The Effect of a Tonic Drone Accompaniment on the Pitch Accuracy of Scales Played by Beginner Violin and Viola Students Disserta

The Effect of a Tonic Drone Accompaniment on the Pitch Accuracy of Scales Played by Beginner Violin and Viola Students

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Charles Clair Laux, Jr., B.M., M.M.

Graduate Program in Music

The Ohio State University

2015

Dissertation Committee:

Dr. Robert Gillespie, Advisor

Dr. Jan Edwards

Prof. Mark Rudoff

Charles Clair Laux, Jr.

2015

Abstract

The purpose of the study was to determine the effect of drone-based accompaniment on the development of pitch accuracy of C-major and D-major scales on beginning-level violin and viola students. Participants were 50 second-year, beginning- level violinists and violists from three middle schools in a large suburban school district in the Southeast. Six orchestra classes were randomly assigned to one of three groups; pitch matching (n=15), drone (n = 15), and pitch matching plus drone (n = 20). Groups differed only by the audio accompaniment used during testing and treatment. The audio accompaniments were made using synthesized square waves that provided pitch- matching, a tonic drone, or pitch matching with tonic drone accompaniment.

This quantitative study used a quasi-experimental pre/posttest design. Each group practiced the D- and C-major scales with the accompaniment track over seven string class periods as part of their daily warm-up routine. Participants were tested performing the scales under accompanied and unaccompanied treatment conditions.

Performed pitches, excluding open strings, were analyzed for cent deviation from equal temperament. The Intonia software program was the measurement tool. In addition to the cent deviations, directional cent deviation data was converted to absolute values and nonparametric sharp/flat values. Participants’ pitch adjustments were also tallied and analyzed. Results indicated no significant improvement in intonation in any of the three

ii groups, and there was an inclination for students to perform flat across the study. It is important to note that pitch adjustments were more frequent, though not significant, in accompanied conditions across all groups in the pretest and significantly greater during accompanied conditions in the posttest.

iii

Dedication

Dedicated to my loving family,

Tricia, Charlie, and Anderson.

Acknowledgments

I would like to express appreciation to my advisor, Dr. Robert Gillespie, for his

time and assistance with this project and for his inspiration, wisdom, and advice that have

helped shape and guide me in my career as a string teacher. I owe you so much! In

addition, I would like to thank the members of my committee, Dr. Jan Edwards, and Prof.

Mark Rudoff for their time and interest in my project. In addition, I would like to thank

Ms. Blair Williams, for assisting me with items while off campus. You are a lifesaver!

Thank you to my many friends and colleagues who have also helped with my

dissertation. Dr. Harry Price: You are not only a wonderful colleague and friend, but also

a phenomenal researcher and thinker. I thank you for your friendship and always being

there for me. To Dr. Patricia Flowers: You have been an inspiration beyond words and I will never forget our talks. Thank you for believing in me. Dr. Jeff Yunek: You are the best editor on the planet. I appreciate your attention to detail and value our friendship.

Thank you to Dr. Michael Hopkins, University of Michigan, for introducing me to the

world of SPSS and being such an inspiring string pedagogue and researcher.

Thank you to all of the students, faculty, and staff at the Kennesaw State

University School of Music. It has been an honor and pleasure to work with such fine

musicians, scholars, and pedagogues. To Dr. Lewis VanBrackle, Kennesaw State

University, for the generosity of your time in assisting me on multiple occasions with statistics. I have learned so much from you. Go Owls!

I would like to thank the students, parents, faculty, and administration of the schools and school district, as I would not have been able to complete this document without your time, energy, and willingness to help. I would like to send special thanks to

Ms. Corie Benton, Ms. Ashley Culley, Ms. Tricia Laux, Mr. Jacob Bitinas, Mr. Paul

O’Keefe, and Mr. Michael Tompkins for your pedagogical expertise and willingness to work with me on this project.

Most importantly, I would like to thank my beautiful wife, Tricia, and wonderful sons Charles III and Anderson for your continued love, patience, and understanding over the years. You are everything to me. This Never Happened Before… I love you!!

Vita

1992...... Mentor High School, Mentor, Ohio

1996...... B.M. Music Education, Ohio University

1996-2003 ...... Orchestra Director, Clark County School

District, Las Vegas, Nevada

1996-2007 ...... Adjunct Faculty, College of Southern

Nevada, North Las Vegas, Nevada

2001...... M.M. Music Education, University of

Nevada, Las Vegas

2003-2007 ...... Orchestra Director, Orange County Public

Schools, Orlando, Florida

2006-2008 ...... Adjunct Faculty, Valencia College, Orlando,

Florida

2007-2008 ...... Graduate Teaching Associate, Department

of Music, The Ohio State University

2008-2009 ...... Orchestra Director, New Albany-Plain Local

Schools, New Albany, Ohio

2009-2012 ...... Orchestra Director, Hilliard City Schools,

Hilliard, Ohio

vii

2012-present ...... Assistant Professor of Music Education,

Kennesaw State University, Kennesaw,

Georgia

Publications

Laux, C. (2010). String Education Technology Blog. http://www.stringedtech.com

Laux, C. (2008). Practical musician: Music & musicians - podcasting 101. Strings, 22(8), 26-28.

Laux, C. (2007). "A Christmas Festival." Ed. Littrell, D, Racin, L. R & Allen, M. (2007). Teaching Music through Performance in Orchestra. Vol. 3. Chicago: GIA Publications, Inc. (343-347).

Laux, C. (2007). "Finale, Symphony No. 2 in C." Ed. Littrell, D, Racin, L. R & Allen, M. Teaching Music through Performance in Orchestra. Vol. 3. Chicago: GIA Publications, Inc. (165-169).

Fields of Study

Major Field: Music

Minor: Educational Technology

viii

Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments ...... v

Vita ...... vii

List of Tables ...... xi

List of Figures ...... xiii

Chapter 1: Introduction ...... 1

Chapter 2: Review of Related Literature ...... 16

Chapter 3: Research Design and Methodology ...... 47

Chapter 4: Results ...... 66

Chapter 5: Summary, Conclusions, Recommendations, and Implications ...... 99

Bibliography ...... 124

Appendix A: Questionnaire ...... 145

Appendix B: Assent Form ...... 147

Appendix C: Permission Form ...... 151

Appendix D: Scale Sheet Music for Violin and Viola ...... 155

Appendix E: Lesson Script for Classroom Teachers ...... 158

Appendix F: Directions for Research Assistants ...... 165

Appendix G: Institutional Review Board Approval Letter ...... 169

Appendix H: Raw Cent deviation Scores for Each Participant ...... 171

List of Tables

Table 3.1: Participants by group and site ...... 49

Table 3.2: The combinations of scale delivery during testing ...... 54

Table 4.1: Participants by group ...... 69

Table 4.2: Shapiro-Wilk Test of normality ...... 70

Table 4.3: Absolute cent deviation for pre- and posttest ...... 71

Table 4.4: Analysis of variance for pre- and posttest absolute cent deviation ...... 72

Table 4.5: Tukey HSD for pre- and posttest absolute cent deviation ...... 73

Table 4.6: Pre- and posttest unaccompanied and accompanied absolute cent deviation . 74

Table 4.7: Analysis of Variance for Pre- and Posttest Absolute Cent Deviation ...... 75

Table 4.8: Tukey HSD for pre- and posttest unaccompanied and accompanied absolute

cent deviation ...... 76

Table 4.9: Total directional cent deviation ...... 78

Table 4.10: Pre- and posttest directional dent deviation, by group ...... 79

Table 4.11: Sharp and flat response percentages of unaccompanied and accompanied

scale performances ...... 80

Table 4.12: Percentages of sharp and flat responses, unaccompanied and accompanied, by

group ...... 81

Table 4.13: Note names, scale degrees, and fingerings used for the D-major scale analysis

...... 82

Table 4.14: Note names, scale degrees, and fingerings used for the C-major scale analysis

...... 82

Table 4.15: Sharp and flat percentages of each performed note, by group ...... 84

Table 4.16: Sharp and flat percentage of scale degrees in the D-major scale ...... 88

Table 4.17: Sharp and flat percentage of scale degrees in the C-major scale ...... 89

Table 4.18: Pre- and posttest pitch adjustment count means ...... 92

Table 4.19: Analysis of Variance for Pitch Adjustment Count Means ...... 93

Table 4.20: Tukey HSD for pitch adjustment count means ...... 94

Table 4.21: Participants who adjusted pitch in pre- and posttests ...... 95

Table 4.22: Total mean cent deviation of adjusted pitches ...... 96

Table 4.23: Analysis of variance for mean cent deviation ...... 96

Table 4.24: Absolute cent deviation of unaccompanied and accompanied adjusted

pitches, by group ...... 97

Table 4.25: Analysis of variance of unaccompanied and accompanied adjusted pitches 98

Table 5.1: Interval adjustment for a major scale from equal temperament to just

intonation ...... 106 xii

List of Figures

Figure 3.1: Intonia graphic display ...... 60

Figure 3.2: Example of sound sample selection in Intonia ...... 61

Figure 4.1: Adjusted pitch in the Intonia software application ...... 90

Figure 4.2: Unadjusted pitch in the Intonia software application ...... 90

Figure 5.1: Major and Dorian finger pattern illustrations ...... 109

xiii

Chapter 1: Introduction

Intonation is a term used to describe a set of mental and physical skills that pertain to the accurate perception or performance of pitch frequency (Morrison & Fyk,

2002). Correct intonation implies that all pitches are played or sung at the precise frequency to a selected standard. Conversely, inaccurate intonation results when pitches are played or sung above or below the desired frequency.

In music, pitch accuracy is measured according to particular standards, also known as musical temperaments or tuning systems, which assign each musical pitch to a precise audio frequency (e.g. Benson, 2008; Coy, 2012; Latten, 2003). Intonation is a fundamental aspect to quality musical performance. Because intonation is thought of in terms of “in tune” and “out of tune,” judgment of correct pitch accuracy is often subjective within a musical context. “It is evident that the issue of intonation is not merely a matter of skill and execution but a question of utmost importance to the constitution of the art form” (Coy, 2012, p. 3).

No other aspect of music teaching poses more of a challenge to ensemble directors than that of intonation (McAdow, 1952; Kohut, 1973; Brick, 1983). On a string instrument, moving or altering the placement of fingers on the fingerboard adjusts pitch intonation. There are a variety of reasons that may cause string students to have intonation problems: (a) changing environmental conditions such as humidity or

1 temperature; (b) poor instrument/string quality (Alexander, 2008); (c) disproportion of the instrument’s components such as incorrect bridge placement that effects string length;

(d) the teacher’s failure to introduce and reinforce concepts that promote an awareness of intonation (Laycock, 2012), and (e) students’ ability to discriminate pitch.

Erickson’s (1973) study confirmed that students could learn to play with greater pitch accuracy when teachers used systematic procedures. To address the important concept of intonation in young string players, this study will examine the use of specific drone-based audio accompaniments to improve the pitch accuracy of string players in an orchestra class. Teachers will use modeling and other pedagogical strategies to show students how to evaluate intonation and adjust pitch accordingly on scales when playing with an accompaniment track. Following this instruction, students will practice scales in class and reinforce intonation skill through this repetition. In music, a drone is an accompaniment where a single pitch or chord is continuously sounded (Erickson, 1973).

For many years, practitioners have praised drones as an intonation tool when practicing or improvising (e.g. Alexander, 2008; Curry, 2011; Flunker, 2010; & Griswold, 1998) however these authors only provide anecdotal evidence to support their claims.

Need For The Study

An important goal for instrumental music teachers is to help students play their best. A focus for teachers of stringed instruments is to find strategies that help their students perform with accurate intonation. The ability to perform with accurate intonation is an important skill that must be developed by all musicians (Hovey, 1976; Klotman,

1981) and is one of the most important and difficult tasks that teachers encounter due to its complexity (Dillon, 2003; Hovey, 1976; Mongeon, 2004).

Unfortunately there are few resources that address the learning of intonation directly. Accurate intonation requires a theoretical understanding to mentally establish the correct pitch frequency and the technical skills to produce and control that pitch (Coy,

2012). Some teachers/conductors leave students on their own to discover how intonation functions in musical practice (Rizzolo, 1969). When a teacher lacks dedicated intonation teaching strategies or provides corrective feedback without explanation, the results can leave students with incomplete or even inaccurate comprehension of intonation and how to achieve its accuracy.

Certain aspects of music do not allow for quantitative inquiry, however intonation can be evaluated and educators should be familiar with the techniques involved (Lehman,

1968). For many years, pedagogues have suggested a need for teachers to focus on strategies to improve students’ pitch accuracy and discrimination (e.g., Hovey, 1976;

Klotman, 1981; Raab, 1978; Swift, 2003; Timm, 1943; Whitcomb, 2007). Intonation is considered one of the most influential factors affecting quality of performance (e.g.

Geringer & Madsen, 1998; Hovey, 1976). Nilo Hovey (1976) stated, “Perhaps nothing detracts more from a satisfying performance than out-of-tune playing, and yet no problem in instrumental music is more complex than that of achieving the highest standards of intonation” (p. 25).

Purpose of the Study

The purpose of the study is to determine the effect of drone-based accompaniments on the development of pitch accuracy in scales among beginning-level violin and viola students.

Significance of the study

Practicing scales, exercises, and excerpts with drones has long been a teaching strategy used by teachers but its effectiveness has not been quantitatively assessed.

Practitioners (e.g. Coy, 2012; Curry, 2011; Griswold, 1988; Hopkins, 2012; Reel, 2005;

Watkins, 2004; Whitcomb, 2007) have suggested the use of drones for improvisation and to aid students with the pitch accuracy of tuning open strings, scales, melodies and more.

In addition to the numerous references in practitioner journals, the availability of commercial drone recordings (e.g., Sloane, 2003; Schwartz, 2010; Apprentice Music,

2013) suggests the use of drones in instrumental practice is commonplace. However, practitioners’ claims are mainly supported by anecdotal evidence. The effectiveness of the use of a drone has not been systematically investigated.

Intonation has been a significant topic of research and discussion within the field of music education. Professional writings stress the importance of intonation in performance (e.g. Ish, 1958; McAdow, 1952) and pitch discrimination and accuracy are recognized as continuing problems in musical performance for young instrumentalists

(Brick, 1983).

The use of technology provides one method of assisting students in developing intonation accuracy with students. Throughout history musicians have had to rely on their development of aural perception to improve their intonation. Significant research

4 pertaining to intonation has a long and distinguished history and can be traced to the pioneering work of Carl Seashore (1938). Many pedagogical texts emphasize the particular tuning difficulties of each instrument and methods to improve intonation

(Barbour, 1972; Barrett, 1972; Garofalo, 1996; Genevro, 1997; Grunow et al., 1999;

Putnik, 1970; Rainey, 1985; Ross, 2002; Ross et al., 2004; Stein, 1958, Jagow, 2012).

With the development of technology, musicians may now depend on electronic tuners to decide their intonation accuracy. Griswold (1988) states that while the visual display of an electronic tuner can be a positive first step toward teaching students to play in tune, an overuse or misuse of this practice can lead to a reliance on the devices and leave the musician’s ears somewhat untrained, preventing students from developing aural skills necessary to discriminate exact pitch.

String pedagogues have suggested a need for teachers to focus on strategies to improve students’ pitch accuracy and discrimination (Klotman, 1981; Raab, 1978). If teachers are not persistent with the correction of intonation issues, students can become less sensitive toward making necessary adjustments (Cohen, 1980). Raab (1978) made the suggestion for students to understand the concept of sympathetic vibrations, while

Klotman (1981) suggested listening for beats when playing unisons or octaves. This study investigates these suggestions by having students listen for intervals of ascending and descending pitches while performing major scales. After initial training, specific consonances and dissonances may become apparent to students as they hear their performed pitch compared to a drone pitch.

String players were selected as subjects in the study because of their need to

5 improve intonation and the ease of adjusting intonation by a subtle movement of a finger on the fingerboard.

The measurement of pitch accuracy of students playing scales has been selected as the medium for evaluating intonation in this study because experts agree that scales are one of the best ways to demonstrate accurate intonation and develop a sense of pitch relationship. Galamian (1985) states “great importance lies in the fact that [scales] can serve as a vehicle for the development of a large number of technical skills in either the right or left hand” (p. 102). He adds that scales are useful because they build a foundation for accurate intonation, help establish good posture, dexterity, tone quality and can be used in the study of bowings, bow division, dynamics and vibrato. While a multitude of pedagogical strategies have been developed to help students’ pitch accuracy, there has been little research to determine wether the use of a sustained tonic drone pitch will affect the pitch discrimination of beginning string students, regardless of the subject age.

The significance of intonation’s effect on quality performance and the complexity of intonation for pedagogues leads to important questions: Why do some string students play with accurate intonation while others have a more difficult time discerning pitch?

Are the differences in intonation accuracy due to differences in how students listen, the context in which they play, or other factors? What teaching strategies can be used to assist students to understand the concept of intonation so that they may play with improved pitch accuracy? Given the importance of intonation on performance quality and the crucial nature of beginning instruction on student success, if the use of drones is shown to be an effective in developing students’ pitch accuracy, the data and procedures

6 from this study could assist teachers in using drones with their students.

Primary Research Questions

This study was designed to address the following research questions:

1. Do beginning string students play with greater pitch accuracy following

training with tonic drones compared to pitch matching alone, or pitch

matching with tonic drone accompaniments?

2. Does the pitch accuracy of students who have learned to play scales initially

with the use of an accompaniment track change once students play the same

scales without an accompaniment track?

3. Are intonation tendencies toward sharpness or flatness for particular scale

degrees different for students when they play with a drone accompaniment

compared to when they play without a drone accompaniment?

4. Do students more frequently attempt to adjust the accuracy of their pitches

when playing with a tonic drone compared to those who use pitch matching

alone, or pitch matching with tonic drone accompaniments?

5. Do students adjust the intonation of their pitches to be more accurate when

playing scales with a drone accompaniment compared to pitch matching

alone, or pitch matching with tonic drone accompaniments?

Hypotheses

1. Following training, violinists and violists who practice scales using a tonic

drone accompaniment will perform with better intonation accuracy than those

students who practice with pitch matching only. The reverse hypothesis is that

there will be no difference in pitch accuracy among those students who

practice with a tonic drone accompaniment and those who practice with pitch

matching only.

2. After practicing with a drone-based accompaniment, violinist and violists will

play scales with greater pitch accuracy regardless of accompaniment. The

reverse hypothesis is that drone-based accompaniments have no impact on a

violinists’ and violists’ ability to play scales with greater pitch accuracy

without accompaniment.

3. Violinists and violists will show differences in intonation tendencies for

particular scale degrees when playing with a drone accompaniment compared

when they play without a drone accompaniment. The reverse hypothesis is

that there are no differences in tendencies toward sharpness when playing

with a drone accompaniment compared to no drone accompaniment.

4. Students will adjust pitch more accurately when playing scales with a drone-

based accompaniment compared to playing with pitch matching

accompaniment. The reverse hypothesis is that a drone-based audio

accompaniment will have no effect on the adjustment accuracy when

compared with pitch-matching accompaniment.

5. Students who practice scales with a tonic drone accompaniment will self-

correct intonation errors more frequently than those who use pitch-matching

accompaniments. The reverse hypothesis states that an accompaniment will

not impact a student’s ability to self-correct intonation errors.

Research Design

Participants

This quantitative study used a quasi-experimental pre-/post-test design. The participants of the study were fifty (n = 50) second year (seventh grade) violinists and violists enrolled in their school orchestra programs. A beginning violinist/violist is defined as having less than two years playing experience.

Participants were selected from three middle schools within a large, suburban public school district. To qualify, subjects must have had between 10 to 11 months of violin/viola playing experience. Those who were enrolled in or had taken private violin/viola lessons and/or received additional violin/viola training prior to their first year of instruction (sixth-grade) were excluded from the study. Prior to the study, participants were asked to complete a brief questionnaire that confirmed their eligibility to participate

(See Appendix A)

Performance Materials

Participants were recorded performing D- and C-Major one-octave scales, ascending and descending. These two scales enabled participants to utilize the two most common finger patterns for beginning-level violin and viola players: (a) the major tetrachord, used in the D Major scale, where the second and third fingers produce a half step on the fingerboard, and (b) the Dorian tetrachord, used in the C Major scale, where the first and second fingers produce a half step on the fingerboard. The left hand technique for these scales is the same for violins and violas so the difference between instruments was not measured in this study.

Data Collection Proceedures

Audio recordings of individual student performances were captured with a digital audio recorder equipped with lavalier microphone attached to the participant’s strings, behind the bridge. Participants played the one-octave D-major and C-major scales with a pre-recorded audio accompaniment. The accompaniment consisted of a verbal count-off, a metronome click track, and one of the following harmonic accompaniments: (a) pitch matching, where pitches of the scale to be performed were presented ascending and then descending; (b) a drone, where the tonic pitch was sustained throughout the duration of the scale performance; and (c) pitch matching while a sustained tonic drone pitch was sounded. In addition to the accompanied performances, all participants performed both scales without accompaniment.

Definition of Key Terms

The following terms are important in understanding the technical aspects of measuring intonation and will be used in the present study.

Directional cent deviation is a tone’s average measured deviation, expressed in

cents, either above or below the chosen tuning standard, indicating the tone’s

relative sharpness or flatness as a positive or negative value, respectively.

Cent is the unit of pitch in equal temperament, defined to be exactly 1/100 of an

equal-tempered semitone (semitones are 100 cents apart)

Cent deviation data is a tone’s average measured deviation, expressed in cents,

away from chosen tuning standard.

Absolute cent deviation is the measure of cent deviation noted as positive value, regardless of pitch direction (sharpness or flatness).

A drone, in music, is a harmonic or monophonic effect or accompaniment where a note or chord is continuously sounded throughout. For this study, a monophonic drone based on the tonic (starting) note of each tested scale will be used.

Equal temperament is a system of tuning, wherein the octave is divided into 12 semitones of equal ratios. For the purpose of this study, equal temperament will be used as the standard for measuring intonation.

Frequency is the rate of vibration of a physical object creating a sound, expressed in cycles per second. The unit of measurement for frequency is Hertz (Hz). The standard of tuning frequency of 440 Hz (A4) will be used by the researcher to tune all subjects’ instruments prior to testing. For the purpose of this study, pitch and frequency will be used synonymously.

Harmony is created when two or more different pitches are sounded simultaneously. Harmony and harmonization are used with similar meaning. For the purpose of this study, harmonization occurs when a performed pitch is played simultaneously with another, such as a pitch that is sounded while a drone pitch is played at the same time.

Intonation refers to the pitch accuracy of a musical instrument, relative to a standard of equal temperament. Recordings of subjects’ scale intonation will be measured through the use of a software program called Intonia. The software uses

a variety of measurements to calculate pitch accuracy and provides a read out in

cent deviations. Pitch accuracy and intonation are used synonymously.

Just Intonation, also referred to as Pure Intonation, is a system of tuning in

which the frequencies of notes are related by superparticular ratios. The two notes

in any just interval are a part of of the same harmonic series. Justly tuned intervals

are usually written as ratios (e.g. 3:2).

A Metronome Click Track for the purposes of this study is an audio track that

contains a verbal count-off and a metronome click sound. This track will be used

to record the “unaccompanied” scale performances -- those that do not include

pitch-matching or drone-based accompaniment. Its sole purpose is to provide

students with a framework for playing the scales in measured time (48 BPM).

