04 ex8 - 0.35 Minim: 0.21 Crotchet: 0.04 0: 0.1

377 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Crotchet: 0.36 Quaver: 0.04 1: 0.72 Quaver: 0.36 2: 0.14 3: 0.03 ex9 0.42 Minim: 0.17 Crotchet: 0.08 0: 0.08 Crotchet: 0.5 1: 0.79 Quaver: 0.25 2: 0.08 4: 0.04 ex10 - 0.5 Minim: 0.08 Minim: 0.04 0: 0.05 Crotchet: 0.5 Crotchet: 0.12 1: 0.58 Quaver: 0.25 2: 0.21 3: 0.09 4: 0.07 ex11 0.57 Minim: 0.12 Quaver: 0.04 1: 0.64 Crotchet: 0.42 2: 0.07 Quaver: 0.42 ex12 - 0.4 Quaver: 0.71 Quaver: 0.29 1: 0.5 2: 0.08 3: 0.33 4: 0.08 ex13 0.44 Crotchet: 0.17 Quaver: 0.08 0: 0.17 Quaver: 0.75 1: 0.39 2: 0.28 3: 0.17 ex14 0.52 Minim: 0.25 Quaver: 0.15 0: 0.05 Crotchet: 0.25 1: 0.57 Quaver: 0.35 2: 0.29 3: 0.05 4: 0.05 ex15 0.62 Minim: 0.2 Quaver: 0.1 0: 0.09 Crotchet: 0.23 1: 0.82 Quaver: 0.47 2: 0.06 3: 0.03 ex16 - 0.69 Minim: 0.08 - 1: 0.7 Crotchet: 0.62 2: 0.14 Quaver: 0.12 3: 0.08 Semiquaver: 0.17 4: 0.05 5: 0.03 ex17 0.57 Minim: 0.67 Crotchet: 0.08 0: 0.13 Semiquaver: 0.25 1: 0.8 2: 0.07 ex18 - 0.22 Minim: 0.5 Crotchet: 0.09 0: 0.19 Crotchet: 0.28 1: 0.33 Quaver: 0.12 2: 0.19 3: 0.1 4: 0.1 ex19 0.51 Minim: 0.03 Crotchet: 0.07 0: 0.13

378 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Crotchet: 0.34 1: 0.7 Quaver: 0.08 2: 0.02 Semiquaver: 0.11 3: 0.04 4: 0.04 7: 0.02 ex20 - 0.53 Semibreve: 0.12 - 0: 0.1 Crotchet: 0.46 1: 0.55 Dotted Quaver: 0.12 2: 0.26 Quaver: 0.25 3: 0.03 Semiquaver: 0.04 5: 0.06 ex21 0.54 Minim: 0.06 Crotchet: 0.17 1: 0.42 Crotchet: 0.5 2: 0.21 Dotted Quaver: 0.09 3: 0.04 Quaver: 0.15 4: 0.04 Semiquaver: 0.03 ex22 - 0.21 Minim: 0.25 - 0: 0.2 Crotchet: 0.31 1: 0.25 Dotted Quaver: 0.33 2: 0.3 Semiquaver: 0.11 3: 0.15 4: 0.1 ex23 0.4 Crotchet: 0.7 Crotchet: 0.11 0: 0.02 Dotted Quaver: 0.14 1: 0.43 Semiquaver: 0.05 2: 0.19 3: 0.12 4: 0.05 5: 0.05 ex24 0.52 Semibreve: 0.05 Minim: 0.03 1: 0.78 Minim: 0.31 Crotchet: 0.03 2: 0.09 Crotchet: 0.3 3: 0.11 Quaver: 0.07 4: 0.02 ex25 0.38 Semibreve: 0.1 Crotchet: 0.05 0: 0.18 Minim: 0.15 1: 0.51 Crotchet: 0.52 2: 0.09 Quaver: 0.05 3: 0.02 4: 0.02 7: 0.02 ex26 0.52 Semibreve: 0.12 Minim: 0.04 0: 0.04 Crotchet: 0.5 Crotchet: 0.06 1: 0.81 Quaver: 0.27 2: 0.1 3: 0.02 4: 0.02 ex27 - 0.58 Semibreve: 0.27 - 0: 0.03 Minim: 0.13 1: 0.54 Crotchet: 0.47 2: 0.36 Quaver: 0.13 3: 0.08 ex28 - 0.49 Minim: 0.12 Crotchet: 0.04 0: 0.09