Performance is defined in this study as the intonation of subjects playing their

own instrument (violin or viola) on sixteen notes of ascending and descending

one-octave major (Ionian) scale patterns.

A scale is a set of musical notes, in order by a fundamental frequency or pitch.

For this study, the one-octave D-major and C-major scales will be used. These

scales will force subjects to utilize two the most common finger patterns for

beginning-level violin and viola players: (a) the major tetrachord, where the

second and third fingers produce a half step, and (b) the Dorian tetrachord, where

the first and second fingers produce a half step.

Assumptions, Limitations, and Scope (Delimitations)

For the purposes of this study, intonation refers to pitch accuracy as it is measured to conform to equal temperament (here after referred to as ET). ET has been selected because a majority of intonation-based research studies have used ET. Historically research suggests that it is used most often in performances of Western Music (Karrick,

1998; Mongeon, 2004; Rakowski, 1990). Ward (1961) tested amateur musicians and young music students listening to ascending diatonic scales and concluded that the participants could not distinguish melodic sequences presented in just intonation from those in ET. The present study does not attempt to compare tuning systems or pitch standards; however, when studying intonation the theoretical relevance of available tuning systems should always be contemplated (Kopiez, 2003).

This study involves second-year (seventh grade) violin and viola students performing ascending and descending major scale patterns. The topic of temperament is widely debated among scholars, pedagogues, and practitioners alike (Kopiez, 2003;

Ostling, 1974; Ward, 1961). While the use other temperament standards such as just

(pure) and Pythagorean temperament were explored and considered, it must recognized that the subjects of the proposed study are amateurs and are most likely discovering their own ability to listen and adjust intonation for the first time. The ability to conceptualize and adhere to a particular tuning system may be beyond a subject’s present musical aptitude. It should be noted, that a future investigation of temperamental preference in scalar and non-scalar passages would be valuable, particularly with participants who are more experienced.

It is common practice for teachers to install finger placement markers (adhesive tape, etc.) on the fingerboards of students’ instruments to aid with left shape and initial finger placement. Students often rely on these markers to visually make judgments about their own pitch accuracy. The participants in this study all played on instruments with finger placement markers installed. It would have been ideal for the purposes of this study to ask teachers to remove all finger placement markers from participants’ instruments. However, as a researcher in an educational setting, it is inappropriate to ask teachers to radically change their teaching methods just for the sake of a research study.

The student’s use of finger placement markers is considered an additional limitation of this study.

A true-control group (scale practice with no harmonic accompaniment) was desirable, though not required for the design of the study. The researcher was limited by a finite number of students available to serve as subjects in the study. Six treatment groups were critical to the design of the study. Students available for the study needed to comprise the treatment groups. No students were available for a control group after treatment groups were formed.

The results of this study should not be generalized to other scale patterns or modes, non-scalar music, or subjects of different ages or other levels of musical achievement. Any equipment limitations and fluctuations in recording or playback levels and selection of sampled sounds are assumed to be randomly distributed across individuals, trials, and groups.

Summary

It has been shown that intonation is a viable topic for research and there is a need for in-service teachers to learn about teaching strategies that will help them focus on teaching the concepts of intonation. While there have been many studies involving pitch perception and pitch accuracy in performance, quite often the methods for improving intonation skills outlined in research journals are not appropriate for incorporation into public school instrumental music programs. There is a need for more research on intonation because we should make certain that we providing students with the best teaching strategies available, particularly as it applies to the pedagogical needs of teachers of beginning instrumentalists.

Chapter 2: Review of Related Literature

Introduction

In music, intonation refers to the ability of a vocalist or instrumentalist to accurately sing or play pitches to a particular frequency standard or musical temperament

(Morrison & Fyk, 2002). Performing with accurate intonation requires a theoretical understanding to mentally establish the correct pitch frequency and the technical skills to produce and control that pitch (Coy, 2012). Good intonation, as defined by Morrison

(2000), is “the ability to adjust performed pitches to minimize or eliminate perceived discrepancies” (p. 39). Morrison states that the main concern of intonation discrepancy in a school ensemble setting is the performance of simultaneous (harmonic) sounding pitches, rather than those in a melodic setting, as might be the case in a solo performance.

The ability to perform with accurate intonation is an important, yet attainable, skill that must be developed by all musicians However, it is a skill that is particularly difficult to teach because of its complexity (Hovey, 1976; Klotman, 1981).

Intonation is considered one of the most influential factors affecting the quality of a performance (e.g., Hovey, 1976; Geringer & Madsen, 1998). Nilo Hovey (1976) stated, “Perhaps nothing detracts more from a satisfying performance than out-of-tune playing, and yet no problem in instrumental music is more complex than that of achieving the highest standards of intonation” (p. 25).

In string teaching, pedagogues have suggested that developing intonation skills in string students should be a primary concern for teachers (Klotman, 1981; Raab, 1978) because developing students’ intonation is one of the most important, yet most complicated, tasks that teachers encounter (Dillon, 2003; Hovey, 1976; Mongeon, 2004).

For many years, pedagogues have suggested a need for teachers to incorporate strategies to improve students’ pitch accuracy and discrimination (e.g., Hovey, 1976; Klotman,

1981; Raab, 1978, Swift, 2003; Timm, 1943; Whitcomb, 2007). Unfortunately there is little research on strategies that actively address how teachers might aid their students in learning this skill. Therefore, many teachers/conductors allow students often leave students on their own to discover how intonation functions in musical practice (Rizzolo,

1969). When a teacher lacks dedicated intonation teaching strategies or provides corrective feedback without explanation, the results can leave students with incomplete or even inaccurate comprehension of the topic (Coy, 2012).

Research on intonation in the performance of stringed instruments can be traced back nearly 80 years, first in the work of Carman (1936) and Green (1936). This review will include the history of intonation research along with common trends of both researchers and practitioners. The review will be organized into two main sections. The first section will cover related, non-string specific studies and will be divided into eight topics (1) the relationship between perception and performance tasks, (2) aural models,

(3) preference for tuning systems, (4) the effect of age, experience, and training, (5) the effects of stimulus type, (6) the effect of direction, (7) the effect of harmonic context/accompaniment, (8) the effect of tuning stimuli, and (9) the impact of technology.

The second section of this review will include those studies that are string-specific.

Topics will address the use of finger placement markers (FPMs) the use of drones in

string teaching and playing.

Non-string specific intonation research

1. Relationship between perception and music production tasks

There are many studies that examine the ability to perceive (mentally gauge) pitch. The initial research focused only on the ability to hear intervals, and transitioned into assessing the ability to hear intonation in performance. Siegel & Siegel (1977) explored categorical perception of tonal intervals. Researchers asked six subjects to identify 13 different intervals (thirds, fourths, and fifths). Some of the intervals were in tune and some were purposefully out of tune in .2 semitone increments. It was found that

subjects could classify intervals with 95 percent accuracy, but all were very poor at

determining if intervals were tuned sharp or flat. After testing, participants judged 63% of

the intervals to be in tune, however only 23% were accurate.

Most studies investigating pitch perception also include the addition of a

performance task through singing, playing an instrument, or other means of adjusting

pitch. Researchers have found positive, yet not significant relationships when making

comparisons between intonation perception and actual performance (e.g. Geringer, 1978;

Geringer, 1983; Geringer & Witt, 1985; Yarbrough, Karrick, & Morrison, 1995;

Yarbrough, Morrison, & Karrick, 1997). Other studies have found mixed results in

correlations betwen pitch perception and intonation accuracy (e.g. Demorest, 2001;

Demorst and Clements, 2007; Morrison, 2000). Inconsistent findings were related to the

18 varying populations under study or differences in performance task (Demorest, 2001, p.

68). Researchers have concluded that the ability to aurally discriminate pitch is an important prerequisite to the proficiency in pitch-matching performance tasks (Madsen &

Geringer, 1976).

Geringer (1978) investigated intonation performance and perception of ascending scales using ninety-six undergraduate and graduate music students. Subjects were randomly selected and were assigned to experimental groups based on their instrument type (string, wind, vocalists, and keyboard), while others served as a control group.

Subjects were asked to perform ascending scalar patterns on their instrument (wind and string players) or with their voice (vocalists/keyboardists), with and without piano accompaniment. Those in the experimental group were told that most people play sharp and their performance, too, was consistently sharp. The subjects in the control group were simply asked to play as accurately as possible. Following performance, each subject went to a different room to complete the perception task. They were asked to adjust the pitch of their scale performances using a variable pitch tape recorder dial. Results indicated a tendency toward sharp intonation. In addition, subjects’ perception of intonation was significantly sharper and less accurate than their performed intonation. Geringer also found that the perception of intonation of unaccompanied scales was significantly less accurate than the perception of intonation of accompanied scales and the performed intonation of both accompanied and accompanied scales. It was also found that accompanied scales were performed and perceived with significantly less absolute deviation, with a tendency to be less sharp than the unaccompanied scales.

2. Aural Models

Since the late 1950’s, researchers have devoted attention to tape-recorded aural models to determine how aural models affect aural comprehension (Spohn, 1959), harmonic dictation (Daniels, 1964), sight-singing (Kanable, 1969), vocal performance

(Arant, 1970), and musical performance (Rizzolo, 1969; Anderson, 1981). Charles Spohn

(1959) completed one of the earliest studies using pre-recorded material to improve aural comprehension skills. He found that participant’s aural skills were more accurate and learned more efficiently compared to those in traditional classroom situations. These findings led to the use of similar programed instruction in the music curriculum at the university (Tromblee, 1972).

Kanable’s (1969) developed a self-instructional method to improve sight-singing skills in high school students using a tape recorder. When compared to those with traditional instruction, results showed no significant differences, suggesting that students who were motivated could learn sight-singing skills via a taped program.

Rizzolo (1969) used a taped program to improve sensitivity to intonation among thirty-eight university music students. The purpose of his study was to develop a tool that could be used to increase a conductor’s ability to correct intonation errors in an ensemble setting. The study used two groups: (1) the control group, which received traditional music training, such as solo playing, private lessons, small and large ensemble rehearsals, and (2) the experimental group which added the taped instruction created for the study.

The taped instruction consisted of a small professional ensemble performing simple harmonies with one voice performed purposely slightly out of tune. Participants were

20 provided with notation and were asked to indicate which voice was either sharp or flat.

While Rizzolo noticed some positive correlations in the scores of the group using taped instruction, the results were not statistically significant.

Anderson (1981) studied the use of tape-recorded aural models with sixth-grade clarinets during home practice. Compared with the control group of those students who had no help with home practice, he found that the aural models had no significant effect on student performance or sight-reading skills.

The effect of tonal pattern training on intonation of sixth grade band and orchestra students was conducted by Mora (2007). In this experiment, teachers in band and orchestra classes modeled two short tonal patterns for eleven weeks as part of a daily warm-up. The control group warm-up did not include tonal patterns. Results of the posttest of the warm-up with tonal pattern group showed significantly higher intonation scores for band students and improvement, though not significant, for orchestra students.

She concluded that modeling tonal patterns as a part of daily warm-up activities within the orchestra and band classroom could have a positive effect on intonation accuracy.

3. Preference for tuning systems

In music, pitch accuracy is measured according to particular standards, also known as musical temperaments or tuning systems. These standards assign each musical pitch a precise audio frequency (e.g. Benson, 2008; Coy, 2012; Latten, 2003). The frequencies are mathematically derived from whole number ratios or other means

(Benson, 2008). There are many temperaments or standards that have been used throughout history; the most common examples of temperaments include Pythagorean,

just intonation (or pure intonation), and equal temperament (Loosen, 1993; Mason,

1960). Noting that many string players utilize Just Intonation when performing alone

(Carman, 1936), studies have shown that their performances generally do not strictly

adhere to one particular standard. Instead, performers often use a mixture of

temperaments depending on context (e.g. Greene, 1937; Kantorski, 1986; Nickerson,

1949a; Ostling, 1974; Sogin, 1989; Yarborough & Ballard, 1990).

Due to the nature of string instruments and their fixed open string tuning,

preferences for tuning systems have been a topic of debate for many years. Carman

(1936) studied two commercial phonographs of professional violinists performing in the

key of G melodic minor and observed how closely the performers adhered to either just

or equal temperament. He found that, in general, both artists adhered to just intonation

with exceptions on in certain instances where Pythagorean intonation was used to

enhance certain expressive qualities. The methods in this experiment required an

advanced knowledge of electronics, mathematics, and acoustics. Due to the limited

technology at the time, pitch accuracy measures were complex and difficult to assess.

Paul Green (1936) studied six violinists in unaccompanied performances to determine whether they systematically expand or contract musical intervals compared to a particular tuning system. Frequency data was collected and as was data for a variety of different intervals. Green found that the violinists did not strictly adhere to just or equal temperament. His study found that the intervals of major seconds and major thirds were expanded, while minor seconds and minor thirds were contracted. Perfect fourths fell

22 within the theoretical scale values. Similar to Carman’s study, Green concluded that the average of all five intervals approximated Pythagorean intonation.

Nickerson (1949a, 1949b, 1949c, 1950) examined advanced string players’ conformity to a particular tuning standard and found in both solo and ensemble performances of the same melodic material a preference for Pythagorean intonation slightly dominated. He claimed that there was a general assumption that musicians were being culturally conditioned to tune to equal temperament as taken from a musical keyboard. His findings refuted this generalization (1949).

Bisel (1987) examined the preference of four tuning systems (Pythagorean tuning, just intonation, one-quarter comma meantone tuning, and equal temperament) by playing four melodic and four harmonic computer-generated examples to college music majors and non-music majors. For melodic examples, he found that music majors’ tuning preferences, in ranked order, were: (1) Pythagorean tuning, (2) equal temperament, (3) one-quarter comma meantone; and (4) just intonation. All of differences on both the melodic and harmonic material were found to be significant at the p < .05 level. For harmonic examples the preferences ranked differently: (1) one-quarter comma meantone tuning, (2) equal temperament, (3) Pythagorean tuning, and (4) just intonation. The differences among tuning preferences in harmonic examples were also significant except the difference between Pythagorean tuning and just intonation.

4. Effect of Age, Experience, and Training

It has been shown that age, experience, and training impact the ability of subjects to discriminate and match pitch (e.g. Geringer, 1983; Hopkins, 2014, in press; Madsen,

Edmonson, and Madsen, 1969; Morrison, 2000; Yarbrough, Karrick, & Morrison, 1995;

Yarbrough, Morrison, & Karrick, 1997).

Geringer (1983) studied pitch-matching and pitch-discrimination abilities of 144 preschool and fourth grade children. After creating ability-based groups using a pitch discrimination test, he found significant differences in pitch-matching skills between age groups, but not between the created ability groups. He also stated that pitch-matching ability may be influenced by a students’ physical maturity and pitch discrimination skill may be a function of learning (p. 98).

Two hundred subjects, ages seven through adult, participated in pitch discrimination a study by Madsen, Edmonson, and Madsen (1969). The study measured subjects’ ability to determine slight variances in pitch. It was found that the ability to discriminate was impacted by age, but also by the amount of musical training.

Interestingly, the researchers found that younger students judged pitches “incorrectly and sharp,” while older subjects demonstrated a “proclivity toward flatness” (p. 1468).

Yarbrough, Karrick, & Morrison (1995) investigated the knowledge of directional mistunings on the tuning accuracy of beginning and intermediate wind players. The study utilized 197 instrumental wind players to complete two tasks: (1) a performance task: tune to a prerecorded stimulus pitch, F or B-flat, with their own instrument, and (2) a perception task: turn the tuning knob of a variable pitch keyboard. Students were randomly distributed into three groups: (1) those that were told the tuning pitch was mistuned sharp; (2) those that were told the tuning pitch was mistuned flat; and (3) those that received no information regarding the mistuning. Results indicated that years of

24 instruction significantly affected subjects' tuning accuracy and no significant differences were found due to treatment, instrument type, or tuning pitch. Additionally, it was found that pitches mistuned from above provided generally sharp responses, those mistuned from below provided flat responses. As experienced increased, data showed that students made improvement in both performance and perception accuracy. Pitch responses tended to err in the sharp direction in students with more experience.

A similar pitch perception and performance study by Yarbrough, Morrison, &

Karrick (1997) investigated if experience, private instruction, and knowledge of directional mistunings effects tuning performance and perception. The researchers asked

113 high school wind players with over five or more years of experience to perform tasks similar to those in the previous study (Yarbrough, Karrick, & Morrison, 1995).

Experiment groups were also identical to the 1995 study. Of the 113 students, 42 received private lessons and results indicated that a participant’s participation in private instructions had a significant effect on the tuning accuracy and pitch perception. There were no significant differences due to the treatment or participant’s years of experience, and there was no relationship between performance and perception responses. As found by other researchers, participants performed significantly sharp, regardless of experience, private instruction, or direction of the original mistuning.

Morrison’s (2000) study examined the effect of age and experience on intonation accuracy. Implementing two experiments, Morrison tested band students in elementary, middle school, junior high, and high school, each with varying amounts of instruction.

Participants were asked to tune to a prerecorded tuning pitch, and then perform along

25 with a prerecorded four-measure melody. The tuning pitch and selected target pitches were measured for cent deviation. Morrison found correlations between pitches from the melodic sequence, but not between the tuning pitch and melody pitches. He also found that participants performed sharp across both experiments. In addition, accuracy and sharpness increased among students who were more experienced.

5. Effect of Stimulus Type

There have been numerous studies investigating the effect of stimulus type (e.g.

Corso, 1954; Cassidy, 1989; Cummings, 2007; Alexander, 2011; Byo, Schlagel & Clark,

2011; Worthy, 2000). Research suggests that the ability to judge intonation may be affected by the similarities or differences in timbre of the comparison pitch (Geringer &

Worthy, 1999; Worthy, 2000). It is commonplace for instrumental music teachers to broadcast a reference pitch for the purpose of tuning. There are many ways for a reference pitch to be produced. Teachers may choose to use an electronic tuner, a pitch fork, a pitch pipe, a variable-pitch instrument, or a fixed-pitch instrument, such as a piano, to provide the tuning stimuli (Lamb & Cook, 2002). Stimuli can be categorized into two main types: pure-tones and complex tones. Pure-tones contain the fundamental frequency with few, if any, overtones and are produced by electronic tuners or computer synthesis. Acoustic instruments produce complex tones that are comprised of the fundamental frequency along with overtones, which provide the characteristic tone of the particular instrument (Alexander, 2011).

A study of unison tunings by Corso (1954) investigated two factors of tuning unison intervals: (1) the harmonic structure of the reference tone, and (2) the method of

presentation (simultaneous or successive). Corso studied four different musical

instruments using five difference reference pitches and found that neither factor had a

significant impact on tuning accuracy. He hypothesized that unison tuning of musical instruments is dependent upon pitch-matching judgments rather than the discrimination

of beats from a reference tone.

Geringer & Worthy (1999) found participants rated stimuli that were relatively

brighter in tone quality as sharper in intonation, and conversely, stimuli of relatively

darker tone quality were judged to be flatter in intonation. The study utilized high school

students, college music majors and non-majors who listened to electronically altered

recorded tones played by clarinet, trumpet, and trombone.

Worthy (2000) found that varying tone-quality conditions, those labeled bright or

dark, had significant effects on the perception and performance of pitch. His study took a

different approach to stimulus by examining the effects among the changes of tone

quality on the perception and performance of pitch. Subjects judged tones as bright in

tone quality sharper in pitch than reference tones and also performed sharp when

matching bright stimuli. Subjects judged tone as dark in tone quality when pitch was

flatter than the reference tones and also performed flatter when matching dark stimuli.

Byo, Schlegel & Clark (2011) examined the effects of the tuning stimulus timbre

and octave. Researchers measured tuning accuracy in 72 high school wind players by

providing reference pitches performed by flute, oboe, clarinet, and tuba. Results indicated

no significant difference due to instrument. However there were differences due to

27 stimulus. Students performed more out of tune when tuning to the tuba, as opposed to the other instruments.

6. Effect of Direction

The effects of performance direction on the intonation accuracy of scalar passages and melodic intervals have been thoroughly investigated (Edmonson, 1972; Duke, 1985;

Geringer, 1978; Kantorski, 1986; Madsen, 1963, 1966; Mason, 1960; Papich & Rainbow,

1974; Salzberg, 1980; Sogin, 1989). When performing musical tasks, researchers have found pitch deviation tendencies toward playing sharp (e.g. Madsen, 1962, 1966, 1974;

Madsen, Edmonson, & Madsen, 1969; Madsen & Geringer, 1976; Madsen, Wolf, &

Madsen, 1968; Mason, 1960; Papich & Rainbow, 1974; Salzberg, 1980; and Small,

1937); however, generalized pitch accuracy findings were not consistent and results varied depending the assigned performance task. Duke (1995) refuted these findings; he found that college students showed some degree of flatness in their performances

Madsen (1963, 1966) tested the effect of scale direction on intonation accuracy and found descending scales were performed more accurately descending than ascending by college-level violin, voice, and piano majors. College wind players who were informed of a sharpness inclination in the performance of ascending scales subsequently performed with increased sharpness (Geringer, 1978). There were concurring results toward sharpness in research that studied the intonation of string instrumentalists (e.g.

Kantorski, 1986; Papich & Rainbow, 1974; Sogin, 1989; and Salzberg, 1980) that will be described in detail in the next section

Conversely, Mason (1960) and Duke (1985) both found no difference in intonation accuracy between ascending and descending directions. Duke (1985) observed that wind instrumentalists' intonation accuracy of melodic intervals was not significantly affected by direction. Duke studied junior high school, high school, and college undergraduates wind instrumentalists' accuracy of selected musical intervals and examined intonation patterns in both melodic and harmonic contexts. Subjects performed various diatonic intervals both melodically and harmonically. Results indicated no significant differences in overall intonation accuracy in relationship to performed ascending and descending directions or among the tested intervals. There were significant differences among flatness and sharpness with the direction of the intervals. When subjects descended, the intervals were performed slightly sharper; when subjects ascended, intervals were performed slightly flatter with younger subjects performing slightly sharper compared to more experienced musicians. Kantorski (1986) also found that arpeggios were performed with less accurate intonation than scales and melodies.

Yarbrough and Ballard (1990) observed that college-age string instrumentalists performed increasingly sharp when ascending.

Edmonson (1972) found that college music majors sang ascending melodic intervals significantly more accurately than descending ones. He measured intervals such as the perfect fourth, perfect fifth, major sixth, and minor third, each starting on f-sharp.

No significant interaction was found in the interval direction, however, Edmonson made several noteworthy observations. In the two subjects with perfect pitch, both performed below the composite mean of the group. In addition, he did not control for gender as a

29 variable. His findings revealed that males underperformed females, claiming that certain situations might have been the cause, and warned that his results should be viewed with caution.

7. Effect of Accompaniment/Harmonic Context

Harmony can provide the performer with an aural reference that may enhance the ability to make decisions about the accuracy of the performed pitch (Gordon, 1997;

Schleuter, 1984). Researchers have examined the impact of harmonic accompaniment on the development of instrumentalists' intonation (e.g. Sheldon, Reese, & Grashel , 1999;

Schleuter, 1997) while others have investigated whether pitch is better heard and understood in a melodic context rather than in isolation (Fyk, 1994; Rakowski, 1990).

Corso (1954) found that neither harmonic structure nor method of presentation of the reference tone had a significant effect upon tuning accuracy. This confirmed his hypothesis that tuning instruments is dependent on pitch-matching ability rather than the discrimination of beats. Corso’s study measured two factors that relate to the tuning of unison pitches: (1) the harmonic structure of the reference tone, and (2) the method of presentation of the reference tone during the tuning process.