379 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Crotchet: 0.5 1: 0.67 Quaver: 0.33 2: 0.18 3: 0.04 4: 0.02 5: 0.02 ex29 0.46 Semibreve: 0.14 Crotchet: 0.05 0: 0.08 Minim: 0.5 1: 0.64 Crotchet: 0.31 2: 0.11 3: 0.06 4: 0.06 5: 0.03 7: 0.03 ex30 - 0.53 Minim: 0.38 - 1: 0.48 Crotchet: 0.08 2: 0.33 Quaver: 0.54 3: 0.09 4: 0.03 ex31 - 0.67 Minim: 0.2 - 0: 0.04 Crotchet: 0.17 1: 0.83 Quaver: 0.63 3: 0.07 5: 0.02 ex32 - 0.49 Minim: 0.13 - 0: 0.02 Crotchet: 0.65 1: 0.62 Quaver: 0.22 2: 0.17 3: 0.04 4: 0.06 5: 0.02 ex33 - 0.58 Semibreve: 0.12 - 0: 0.07 Minim: 0.16 1: 0.74 Crotchet: 0.54 3: 0.02 Quaver: 0.14 ex34 0.68 Semibreve: 0.06 Crotchet: 0.02 1: 0.74 Minim: 0.09 2: 0.17 Crotchet: 0.5 3: 0.06 Quaver: 0.07 5: 0.04 Semiquaver: 0.08 ex35 0.31 Minim: 0.29 Crotchet: 0.21 0: 0.09 Crotchet: 0.29 1: 0.61 Quaver: 0.05 2: 0.04 3: 0.09 4: 0.04 ex36 - 0.58 Minim: 0.05 - 1: 0.47 Crotchet: 0.52 2: 0.24 Dotted Quaver: 0.07 3: 0.07 Quaver: 0.33 7: 0.03 Semiquaver: 0.02 ex37 0.55 Minim: 0.05 Quaver: 0.06 0: 0.05

380 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Crotchet: 0.42 1: 0.69 Quaver: 0.47 2: 0.12 3: 0.05 5: 0.05 7: 0.02 ex38 0.53 Minim: 0.38 Crotchet: 0.06 1: 0.51 Crotchet: 0.42 Quaver: 0.01 2: 0.08 Dotted Quaver: 0.09 3: 0.08 Quaver: 0.01 5: 0.08 Semiquaver: 0.03 7: 0.05 ex39 - 0.61 Minim: 0.19 - 1: 0.63 Crotchet: 0.31 2: 0.32 Quaver: 0.38 3: 0.05 ex40 0.57 Minim: 0.12 Crotchet: 0.06 1: 0.48 Crotchet: 0.25 2: 0.52 Quaver: 0.56 ex41 - 0.5 Minim: 0.19 - 1: 0.38 Crotchet: 0.38 2: 0.43 Quaver: 0.44 3: 0.19 ex42 0.42 Semibreve: 0.12 Crotchet: 0.04 1: 0.37 Minim: 0.33 2: 0.47 Crotchet: 0.25 3: 0.11 Quaver: 0.19 4: 0.05 ex43 0.54 Semibreve: 0.12 Minim: 0.06 0: 0.05 Minim: 0.05 Crotchet: 0.06 1: 0.77 Crotchet: 0.25 2: 0.14 Quaver: 0.2 3: 0.05 ex44 0.53 Minim: 0.09 Crotchet: 0.06 1: 0.32 Crotchet: 0.25 2: 0.58 Quaver: 0.47 3: 0.05 4: 0.05 ex45 - 0.39 Minim: 0.12 - 1: 0.58 Crotchet: 0.19 2: 0.11 Quaver: 0.41 3: 0.16 4: 0.11 5: 0.05 ex46 0.44 Semibreve: 0.12 Crotchet: 0.08 1: 0.41 Minim: 0.12 2: 0.29 Crotchet: 0.38 3: 0.12 Quaver: 0.12 4: 0.18 ex47 - - 0.46 Crotchet: 0.38 - 0: 0.04 Quaver: 0.62 1: 0.28 2: 0.48 3: 0.08 5: 0.12 ex48 - 0.48 Semibreve: 0.12 - 0: 0.04