Some research suggests that accompaniment helps develop a sense of tonality

(Krumhansl, 1979, 2001). Tonality is related to intonation in that musicians can adjust pitch slightly to better fit within the context of a musical scale or chord. These adjustment are subjective, artistic decisions made by the performer. For instance, “Musical listeners extract a pattern of relationships among tones that is determined not only by pitch height and chroma, but also by membership in the major triad chord and the diatonic scale

30 associated with the tonal system of the context” (Krumansl, 2001, p. 346). Scheluter

(1997) stated that tonality is a learned skill that requires tonal memory. He discussed the common thread of tonality in all Western music and described it as “a ‘glue’ that provides continuity and expectation the music of our culture” (p. 42).

Positive effects on performance quality when using live piano or intelligent digital piano accompaniment for a period of 6 weeks were found by Sheldon, Reese, & Grashel

(1999). Researchers utilized 45 undergraduate music majors playing secondary instruments and created three groups: (1) live accompaniment, (2) intelligent digital accompaniment, and (3) no accompaniment. Subjects were rated for performance quality in six categories. Students performed better when playing the solo twice in a row, compared to playing solo and then with either piano or intelligent accompaniment, showing the importance of consistency in performance condition.

Cummings (2007) examined instrument type (violinists and flutists) who played pitches along with four different harmonic contexts: in unison (pitch matching), a perfect fifth (performing with the root), triadic fifth (performing with the root and major third), and triadic third (performing with the root and fifth). When comparing instrument types, he found that violinists played more accurately than flutists, and also found a significant difference in the triadic third context, with violins playing almost seven cents flatter than flutists.

The use of a tonal center or final resting tone to develop a student’s sense of tonality and improve instrumentalists' intonation was thoroughly discussed by Schleuter

(1997). He recommended a variety of techniques that reinforce the ability of students to

31 become more familiar with listening to the tonic pitch. These exercises include identifying the tonic while singing or playing the a tune or phrase, listening to recordings or other performances, having students play along with a melody only when the tonic note is heard, and counting the number of times the tonic pitch is heard.

It is interesting to compare the effects of accompaniment because of the discrepancies in results. English (1985) showed that more piano accompaniment hinders intonation gains, while Sheldon, Reese, & Grashel (1999) found that continuous use of live or intelligent digital piano showed positive gains in intonation accuracy. The present study utilized simple pitch matching and tonic drones that might be considered a lighter accompaniment and provide a players with reference point for intonation without being overbearing.

8. The Effect of Stimuli

Research has explored the effect of stimuli on tuning accuracy. Varying factors of stimuli include whether the sound is produced acoustically or via synthesis, whether it matches or contrasts the participants' response, the duration, and the relative octave of the tuning stimuli. It can be debated which stimulus, acoustic or synthesized, is more beneficial to real-world tuning applications. Although there are some studies that have used acoustic stimuli (e.g., Duke, 1985; Ely, 1992; Geringer, 1983; Geringer & Witt,

1985; Geringer & Worthy, 1999; Madsen & Geringer, 1999; Yarbrough, Green, Benson,

& Bowers, 1991), a synthesized stimulus provides a particular advantage, allowing the researcher complete control over frequency, amplitude and overtones (Cummings, 2007).

The timbre of tuning stimuli can impact a musician’s ability to perceive and tune pitch. Cassidy (1989) concluded that tuning pitches with the same timbre had no advantage over tuning tones with different timbres. The sawtooth waveform is an approximation of the wave shape produced by bowed string instruments (Benson, 2008;

Platt & Racine, 1985), with fewer complex overtones. A study by Platt and Racine (1985) also revealed greater tuning accuracy when using sawtooth wave stimuli compared to sine waves. Sine waves were found to cause intonation inaccuracies when tuning to an upper octave (e.g. Cassidy, 1989). Cassidy’s (1989) study found that participants tuned most accurately to a same octave pitch using a sawtooth wave and to a lower octave pitch when the sine wave and square wave were used.

Several studies confirm the findings that tuning accuracy improved when participants were provided complex versus simple tones, such as sine waves (Sergeant,

1973). Spiegel & Watson (1984) found that square waves easier for musicians and nonmusicians to discriminate when compared with sine waves, particularly in frequencies below 1768 Hz. Sergeant (1973) deemed pure tones (sine waves) as unsuitable for use in free field group tests, due to the varying level of signal intensity, a factor that directly relates to this study and the choice of tuning stimuli. Rakowski (1990) found more accurate responses to simple tones under certain conditions, however other researchers

(e.g. Corso, 1954; Ely, 1992; Price, 2000) did not find significance in tuning accuracy when comparing complex and simple timbres.

Byo, Schlegel, & Clark (2011) found that students were more successful tuning to a pitch that matched their register over a reference pitch that was below their pitch.

Simple timbres, such as sine, square, and sawtooth waves, are generally more accurately recognized than complex sounds that are rich in overtones (Fletcher, 1934).

The duration of a stimulus can impact to discriminate and match pitch. Turnbull

(1944) found that as the duration of a stimulus tone decreases, precision of discrimination diminishes. These findings were confirmed by and furthered by Fyk (1985, 1987) who studied the duration of tones necessary for satisfactory pitch matching precision using university music students. She found that the participants could accurately match pitch with tones that were less than a second in duration. In addition to the duration of the stimulus tone, there are other factors that affected the outcome, such as ear training courses, and frequency of the pitch. As the frequency of a pitch rises, a shorter duration is required for satisfactory pitch matching performance (Fyk, 1987).

9. Impact of Technology

Technological developments have played an important role in advancing the measurement of intonation, allowing sound to be analyzed more accurately and efficiently then ever. In early studies, magnetic tape recorders were used to capture performances. These devices were less accurate in capturing nuance than current digital devices due to their noise and distortion levels. Prior to digital readouts, some researchers had judges watch the measurement needle on electronic tuners (e.g. Yarbrough and

Ballard, 1990), however this method still left some margin for error due to human judgment. Since the early 1990’s, researchers have used digital readouts to facilitate and verify their results (e.g. Britten, 1993; Ely, 1992; Yarbrough, Karrick, & Morrison, 1995;

Yarbrough, Morrison, & Karrick, 1997; Karrick, 1998; Morrison, 2000; Worthy, 2000;

Mongeon, 2004; Cummings, 2007; and Ballard, 2011).

Yarbrough and Ballard (1990) used judges who watched the needles on electronic tuners and found observation reliability to be about 85%. Since the judgment of intonation was based upon one’s visual interpretation of the tuner display, results were less reliable. As technology improved, researchers turned to digital devices to provide readouts of frequency (e.g., Brittin, 1993; Duke, 1985; Ely, 1992; Yarbrough, Karrick, &

Morrison, 1995; Yarbrough, Morrison, & Karrick, 1997).

Meyer (1993) developed a computer system to discover how pitch discrimination in violinists could improve when aural perception is reinforced with visual perception.

While the computer system may pose to be a valuable tool, the document focuses more on the development of the computer system and lacks the inclusion of actual testing or measurements of the system’s accuracy, validity, or reliability.

Recent technological advances, using personal computers and analysis software, have made frequency measures easier and more reliable. The most recent intonation studies have used this technology (Ballard, 2011; Cummings, 2007; Karrick, 1998;

Morrison, 2000; Worthy, 2000). The present study made use of computer-based digital audio frequency analysis technology with software that has not appeared in published research. Intonia (2008), a java-based computer application developed by Jerry Agin, graphically displays pitch and provide rapid cent-deviation calculations. This feature allows the researcher to quickly analyze performances, measuring cent deviation with unparalleled accuracy.

While technology has improved the way researchers measure intonation accuracy, it must be noted that overuse of an electric tuner or device during practice may also hinder a student’s progress with intonation. Griswold (1988) states that the visual reading of electronic tuners is fine as a first step but their overuse may divert students away from developing their aural skills. Coy (2012) agreed with Griswold and also pointed out that most tuners only support equal temperament, thereby limiting real-world applications to intonation adjustment.

Technological tools available to examine pitch perception have evolved considerably over the past century. Michael Hopkins (in press) sites the methodological approach by Burns & Ward (1978) coining the term “method of adjustment” (MOA) that describes how research participants have been asked to adjust pitch. Many studies have presented participants with a fixed reference tone, and have been asked by researchers to manually adjust a second tone using a lever, slider, or knob controller to form an interval along with the fixed tone. Pitch perception using various MOA have been examined by many researchers (e.g. Elliot, Platt & Racine, 1987; Burns & Ward, 1978; Hopkins, in press; Moran & Pratt, 1926; Ward, 1954; and Vurma & Ross, 2006). Studies by

Demorest (2001), Demorst & Clements (2007), Morrison (2000), Yarborugh, Karrick, &

Morrison (1995), and Yarbrough, Morrison & Karrick (1997) have used various MOA to examine relationships between pitch perception and music production tasks.

String-Specific Intonation Studies

Due to the susceptibility of string instrumentalists to make intonation errors, many researchers chose to focus on string participants only for pitch perception and intonation

36 accuracy (e.g. Geringer & Witt, 1985; Kantorski, 1986; Loosen, 1993; Salzberg, 1980;

Smith, 1995; Sogin, 1989; Hopkins, in press). String participants have been asked to perform variety of tasks such as tuning open strings (Geringer and Witt, 1985; Alexander,

2011; Hopkins, in press); performing scalar passages, (Geringer, 1978, Salzberg, 1980;

Kantorksi, 1986; Loosen, 1993; Yarbrough & Ballard, 1990); playing arpeggios

(Salzberg, 1980); playing melodies (Salzberg, 1980) and playing harmonies, such as double stops (Salzberg, 1980).

A variety of pedagogical models and strategies for performers of string instruments have been researched to determine their effectiveness on intonation. These involve kinesthetics (Jacobs, 1969), hand position on the instrument (Cowden, 1972), the use of finger placement markers (Smith, 1985, 1987; Bergonzi, 1997), the use of piano accompaniment (English, 1985), harmonic approach (Maag, 1974), aural vs. visual approach (Meyer, 1993; Nuñez, 2002), and physical exercises (Mongeon, 2004).

Jacobs (1969) found that beginning string students with no prior musical training tended to rely solely on their kinesthetic and tactile perceptions to correct pitch errors, rather than aural skills. The study utilized two groups of adolescent violinists, those with and without previous musical training. Participants with music training were “highly disturbed whenever they played out of tune. Their attention bore immediately upon tones and not upon the movements by which the tones are produced” (p. 114). Jacobs’ research should provide a cautionary measure to teachers about teaching “the learning of means,” or the physical actions of playing violin rather than focusing on the aural aspect of intonation development.

Cowden (1972) explored beginning violinists’ intonation accuracy using the comparison of a first- and third-position approach, and found that both approaches showed similar gains in pitch accuracy. First position is the most common position used when teaching beginning students, while third position, where a player’s left hand is placed higher on the fingerboard, is traditionally reserved for advanced study. Those in the control group played in first-position only and the experimental group played in third- position.

Maag (1974) compared the effects of diatonic and pentatonic approaches on beginning string students' intonation with 146 fourth- and fifth-grade beginning string students. After six months of instruction, it was found that the pentatonic group had significantly improved performance pitch accuracy, as judged by a panel of experts.

Salzberg’s (1980) study examined intonation accuracy of 50 college-age string players performing four musical tasks (a scale, an arpeggio, double stops, and a melody) in two conditions, blindfolded and not blindfolded. After analysis, she found that performances were generally sharp and attributed this to possible errors in the referenced research. Salzberg found that the melody was performed with the most accurate intonation and the arpeggio was the least accurate. No significant difference was found in regards to the visual stimulus (blindfolded versus not blindfolded). Subjects were grouped by instruction type: verbal feedback, tape-recorded playback, model performance, free practice, and no instruction. Those in the verbal feedback group were told if they were sharp, flat, or in-tune. In the tape-recorded playback group, subjects listened to their performances after the first set of trials. The model performance group

were played a tape recording of a professional player. The free performance group had

one minute to practice between pairs of trials, while the control group did not receive any

instruction. Citing previous research (Greene, 1937; Nickerson, 1949c) favoring the use

of Pythagorean temperament in string playing, Salzberg chose to use this tuning system

as her standard for measurement. The use of Pythagorean temperament is unique when

compared to a majority of previous intonation research.

A tuning perception and production study by Geringer and Witt (1985) found that experienced players demonstrated more frequent agreement between their tuning and verbal judgment, however neither group showed strong agreement between the two tasks.

Researchers asked 60 high school and 60 college students to tune three different A string pitches (A 440 Hz., 25 cents sharp, and 15 cents flat) and then respond with a verbal assessment of the accuracy of the tuning stimulus.

The use of piano accompaniment with beginning string players has long been a practiced used by practitioners, however has not been shown in research to improve intonation. In Elizabeth Green’s seminal text Teaching Stringed Instruments In Classes

(1966), she strongly recommends using piano accompaniment with beginning level string

players to improve intonation. She does provide words of caution instructing teachers to

guard against playing too loudly as not to drown out the students’ sound.

English (1985) studied the effect of piano accompaniment on intonation and

rhythmic accuracy on beginning string classes using three groups: those that used piano

accompaniment 100 percent of the time, 50 percent of the time, and no piano

accompaniment. The participants who used no piano accompaniment made the greatest,

39 statistically significant gains in intonation and rhythmic accuracy. Interestingly, the group that used piano accompaniment 50 percent of instructional time were superior to those that used the accompaniment 100 percent of the time, thus showing a significant relationship between the absence of piano accompaniment and performance achievement.

Kantorski (1986) studied the effects of accompaniment and register in 48 college- aged string players (12 each of violinists, violists, cellists, and double bassists) and found that performers played with greater pitch accuracy in lower registers. Subjects performed accompanied whole-tone scalar passages in upper and lower registers. Kantorski measured the combined absolute cent deviation values of tetrachords rather than individual pitches. It was also found that subjects were consistently sharp, significantly so while descending and in upper registers.

Smith’s two studies (1985 and 1987) investigated the use of fingerboard placement markers (FPMs). She found that FPMs made no significant difference in intonation accuracy when measured by a panel of judges using a five-point Likert scale.

The 1985 study used 18 music education majors who were enrolled in a string techniques course; the 1987 study used fourth- and fifth-grade string students enrolled in large-group string classes. Both studies divided participants into three groups; those that used FPMs for the entire treatment period, 50% of the time, and no FPMs.

Bergonzi’s (1997) findings refuted the results of Smith’s (1985, 1987) studies involving finger placement markers. He found that students using FPMs made significant gains in intonation accuracy. In addition to FPMs, Bergonzi also studied harmonic context with sixth-grade beginning string students, measuring differences in left-hand

40 technique, intonation, and general performance skills. Students who utilized harmonic accompaniment (synthesized piano and a drum track) during instruction and practice also made overall intonation performance gains.

Sogin (1989) researched a string player's adjustment of intonation in ascending and descending pitch sets. He found that subjects played with increased sharpness at the end of the pitch than at the beginning. Sharpness increased when performing descending patterns, and the pitches were played sharp both with and without vibrato. Forty-eight college and professional string instrumentalists (12 each on violin, viola, cello, and double bass) were measured by playing an unfamiliar pitch set (E-flat, F, G-sharp, A- sharp). Sogin recorded subjects and measured deviation between the lowest and highest recorded frequencies; a method that produced two data points for each pitch. Sogin is assessing pitch precision, rather than pitch accuracy as in other studies within the literature. This method may be less controversial, in terms of personal judgment and the adjustment to a particular temperament, than trying to argue at what point a performed pitch becomes out-of-tune.

Yarbrough & Ballard (1990) measured the effects of accidentals, scale degrees, direction, and performer opinion on intonation. Results indicated that students tended to play sharp, regardless of direction. Although not significant, students played more out of tune when ascending than descending (p.20). Thirty-nine string players (18 violinists, 8 violists, 9 cellists, and 4 bassists) were asked to play twelve five-note scalar patterns. The patterns were arranged so that the notes F-sharp, B-natural, and B-flat would serve as leading tones and thirds of a scale. All twelve patterns were played slowly ascending and

41 descending. Observers watched the needle of a tuner to calculate cent deviation of the first note. To obtain data on the relationship of the following four notes, the deviation score of the first note was added or subtracted to the note. This method of calculation then marked the first note of each pattern as “in tune” and the intonation of the subsequent notes was related to the intonation of the first.

Loosen (1993) studied eight professional violinists and their pitch accuracy using an unaccompanied three-octave C major scale finding a preference toward ET and

Pythagorean temperament over Just Intonation. Rather than using the familiar model of measuring frequencies of performed pitches, the study measured interval size between performed pitches and how the performances conformed to particular tuning systems. He also found that the tonic note (C) was adopted as an “absolute cognitive reference point”

(p. 525).

A study by Nuñez (2002) found no significant differences when comparing aural versus aural/visual teaching methodologies. Using a pre-/post-test design to collect absolute cent deviation from equal temperament, Nuñez measured pitch accuracy of seven pitches performed by 68 second-year, seventh grade, violinists and violists.

Mongeon (2004) found that implementation of routine left-hand stretching exercises improved the intonation accuracy and technical facility of upper string instrumentalists. Sixty students, all with 3 years or less of playing experience, were either randomly assigned to the experimental group, which performed routine left hand stretching exercises prior to playing, or the control group, which did not receive any physical exercises. Students were evaluated on pitch accuracy and technical facility in a

42 pre-/post-test format. Intonation was measured by calculating absolute cent deviation from equal temperament. Judges analyzed videos of students playing, without sound, to measure technical facility.

Cummings (2007) explored the effects of instrument type, stimulus timbre, and harmonic context (i.e. diatonic triads) on tuning accuracy of college-level violinists and flautists. Participants performed sustained tones along with prerecorded accompaniment stimuli of various timbres. Results indicated that there are some independent associations regarding tuning accuracy and factors of instrument type, stimulus timbre, and harmonic context. Consequently, even experienced musicians react differently to these factors.

Alexander (2011) found no significant differences when comparing two types of stimuli. His study measured open A-string tuning ability among 139 high school string orchestra, students. He examined two different stimuli, proximity to the stimuli, and possible differences between string instrument types. Significant differences were found on the variable of distance, particularly in the tuning of cellists who were farthest away from the tuning source.

Hopkins (in press) found a moderate relationship between perceptual accuracy and instrument tuning accuracy using a self-developed instrument for assessment, the

Violin Tuning Perception Test. This study involved open-string tuning skill of middle school students. Hopkins also found that students more frequently tuned strings flat and that G-string tuning was least accurate.

Practitioners’ Recommendation of Drone Use

Many practitioners have advocated the use of drones as a tool to improve

intonation (e.g. Alexander, 2008; Ball, n.d.; Colley, 1993; Curry, 2011; Flunker, 2010;

Griswold, 1998; Watkins, 2004), however there are no research studies to support these

claims. Major string practitioner journals such as the American String Teacher, String

Magazine, and The Strad have published articles from teachers and researchers that

instruct others to use drones or other simliar reference pitches to develop inotnation

skills. These authors have suggested the use of drones based on anecdotal evidence.

Watkins (2004) states that "Practicing with a drone becomes an excellent way for

students to work because they are more attuned to the variety of consonant relationships

and much less likely to reject dissonant relationships as sounding bad" (p. 88). Hopkins

(2012) recommends using an electric tuner as the reference pitch and says “Playing scales

against a sustained tonic drone pitch can also be very useful for developing intonation

awareness” (p. 26).

The use of drones in an ensemble setting was advised by Flunker (2010) who

stated that drones can be used to train the ear for purposes of intonation and tone

production to achieve a “complete sound” (p. 36).

Curry (2011) encouraged students to analyze the problem of intonation by using recordings of drones when practicing scales, particularly so that they may check intonation of the consonant scale degrees (tonic, third, fourth, fifth, and sixth).

To increase tuning sensitivity and help pitch become more stable and reliable,

Coy (2012) recommended slow, repetitive practice with a drone pitch, beginning with

scales and scalar patterns to “train the brain and muscles with typical adjustments in the

context of each key” (p. 46). He stated that once the scales were mastered, that more

44 complex material, like etudes, should follow.

In addition to the published articles in practitioner journals, the availability of commercial drone recordings suggest that their use is widespread. The Tuning CD by Ball

(n.d.) is a compact disk of two-minute drones. The drones provided on The Tuning CD are synthesized and contain a pitch’s fundamental along with various harmonies that may aid tuning, such as a perfect. In his instruction manual, Ball claimed that playing with drones can fine-tune intonation skills and improve the ability to play all intervals with faster adjustment speed and more confidence. Ball also stated that modes and scales can be heard and understood with greater clarity by playing with drones. He recommended playing scales and modes with tonic drones and also advised using a drone based on the dominant (fifth scale degree) pitch. An example of this technique would be to perform and F-major scale while sounding a C pitch.

Cello Drones, by Marcia Sloane (2003) contains drones on all 12 chromatic pitches to be used for “tuning and improvisation in major, minor, modal, and scales of your own creation.” Like The Tuning CD, the tracks are rich, complex tones. Sloane stated that each track consists of a total of 5 sustained tones: 3 octaves of the tonic (the fundamental) and 2 octaves of the dominant (fifth scale degree). The cello sounds have been somewhat manipulated through software to ensure pitch accuracy.

Another commerically-available product, Chromatic Violin, is a CD of violin drones by Apprentice Music (2014). The website claims that tuning to another violin is vastly superior to a tuner and the “artificial sound from a synthesizer.” The author recommends using the drones when practicing scales and repertoire. The author also

states that, after practicing, the user will be able to hear the drone even after it has been

turned off, cliaming that it will improve the user’s sense of audiation.

Colley’s (2015) Tuneup Intonation Training System was developed to “enable any

musician, no matter the natural aptitude, to develop a firm grasp of pure, perfect

intonation.” The system uses a method for ensemble directors to help improve a student’s

ability to hear pure intervals. The first exercise in the system uses a tonic drone and

includes pedagogy to allow students to associate how the pitch of each note fits and

relates to the tonic in every key. The system develops with a series of more complex

exercies that allow ensemble directors to intergrate the system into their daily routines.

Implications for the Current Study

The above research displays some of the complexities with intonation, the

difficulties in achieving clear results through research, and the many factors that affect intonation perception and performance. The sheer quantity of literature demonstrates the importance of intonation in the practice and performance of music.

While the related literature is vast, there are still voids. In particular, there are not

studies that investigate the effect of a drone on intonation accuracy on beginning-level

string instrumentalists. This lack of research literature on drones is jarring, given the

numerous recommendations of their use by highly qualified practitioners. Results of a

systematic study on the use of drones to improve the pitch accuracy of beginning string

students may help pre-service and licensed string teachers in the schools as they teach

their students to play in tune accurately.

Chapter 3: Research Design and Methodology

Purpose of the study

The purpose of the study was to determine if practicing scales with a tonic drone audio accompaniment might increase the pitch accuracy of beginning-level violin and viola players. There were three accompaniments used: pitch-matching (PM), tonic drone

(D), and pitch matching with a tonic drone (PMD).

The research questions related to the purpose of the study were:

1. Do beginning string students play with greater pitch accuracy following

training with tonic drones compared to pitch matching alone, or pitch

matching with tonic drone accompaniments?

2. Does the pitch accuracy of students who have learned to play scales initially

with the use of an accompaniment track change once students play the same

scales without an accompaniment track?

3. Are intonation tendencies toward sharpness or flatness for particular scale

degrees different for students when they play with a drone accompaniment

compared to when they play without a drone accompaniment?

4. Do students more frequently attempt to adjust the accuracy of their pitches

when playing with a tonic drone compared to those who use pitch matching

alone, or pitch matching with tonic drone accompaniments?

5. Do students adjust the intonation of their pitches to be more accurate when

playing scales with a drone accompaniment compared to pitch-matching

alone, or pitch matching with tonic drone accompaniments?

Participants

This quantitative study used a quasi-experimental pre/posttest design. The participants of the study were 50 second-year, seventh-grade, violinists and violists enrolled in their school orchestra programs. For the purposes of this study, a beginning violinist/violist was defined as having less than two years playing experience, regardless of age. The design of the study intended for procedures to take place in a string/orchestra classroom environment. Participants were selected from three middle schools within a large, suburban public school district in the southeast. Each school had two seventh-grade orchestra classes and participants were randomly chosen from those who choose to and were qualified to participate. To qualify, students must have had a minimum of 10 to 11 months of violin/viola playing experience. Students were also excluded from the study if they were enrolled in private lessons at the time of the study, had previously taken private violin/viola lessons, or received any additional violin/viola group training prior to their first year of instruction (sixth-grade). The three middle schools were in close geographic proximity (within a 5 mile radius) and had similar school ratings, demographics, and socioeconomic status levels.

According to Madsen & Geringer (1976), "The relationship between perceptual discrimination and performance responses is largely inferential, although aural discrimination ability would appear to be a major prerequisite to intonational

48 proficiency” (p. 13). All participants of this study had approximately ten months of daily group study on their instruments. However, there are several assumptions made by the investigator regarding participants' previous knowledge and experiences. First, it was assumed that students have had some amount of aural training in class or were previously instructed by their teacher to adjust performed pitches or correct intonation errors. In addition, given the rate of progress for beginning string students who meet daily, it was assumed that participants already had learned to perform both the D-major and C-major scales at least at a fundamental level as a part of the regular string-class playing experience.

The six school orchestra classes were randomly assigned to one of three treatment groups (pitch-matching, tonic drone, and pitch matching with a tonic drone), and students in that class who chose to participate in the study were also assigned to that particular group (See Table 3.1).

Table 3.1

Sample by group and site

Group Site 1 Site 2 Site 3 Total

Pitch Matching 0 11 4 15

Pitch Matching 11 0 4 15

Drone plus Pitch Matching 20 0 0 20

TOTAL: 50

Initially, participants were asked to complete a brief questionnaire to confirm their eligibility to participate (see Appendix A). Because this study involved minors as the participants, the IRB required the students and their parents to complete assent (See

Appendix B) and permission forms (See Appendix C) to participate. All identifying information was kept secured and confidential.

Performance Materials

Participants were recorded performing D- and C-major one-octave scales, ascending and descending. It was assumed that participants knew the scales from memory, however they were provided with notation of the scales that included note letter names and appropriate fingerings (See Appendix D) upon entering the testing room.

On the violin and viola, the one-octave D-major scale started on the open D string and ascended to the third finger on the A string. The one-octave C-major scale started with the third finger on the G string (middle C) and ascended to second finger on the A string. These two scales enabled participants to utilize the two most common finger patterns for beginning-level violin and viola players: (a) the major tetrachord, used in the

D-major scale, where the second and third fingers produce a half step, and (b) the Dorian tetrachord, used in the C-major scale, where the first and second fingers produce a half step. The left-hand technique required for the one-octave D- and C-major scales is nearly the same for violins and violas; the only difference is that the violas begin each scale one string higher than violins. Therefore, the difference between violinists and violists was not measured in this study.

Preparing the audio accompaniment tracks

Three versions of accompaniment tracks for the C-major and D-major scale were created for use in this study and served as the independent variable. They were: pitch matching (PM), tonic drone (D), and pitch matching with a tonic drone (PMD). Subjects in the study were divided into three experimental groups based on these accompaniments.

An additional accompaniment track, a metronome click track, did not contain a pitch matching or done-based harmonic accompaniment.

The accompaniment tracks were created using Apple Logic Pro 9 (Apple, Inc.,

2013) multi-track digital audio workstation software. All accompaniments were multi- track audio files that included the following tracks: (a) a narration announcing the scale to be performed; (b) four-beat verbal count-off; and, (c) a metronome click. On each track, a recorded voice announced the scale to be performed, followed by a slight pause and then a four-beat vocal count off with metronome click to help ensure consistency of pitch durations. To allow participants enough time to compare their pitch to the drone and make an adjustment (if necessary), the researcher determined a three-second pitch duration would be sufficient. In order to achieve this duration on the audio track, the metronome click was set to 48 BPM. Participants were asked to perform scales in half notes at this tempo and this produced a 2.91 second sample for each pitch. Also, the three-second duration provided the researcher with an adequate length of pitch to be analyzed for cent deviation and pitch adjustment, when necessary.

It can be debated which stimulus, acoustic or synthesized, is more beneficial to real-world tuning applications. Although there are some studies that have used acoustic stimuli (e.g., Duke, 1985; Ely, 1992; Geringer, 1983; Geringer & Witt, 1985; Geringer &

Worthy, 1999; Madsen & Geringer, 1999; Yarbrough, Green, Benson, & Bowers, 1991), a synthesized stimulus provides a particular advantage, allowing the researcher complete control over frequency, amplitude and overtones (Cummings, 2007).

In this study, square waves were selected to produce all stimuli. This decision was made based on recommendations from the related literature on tuning timbres (e.g.

Cassidy, 1989; Platt and Racine, 1985; Rakowski, 1990; Sergeant, 1973; Spiegel &

Watson, 1984). Spiegel & Watson (1984) found that square waves were easier for musicians and non-musicians to discriminate when compared with sine waves, particularly in frequencies below 1768 Hz. The drone pitches were generated from an oscillator at the same amplitude. The scale's starting pitch, the tonic, was either a

C=261.63 Hz or D= 293.66 Hz, that matched the starting note of each scale. Students are more successful tuning to a pitch that matches their register (Byo, Schlegel, & Clark,

2011). As stated previously, the ascending and descending scale pitches were created using equal temperament.

The audio track for each group differed only by the harmonic accompaniment.

They were: pitch-matching (PM) that included ascending/descending scale stimulus pitches, drone-only (D) that included a sustained tonic drone pitch, and pitch-matching and drone (PMD) group that included both ascending/descending scale pitches and a sustained tonic drone. This design isolated the drone pitch as the independent variable.

Tracks were mixed, normalized, and bounced to uncompressed 16 bit audio files in Waveform Audio File Format (WAV). Digital recording and rendering to uncompressed files results in zero loss in audio fidelity or fluctuation in pitch. There were

52 a total of eight versions of stereo audio tracks created: the D-major scale with pitch- matching (D-PM), tonic drone (D-D), or pitch-matching plus tonic drone accompaniment

(D-PMD), the C-major scale with pitch-matching (C-PM), tonic drone (C-D), or pitch- matching plus drone accompaniment (C-PMD), and two tracks without pitch, one for D- major (D-U) and C-major (C-U). These tracks contained an announcement of the scale name, a four beat count off, and metronome click. The uncompressed audio files were burned to compact discs and labeled for use in each recording room.

Methodology

For pre- and posttests, participants were recorded performing the two scales twice, one with an accompaniment track and once without accompaniment. It was confirmed with the classroom teachers, in the sequence of their string curriculum, that students had learned the D-major scale first, and the C-major second. To eliminate confusion for the young participants, the D-major scale was delivered first, followed by the C-major scale. To control for the order effect, the delivery of the treatment

(accompanied or unaccompanied) was randomized; half of the participants played scales first with an accompaniment followed by no accompaniment, while others did the opposite. This aspect of the experiment was critical, as intonation data was compared under accompanied and unaccompanied conditions.

On the CD there were four possible combinations of scale delivery for each treatment group (see Table 3.2). The different scale accompaniments were combined in

Logic as to create a continuous performance track for each group of participants.The

53 playback of a single track during testing ensured an equal duration of time between scale performances and helped ensure the correct delivery order of accompaniments.

Table 3.2

The combinations of scale delivery during testing

Da Du Ca Cu 1. Da Du Cu Ca 2. Du Da Ca Cu 3. Du Da Cu Ca 4.

Key: Da = D-major scale, accompanied

Du = D-major scale, unaccompanied

Ca = C-major scale, accompanied

Cu = C-major scale, unaccompanied

Participants were evaluated solely on the accuracy of their intonation for each scale degree. Other performance criteria, such as instrument position and tone, were not evaluated. Only pitches played with left hand fingers pressed down on the fingerboard were measured. In other words, open string intonation, those pitches that are produced by only playing strings with no fingers touching the fingerboard, was not evaluated. The researcher or a research assistant tuned each of the participant’s instruments with an electronic tuner calibrated to A440. Playing the A string without fingers on the

54 fingerboard produces the pitch A and playing the D string without fingers on the fingerboard produces the pitch D.

Data consisted of cent deviations from equal temperament tuning for each fingered pitch; this resulted in the collection of 44 data points per student on each pre- and posttest. The 44 data points were derived from four scales, each consisting of 11 measurable pitches. For example, in the one-octave D-major scale, the pitches performed were D (open string, not measured), E (first finger), F-sharp (second finger), G (third finger), A (open string), B (first finger), C-sharp (second finger), D (third finger), C-sharp

(second finger), B (first finger), A (open string), G (third finger), F-sharp (second finger),

E (first finger) and D (open string). See Appendix D for the notated scales with fingerings.

Alternate tuning systems such as just intonation or Pythagorean tuning were considered for data analysis, but ultimately discarded for several reasons. First, adhering to one of these tuning systems was problematic because the participants were beginning- level players and most likely not proficient in discriminating such a specific level of precision. Second, historically, unless focused on temperament, most intonation research study used cent deviation from equal temperament as the measurement standard (e.g.

Byo, Schlegel & Clark, 2011; Geringer, 1976, 1983; Geringer & Witt, 1983; Rakowski,

1990; Nuñez, 2002; Mongeon, 2004,; Sogin, 1987).

Another area of concern of using just intonation as the measurment standard is with regards to playing open strings; the pitches sounded by the open strings are untunable while a subject is performing. Just intonation requires scale intervals precisely

55 tuned to pure harmonics of the natural overtone series. Harmonics are superparticular ratios above of a fundamental frequency, and are a natural phenomenon of a vibrating string. Given the scales to be performed, the only open strings used are the D and A strings.

Data Collection Procedures

Recording of participants took place in an isolated, well-ventilated environment, free from as much extraneous noise and other distractions as possible in a school environment. It has been shown that greater pitch discrimination is possible with participants who were tested in an isolated environment (Sergeant, 1973), this was not entirely possible in a school setting.

To ensure all students from each of the three sites were recorded on the same day, a team of research assistants was used. Assistants were college music professors and upper-level undergraduate music majors. Each site required a manager, who was in charge of taking participants to a recording room; an experienced violinist/violist who tuned each of the participant’s instruments; and a person who operated the audio recorders and led participants through the script.

Prior to entering the recording area, participants were given a card that identified their participant ID, name, treatment group, CD accompaniment track number, and instrument to the research assistant.In addition, the participant’s instrument was tuned precisely using a Korg CA-1 tuner calibrated to A440 by the research assistant.

Upon entering the recording area, participants were greeted and then heard verbal instructions. The script used during recording was as follows:

[Student enters the room, his/her instrument has been tuned.]

Say: Hello, may I please have your card? [Take card from student]

Say: Hello [insert student name]. Thank you for agreeing to participate. Is it okay if I clip this microphone to your instrument? [Clip microphone to strings behind bridge]

Say: Ok, let’s begin. This is an experiment concerned with scales and intonation, or playing in tune. You will be recorded performing two different scales - the D- major scale, and the C-major scale, two times each. If you need them, the scales are printed on the sheet music on the stand in front of you. [Point to the correct sheet (violin or viola)]

Say: You will hear verbal instructions telling you which scale to play, followed by a four beat count-off. After the fourth beat, you will be expected to perform the scale, both ascending and descending (up and down). Also, as a reminder: You will NOT repeat the top note of the scale. As you play, sometimes you will hear a harmonic accompaniment and sometimes you will only hear a metronome click. The metronome click will be slow, so be sure to use a slow bow and stay with the click.

Say: Please try to perform the scales as accurately as possible and maintain a steady tempo, playing each note for two full counts. You should listen to the accompaniment as you play and match your pitch to the accompaniment the best you can.

Say: Between each of the scales you will hear some white noise, and will have a short time to prepare for the next scale. Before we begin, do you have any questions?

[Start the audio recorder and ensure that recording is taking place by looking at the display. You should see: 1.) The recording timer counting up and 2.) Activity on the audio level meters.

While recording audio, announce the student’s participant ID.

Say: This is participant # [Insert student participation ID number]. Then begin the CD player, advancing to the track number that is marked on his/her sheet: #1, 2, 3, or 4.]

[Student will follow prompts on audio recording to perform D-major scales two times, and C-major scale two times. Feel free to remind them what scale they are

playing between takes (during the white noise). Once they have completed, remove the microphone from their instrument.]

Say: Thank you for playing today! [Put the student’s card in your folder.]

A Tascam Model DR-05 Linear Pulse-code modulation (PCM) digital audio

recorder equipped with an attached Audio-Technica ATR-3350 lavaliere microphone was used to record the participant’s performances. Audio quality was set to 44.1 kHz/16 bit

(CD quality) to obtain a high fidelity audio recording. The lavaliere microphone was clipped onto the strings, just behind the bridge to obtain a direct sound from the

instrument and reject extraneous noise, the audio accompaniment track, and room

acoustics. This direct recording technique improved the accuracy of the analysis

software. The metal clip on the microphone was affixed with a small amount of foam

padding to prevent rattling from string vibrations.

Students were provided with printed notation of the scales to play from if they

wished (See Appendix D). Participants listened to audio tracks through the stereo

speakers of a portable compact disc stereo system, Memorex Model MP3851. Research

assistants controlled the delivery of the audio tracks.

After the verbal instructions were stated and any questions answered, white noise

was played through the loudspeakers for five seconds to allow participants to provide

feedback to the researcher indicating that the track volume being set at a comfortable

level (Benson, 2008). The participants were then led through the performances of four

scales.

Via the CD playback recording, each subject was given the directions, "[D or C] major scale. [pause] One, Two, Three, Four…" A click track in the audio recording guided participants through the performance of the first scale. Between each scale performance, participants were played seven seconds of white noise to help clear their tonal memory (Brown, 1991; Cummings, 2007). This process continued until all of the scales were performed; two D-major scales and two C-major scales, with accompaniment delivered randomly. During recording, the researcher monitored and calibrated the recording apparatus as necessary to achieve a consistent recording level for each participant. After all of the scales were performed, the participants were thanked for playing. This recording process was exactly the same for pre- and posttests.

Measures

Each participant’s recorded digital sound file was downloaded onto an Apple

MacBook Pro and opened using the Intonia software program. Intonia was a software application written by Gerald Agin (2010) in the Java programming language and is cross-platform, compatible with Apple Macintosh OSX, Microsoft Windows, and Linux operating systems. A version for Andriod was released in 2014. An industry-standard

Fast Fourier transform calculation turned the sound energy into digital computer data

(Agin, 2013). The data was then represented in a grid-based graphic display on the screen to show each pitch as shown in Figure 3.1.

Figure 3.1. Graphical Grid Interface of Intonia Software

The software features options that allow the user to customize the reference tuning frequency, temperament, and more. The tuning standard of A440 and equal temperament were used for this study. Each performed pitch, excluding open strings, was measured for intonation accuracy. Sample fragments of pitches were selected and analyzed for cent deviations.

For each pitch, approximately a middle one-second fragment of sound was selected and analyzed for cent deviation. Mongeon (2004) also used this technique of pitch selection and analysis in a similar fashion using Amadeus II software. The

beginning and end sample of each pitch performance was discarded to remove attack

transients from bow direction change sounds that can alter pitch. Once a sound sample

selection was made, a simple keystroke was used to show deviations from equal

temperament. The directional deviation score was record recorded for each performed

pitch. See figure 3.2 for an example of sample selection and cent deviation calculation.

Figure 3.2. Example of sound sample selection in Intonia

The technique of converting a sound frequency readout to a cent deviation score to measure pitch accuracy has been used in previous research (e.g. Duke, 1985; Karrick,

1998; Kopiez, 2003; & Morrison, 2000). Typically, a mean frequency of audio samples was converted to a cent deviation score, and served as the measure of accuracy for the

61 particular task. In many studies, recorded pitch durations have ranged between one and three seconds, making the mean frequency method a logical choice for analysis

(Cummings, 2007). The software used in this study allowed the researcher to bypass the manual calculation of frequency means, and instantly produce a cent deviation calculation reading. In instances where participants made intonation adjustments to a pitch, a sampled area was selected after the pitch was stabilized to a steady state.

Cent deviation data for each scale pitch, except for open string pitches, was collected and allowed for direct comparisons between treatment groups. A score of zero

(0) indicated that the pitch was precisely in tune according to ET. Any other value, was measured in cent deviations, indicated the amount of error in the pitch from equal temperament. Errors were recorded as positive (sharp) and negative (flat) numbers and then were converted to absolute values (positive numbers) regardless if the pitch was played sharp or flat to produce absolute deviation. Directional scores that show relative sharpness or flatness are useful in determining trends in pitch direction, but they were problematic when computing means, as the positive and negative data points cancel out one another as they go above and below the ET value of zero. This problem does not occur with absolute means. To examine relative sharpness and flatness, directional data

(both positive and negative values) were also collected and examined.

Comparisons of the mean error score were done for individual pitches, each of the scales, and for all of the scales combined. This calculation was designed to reveal the pitches and scales that vary most between groups and show the differences (if any) between treatment groups and for all of the scales combined.

Reliability Measure

The data measurement instrument and pitch analysis method was confirmed for

reliability by an independent observer who was a internationally-published music

education researcher with over 35 years experience. Twenty percent of the audio

recordings were randomly selected and analyzed by the observer using the Intonia

software. These analysis procedures are described in detail later. The selected segment of

each pitch used for measurement in this study is somewhat approximated and is a

subjective judgment of the researcher. While every attempt was made to ensure

uniformity in pitch selection, there are many variables that impacted the recorded

durations of each pitch, and it would have been nearly impossible for two different

researchers to select exactly the same start and end point for each pitch.

Intonation Adjustments

While performing, a musician must be alert and willing to make necessary adjustments in characteristics such as rhythm, tempo, and pitch. A valuable skill for string players is the ability to recognize and correct an intonation error immediately while playing. To measure the frequency of intonation adjustments, scale performances were screened for the adjustment of intonation. If a subject attempted to adjust/correct pitch by moving a fingered note on the fingerboard, regardless of outcome, the particular pitch was counted. Adjustment tallies identified what particular notes/scale degrees were most often adjusted.

In addition to simply counting the number of adjustments, the difference in deviation of the adjusted starting pitch and the ending pitch was measured. This

63 measurement allowed the researcher to determine the impact of the adjustment: positive

(correct) or negative (incorrect).

Treatment/Classroom Instruction

Each class was randomly assigned to one of the three treatment groups. All students in the class, regardless of participation in the study, performed scales while playing along with the assigned audio track. Classes were assigned to a particular group that was determined by the version of the audio track: pitch-matching, drone, or pitch matching plus drone. The participants had training on the scales via daily classroom instruction for approximately 5-10 minutes per day, over a period of seven school days using the provided recorded audio track. Before class began, the classroom teachers were told to ensure the open-string tuning accuracy of every student instrument. Then, as the class warm-up activity, teachers used the provided accompaniment tracks to practice the scales with the students.

Students were instructed on the scales via group string instruction for seven class periods. Classroom teachers were provided with a script (See Appendix E) for each day and provided instruction using the following schedule:

• Pre-Test: All participants were recorded on the same day

• Day 1: Teacher explained the tracks, along with a modeled demonstration; Begin

D- and C-major scale training

• Day 2: Pitch adjustment demonstration and game; D- and C-major scale training

• Day 3, 4, 5, 6, and 7: Reinforcement through repetition of D- and C-major scales.

Order and delivery of the scales changed slightly each day.

• Post-Test: All participants were recorded on the same day

On the first day, the objective was to allow students to become familiar with

playing with an accompaniment track. For the first two days, the teacher modeled scales

with the accompaniment tracks for students. Modeling has been shown to be effective teaching strategy (Hamann & Gillespie, 2012; Mann, 2008). Specific directions were given that would help students obtain a large, full sound, as good bow control is important in keeping a pitch stable. Students were also praised with positive

reinforcement.

The lessons also contained information about the value of accurate intonation and

included some teaching strategies to make students aware of their ability to adjust fingers

on the fingerboard to correct intonation errors. It is valuable for the teacher to lead the

students to philosophically believe that playing with accurate intonation is important

(Alexander, 2008). Each day, 4-6 repetitions of the scales were used as the class warm-

up. Each group received an equal amount of in-class training on the two scales. The

delivery of instruction and pedagogy did not vary between groups except the specific

audio track used to accompany students in each group. While the students were expected

to have played a one-octave D-major and C-major scales prior to this study, the

classroom teachers were instructed to review the notes and fingerings prior to pre-test

data collection. The class was instructed not to practice the material at home and the

tracks were not available for use outside the classroom.

Chapter 4: Results

Introduction

The purpose of the present study was to investigate the effect of a tonic drone accompaniment on the pitch accuracy of beginning-level violinists and violists. The research questions of the study were:

1. Do beginning string students play with greater pitch accuracy following

training with tonic drones compared to pitch matching alone, or pitch

matching with tonic drone accompaniments?

2. Does the pitch accuracy of students who have learned to play scales initially

with the use of an accompaniment track change once students play the same

scales without an accompaniment track?

3. Are intonation tendencies toward sharpness or flatness for particular scale

degrees different for students when they play with a drone accompaniment

compared to when they play without a drone accompaniment?

4. Do students more frequently attempt to adjust the accuracy of their pitches

when playing with a tonic drone compared to those who use pitch matching

alone, or pitch matching with tonic drone accompaniments?

6 6

5. Do students adjust the intonation of their pitches to be more accurate when

playing scales with a drone accompaniment compared to pitch matching

alone, or pitch matching with tonic drone accompaniments?

Participants

Sixty-four students initially agreed to participate in the study. However, nine students did not complete either pre- or posttest due to school absences on one of the testing days and thus were eliminated from the study. All participants from each of the three sites were recorded on the same day during their orchestra class meeting time.

Outliers

It is appropriate to remove outliers from the population based on subjective reasoning, errors in measurement, or previous research models (King & Minium, 2008).

Five outliers were identified in the data, as assessed by the inspection of pretest and posttest absolute deviation data in a boxplot. One participant’s combined total deviation score on both pre- and posttests of 5213.8 cents was more than three standard deviations away from the next highest score and appears inconsistent with the rest of the data.

Another participant had a pre-test absolute deviation score of 2329.3, over two standard deviations away from the next highest score. Upon reevaluation of this participant’s audio recording, it was apparent that the participant’s left hand was positioned at the incorrect place on the fingerboard, resulting in notes that were incorrect and not simply out of tune. No attempt was made by the participant to correct the mistake. This participant’s posttest score was in the normal distribution, however both the pre- and posttest scores were removed from the data set.