381 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Minim: 0.08 1: 0.39 Crotchet: 0.21 2: 0.46 Quaver: 0.4 3: 0.11 ex49 - 0.58 Minim: 0.09 - 1: 0.6 Crotchet: 0.25 2: 0.28 Quaver: 0.66 3: 0.12 ex50 0.52 Minim: 0.12 Crotchet: 0.06 1: 0.67 Crotchet: 0.12 2: 0.24 Quaver: 0.59 ex51 - - 0.38 Semibreve: 0.09 - 0: 0.11 Minim: 0.25 1: 0.69 Crotchet: 0.34 2: 0.11 Quaver: 0.31 3: 0.09 ex52 - 0.54 Minim: 0.06 Crotchet: 0.06 0: 0.05 Crotchet: 0.5 1: 0.68 Quaver: 0.38 2: 0.16 3: 0.11 ex53 - 0.62 Minim: 0.25 Crotchet: 0.03 1: 0.47 Crotchet: 0.44 2: 0.18 Quaver: 0.28 3: 0.18 4: 0.03 ex54 - - 0.58 Minim: 0.31 - 1: 0.49 Crotchet: 0.34 2: 0.08 Quaver: 0.34 3: 0.19 4: 0.11 ex55 0.48 Minim: 0.12 Crotchet: 0.06 1: 0.81 Crotchet: 0.25 2: 0.1 Quaver: 0.56 3: 0.1 ex56 - 0.43 Minim: 0.12 - 1: 0.5 Crotchet: 0.25 2: 0.25 Quaver: 0.62 3: 0.21 4: 0.04 ex57 0.38 Minim: 0.12 Crotchet: 0.12 1: 0.6 Crotchet: 0.44 2: 0.2 Quaver: 0.31 3: 0.13 4: 0.07 ex58 0.42 Minim: 0.12 Crotchet: 0.12 0: 0.06 Crotchet: 0.25 1: 0.33 Quaver: 0.5 2: 0.28 3: 0.11 4: 0.06 ex59 0.46 Semibreve: 0.25 Crotchet: 0.08 0: 0.04 Crotchet: 0.33 1: 0.74 Quaver: 0.33 2: 0.13 3: 0.04 4: 0.04

382 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

ex60 0.65 Semibreve: 0.38 Crotchet: 0.08 1: 0.74 Minim: 0.08 2: 0.11 Crotchet: 0.17 3: 0.05 Quaver: 0.29 7: 0.05 ex61 - 0.45 Minim: 0.42 - 0: 0.1 Crotchet: 0.46 1: 0.57 Quaver: 0.12 3: 0.1 4: 0.1 5: 0.05 ex62 - 0.41 Minim: 0.12 Crotchet: 0.16 0: 0.29 Crotchet: 0.38 1: 0.48 Quaver: 0.34 2: 0.1 3: 0.03 4: 0.06 7: 0.03 ex63 - 0.59 Minim: 0.06 Crotchet: 0.22 1: 0.64 Crotchet: 0.56 2: 0.18 Quaver: 0.16 3: 0.09 4: 0.09 ex64 0.43 Semibreve: 0.09 Minim: 0.12 0: 0.07 Minim: 0.12 Crotchet: 0.03 1: 0.45 Crotchet: 0.34 2: 0.1 Quaver: 0.28 3: 0.07 4: 0.07 ex65 - 0.44 Minim: 0.19 Crotchet: 0.03 0: 0.09 Crotchet: 0.59 1: 0.62 Quaver: 0.19 2: 0.12 3: 0.06 4: 0.09 ex66 - - 0.47 Minim: 0.31 - 1: 0.33 Crotchet: 0.47 2: 0.42 Quaver: 0.22 3: 0.06 4: 0.09 5: 0.09 ex67 - 0.32 Semibreve: 0.12 - 0: 0.21 Crotchet: 0.38 1: 0.44 Quaver: 0.41 2: 0.33 3: 0.03 ex68 - 0.5 Crotchet: 0.67 Crotchet: 0.04 0: 0.14 Quaver: 0.29 1: 0.45 2: 0.24 3: 0.07 5: 0.03 7: 0.07 ex69 - 0.43 Semibreve: 0.12 - 1: 0.46 Minim: 0.17 2: 0.25