In addition, three students had unusually high posttest scores compared to their

pre-test and these cases were examined. The field notes taken by the research assistants

revealed inappropriate behavior of the adolescent subjects and it was concluded that the

participants may have purposefully skewed their posttest performances. Results showed

two participants’ absolute deviation score roughly doubled (from 1033.2 to 2446.8 and

1239 to 2329.8), and another participant’s score nearly tripled (from 738.8 to 2051.2)

from pre-test to posttest.

These outliers were removed as their scores severly impacted the data set. Of the

five outliers, three were from the pitch-matching (PM) group and two were from the

pitch-matching plus drone (PMD) group.

A total of 14 participants, nine with incomplete data sets, and five outliers were

removed from the data set and were not included in any analysis. Consequently, 50

students participated in the study.

Treatment Groups

Intact classes were randomly assigned into one of three treatment groups: pitch

matching (n=15), drone (n=15), and pitch-matching plus drone treatment group (n=20).

Table 4.1

Participants by group

Pitch-matching (PM) 15 Drone (D) 15 Pitch matching plus drone (PMD) 20 Total 50

Treatments involved the use of audio accompaniment tracks while practicing scales. The accompaniment for each group differed only by the criteria for each treatment group. The group treatments were: pitch-matching (PM), that included ascending/descending scale stimulus pitches; drone-only (D), that included a sustained tonic drone pitch; and pitch-matching and drone (PMD); that included both ascending/descending scale pitches and a sustained tonic drone. Participants had training on these scales via daily classroom instruction for approximately 5-10 minutes per day, for seven school days, using the provided recorded audio track for each group.

Data Collection Procedures

For pre- and posttests, each participant was individually recorded performing the

D-major and C-major scales twice, one track with accompaniment and one without. A digital audio recorder equipped with an attached lavaliere microphone was used to record the participant’s performances. Participants listened to audio tracks through the stereo speakers of a portable compact disc stereo system while performing the scales.

Data Sets

Cent deviation data for each scale pitch, except for open string pitches, was analyzed and used for direct comparisons between treatment groups. The pre-test and post-test scores of each student comprised a data set: 50 students participated in the study, resulting in 50 data sets, one data set per student. All 50 data sets were analyzed and raw data can be found in Appendix 4.1.

Pretest scores of all participants were normally (p > .05) distributed with a skewness of 0.426 (standard error = 0.337) and kurtosis of -0.41 (standard error = 0.662).

These scores were also normally (p > .05) distributed within each group as shown in

Table 4.2.

Table 4.2

Shapiro-Wilk test of normality

Group Statistic df Sig. Pre-Test Absolute Cent D .927 15 .246 Deviation Scores PM .899 15 .092 PMD .935 20 .194

Absolute Cent Deviation

All data was organized in Microsoft Excel (v. 14.4.7, Mac OS) and imported to

Statistical Package for the Social Sciences (SPSS, v. 22, Mac OS) software for analysis.

The main area of experimental interest was the comparison of intonational performance differnces between the three treatment groups, PM , D, and PMD.

Descriptive statistics reveal virtually no differences between pre- and posttest mean scores as shown in Table 4.3.

Table 4.3

Absolute cent deviation for pre- and posttest

N Mean Std. Deviation Std. Error Pretest PM 15 866.4 307.76 79.46 D 15 846.0 382.85 98.85 PMD 20 899.6 246.30 55.07 Total 50 873.5 304.94 43.12 Posttest PM 15 856.3 409.04 105.61 D 15 872.4 381.66 98.54 PMD 20 889.2 228.57 51.11 Total 50 874.3 331.47 46.88

An Analysis of Variance (ANOVA) was used to analyze data to determine if differences existed between the three groups of students, pre- and posttest as shown in

Table 4.4. The within-subject variables were tested with one of the three pre-selected accompaniments and with no harmonic accompaniment (a metronome click track). The between-subject variables were instrument (violin or viola), and the subjects’ attending schools. These were not analyzed.

Table 4.4

Analysis of variance for pre- and posttest absolute cent deviation

Sum of Squares df Mean Square F Sig. Pretest Between Groups 25720.1 2 12860.1 .133 .875

Within Groups 4530642.1 47 96396.6

Total 4556362.5 49 Posttest Between Groups 9347.8 2 4673.9 .041 .960

Within Groups 5374379.8 47 114348.5

Total 5383727.5 49

Post hoc test results are shown in Table 4.5.

Table 4.5

Tukey HSD for pre- and posttest absolute cent deviation

Mean 95% Confidence Interval Dependent (I) Difference Lower Upper Variable Group (J) Group (I-J) Std. Error Sig. Bound Bound Pretest PM D 20.4 113.37 .982 -253.98 294.76 PMD -33.2 106.05 .947 -289.85 223.45 D PM -20.4 113.37 .982 -294.76 253.98 PMD -53.6 106.05 .869 -310.24 203.06 PMD PM 33.2 106.05 .947 -223.45 289.85 D 53.6 106.05 .869 -203.06 310.24 Posttest PM D -16.1 123.48 .991 -314.92 282.74 PMD -32.9 115.50 .956 -312.41 246.64 D PM 16.1 123.48 .991 -282.74 314.92 PMD -16.8 115.50 .988 -296.32 262.73 PMD PM 32.9 115.50 .956 -246.64 312.42 D 16.8 115.50 .988 -262.73 296.32

Accompanied and unaccompanied performances were also examined. Results revealed slight improvement in pitch accuracy across all groups when accompanied, though not significant. Table 4.6 shows descriptive statistics.

Table 4.6

Pre- and posttest unaccompanied and accompanied absolute cent deviation

N Mean Std. Deviation Std. Error Pretest PM 15 494.867 190.9225 49.2960 Unaccompanied D 15 429.447 217.5563 56.1728 PMD 20 467.575 125.8095 28.1319 Total 50 464.324 175.3209 24.7941 Pretest PM 15 371.507 178.8482 46.1784 Accompanied D 15 416.533 188.9794 48.7943 PMD 20 432.000 164.7928 36.8488 Total 50 409.212 174.7471 24.7130 Posttest PM 15 451.727 258.2109 66.6698 Unaccompanied D 15 450.913 241.1505 62.2648 PMD 20 462.560 132.1600 29.5519 Total 50 455.816 206.0786 29.1439 Posttest PM 15 404.560 176.6215 45.6035 Accompanied D 15 421.467 168.0247 43.3838 PMD 20 426.615 116.6572 26.0854 Total 50 418.454 149.4833 21.1401

Table 4.7

Analysis of variance for pre- and posttest absolute cent deviation

Sum of Mean Squares df Square F Sig.

Pretest Between Groups 32450.6 2 16225.3 .517 .599 Unaccompanied Within Groups 1473682.4 47 31354.9

Total 1506133.1 49 Pretest Between Groups 32515.3 2 16257.6 .522 .597 Accompanied Within Groups 1463774.9 47 31144.1

Total 1496290.2 49 Posttest Between Groups 1521.0 2 760.5 .017 .983 Unaccompanied Within Groups 2079429.3 47 44243.2

Total 2080950.3 49 Posttest Between Groups 4363.8 2 2181.9 .094 .910 Accompanied Within Groups 1090553.6 47 23203.3

Total 1094917.4 49

Table 4.8

Tukey HSD for pre- and posttest unaccompanied and accompanied absolute cent eviation

Mean 95% Confidence Interval (I) Difference Lower Upper Dependent Variable Group (J) Group (I-J) Std. Error Sig. Bound Bound Pretest PM D 65.4 64.65 .573 -91.060 221.900 Unaccompanied PMD 27.3 60.48 .894 -119.082 173.666 D PM -65.4 64.66 .573 -221.900 91.060 PMD -38.1 60.48 .804 -184.502 108.246 PMD PM -27.3 60.48 .894 -173.666 119.082 D 38.1 60.48 .804 -108.246 184.502 Pretest PM D -45.0 64.44 .765 -200.980 110.927 Accompanied PMD -60.5 60.28 .578 -206.374 85.388 D PM 45.0 64.44 .765 -110.927 200.980 PMD -15.5 60.28 .964 -161.348 130.414 PMD PM 60.5 60.28 .578 -85.388 206.374 D 15.5 60.28 .964 -130.414 161.348 Posttest PM D .8 76.81 1.000 -185.065 186.692 Unaccompanied PMD -10.8 71.85 .988 -184.707 163.040 D PM -.8 76.81 1.000 -186.692 185.065 PMD -11.7 71.85 .986 -185.520 162.227 PMD PM 10.8 71.85 .988 -163.040 184.707 D 11.6 71.85 .986 -162.227 185.520 Posttest PM D -16.9 55.62 .950 -151.518 117.705 Accompanied PMD -22.1 52.03 .906 -147.972 103.862 D PM 16.9 55.62 .950 -117.705 151.518 PMD -5.1 52.03 .995 -131.066 120.769 PMD PM 22.1 52.03 .906 -103.862 147.972 D 5.1 52.03 .995 -120.769 131.066

Reliability Results

The data measurement instrument and pitch analysis method was confirmed for reliability by an independent observer who was a music education colleague with over 35 years research experience. The observer examined 20% of the randomly selected audio recordings and analyzed using the Intonia software. Intonia is a computer software application that shows pitch level in a grid-based display. The software allows a sample of audio to be selected and analyzed for cent deviations. The independent observer was provided with directions on how to use the software and familiarized with procedures for selecting a middle second of sound from each pitch to be measured.

Of the 1056 samples cross-analyzed for reliability, 1005 were within 10 cents, providing a reliability level of 93.8%. In a more stringent measurement, 916 of these samples were within 5 absolute cent deviations, providing secondary reliability measure of 86.7 percent.

Directional Cent Deviation

A second analysis of the data was computed that considered the direction of the deviations (sharp/flat, positive/negative). A tendency toward flat intonation (54,670.3) was consistent throughout the study, with the overal deviation of 87,390.2 (See Table

4.9). Thus the ratio of total cents flat to total cents sharp in the pretest was approximately

1.67 to 1.

Table 4.9

Total Directional Cent Deviation

N Sum Mean Std. Deviation Sharp 50 32719.9 654.4 521.14 Flat 50 54670.3 1093.4 532.51

The total deviation of the pre-test was 43,676.8, of which 23,891.6 were in the flat direction, amounting to approximately 54.7%. The total deviation of the posttest was

43,713.5, of which 30,778.8 were in the flat direction, and amounted to approximately

70.4%. See Table 4.10 for descriptive statistics for the pre- and posttest directional cent deviation.

Table 4.10

Pre- and posttest directional cent deviation means, by group

Pretest Posttest

Std. Std.

N Mean Deviation Std. Error Deviation Std. Error Mean Sharp PM 15 746.3 605.76 156.41 1081.7 53.0 1668.1 D 15 488.7 347.60 89.75 681.2 78.4 1473.8 PMD 20 709.7 556.27 124.39 970.1 45.6 2380.3 Total 50 654.4 521.13 73.70 802.5 45.6 2380.3 Flat PM 15 -976.4 386.57 99.81 -762.3 -1613.0 -436.3 D 15 -1229.6 607.27 156.80 -893.3 -2325.6 -340.1 PMD 20 -1079.0 569.01 127.23 -812.7 -2250.0 -4.5 Total 50 -1093.4 532.51 75.31 -942.1 -2325.6 -4.5

Directional cent deviation data was converted to a nonparametric sharp or flat value and recorded. Responses were tallied and converted to percentages that were compared. Raw data would not be useful to examine, as groups are unequal size. Table

4.11 shows percentages of sharp/flat responses of accompanied and unaccompanied performances. Results reveal no significant differences within pre- and posttests. While not significant, there was an increase in flat responses in the posttest.

Table 4.11

Sharp and flat response percentages of unaccompanied and accompanied scale performances

Pretest Postttest Unaccompanied Accompanied Unaccompanied Accompanied D-major scale Sharp 43% 41% 33% 33% Flat 57% 59% 67% 67%

C-major scale Sharp 49% 49% 36% 34% Flat 51% 51% 64% 66%

In a comparison between treatment groups, the drone group (D) produced more flat responses overall as shown in Table 4.12. The pitch-matching (PM) and pitch- matching plus drone (PMD) groups were similar, except for in the posttest D-major scale

Table 4.12

Percentages of sharp and flat responses, unaccompanied and accompanied, by group

D-major scale Pretest Posttest Unaccompanied Accompanied Unaccompanied Accompanied Sharp 46% 41% 28% 24% PM Flat 54% 59% 72% 76% Sharp 38% 41% 28% 29% D Flat 62% 59% 72% 71% Sharp 45% 42% 39% 42% PMD Flat 55% 58% 61% 58%

C-major scale Pretest Posttest Unaccompanied Accompanied Unaccompanied Accompanied Sharp 52% 55% 41% 36% PM Flat 48% 45% 59% 64% Sharp 45% 41% 31% 30% D Flat 55% 59% 69% 70% Sharp 50% 50% 36% 36% PMD Flat 50% 50% 64% 64%

Intonation tendencies of selected scale degrees were examined to determine if

there were patterns of sharpness or flatness for certain pitches on scale. The scale degrees

selected represent pitches that were performed with left hand fingers pressing down on the fingerboard. Those pitches performed by playing open strings were not analyzed. In the D-major scale the selected scale degrees were the second (E), third (F#), fouth (G), sixth (B), seventh (C#), and octave (D). Table 4.13 shows the note names, scale degree, and fingering for each of the analyzed pitches in the D-major scale.

Table 4.13

Note names, scale degrees, and fingerings used for the D-major scale analysis

Letter D E F# G A B C# D name

Scale 8 1 (tonic) 2 3 4 5 6 7 degree (octave) Open Open string, string, Fingering 1st 2nd 3rd 1st 2nd 3rd not not measured measured

For the C-major scale, the tonic (C), third (E), fourth (F), fifth (G), seventh (B), and octave (C) were selected. Table 4.14 shows those in the C-major scale.

Table 4.14

Note names, scale degrees, and fingerings used for the C-major scale analysis

Letter C D E F G A B C name

Scale 1 8 2 3 4 5 6 7 degree (tonic) (octave) Open Open string, string, Fingering 3rd 1st 2nd 3rd 1st 2nd not not measured measured

As previously mentioned, directional cent deviation data showed non-significant tendencies in pitch toward the flat direction. Table 4.15 represents the sharp/flat 82 percentages of each performed note within the 8 scales. In all scales performances, there were fewer notes played sharp in post tests. The shaded cells show the notes that were played more frequently in the sharp direction. Analysis revealed that 49 notes in the pretest data were sharp, (37.1%) and only 19 notes were performed sharp a majority of the time (14.4%) in the posttest data. In both pre- and posttests, only five notes (1.9%) had an equal number of sharp and flat responses. There were 27 notes played sharp

(20.4%) in the pre- and posttest performances of the D-major scale, while 41 notes were played sharp in the C-major scale (31%).

Table 4.15

Sharp and flat percentages of each performed note, by group

Pretest, D-major, Unaccompanied Ascending Descending E F# G B C# D C# B G F# E Sharp 60% 60% 67% 40% 40% 40% 20% 33% 47% 33% 67% PM Flat 40% 40% 33% 60% 60% 60% 80% 67% 53% 67% 33% Sharp 47% 40% 60% 47% 13% 33% 13% 40% 53% 20% 47% D Flat 53% 60% 40% 53% 87% 67% 87% 60% 47% 80% 53% Sharp 50% 30% 70% 35% 40% 55% 45% 40% 60% 25% 45% PMD Flat 50% 70% 30% 65% 60% 45% 55% 60% 40% 75% 55%

Posttest, D-major, Unaccompanied Ascending Descending E F# G B C# D C# B G F# E Sharp 53% 40% 33% 20% 13% 20% 33% 13% 13% 13% 60% PM Flat 47% 60% 67% 80% 87% 80% 67% 87% 87% 87% 40% Sharp 20% 33% 40% 33% 33% 20% 20% 33% 40% 13% 27% D Flat 80% 67% 60% 67% 67% 80% 80% 67% 60% 87% 73% Sharp 45% 40% 60% 25% 20% 65% 20% 20% 70% 30% 30% PMD Flat 55% 60% 40% 75% 80% 35% 80% 80% 30% 70% 70%

continued 84

Table 4.15 continued

Pretest, D-major, Accompanied Ascending Descending E F# G B C# D C# B G F# E Sharp 53% 53% 53% 33% 13% 47% 20% 33% 53% 40% 53% PM Flat 47% 47% 47% 67% 87% 53% 80% 67% 47% 60% 47% Sharp 40% 53% 67% 33% 40% 40% 13% 33% 47% 27% 53% D Flat 60% 47% 33% 67% 60% 60% 87% 67% 53% 73% 47% Sharp 45% 45% 70% 35% 30% 55% 30% 45% 45% 30% 35% PMD Flat 55% 55% 30% 65% 70% 45% 70% 55% 55% 70% 65%

Posttest, D-major, Accompanied Ascending Descending E F# G B C# D C# B G F# E Sharp 40% 13% 27% 13% 13% 13% 20% 13% 40% 33% 33% PM Flat 60% 87% 73% 87% 87% 87% 80% 87% 60% 67% 67% Sharp 33% 33% 27% 33% 20% 20% 20% 33% 33% 40% 27% D Flat 67% 67% 73% 67% 80% 80% 80% 67% 67% 60% 73% Sharp 35% 50% 70% 30% 35% 65% 20% 25% 70% 30% 30% PMD Flat 65% 50% 30% 70% 65% 35% 80% 75% 30% 70% 70%

continued 85

Table 4.15 continued

Pretest, C-major, Unaccompanied Ascending Descending C E F G B C B G F E C Sharp 60% 67% 40% 53% 40% 53% 33% 53% 60% 60% 47% PM Flat 40% 33% 60% 47% 60% 47% 67% 47% 40% 40% 53% Sharp 67% 40% 47% 60% 33% 33% 27% 47% 53% 40% 47% D Flat 33% 60% 53% 40% 67% 67% 73% 53% 47% 60% 53% Sharp 65% 55% 45% 70% 30% 35% 30% 55% 50% 40% 70% PMD Flat 35% 45% 55% 30% 70% 65% 70% 45% 50% 60% 30%

Posttest, C-major, Unaccompanied Ascending Descending C E F G B C B G F E C Sharp 53% 27% 47% 47% 20% 47% 20% 27% 53% 53% 53% PM Flat 47% 73% 53% 53% 80% 53% 80% 73% 47% 47% 47% Sharp 40% 20% 20% 27% 20% 20% 33% 47% 33% 27% 53% D Flat 60% 80% 80% 73% 80% 80% 67% 53% 67% 73% 47% Sharp 65% 30% 25% 40% 20% 20% 20% 50% 35% 40% 55% PMD Flat 35% 70% 75% 60% 80% 80% 80% 50% 65% 60% 45%

continued 86

Table 4.15 continued

Pretest, C-major, Accompanied Ascending Descending C E F G B C B G F E C Sharp 60% 53% 67% 60% 53% 33% 40% 53% 53% 80% 47% PM Flat 40% 47% 33% 40% 47% 67% 60% 47% 47% 20% 53% Sharp 60% 40% 40% 53% 13% 27% 27% 47% 47% 53% 40% D Flat 40% 60% 60% 47% 87% 73% 73% 53% 53% 47% 60% Sharp 75% 45% 50% 75% 35% 35% 35% 65% 35% 35% 65% PMD Flat 25% 55% 50% 25% 65% 65% 65% 35% 65% 65% 35%

Posttest, C-major, Accompanied Ascending Descending C E F G B C B G F E C Sharp 47% 47% 53% 33% 13% 40% 20% 27% 33% 27% 60% PM Flat 53% 53% 47% 67% 87% 60% 80% 73% 67% 73% 40% Sharp 33% 33% 27% 33% 13% 20% 20% 33% 20% 47% 47% D Flat 67% 67% 73% 67% 87% 80% 80% 67% 80% 53% 53% Sharp 35% 25% 25% 40% 30% 30% 30% 55% 30% 30% 70% PMD Flat 65% 75% 75% 60% 70% 70% 70% 45% 70% 70% 30%

Table 4.16 shows the sharp and flat percentage for each of the measured scale degrees in the D-major scale. The pitch perfomed flat most often was the C-sharp, both ascending and descending. In the key of D-major, this pitch is the seventh scale degree or leading tone.

Table 4.16

Sharp and flat percentage of scale degrees in the D-major scale

D-major scale Ascending Descending E F# G B C# D C# B G F# E Pretest, Sharp 52% 42% 66% 40% 32% 44% 28% 38% 54% 26% 52% Unaccompanied Flat 48% 58% 34% 60% 68% 56% 72% 62% 46% 74% 48% Pretest, Sharp 46% 50% 64% 34% 28% 48% 22% 38% 48% 32% 46% Accompanied Flat 54% 50% 36% 66% 72% 52% 78% 62% 52% 68% 54% Posttest, Sharp 40% 38% 46% 26% 22% 38% 24% 22% 44% 20% 38% Unaccompanied Flat 60% 62% 54% 74% 78% 62% 76% 78% 56% 80% 62% Posttest, Sharp 36% 34% 44% 26% 24% 36% 20% 24% 50% 34% 30% Accompanied Flat 64% 66% 56% 74% 76% 64% 80% 76% 50% 66% 70% Sharp 56% 40% 40% 50% 27% 33% 28% 48% 42% 44% 56% TOTAL Flat 45% 60% 60% 50% 73% 68% 72% 53% 59% 57% 45%

The percentage of sharp and flat scale degrees for the C-major scale are shown in

Table 4.17. The seventh scale degree or leading tone (B), was perfomed flat most often which paralells the D-major scale tendency.

Table 4.17

Sharp and flat percentage of scale degrees in the C-major scale

C-major scale Ascending Descending C E F G B C B G F E C Pretest, Sharp 64% 54% 44% 62% 34% 40% 30% 52% 54% 46% 56% Unaccompanied Flat 36% 46% 56% 38% 66% 60% 70% 48% 46% 54% 44% Pretest, Sharp 66% 46% 52% 64% 34% 32% 34% 56% 44% 54% 52% Accompanied Flat 34% 54% 48% 36% 66% 68% 66% 44% 56% 46% 48% Posttest, Sharp 54% 26% 30% 38% 20% 28% 24% 42% 40% 40% 54% Unaccompanied Flat 46% 74% 70% 62% 80% 72% 76% 58% 60% 60% 46% Posttest, Sharp 38% 34% 34% 36% 20% 30% 24% 40% 28% 34% 60% Accompanied Flat 62% 66% 66% 64% 80% 70% 76% 60% 72% 66% 40% Sharp 56% 40% 40% 50% 27% 33% 28% 48% 42% 44% 56% TOTAL Flat 45% 60% 60% 50% 73% 68% 72% 53% 59% 57% 45%

Pitch Adjustments

The researcher analyzed each of the audio recordings for the adjustment of pitch.

For the purposes of this study, a pitch adjustment was tallied when a participant altered the placement of a finger of the left hand on the fingerboard while performing a pitch.

The adjustment made the pitch higher or lower. Each time this occurred, the adjusted pitch was tallied.

A pitch was tallied as being adjusted if it was shown to have an inconsistency as displayed on the visual display of the pitch analysis made by the Intonia software, and confirmed aurally by listening for a fluctuation in pitch. See Figure 4.1 for an example of the visual display of an ajusted pitch in Inonia. When an adjustment was both observed and heard aurally, the pitch adjustment occourance was noted.

Figure 4.1. An adjusted pitch in the Intonia software application

See Figure 4.2 for an example of an unadjusted pitch on the Intonia visual display.

Figure 4.2. An unadjusted pitch in the Intonia software application

On occasion, fluctuations in pitch occurred due to exceptionally slow bow speed during bow direction changes performed by the participant. What looked like an intonation adjustment from the visual display in Inonia, however, was actually a performance error. Pitch deviation and poor tone quality near the frog and tip are caused by the slowing of the bow and is a typical characteristic of an inexperienced string player.

When changing bow direction from a down bow to up bow, and vice versa, the bow physically comes to a stop. An experienced string player has the skill to make direction changes smooth and connected, without slowing the bow, so they are less noticeable.

Contrarily, an inexperience player will sometimes slow the bow prior to a change in direction that can result in a flattening of pitch.

The occurances of technical errors were not classified as intonation adjustments.

Had the researcher only relied on the Intonia visual display to detect adjustment in intonation, the above mentioned performance errors might have been mistakenly identified as an intentional pitch adjustment. The performance errors may display fluctuations in pitch level, however, only those pitch adjustments made by a participant moving a finger on a string were tallied as pitch adjustments for the purposes of this study. The adjustments made by participants moving fingers on the figerboard were identified both by the Intonia software and aurally by ther researcher.

The numbers of identified pitch adjustments were converted to mean values and revealed that participants adjusted their pitch more frequently when accompanied than when unaccompanied. Representative descriptive statistics can be found in Table 4.18.

Table 4.18

Pre- and posttest pitch adjustment count means

Pretest Posttest Std. Std. Std. Std. N Mean Deviation Error Mean Deviation Error Pitch Matching (PM) 15 3.80 3.529 .911 5.73 3.731 .963

Drone (D) 15 2.67 2.554 .659 2.20 2.007 .518 Pitch Matching + 20 2.80 2.167 .484 4.40 2.798 .626 Drone (PMD) Total 50 3.06 2.736 .387 4.14 3.182 .450

The pitch matching group showed the greatest number of adjustments overall.

Adjustment amounts increased in participants using an accompaniment in both the pre- and posttests. Significant differences were found between groups in the ANOVA with a result of .006 (p < .01) as shown in Table 4.19.

Table 4.19

Analysis of variance for pitch adjustment count means

Sum of Mean Squares df Square F Sig. Pretest Between Groups 11.887 2 5.943 .787 .461

Within Groups 354.933 47 7.552

Total 366.820 49 Posttest Between Groups 95.887 2 47.943 5.631 .006

Within Groups 400.133 47 8.513

Total 496.020 49

Post hoc tests reveal significant differences in posttest adjustment count means between PM and D groups (See Table 4.20).

Table 4.20

Tukey HSD for pitch adjustment count means

95% Confidence Mean Interval Dependent (I) (J) Difference Std. Lower Upper Variable Group Group (I-J) Error Sig. Bound Bound Pretest PM D 1.133 1.003 .501 -1.30 3.56 Absolute PMD 1.000 .939 .540 -1.27 3.27 Cent D PM -1.133 1.003 .501 -3.56 1.30 Deviation PMD -.133 .939 .989 -2.40 2.14 PMD PM -1.000 .939 .540 -3.27 1.27 D .133 .939 .989 -2.14 2.40 Posttest PM D 3.533* 1.065 .005 .95 6.11 Absolute PMD 1.333 .997 .382 -1.08 3.75 Cent D PM -3.533* 1.065 .005 -6.11 -.95 Deviation PMD -2.200 .997 .080 -4.61 .21 PMD PM -1.333 .997 .382 -3.75 1.08 D 2.200 .997 .080 -.21 4.61 *. The mean difference is significant at the 0.05 level.

Accuracy after adjustment

The following analysis addresses only the accuracy of the pitches that were adjusted; non-adjusted pitches are not included. The analysis of cent deviations examined if an adjustment produced more accurate intonation under each treatment condition.

Unaccompanied scales pitch adjustments also were assessed.

All of the combined pre- and posttest scores were compared, regardless of treatment. The results showed that a total of 33 participants (66%) adjusted pitch at least

94 once during the pretest and 42 participants (84%) adjusted pitch during the posttest, an increase of 18%. Table 4.21 reveals the number and percentages of participants that made intonation adjustments in pre- and posttests. More participants from each group made adjustments in the posttest, with the pitch-matching group revealing the greatest increase

(26%), compared to the increases made by the PMD (20%) and the D (6.6%) groups.

Table 4.21

Participants who adjusted pitch in pre- and posttests

Treatment Group Pretest Posttest Pitch-matching (PM) 10 (66.6%) 14 (93%) Drone (D) 9 (60%) 10 (66.6%) Pitch matching plus drone (PMD) 14 (70%) 18 (90%) Total 33 (66%) 42 (84%)

The mean adjustment accuracy scores show a similar pattern to the pitch accuracy scores of all participants; there were only slight, yet not significant, changes in pitch accuracy from pre- to posttest (see Table 4.22). Both the PM and D groups show a small amount of improvement and the PMD group’s mean score was slightly elevated in the posttest.

Table 4.22

Total mean cent deviation of adjusted pitches

Posttest Pretest Std. Std. N Mean Deviation N Mean Deviation Pretest PM 10 15.740 10.9003 14 12.864 8.5437 D 9 12.978 10.2120 10 10.130 6.8479 PMD 14 12.179 7.4588 18 14.728 9.1934 Total 33 13.476 9.1923 42 13.012 8.4740

An Analysis of Variance was used to examine any differences between and within groups; significant differences were not found (see Table 4.23).

Table 4.23

Analysis of variance for mean cent deviation

Sum of Mean Squares df Square F Sig. Pretest Between Groups 77.057 2 38.53 .440 .648 Within Groups 2626.863 30 87.56 Total 2703.921 32 Posttest Between Groups 136.355 2 68.18 .947 .397 Within Groups 2807.789 39 72.00 Total 2944.144 41

Next, the unaccompanied and accompanied adjusted pitches were analyzed using an Analysis of Variance. Once again, no differences were found between treatment 96 groups. Pitch accuracy did not significantly improve among those who adjusted pitch,

Table 4.24 and 4.25 shows descriptive statistics and the ANOVA.

Table 4.24

Absolute cent deviation of unaccompanied and accompanied adjusted pitches, by group

Unaccompanied Pretest Posttest Std. Std. N Mean Deviation N Mean Deviation PM 9 16.356 12.6234 14 13.143 9.9837 D 6 10.683 10.6747 8 11.638 9.0410 PMD 9 12.211 11.4448 11 16.491 11.6227 Total 24 13.383 11.4740 33 13.894 10.2189

Accompanied Pretest Posttest Std. Std. N Mean Deviation N Mean Deviation PM 10 13.430 10.8807 12 13.575 9.8109 D 9 14.656 12.1617 9 10.644 6.5966 PMD 13 10.823 6.4528 18 13.872 10.2933 Total 32 12.716 9.5613 39 13.036 9.2845

Table 4.25

Analysis of variance of unaccompanied and accompanied adjusted pitches

Sum of Mean Squares df Square F Sig. Pretest Between 135.614 2 67.807 .492 .618 Unaccompanied Groups Within 2892.419 21 137.734 Groups Total 3028.033 23 Pretest Between 85.536 2 42.768 .451 .641 Unaccompanied Groups Within 2748.426 29 94.773 Groups Total 2833.962 31 Posttest Between 122.817 2 61.408 .572 .570 Unaccompanied Groups Within 3218.802 30 107.293 Groups Total 3341.619 32 Posttest Between 67.549 2 33.774 .379 .687 Accompanied Groups Within 3208.101 36 89.114 Groups Total 3275.650 38

Chapter 5: Summary, Conclusions, Recommendations, and Implications

Summary

The purpose of the study was to determine if practicing scales with a tonic drone audio accompaniment might increase the pitch accuracy of beginning-level violin and viola players.

The research questions related to the purpose of the study were:

1. Do beginning string students play with greater pitch accuracy following

training with tonic drones compared to pitch matching alone, or pitch

matching with tonic drone accompaniments?

2. Does the pitch accuracy of students who have learned to play scales initially

with the use of an accompaniment track change once students play the same

scales without an accompaniment track?

3. Are intonation tendencies toward sharpness or flatness for particular scale

degrees different for students when they play with a drone accompaniment

compared to when they play without a drone accompaniment?

4. Do students more frequently attempt to adjust the accuracy of their pitches

when playing with a tonic drone compared to those who use pitch matching

alone, or pitch matching with tonic drone accompaniments?

5. Do students adjust the intonation of their pitches to be more accurate when

playing scales with a drone accompaniment compared to pitch-matching

alone, or pitch matching with tonic drone accompaniments?

The study was a quasi-experimental pre/posttest design. Participants were 50 seventh-grade violin and viola students in the second-year, from three middle schools in a large suburban public school district in the Southeast. Students were tested for performance pitch accuracy on the D- and C-major scales with and without a harmonic accompaniment. All participants had less than two years playing experience with no instruction other than whay they received in their school string class.

Participants in were divided into groups by their string class period. Each of the three schools had two seventh-grade orchestra classes, for a total of six classes. The six classes were randomly assigned to one of three treatment groups: pitch-matching (PM), tonic drone (D), and pitch matching with a tonic drone (PMD). There were 15 participants in the PM group, 15 in the D group, and 20 in the PMD group. The groups were different only in the harmonic audio accompaniment that was to be used during testing and the treatment period.

Participants were recorded, on the pre- and posttest, performing the D-major and

C-major scales twice, once with a harmonic accompaniment and once without, for a total of four scale performances. Participants performed along with audio accompaniments that were played over loudspeakers by a CD boom box. The delivery of the accompanied and unaccompanied performances was randomized. The researcher or a research assistant tuned open strings (to A440 standard) with an electronic tuner, then a lavaliere microphone was affixed to the students’ instruments and performances were recorded

100

using a digital PCM audio recorder.

Recorded audio was analyzed for pitch accuracy using Intonia software. Intonia is

a computer application that opens audio files, graphically displays pitch, and delivers cent

deviation analysis. For each pitch, approximately a one-second fragment of sound was

selected and analyzed for cent deviation. Only pitches played with left hand fingers

pressed down on the fingerboard were selected for pitch accuracy measurement. Open

string intonation, those pitches that are produced by playing strings with no fingers

touching the fingerboard, were not evaluated.

Data consisted of cent deviations from equal temperament tuning for each

fingered pitch; this resulted in the collection of 44 data points per student on each pre-

and posttest. The 44 data points were derived from four scales, each consisting of 11

measurable pitches.

The treatment consisted of participants practicing scales in groups within their school orchestra class using the different audio accompaniments. Treatment lasted for a period of seven school days. Scripts of the daily lessons were provided to the classroom teachers to lead students through the scale-practicing procedures.

Recording procedures were repeated for the posttest. Both the pretests and posttests were analyzed for cent deviation from equal temperament. Then the analyses of the pretests were compared to those found in the posttests.

Conclusions

Results revealed no differences in pitch accuracy overall, within, or between groups from pretest to posttest. Additionally there were no differences in accompanied

101

compared to unaccompanied performances.

Nonparametric analysis included examining pitch distance from equal

temperament and whether they were performed sharp or flat. A value of “sharp” or “flat”

was assigned to each measured pitch based upon the directional cent deviation score. If a

pitch was sharp, by any amount, it was labeled sharp, the same held true for all flat

pitches. The sharp and flat values were tallied for each pitch and were categorized by

group. Results revealed that those pitches identified as different from the expected pitch were more often flat than sharp, although not significant. The tendency was for students in all groups to play pitches flat compared to the standard appeared in both the pre- and posttests. The evidence of students playing flat, when not matching the standard, contradicts much research that shows string players err towards playing sharp (e.g. Duke,

1985, Geringer, 1983, Karrick, 1998, Worthy, 2000). Nonparametric analysis does not show the amount of flatness or sharpness, but provides a simplified view of pitch direction.

Scale performances were screened for intonation adjustments, and any pitch adjustments were tallied. A pitch was considered adjusted if the participant made a change to the pitch by altering the placement of a left-hand finger on the fingerboard.

Results showed increases in the frequency of pitch adjustments when participants performed with an audio accompaniment compared to unaccompanied performances. The increase in the frequency of adjustments when using accompaniment was present during the pretest and showed significance in the posttest results. Specifically, students in the pitch-matching group adjusted more often than the drone group, and significantly more

102

frequently than those in the pitch matching plus drone group. Performing with an

accompaniment can change the way musicians think about their performance. Playing with an accompaniment requires that the musician make adjustments to a performance in terms of balance, blend, tone production, and intonation. In this study, the drone and pitch matching accompaniments caused students to listen and make adjustments to

intonation. Because there were more intonation adjustments that occurred in the pre-test,

even before training with an accompaniment, it displays the power that accompaniment

can have on a musician of any age or experience level when performing with a reference

stimulus that is sounding at the same time.

Although it was my hypothesis that participants would make significant gains in

pitch accuracy after practicing with drone-based accompaniments, this study does not

show any significant gain from pretest to posttest under accompanied versus

unaccompanied conditions, overall, or between groups. Variables that may have impacted

the results, to be described in detail later, include the factors of age, experience, level of

instrument technique, treatment duration, timing of testing within the academic year, and

type of instruction received.

In the analysis of directional (flat and sharp) cent deviation, it was found that flat

deviation outweighed sharp at a ratio of 1.67 to 1, across all performances. The

preference for flatness even increased in the posttest results following treatment. This

finding is in contradiction with much of the prior research. Numerous studies have shown

that an overall inclination to perform sharp was prominent in both experienced and

inexperienced musicians (e.g. Duke, 1985, Geringer, 1983, Karrick, 1998, Salzberg,

103

1980, Small, 1937, Worthy, 2000) and in a variety of contexts involving pitch perception

and performance (e.g. Geringer & Witt, 1985; Kantorski, 1986; Madsen, 1974; Madsen,

Edmonson, & Madsen, 1969; Mason, 1960; Papich & Rainbow, 1974; Salzberg, 1980;

Sogin, 1989; Yarbrough & Ballard, 1990; Cummings, 2007). When comparing the means

of directional deviation, there were no significant differences overall or between groups

from pretest to posttest.

There are many factors that can lead to flatness in young string students. Some of

these elements include the lack of refined aural discrimination skills, incorrect technical

skills, and poor instrument quality. In a recent study, Hopkins (in press) found that

middle school students generally tuned open strings in the flat direction, which concurs

with the results in this study.

Musicians can increase aural discrimination skills through experience and

training, however the participants in this study were beginning-level instrumentalists

without private lessons or additional training beyond their school string class. Many

studies involving intonation in string players have included older, more experienced

students as participants (e.g. Geringer & Witt, 1985; Sogin, 1989; Worthy, 2000).

Perhaps participants in this study had difficulty in discriminating small discrepancies in

pitch because they have had less developed aural training through their limited string

instrument experiences. Unfortunately, most previous research does not examine

beginner-level string players’ intonation tendencies. It appears that this trend toward flatness may be true of young string students and more research should be conducted

104 involving beginning-level string players to confirm this possible tendency toward flatness.

Typically, a student-level instrument is inferior in quality to those played by advanced, more mature students. Lower quality instruments may include tuning pegs that slip, fine tuners that are difficult to turn, and strings that don’t stay in tune. With low quality instruments, it is possible that even in the short time between the when participants were tuned and the time that they performed, the instrument could have gone out of tune.

It is common tuning practice, in string playing, to adjust fingered pitches to an open string (e.g. Reel, 2005; Raab, 1978; Watkins, 2004). This technique essentially utilizes an open string as a reference drone pitch. When a string player tunes consonant pitches with this method they often use just intonation to eliminate beats (Watkins, 2004;

Whitcomb, 2007). In a similar manner, it would be reasonable to assume that just intonation could be used when tuning pitches with drone-based accompaniments (Jagow,

2012). In this study, the large number of flat responses (as measured using the equal temperament standard) on the third, sixth, and seventh scale degrees can suggest that participants may have begun listening and correcting pitch errors that resulted in what may be an inclination to adhere to just intonation. When paralleled with the equal temperament standard, just intonation requires that specific scale degree be altered by different amounts. These adjustments are necessary because equal temperament is a sacrifice from the pure harmonies within the natural overtone series. Table 5.1 shows the

105 amount of a pitch adjustment (in cents) from equal temperament of each major scale interval when a musician performs scales using just intonation.

Table 5.1

Interval adjustment for a major scale from equal temperament to just intonation

Scale Degree 1 2 3 4 5 6 7 8 (Major Scale) Adjustment 0 +4 -14 -2 +2 -16 -12 0 (in cents)

It should be noted that the sixth and seventh scale degrees (the notes B and C- sharp) of the D-major scale and the seventh scale degree (the note B) of the C-major scale were flat most often across all treatment groups. This flatness somewhat coincides with the interval adjustments required for just intonation. Further detailed research is warranted to determine if beginning-level string players adjust pitch when using drones to reject equal temperament and conform to the just intonation standard.

In addition to pitch accuracy, each occurrence of an adjusted pitch in the study was tallied. Analysis revealed that students adjusted pitch more frequently from pretest to posttest under both accompanied and unaccompanied treatment conditions. For example, pretest results displayed a greater number of pitch adjustments when accompanied than when unaccompanied. Perhaps this is because an audio accompaniment provided an aural reference point for participants to better gauge their accuracy. The pretest results confirm the hypothesis that performing with an accompaniment has a positive effect on in the frequency of intonation adjustments made by of beginning-level violinists and violists. 106

In the posttest, pitch adjustments were significantly more frequent than in the

pretest. It is reasonable to assume that the scripted instructions along with systematic

classroom practice of the scales with an accompaniment affected the increased frequency

of adjustments. During the seven-day treatment period between the pre- and posttests, the

instruction delivered by classroom teachers helped participants become more aware of

how pitches are altered by changing placement of fingers on the fingerboard. The posttest

revealed an increase in pitch adjustments across all groups for the accompanied items,

however the pitch-matching group made more frequent adjustments. Perhaps these results

are based on the simple and direct nature of pitch matching accompaniment: it requires a

single skill rather than with drone accompaniment that requires the ability to harmonize.

Pitch-matching can be considered one of the fundamental forms of ear training, as it is required to perform in unison with other people. A more complex method of ear training is harmonization. Tuning to a drone accompaniment or other reference falls in this category; it requires the ability to hear oneself, recognize the desired interval, and adjust pitch to accurately harmonize.

When the D-major and C-major scales were compared, more pitch adjustments were made when students performed the C-major scale in both the pre- and posttest. It is possible that the notes in the C-major scale, and the required left-hand techniques to play a C-major scale, were more recently taught to students in the sequence of their classroom string lessons. As found in most beginner string method books it is typical that the first notes and fingerings learned are those in the D-major scale (e.g. Allen, Gillespie, &

Tellejohn Hays, 2004; Dabczynksi, Meyer, & Phillips, 2002; Phillips, Boonshaft, &

107

Sheldon, 2010; Shade, Woolstenhulme, & Barden, 2010). Other keys and scales are learned after the notes in the key of D-major have been well established. It was confirmed with the classroom teachers at all three sites that the C-major scale was more recently learned than the D-major scale. The newness of the C-major scale may have created a sense of alertness in students that would cause them to pay close attention to pitch details when playing this scale as to ensure that the correct notes were played. When learning the

C-major scale after the D-major scale, it requires that the notes F-sharp and C-sharp be altered to F-natural and C-natural. The alteration of these notes requires a new left-hand technique; a new pattern of whole steps and half steps must be played with the left hand to produce the F-natural and C-natural.

Each adjusted pitch was tallied for frequency and results indicated that, while not significant, the most frequently adjusted pitch was F-natural, the fourth scale degree of the C-major scale. It is played with a second finger placed on the D-string, one-half step away from the first finger E that is performed with the first finger. Perhaps the F-natural may have been the note most frequently adjusted because it was the note most recently introduced to students in their learning sequence at the time of testing. The teaching of F- natural was done at nearly the same time in each of the three school sites used in the study. I verified this post hoc from the string teacher at each of the three schools: F- natural was the newest note learned among all of the pitches in both the D-major and C- major scales used to measure the intonation skills of the students in the posttest. When an important task or new concept is introduced to young students, it can create a sense of urgency that draws attention to that particular task, that is, students focus on the task most

108 recently learned. In the pedagogical sequence used with beginning violin and viola students, the notes in the key of D-major are learned first. The notes in the D-major scale are D, E, F#, G, A, B, C#, and D (ascending and descending). The note F-sharp is played with a second finger on the D-string that is one whole step away from E, the first finger.

The D-major scale is played with second and third fingers closer together on the fingerboard to form a half step on the D and A string. The pitches on a single string can be grouped into a unit known as a finger pattern (Allen, Gillespie & Tellejohn Hayes,

2004; Bornoff, 1948; Hamann & Gillespie, 2013). The use of finger patterns as a teaching tool can help students organize information and provide a visual representation of the hand on the fingerboard. See Figure 5.1 for illustrations of the major finger pattern

(where second and third finger patterns create a half step) and Dorian finger pattern

(where first and second fingers create a half step).

Figure 5.1a: Major finger pattern Figure 5.1b: Dorian finger pattern

Figure 5.1. The figures illustrate the two finger patterns used by violinists and violists in this study. The major finger pattern is used to play the one-octave D-major scale and the Dorian finger pattern is used to play the C-major scale. From “Essential Elements for Strings” by M. Allen, R. Gillespie, and P. Hayes 2004, p. 10 & 38. Copyright 2004 by Hal Leonard Corporation. Used with permission.

109

As previously mentioned, students in school string classes typically learn notes in the D-major scale prior to those in the key of C-major. To play the notes in a D-major scale, a violinist or violist must place their first finger one whole step away from the nut.

This produces the pitch E on the D string, and B on the A string. Following this, the second is placed a whole step away from first finger, and the third finger is placed close to the second finger to form a half step. This produces the notes F-sharp and G on the D string, and C-sharp and D on the A string. Playing notes in the key of C-major requires that the learned F-sharp from the D-major scale to be altered to an F-natural, and the learned C-sharp from the D-major scale be altered to a C-natural. Moving the second finger down one half step on the fingerboard create these new notes and a new pattern of whole steps and half steps in the left hand. In the key of C-major, the first and second fingers form a half step. The four notes played on a single string with the first, second, and third fingers form a tetrachord; a four-note pattern. These finger patterns are used in string pedagogy to provide a framework for whole steps and half steps within the left hand. Alteration of the second finger changes the pattern in the left-hand from a major tetrachord to a Dorian tetrachord. For example, the notes D, E, F-sharp, and G are the notes in the major tetrachord on the D string, and the notes D, E, F-natural, G are the notes in the Dorian tetrachord.

Madsen and Geringer (1976) speculated that a degree of aural discrimination is an important prerequisite to performance proficiency. It may be assumed, because of the wide range of measurements and severity of some of the inaccuracies, that some subjects did not possess a level of judgement necessary to adequately complete the task of

110

changing F-sharp to F-natural and C-sharp to C-natural when playing a D-Major scale

compared to a C-Major scale. Perhaps, more experienced participants would have

demonstrated the benefits of drone-based accompaniments because they would have had

more time performing in groups and more experiences playing literature with these

harmonies.