383 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Crotchet: 0.5 3: 0.08 Quaver: 0.21 4: 0.04 ex70 - 0.35 Minim: 0.12 Minim: 0.06 0: 0.13 Crotchet: 0.53 Crotchet: 0.06 1: 0.53 Quaver: 0.22 2: 0.03 3: 0.1 4: 0.13 5: 0.07 ex71 - 0.5 Crotchet: 0.36 Crotchet: 0.07 0: 0.13 Quaver: 0.32 Quaver: 0.05 1: 0.6 Semiquaver: 0.2 2: 0.18 3: 0.09 ex72 0.71 Minim: 0.09 Minim: 0.04 1: 0.65 Crotchet: 0.22 Crotchet: 0.04 2: 0.18 Quaver: 0.15 3: 0.08 Semiquaver: 0.08 4: 0.02 ex73 0.57 Minim: 0.08 Crotchet: 0.04 1: 0.64 Crotchet: 0.48 2: 0.15 Dotted Quaver: 0.12 3: 0.11 Quaver: 0.1 4: 0.06 Semiquaver: 0.04 5: 0.04 ex74 0.62 Minim: 0.19 Minim: 0.04 1: 0.6 Crotchet: 0.19 Crotchet: 0.04 2: 0.06 Quaver: 0.38 3: 0.04 4: 0.08 5: 0.02 ex75 0.68 Minim: 0.08 Crotchet: 0.17 1: 0.67 Crotchet: 0.46 2: 0.09 Dotted Quaver: 0.11 3: 0.09 Quaver: 0.15 4: 0.04 Semiquaver: 0.04 7: 0.02 ex76 - 0.55 Minim: 0.06 Minim: 0.04 0: 0.03 Crotchet: 0.25 1: 0.44 Quaver: 0.52 2: 0.21 3: 0.09 4: 0.02 5: 0.06 ex77 0.7 Minim: 0.06 Crotchet: 0.1 0: 0.04 Crotchet: 0.42 1: 0.61 Quaver: 0.38 2: 0.11 3: 0.07 4: 0.02 5: 0.02 ex78 - 0.39 Crotchet: 0.21 Crotchet: 0.04 0: 0.15 Dotted Quaver: 0.03 Quaver: 0.08 1: 0.65 Quaver: 0.33 2: 0.02

384 APPENDIX H.ALGORITHM PARAMETERS USEDTO GENERATE GRADE 3 EXERCISES

Semiquaver: 0.3 3: 0.07 4: 0.04 5: 0.02 ex79 0.65 Minim: 0.12 Crotchet: 0.12 1: 0.6 Crotchet: 0.42 2: 0.08 Quaver: 0.33 3: 0.04 4: 0.04 5: 0.06 ex80 0.42 Minim: 0.07 Crotchet: 0.19 1: 0.59 Crotchet: 0.39 2: 0.14 Quaver: 0.23 3: 0.1 4: 0.02 6: 0.02 ex81 - 0.46 Minim: 0.08 Crotchet: 0.23 0: 0.04 Crotchet: 0.1 1: 0.41 Quaver: 0.58 2: 0.24 3: 0.1 14: 0.02 ex82 - 0.54 Minim: 0.04 Crotchet: 0.08 0: 0.06 Crotchet: 0.31 Quaver: 0.07 1: 0.61 Quaver: 0.49 2: 0.14 3: 0.08 4: 0.04 5: 0.04

385