As students gain experience they should become more proficient with basic

instrument technique, such as body and instrument posture, left hand position, and tone

production. The mastery of these basic skills allows students to begin focusing on more

complex issues, such as intonation. In addition, as students progress in their musical

development, they are afforded the opportunity to harmonize more often than in

beginning level classes. Through dedicated instruction on how to listen for harmony and

experiences playing harmonically with others, students may become more aware of correcting and adjusting their pitches, and therefore, may increase their responsiveness to a drone-based harmonic accompaniment in their individual practice.

Researchers have shown that age and experience effect pitch perception and performance (e.g. Hopkins, in press; Yarbrough, Green, Benson, & Bowers, 1991;

Yarbrough, Karrick & Morrison, 1995; Yarbrough, Morrison & Karrick, 1997). Some students had difficulty producing an acceptable tone and seemed to be focused merely on the task of playing the correct notes. The task of playing the notes in tune may have been a factor participants were not mentally or technically prepared for yet Hopkins’ (in press) study of open string tuning suggests that beginning-level string players had not yet developed the pitch perception necessary to accurately tune a stringed instrument.

111

It is my view that using drone-based accompaniments would increase pitch accuracy following treatment. The anecdotal evidence based on more than a decade of teaching experience using similar drone-based scale accompaniments that gain in intonation accuracy could be made by second-year string players. While no formal research was conducted, in my years working with beginning-level string students it was noticed that students’ pitch accuracy improved after playing with drone-based accompaniments and particularly an accompaniment that simulated the pitch matching plus drone track used in this study. In addition, in this study, students seemed to demonstrate they were better able to listen for mistakes and adjust their pitch to match the drone. Unfortunately, the data from this study do not support this view. Since I am not willing to give up this perspective yet, more research is needed in this area. It is possible that the length of treatment time was too short or that the instruction by the teachers was not specific and systematic to train students how to listen to intervals to tune to the drone.

While the age and experience level of a student can impact pitch discrimination and performance (e.g. Morrison, 2000; Stauffer, 1995; Yarbrough, Morrison, & Karrick,

1997; Yarbrough, Green, Benson & Bowers, 1991), likewise, the duration of treatment time can also be a factor. The current study provided treatment for a total of seven class periods only using the accompaniments as part of the daily warm up. Perhaps this length of instruction was not adequate enough for students to fully develop their aural with technical skills and, ultimately, demonstrate improved intonation from using accompaniments. A longer treatment period that allows more time to the practice of scales should be considered in future research.

112

As a by product of the intonation training, student’s bow control and tone quality appeared to improve, as the training required students to sustain each pitch for a duration of about 3 seconds. Playing long tones requires that a string player slow the bow to a speed that will allow for the required duration. It also requires fine adjustments to the applied amount of weight or pressure on the bow and to the bow’s contact point on string.

Tone can be altered with variants in bow speed, weight, and contact point. Playing loudly on a long pitch durations requires good bow control (control over the above mentioned factors) to maintain an even tone.

The timeframe of data collection within the academic school year may have also impacted the results. Data was collected in the second week of the school year, and it began at the end of the students’ the first week of playing instruments following a two- month summer break. Many students do not practice their instruments frequently during the summer months and must relearn technical skills and concepts upon returning the following school year. Perhaps if the data been collected a few weeks later in the school year following a period of review, students would have had more time to reacquaint themselves with their instruments and their playing skills.

The effect of stimuli has been thoroughly investigated and was carefully considered when determining what stimulus would be used for this study. Synthesized stimuli are simple to create and allow the researcher complete control over frequency selection and amplitude. Synthesized square waves were used as the stimuli in this study and were chosen based on recommendations from previous research (e.g. Cassidy, 1989;

Platt and Racine, 1985; Rakowski, 1990; Sergeant, 1973; Spiegel & Watson, 1984).

113

Spiegel & Watson (1984) found square waves to be easier for musicians and nonmusicians to discriminate when compared to other synthesized timbres. Indeed, Fyk

(1987) concluded that the quality and familiarity of sound greatly affects the precision of pitch matching. It may be that these synthesized tones were not aesthetically appealing and might not have provided the acoustic complexities and characteristic warmth that students typically experience on string instruments.

Pitch accuracy also can be affected by individual factors or in combination.

Failure to recognize a pitch that is out of tune is sometimes seen as the primary cause of inaccurate intonation. However, in this study involving very inexperienced string players,

I observed a variety of technical playing problems, such as body posture, left hand position, and bow technique, all of which can impact students’ abilities to play in tune.

Generally, technical errors may increase the likeliness that a student will play with poor intonation. For example, playing with unnatural posture limits dexterity and facility of the arms, hands, and fingers. Regardless of how well trained the students aural skills are, problems with a students’ technique can cause physical barriers for the appropriate placement of fingers on the fingerboard. Incorrect left hand position can also diminish the effectiveness of the fingers on the strings to make pitch adjustments while playing.

A common playing problem of beginning string players is a faulty instrument playing position. Generally, when a violin or viola is positioned properly on the left shoulder, it should remain at approximately a 45-degree angle left of the enter body

(Lamb & Cook, 2002). This placement allows the left arm to be in a relaxed position, even while extended, and allows the musician to play on any of the four strings without

114

tension. If the instrument moves toward the front of the body, it becomes more difficult

for the left hand to reach around the neck of the instrument, causing tension.

Additionally, the instrument needs to be positioned on a horizontal plane, generally

parallel to the floor. This allows the bow to effectively make use of gravity to remain at

the proper contact point between the bridge and fingerboard for optimum tone production

and more accurate intonation. If the horizontal plane of the instrument is broken, it puts

the instrument in a downward angle and this position allows the bow to slide near the

fingerboard, reducing tone quality and, with the incorrect amount of bow pressure, leads

to flatter intonation. For example, when the bow is drawn with a contact point on the

string, but over the fingerboard, it is very easy to flatten the pitch by applying even a

moderate amount of pressure to the bow.

Another variable that may have affected the results of this study was the use of

finger placement markers (Bergonzi, 1991). On bowed stringed instruments, the fingerboards are not marked to show where fingers should be placed to produce different pitches. Finger placement markers can come in the form or adhesive dots, tape, pencil markings, or other materials. The application of finger placement markers on student

instruments is a common practice used by beginning string teachers to assist students

with keeping a proper hand shape and teach initial finger placement (Hamann &

Gillespie, 2013; Lamb & Cook, 2002). There are philosophical differences among string

pedagogues regarding if finger placement markers should be used on beginners’

instruments. While research has shown positive effects on intonation accuracy with the

use of finger placement markers (Bergonzi, 1991), the pedagogues debate whether or not

115 students should rely solely on their aural aptitude to determine pitch, or if finger placement markers should be used to visually and tactually assist students with pitch accuracy. Unfortunately, the use of finger placement markers may allow students to attempt to visually determine their pitch accuracy rather than make decisions using aural skills. As a researcher in an educational setting, it is difficult to ask teachers to significantly change their teaching methods The teachers whose students served as subjects in the present study use finger markers as an intonation and left-hand shape aid with their beginning students. Therefore, the use of finger placement markers on the subjects’ instruments should be considered a limitation of the study. Future research should examine the effect of finger placement markers on intonation performance within a harmonic context.

In string playing, problems with the left hand often are addressed when solving intonation problems, but the right hand (bow hand) can also pose its own set of technical problems that contribute to poor intonation (Hamann & Gillespie, 2013). For example, if a string player does not maintain a consistent bow speed, intonation can fluctuate, especially if exceptionally slow bow speeds are used. We should also note that intonation problems are magnified at the tip and the frog of the bow. In string instrument bowing, the bow must be held by one end, at the frog. The end held with the hand is referred as the lower part of the bow (near the frog) and the area away from the hand is the upper part (near the tip). Because the lower part of the bow contains the weight of the hand, more weight can be applied when playing in this part of the bow. With inexperienced players, too much weight is sometimes applied, in error. Excessive weight on the string

116 forces the string to bend, and causes the pitch of that string to dip, or become temporarily flat. It was a common mistake among the participants of this study, as observed by me, that students would use too much weight near the frog of the bow, thus altering (in the flat direction) the pitch of the performed note.

Accompaniments can be a valuable tool to provide an aural reference point for musicians to use for tuning performed pitches (e.g. Coy, 2012), but are there limitations to this benefit? Can accompaniments mask poor intonation to the point where musicians chooses to no longer listen to their own pitches? When considering the results of increased adjustment frequency means in the present study, perhaps each of the accompaniments were beneficial to the participants by fostering their willingness to adjust pitch. However, after analyzing the cent deviation data and finding no significant result, one must also consider the notion that accompaniments may have a detrimental effect on the performance, particularly if used improperly. For example, students must be taught how to obtain a balance of listening to their own playing while simultaneously listening to, analyzing, and adjusting their pitches to an accompaniment.

Suggestions for Further Research

Further research is needed to address the topic of beginning-level string players and their ability to aurally discriminate pitch and perform with accurate intonation.

Specifically, more research on the use of drones as an intonation practice tool may provide data to support the recommendations for use of a drone when helping students learn to play in tune.

Based on the findings, my recommendations for further research include:

117

1. A modified replication of this study with longer treatment times might be

what is needed. Given the inexperience of these players, more time may be the

issue.

2. Slightly more experienced string students in the study might yield more

positive results. They might be able to better understand the concepts with

more experiences.

3. A larger sample might display significant differences in intonation accuracy,

pitch adjustment, and sharp/flat tendencies.

4. The implementation of a true control group; that is, a group that does not use

any accompaniment may also help to provide a baseline isolating the drone’s

effect.

5. Studies that investigate if beginning-level string instrumentalists demonstrate

a preference for Pythagorean, just, or equal temperaments in perception and

performance would be informative, give the appearance of a move toward just

intonation in this study.

6. Projects that study the effectiveness of different aural skill training sequences

for beginning-level string players that include simple pitch-matching activities

or the use of more complex harmonic soundscapes when learning how to play

in tune.

7. Research that involves comparisons of several highly detailed systematic

classroom procedures that assist students with tuning procedures could

provide useful data for in-service string teachers. A detailed, systematic

118

procedure might include scripted lesson plans that walk teachers through

implementing research-based teaching strategies to help their students tune.

For example, in Hopkins’s (2002) article on string orchestra tuning, he

outlines six stages of tuning and summarizes sequences in each stage. A study

could compare the implementation of various teaching strategies and their

effectiveness to achieve one of these stages such as his “Stage 3: Tuning in

sections, one string at a time” (p. 146).

8. Studies that examine the effects of instrument type when using drones and

drone-based audio accompaniments.

9. Intonation studies that compare the effects of age and experience of students

performing in groups. An example of this might group students into third,

fourth, and fifth year players, or beginning, intermediate, and advanced

categories to determine when the effect of a tonic drone on intonation

accuracy becomes apparent.

10. To assess the effects of drone-based accompaniments on a much larger, more

diverse population. Treatment factors could include variables such as: age and

experience, private schools; school and home environments; geographical

location including urban, rural, and suburban populations, socio-economic

status, and instrument type and quality.

11. Teachers’ value technology that helps their students play more in tune. Studies

that involve more recent computer and mobile applications using the

119

techniques examined in this study need to be conducted to determine their

effectiveness to improve student pitch accuracy.

Implications

If music educators wish to improve their students’ pitch accuracy, a significant amount of instructional time should be devoted to ensure students are playing with correct technical facility and that students have had daily in-class training devoted to aural performance skills. Unfortunately there are few resources currently available for string teachers to use that help teach their students to play in tune. Many teachers/conductors sometimes allow students on their own to discover how intonation functions (Rizzolo, 1969). When a teacher lacks dedicated intonation teaching strategies or provides corrective feedback without explanation, the results can leave students with incomplete or even inaccurate comprehension of accurate intonation (Coy, 2012).

It is the job of the teacher to set a high standard for intonation accuracy. If allowed, students will play out of tune simply because it is easier than having to learn how to play in tune. Teachers must consistently monitor the intonation accuracy of their students and find strategies that will help them understand how to correct their own intonation.

How, then, should teachers be trained to know how to adjust intonation?

Obviously a teacher must possess exceptional aural skills, including being able to: 1) efficiently assess the level of intonation of their students; 2) provide specific and immediate intonation feedback to their students regularly; and 3) have access to many

120 research-based teaching strategies to help their students learn how to play with a high standard of intonation accuracy.

The current study has confirmed that varying levels of intonation accuracy exist in beginning-level string players, which leads to a new hypothesis: beginning students must first be very confident in pitch-matching ability to be able to play in tune before they can begin using a drone pitch or other harmonic reference points when tuning. In the initial stage of learning to play a stringed instrument, students study the fundamental physical actions such as body posture, instrument posture, left-hand position, and bow hold. The learned musical exercises and melodies have a very limited note range and are performed by all instruments in unison. Playing in unison is typically taught first to beginners prior to ensemble-part playing. Precise intonation when playing unison in groups requires pitch-matching skill. Students must listen to the teacher and to each other to precisely match the pitch they are performing to others’ pitch. Pitch matching requires students to decide if they sound the same or not; there is little room for error.

In the developing stage, students should have learned to play with some level of confidence, and the musical literature should require the production of simple harmonies with other instruments. At this point, students are still also playing with like instruments which requires pitch-matching skill, but now must also blend and harmonize with other instruments.

Harmonization requires an additional level of aural comprehension because students must understand what their particular harmonic interval sounds like when compared to a reference pitch. Students must listen to their performed pitch, listen to the

121

reference pitch, then make a decision if their notes are in tune or out of tune. Once this

decision has been made, the student must tune it to harmonically match the reference tone

or group of tones, such as a chord. This decision requires more thought and a greater

understanding of musical harmony than that of pitch matching. As students’ instrumental

independence develops and the musical literature becomes more complicated, harmonic

playing becomes even more challenging. Therefore, students’ aural training sequence

needs to begin with pitch matching, and progress into listening and playing simple

harmonies. Teachers should look for ways to integrate research-based teaching strategies

into their teaching so that students may have the opportunity practice pitch matching and,

later, simple harmonization. Intonation training that involves a stimulus reference tone or

a combination of tones best simulates the scenario of performing with others in an

ensemble setting; performers must listen, analyze, and adjust pitch, if necessary, to best

fit into the harmonic landscape.

Conclusion

The current study did not support the hypothesis that playing scales with drone-

based accompaniments improves pitch accuracy of beginning-level string players given

the limitation of this study. The aforementioned factors of experience, aural

comprehension, duration of treatment, type of instruction, and testing time within the academic calendar may have made an impact on the overall results. Perhaps beginners

could increase pitch accuracy when using drones if they are systematically instructed how

to do so. The results revealed the tendency for beginning-level violin and viola students

122

to play flat, most likely due to technical inaccuracies, poor instrument quality, and a

possible inclination to adhere to just intonation.

A significant discovery was made, however, where the results revealed that beginning-level string players adjust pitch more frequently when a harmonic accompaniment was present. This trend was revealed even the pretest, though not significant. Posttest results showed an increase in pitch adjustments that was significant overall and between groups. This factor should be examined further to help determine what kind of accompaniment produces more frequent pitch adjustments.

This study involving drone-based accompaniments on pitch accuracy in beginning-level string players is the first of its kind and has highlighted a variety of factors that impact the students’ ability to learn to play in tune and requires further research. Indeed more inquiry needs to be conducted that will help clarify results of this study, provide a deeper understanding of beginning-level string players’ capabilities, and develop additional research-based teaching strategies that allow teachers to effectively and efficiently teach their students to play more in tune.

123

Bibliography

Apple, Inc. (2013). Logic Pro v. 9.1.1 [computer software]. Cupertino, CA: Apple, Inc.

Apprentice Music, LLC. (2013). Chromatic violin: Violin drones for improving intonation [CD]. Silver Spring, MD: Apprentice Music, LLC.

Agin, J. (15 Nov. 2013). Personal interview.

Agin, J. (2010). Intonia Gerald J. Agin.

Alexander, M. (2008). Teaching tuning to the string orchestra: Classroom procedures for beginning to advanced students. American String Teacher, 58(4), 20-26.

Alexander, M. L., & Henry, M. L. (2012). The development of a string sight-reading pitch skill hierarchy. Journal of Research in Music Education, 60(2), 201-216.

Alexander, M. L. (2000). Comparing the use of pure tones versus complex tones as a reference pitch for tuning the public school string orchestra. University of Houston).

Anderson, J. N. (1981). Effects of tape-recorded aural models on sight-reading and performance skills. Journal of Research in Music Education, 29(1), 23-30.

Arant,E.P. (1970). The development and evaluation of a method of voice instruction utilizing tape-recorded lesson materials.

Ary, D., Jacobs, L.C., Razavieh, A. (1972). Introduction to research in education. New York: Holt, Rinehart and Winston.

Ary, D.,. (2006). Introduction to research in education. Belmont, CA: Thomson/Wadsworth.

Atterbury, B. W., & Silcox, L. (1993). The effect of piano accompaniment on kindergartners' developmental singing ability. Journal of Research in Music Education, 41(1), 40-47.

124

Ballard, D. L. (2006). Relationships between college level wind instrumentalists' achievement in intonation perception and performance. (D.M.E., Indiana University). ProQuest Dissertations and Theses.

Ballard, D. L. (2011). Relationships between college-level wind instrumentalists' achievement in intonation perception and performance. Bulletin of the Council for Research in Music Education, (187), 19-32.

Balzano, G. J. (1982). Musical vs. psychoacoustical variables and their influence on the perception of musical intervals. Bulletin of the Council for Research in Music Education, (70), 1-11.

Barber, B. (1990). Intonation; a sensory experience. American String Teacher, 40(4), 81- 85.

Barbieri, P., & Mangsen, S. (1991). Violin intonation: A historical survey. Early Music, 19(1), 69-88.

Barbour, J. M. (1972). Tuning and temperament; a historical survey. New York: Da Capo Press.

Barnes, G. V. (2008). Challenging the middle school orchestra musician. American String Teacher, 58(3), 38-41.

Barrett, H. (1972). The viola: Complete guide for teachers and students. University, Ala.: University of Alabama Press.

Beery, C. D. B. (1996). The effects of structured singing instruction on beginning instrumental students' performance achievement.

Benson, D. (2008). Music: A mathmatical offering. Retrieved November 18, 2013, from https://homepages.abdn.ac.uk/mth192/pages/html/music.pdf

Benson, W. L. (1995). The effect of tuning stimulus vibrato, timbre, and frequency on tuning accuracy of university, high school, and junior high school instrumentalists.

Bentley, A. (1968). "Monotones": A comparison with "normal" singers in terms of incidence and musical abilities. London: Novello.

Bergan, J. R. (1966). Factors affecting pitch discrimination. Bulletin of the Council for Research in Music Education, (8), 15-21.

125

Bergonzi, L. (1997). Effects of finger markers and harmonic context on performance of beginning string students. Journal of Research in Music Education, 45(2), 197- 211.

Bergonzi, L. S. (1991). The effects of finger placement markers and harmonic context on the development of intonation performance skills and other aspects of the musical achievement of sixth-grade beginning string students. (Ph.D., University of Michigan). ProQuest Dissertations and Theses.

Bisel, L. D. (1987). Seeking a perceptual preference among pythagorean tuning, just intonation, one-quarter comma meantone tuning, and equal temperament. (Ph.D. Thesis, University of Miami).

Borup, H. (2008). Is that in tune, Mr. Mozart? American String Teacher, 58(2), 32-35.

Brick, J. S. (1983). The effects of a self-instructional program utilizing the pitch master on pitch discrimination and pitch accuracy in performance of junior high school trombonists. (Ph.D., University of Miami).

Brittin, R. V. (1993). Effects of upper and lower-register accompaniment on intonation. Journal of Band Research, 29(1), 43.

Brittin, R. V. (2002). Instrumentalists' assessment of solo performances with compact disc, piano, or no accompaniment. Journal of Research in Music Education, 50(1), 63-74.

Brown, R. A. (1996). Dynamics of intonation in performances by artist violinists.

Brown, S. E. (1991). Determination of location of pitch within a musical vibrato. Bulletin of the Council for Research in Music Education, (108), 15-30.

Brunson, T. R. (1970). An adaptation of the suzuki-kendall violin method for heterogeneous stringed instrument classes. University Microfilms.

Byo, J., Schlegel, A., & Clark, N. (2011). Effects of stimulus octave and timbre on the tuning accuracy of secondary school instrumentalists. Journal of Research in Music Education, 58(4), 316-328.

Cadek, O. (1949). String intonation in theory and practice. Music Journal, 7(3), 6.

Canelos, J. J., Murphy, B. A., Blombach, A. K., & Heck, W. C. (1980). Evaluation of three types of instructional strategy for learner acquisition of intervals. Journal of Research in Music Education, 28(4).

126

Carman, G. G. (1936). A study of intonation in violin playing. (M.S., University of Chicago).

Carmody, W. J. (1988). The effects of chamber music experience on intonation and attitudes among junior high school string players. (D.M.A., University of Southern California). ProQuest Dissertations and Theses.

Carterette, E. C., Vaughn, K., & Jairazbhoy, N. A. (1989). Perceptual, acoustical, and musical aspects of the tambura drone. Music Perception, 7(2), 75.

Cassidy, J. W. (1994). The effect of instrument type, stimulus, timbre, and stimulus octave placement on tuning accuracy. In F. Koch, W. Sims & R. Pembrook (Eds.), Missouri journal of research in music education, 1989-1994. (pp. 7-23). University of Missouri-Kansas City, Conservatory of Music, Kansas City, MO: Missouri Journal of Research in Music Education.

Codding, P. A. (1985). The effect of differential feedback on beginning guitar students' intonational performance in tuning strings (computer-assisted instruction (cai)). (Ph.D., The Florida State University). ProQuest Dissertations and Theses.

Cohen, E. (1980). There's more to good pitch than a good ear. American String Teacher, 30(1), 26-27.

Cohen, J. (2009, May 2009). Music & musicians: Strings 101 - mo' better pitch. Strings, 23, 23-23, 25.

Colley, S. C. (2015). Tuneup intonation training system. Retrieved December 12, 2015, from http://tuneupsystems.com/Home_Page.html

Colwell, R. (1970). The evaluation of music teaching and learning. Englewood Cliffs, N.J.: Prentice-Hall.

Colwell, R., & Goolsby, T. (1992). The teaching of instrumental music. Englewood Cliffs, N.J.: Prentice Hall.

Conway, C. (2003). Good rhythm and intonation from day one in beginning instrumental music. Music Educators Journal, 89(5), 26-31.

Cooper, N. (Spring-Summer 1990). Selected factors related to children's singing accuracy. Update: Applications of Research in Music Education, 8(2), 14-18.

Corso, J. F.,. (1954). Unison tuning of musical instruments. Journal of the Acoustical Society of America, 26(5).

127

Cowden, R. L. (1969). A comparison of the effectiveness of first and third position approaches to violin instruction.

Cowden, R. L. (1972). A comparison of first and third position approaches to violin instruction. Journal of Research in Music Education, 20(4), 505-509.

Coy, B. R. (2012). Pitch performance: A rational approach to the acquisition of intonation skills. Ohio State University.

Cummings, P. C. (2007). The effects of instrument type, stimulus timbre, and harmonic context on tuning accuracy. (D.M.A., University of Oregon). ProQuest Dissertations and Theses.

Curry, N. (2011). Dr. nick's steps to practicing intonation on a string instrument. American String Teacher, 61(4), 94-95.

Dabczynski, A. H., Meyer, R., & Phillips, B. (2002). String explorer: A journey into the wonders of string playing. Van Nuys, CA: Alfred Publishing Co.

Dalby, B. F. (1992). A computer-based training program for developing harmonic intonation discrimination skill. Journal of Research in Music Education, 40(2), 139-52.

Daniels, M. L.,. (1964). An investigation of the effectiveness of programed learning in the teaching of harmonic dictation in a beginning college music theory course.

Darling, L. (2004). Focal point: Strings in world music - from west to east: An introduction to Arabic string playing. American String Teacher, 54(2), 78-83.

Davis, L. M. (1981). The effects of structured singing activities and self-evaluation practice on elementary band students' instrumental music performance, melodic tonal imagery, self-evaluation, and attitude. (Ph.D., The Ohio State University). ProQuest Dissertations and Theses.

Dell, C. E. (2003). Singing and tonal pattern instruction effects on beginning string students' intonation skills. (Ph.D., University of South Carolina). ProQuest Dissertations and Theses.

Demorest, S. M., & Clements, A. (2007). Factors influencing the pitch-matching of junior high boys. Journal of Research in Music Education, 55(3), 190-203.

Dillon, J. (2003). "A Christmas Festival." Ed. Littrell, D, Racin, L. R & Allen, M. Teaching Music through Performance in Orchestra. Vol. 2. Chicago: GIA Publications, Inc. (41-46). 128

Donakowski, C. (2012). Intonation: The final frontier. American String Teacher, 62(2), 80.

Droste, D. (2013). High school orchestras: New ideas and old reminders for the new school year. American String Teacher, 63(3), 36-39.

Duke, R. A. (1985). Wind instrumentalists' intonational performance of selected musical intervals. Journal of Research in Music Education, 33(2), 101-111.

Dunnigan, P. (1999). Effects of tempo, bass loudness, and tonic chord degree on the perception and performance of intonation by wind instrumentalists.

Edmonson, F. A., III. (1972). Effect of interval direction on pitch acuity in solo vocal performance. Journal of Research in Music Education, 20(2).

Edmonson, F. A., III. (1967). The effect of interval direction on pitch acuity in solo vocal performance. (Ph.D., The Florida State University). ProQuest Dissertations and Theses.

Eisele, M. J. (1985). Development and validation of a computer-assisted instructional lesson for teaching intonation discrimination skills to violin and viola students. (D.Mus.Ed., Indiana University). ProQuest Dissertations and Theses.

Elliot J., Platt J.R., & Racine R.J. (1987). Adjustment of successive and simultaneous intervals by musically experienced and inexperienced subjects. Perception & Psychophysics, 42(6), 594-8.

Elliott, C. A. (1974). Effect of vocalization on the sense of pitch of beginning band class students. Journal of Research in Music Education, 22(2), 120-128.

Ellis, A. J. (1876). Measurement and settlement of musical pitch. Journal of the Society of Arts, 25, 664.

Ely, M. C. (1988). The effects of timbre on intonational performance and perception by college performers of selected woodwind instruments. (Ph.D., The Ohio State University). ProQuest Dissertations and Theses.

Ely, M. C. (1992). Effects of timbre on college woodwind players' intonational performance and perception. Journal of Research in Music Education, 40(2), 158- 167.

English, W. H. (1985). The relative effectiveness of the amount of piano accompaniment in beginning strings class instruction (orchestra, elementary, pitch, rhythm). (Educat.D., University of Houston). ProQuest Dissertations and Theses. 129

Ericksen, K. E. (1973). A comparison of three teaching procedures used in the development of improving intonation in clarinet performance. (Educat.D., Utah State University). ProQuest Dissertations and Theses.

Erickson, R. (1975). Sound structure in music. Berkeley: University of California Press.

Eros, J. (2009). A case study of three urban music teachers in the second stage of their teaching careers. (Ph.D., University of Michigan).

Etmektsoglou, I. E. (1992). A computer-based evaluation of pitch matching skills of college freshman students in music. (Ph.D., University of Illinois at Urbana- Champaign). ProQuest Dissertations and Theses.

Fanelli, M. (2011). Paul Rolland 1911-2011: A centenary celebration. American String Teacher, 61(1), 20-23.

Fetherston, M. D. (2011). Building memory structures to foster musicianship in the cello studio. (D.M.A., The Ohio State University). ProQuest Dissertations and Theses.

Fischer, S. (2002, Aug 2002). Intonation [string lesson]. The Strad, 113, 860-861.

Fitzpatrick, K. (2008). A mixed methods portrait of urban instrumental music teaching. (Ph.D., Northwestern University).

Fletcher, H.,. (1934). Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure. Journal of the Acoustical Society of America, 6(2).

Forsythe, J. L. (1967). A study vocal pitch acuity in the performance of musical intervals.

Foster, D. (1996). Memories of Paul Rolland: The man and his teaching. American String Teacher, 46(3), 45-48.

Frank, H. E. (2006). The relationship between singing intonation and string playing intonation in beginning violin and viola students. (M.Mus., Michigan State University). ProQuest Dissertations and Theses.

Franke, J. (2013). Violin scales: Strategies for improving intonation. American String Teacher, 63(2), 74-75.

Fyk, J. (1985). Vocal pitch-matching ability in children as a function of sound duration. Bulletin of the Council for Research in Music Education, (85), 76-89. 130

Fyk, J. (1987). Duration of tones required for satisfactory precision of pitch matching. Bulletin of the Council for Research in Music Education, (91), 38-44.

Galamian, I. (1985). Principles of violin playing & teaching. Englewood Cliffs, N.J.: Prentice-Hall.

Garman, B. R. (1992). The effects of accompaniment texture and contextual pitch distance on string instrumentalists' intonational performance. (Ph.D., University of Miami). ProQuest Dissertations and Theses.

Garofalo, R. J.,. (1996). Improving intonation in band and orchestra performance. Ft. Lauderdale, FL: Meredith Music Publications.

Gearhart, F. (2007). The use of "tartini tones" in teaching. American String Teacher, 57(3), 32-34.

Genevro, B. J. (1997). Ways to improve intonation. Teaching Music, 4(4), 30-32.

Geringer, J. M., MacLeod, R. B., & Ellis, J. C. (2014). Two studies of pitch in string instrument vibrato: Perception and pitch matching responses of university and high school string players. International Journal of Music Education, 32(1), 19- 30.

Geringer, J., MacLeod, R., & Allen, M. (2010). Perceived pitch of violin and cello vibrato tones among music majors. Journal of Research in Music Education, 57(4), 351-363.

Geringer, J. M. (1976). Tuning preferences in recorded orchestral music. Journal of Research in Music Education, 24(4)

Geringer, J. M. (1978). Intonational performance and perception of ascending scales. Journal of Research in Music Education, 26(1), 32-40.

Geringer, J. M. (1983). The relationship of pitch-matching and pitch-discrimination abilities of preschool and fourth-grade students. Journal of Research in Music Education, 31(2), 93-99.

Geringer, J. M. (1976). Intonational performance and perception of accompanied and unaccompanied ascending scalar patterns. 131

Geringer, J. M., & Madsen, C. K. (1984). Pitch and tempo discrimination in recorded orchestral music among musicians and nonmusicians. Journal of Research in Music Education, 32(3), 195-204.

Geringer, J. M., & Madsen, C. K. (1998). Musicians' ratings of good versus bad vocal and string performances. Journal of Research in Music Education, 46(4), 522-34.

Geringer, J. M., & Witt, A. C. (1985). An investigation of tuning performance and perception of string instrumentalists. Bulletin of the Council for Research in Music Education, (85), 90-101.

Geringer, J. M., & Worthy, M. D. (1999). Effects of tone-quality changes on intonation and tone-quality ratings of high school and college instrumentalists. Journal of Research in Music Education, 47(2), 135-149.

Geringer, J., & Madsen, C. (1981). Verbal and operant discrimination-preference for tone quality and intonation. Psychology of Music, 9(1), 26-30.

Gibons, S. (2000). Teaching methods: Fiddling around with the Bornoff method. American String Teacher, 50(2), 42-43.

Gillespie, R. (1991). Research in string pedagogy for developing the playing skills of students in string classes. Dialogue in Instrumental Music Education, 15(1), 32- 46.

Goetze, M. (1989). A comparison of the pitch accuracy of group and individual singing in young children. Bulletin of the Council for Research in Music Education, (99), 57-73.

Goodwin, M. A. (1990). The effectiveness of "pitch master" compared to traditional classroom methods in teaching sightsinging to college music students. (Ph.D., University of South Florida). ProQuest Dissertations and Theses.

Gordon, E. (1997). Learning sequences in music : Skill, content, and patterns : A music learning theory. Chicago: GIA.

Greene, P. C. (1937). Violin intonation. The Journal of the Acoustical Society of America, 8(3), 207-207. doi:http://dx.doi.org.proxy.lib.ohio- state.edu/10.1121/1.1901994

Greene, P. C. (1937). Violin performance with reference to tempered, natural, and pythagorean intonation. Iowa City, Iowa: University of Iowa Press.

132

Greer, R. D. (1970). In Gordon, Edwin,, (Ed.), The effect of timbre on brass-wind intonation. Iowa City: University of Iowa Press.

Greer, R. D.,. (1969). The effect of timbre on brass-wind intonation. University of Michigan).

Griswold, H. E. (1988). How to teach aural skills with: Electronic tuners. Music Educators Journal, 74(5), 49-51.

Grunow, R. F., Gordon, E.,& Azzara, C.D. (1999). Jump right in : The instrumental series : Teacher's guide (2nd ed. ed.). Chicago, IL: G.I.A. Publications.

Grutzmacher, P. A. (1987). The effect of tonal pattern training on the aural perception, reading recognition, and melodic sight-reading achievement of first-year instrumental music students. Journal of Research in Music Education, 35(3).

Hajdu, G. (1993). Low energy and equal spacing; the multifactorial evolution of tuning systems. Interface, 22(4), 319-333.

Hall, D. E.,. (1986). Musical acoustics an introduction. Belmont, California: Wadsworth.

Hamann, D. L., & Gillespie, R. (2013). Strategies for teaching strings : Building a successful string and orchestra program. New York: Oxford Univ. Press.

Harbaugh, R. (2009). Studio tips: Ensembles: An owner's manual. American String Teacher, 59(3), 61-63.

Harper, K. (1998). Harmonics and double-stop effects on tuning. American String Teacher, 48(2), 43-44.

Harris, T. J. (1977). An investigation of the effectiveness of an intonation training program upon junior and senior high school wind instrumentalists. (Educat.D., University of Illinois at Urbana-Champaign). ProQuest Dissertations and Theses.

Hayes, T. E. (2009). Achievement of middle school wind instrumentalists in performance and perception of intonation. (Ph.D., Indiana University). ProQuest Dissertations and Theses.

Henning, G. S. (1968). Effect of harmonic components on frequency discrimination. The Journal of the Acoustical Society of America, 44(5), 1386-9.

Hopkins, M. (2002). Six stages of tuning stringed instruments in orchestra. American String Teacher, 52(3), 64-67, 69.

133

Hopkins, M. (2003). Good hand position and posture improve string intonation. The Instrumentalist, 58, 44-44, 46, 48.

Hopkins, M. (2012). Strategies for improving the intonation of your orchestra. American String Teacher, 62(4), 24-28.

Hopkins, M. T. (2013). Teachers' practices and beliefs regarding teaching tuning in elementary and middle school group string classes. Journal of Research in Music Education, 61, 1, 97-114.

Hopkins, M. T. (2014). Pilot-testing of new software for measuring string players instrument tuning skills. Journal of Music, Technology and Education, 7, 1, 5-21.

Hopkins, M. (in press). Eighth-Grade Violinists Instrument Tuning Ability: A Comparison of Pitch Perception and Tuning Accuracy. Journal of Research in Music Education.

Hopper, G. L. (2007). The effect of singing and sliding as a music memorization strategy on the intonation skill of collegiate trombonists. (D.M.A., University of Cincinnati). ProQuest Dissertations and Theses.

Hovey, N. W. (1976). Efficient rehearsal procedures for school bands. Elkhart, Ind.: Selmer Co.

Humphreys, J. T. (1986). Measurement, prediction, and training of harmonic audiation and performance skills. Journal of Research in Music Education, 34(3).

Jacobus, C. (2009). Urban orff: The music and philosophy of carl orff as it relates to no child left behind in urban schools. (M.A., California State University, Dominguez Hills).

Jagow, S. (2012). Tuning for wind instruments : A roadmap to successful intonation. Galesville, Md.: Meredith Music Publications.

Johnson, K. (2008). An examination of factors impacting the quality of music education in the urban environment. (M.S., Tennessee State University). , 67.

Jones, S. A. (2003). The effect of vocalization on pitch discrimination among high school instrumentalists. (Ph.D., University of Minnesota). ProQuest Dissertations and Theses.

Kanable, B. (1969). An experimental study comparing programed instruction with classroom teaching of sightsinging. Journal of Research in Music Education, 17(2), 217-226. 134

Kantorski, V. J. (1984). The effects of differential accompaniment on string instrumentalists' intonational performance in extreme registers (scales, direction, intervals). (Ph.D., The Florida State University). ProQuest Dissertations and Theses.

Kantorski, V. J. (1986). String instrument intonation in upper and lower registers: The effects of accompaniment. Journal of Research in Music Education, 34(3), 200- 210.

Karrick, B. (1998). An examination of the intonation tendencies of wind instrumentalists based on their performance of selected harmonic musical intervals. Journal of Research in Music Education, 46(1), 112-27.

Keislar, D. F. (1991). Psychoacoustic factors in musical intonation: Beats, interval tuning, and inharmonicity. (Ph.D., Stanford University). ProQuest Dissertations and Theses.

Kimber, M. (1992). Teaching a Melodic/Harmonic awareness of intonation. American String Teacher, 42(2), 59-64.

King, B. M., & Minium, E. W. (2008). Statistical reasoning in the behavioral sciences. Hoboken, NJ: John Wiley & Sons.

Klotman, R. (1981, Apr 1981). Teaching intonation. The Instrumentalist, 35, 46.

Kohut, D. L. (1973). Instrumental music pedagogy: Teaching techniques for school band and orchestra directors. Englewood Cliffs, N.J: Prentice-Hall.

Kopiez, R. (2003). Intonation of harmonic intervals: Adaptability of expert musicians to equal temperament and just intonation. Music Perception: An Interdisciplinary Journal, 20(4), 383-410.

Krumhansl, C. L. (2001). Cognitive foundations of musical pitch. New York: Oxford University Press.

Kubiak, P. V. (1983). Improving pitch accuracy and intonation among high school trumpet players with the implementation of pitch level supports. UMI).

Lader, E. C. (1977). The effect of differential treatments on the intonation of string instrumentalists.

Lamb, N., & Lamb Cook, S. (2002). Guide to teaching strings (7th ed.). New York: McGraw-Hill. 135

Latten, J. E. (2003). Exploration of a sequence for teaching intonation skills and concepts to wind instrumentalists. (Ph.D., The Pennsylvania State University). ProQuest Dissertations and Theses.

Latten, J. E. (2005). Exploration of a sequence for teaching intonation skills and concepts to wind instrumentalists. Journal of Band Research, 41(1), 60-87.

Laycock, M. (2012). Here comes the judge. American String Teacher, 62(3), 28-32.

Lee, L. (2013, Feb 2013). 4 steps to better intonation, chord awareness and musical freedom. Strings, 27, 21-22.

Lee, L. (2013, Jul 2013). Think you're in tune? Ahink again. And try these tips. Strings, 27, 19-20.

Lehman, P. (1968). Tests and measurements in music. Engelwood Cliffs, NJ: Prentice- Hall.

Lewis, R. (1998). Chamber music intonation. American String Teacher, 48(2), 39-42.

Lichte, W. H.,. (1941). Attributes of complex tones. Journal of Experimental Psychology, 28(6), 455-480.

Lloyd, L. S. (1940). The myth of equal temperament. Music & Letters, 21(4), 347-361.

Lochstampfor, M. L., & Butler, D. (1990). The effects of timbre on aural skills : An exploration of the attributes of timbre and spectral parsing for sounds used in aural training.

Loosen, F. (1993). Intonation of solo violin performance with reference to equally tempered, pythagorean, and just intonations. Journal of the Acoustical Society of America, 93(1), 525.

Loosen, F. (1994). Tuning of diatonic scales by violinists, pianists, and nonmusicians. Perception & Psychophysics, 56(2), 221-6.

Loosen, F. (1995). The effect of musical experience on the conception of accurate tuning. Music Perception, 12(3), 291.

Lynch M.P., & Eilers, R.E. (1992). A study of perceptual development for musical tuning. Perception & Psychophysics, 52(6), 599-608.

136

Lynch, M. P. (1989). The development of musical tuning perception from infancy to adulthood. Journal of the Acoustical Society of America, 86(S1).

Maag, R. R. (1974). a comparison of the effectiveness of pentatonic versus diatonic instruction in the intonation of beginning string students. (D.M.A., The University of Texas at Austin). ProQuest Dissertations and Theses.

Madsen, C.K., Edmonson, F.A., & Madsen Jr., C.H. (1969). Modulated frequency discrimination in relationship to age and musical training. The Journal of the Acoustical Society of America, 46(6), 1468-72.

Madsen, C. K. (1960). A study of directional harmonic minor scale solo performances.

Madsen, C. K. (1966). The effect of scale direction on pitch acuity in solo vocal performance. Journal of Research in Music Education, 14(4), 266-275.

Madsen, C. K., & Geringer, J. M. (1976). Preferences for trumpet tone quality versus intonation. Bulletin of the Council for Research in Music Education, (46), 13-22.

Madsen, C. K., & Geringer, J. M. (1981). Discrimination between tone quality and intonation in unaccompanied Flute/Oboe duets. Journal of Research in Music Education, 29(4).

Madsen, C. K., & Geringer, J. M. (1999). Comparison of good versus bad tone Quality/Intonation of vocal and string performances: Issues concerning measurement and reliability of the continuous response digital interface. Bulletin of the Council for Research in Music Education, 141(141), 86-92.

Madsen, C. K., Geringer, J. M., & Heller, J. J. (1993). Comparison of good versus bad tone quality of accompanied and unaccompanied vocal and string performances. Bulletin of the Council for Research in Music Education, (119, The 14th International Society for Music Education: ISME Research Seminar), 93-100.

Madsen, C. K., Wolfe, D. E., & Madsen, C. H. (1969). The effect of reinforcement and directional scalar methodology on intonational improvement. Bulletin of the Council for Research in Music Education, (18), 22-33.

Mann, B. A. A. (2008). The effect of vocal modeling on student achievement and attitude. (Ph.D., University of Oregon). ProQuest Dissertations and Theses.

Mason, J. A. (1960). Comparison of solo and ensemble performances with reference to pythagorean, just, and equi-tempered intonations. Journal of Research in Music Education Journal of Research in Music Education, 8(1).

137

McAdow, M. (1952). Intonation Worries and Their Remedies. The Instrumentalist, 7(2).

Mchose, A. I. (1949). Harmonic foundation of string intonation. Music Journal, 7(5), 8.

Meyer, H. (1993). A computer system to improve violin intonation. (Columbia University Teachers College, ProQuest, UMI Dissertations Publishing). ProQuest Dissertations and Theses.

Millar, J. K. (1984). The aural perception of pitch-class set relations: A computer-assisted investigation (ear-training, atonal music). (Ph.D., University of North Texas). ProQuest Dissertations and Theses.

Millsap, T. A. (1999). The daily implementation of sequential sustained tone exercises as a means of improving the ensemble intonation and tone quality of second-year middle school bands. (D.M.A., University of Georgia). ProQuest Dissertations and Theses.

Mongeon, J. (2004). The effects of left-hand exercises on beginning upper string performers' intonation and facility. (Ph.D., University of Miami). ProQuest Dissertations and Theses.

Mora, L. (2007). The effects of tonal pattern training on intonation of sixth grade instrumental music students. (M.A., California State University, Fullerton). ProQuest Dissertations and Theses.

Morrison, S. J., & Fyk, J. (2002). Intonation. In R. Parncutt and G. E. McPherson (Ed.), The science & psychology of music performance (pp. 183-197). Oxford; New York: Oxford University Press.

Morrison, S. J. (2000). Effect of melodic context, tuning behaviors, and experience on the intonation accuracy of wind players. Journal of Research in Music Education, 48(1).

Nelson, D. J. (1983). String teaching and performance: A review of research findings. Bulletin of the Council for Research in Music Education, (74), 39-46.

Nickerson, J. F. (1949a). Comparison of performances of the same melody played in solo and in ensemble with reference to equal tempered, just, and pythagorean intonations. Journal of the Acoustical Society of America, 21(4).

Nickerson, J. F. (1949b). Intonation of solo and ensemble performance of the same melody. Journal of the Acoustical Society of America, 21(6)

138

Nickerson, J. F. (1949c). A comparison of performances of the same melody played in solo and in ensemble with reference to equi-tempered, just, and pythagorean intonations. (Ph.D., University of Minnesota). ProQuest Dissertations and Theses.

Nickerson, J. F. (1950). Comparison of intonation of solo and ensemble performances. Music Journal, 8(2), 21.

Nunez, M. L. (2002). Comparison of aural and visual instructional methodologies designed to improve the intonation accuracy of seventh-grade violin and viola instrumentalists. (Ph.D., University of North Texas). ProQuest Dissertations and Theses.

Ostling, A. H. (1974). Research in pythagorean, just temperament, and equal temperament tunings in performance. Journal of Band Research, 10(2), 13-20.

Papich, G., & Rainbow, E. (1974). A pilot study of performance practices of twentieth- century musicians. Journal of Research in Music Education, 22(1), 24-34.

Petzold, R. G. (1960). Development of auditory perception of musical sounds by children in the first six grades. Madison: University of Wisconsin.

Petzold, R. G. (1966). Auditory perception of musical sounds by children in the first six grades : Cooperative research project no. 1051. Madison: University of Wisconsin.

Phillips, B., Boonshaft, P., & Sheldon, R. (2010). Sound innovations for string orchestra: A revolutionary method for beginning musicians. S.l.: Alfred Music Publishing Co.

Platt Jr., R. R. (1985). Effect of frequency, timbre, experience, and feedback on musical tuning skills. Perception & Psychophysics, 38(6), 543-53.

Podnos, T. H. (1981). Intonation for strings, winds, and singers : A six-month course. Metuchen, N.J.: Scarecrow Press.

Poole, H. W. (1878). Just intonation in music. American Journal of Science, s3-15(89), 359-363.

Powell, S. R. (2010). Wind instrument intonation: A research synthesis. Bulletin of the Council for Research in Music Education, (184), 79-96.

Price, H. E. (2000). Interval matching by undergraduate nonmusic majors. Journal of Research in Music Education, 48(4), 360-372.

139

Pullman, W. S. (1919). An analytic study of music, with scales for testing musical intelligence. (Ped.D., New York University). ProQuest Dissertations and Theses.

Quindag, S. R. (1992). The effects of guided aural versus guided aural-visual modeling on the performance achievement of beginning string instrumentalists. (Ed.D., The University of North Carolina at Greensboro). ProQuest Dissertations and Theses.

Raab, E. (1978). Do you hear what l hear? American String Teacher, 28(1), 22-23.

Rakowski, A. (1985). The perception of musical intervals by music students. Bulletin of the Council for Research in Music Education, (85), 175-186.

Rakowski, A. (April 1990). Intonation variants of musical intervals in isolation and in musical contexts. Psychology of Music, 18(1), 60-72.

Reel, J. (2004). Strings 101: Sound advice - fourteen steps toward improved intonation. Strings, 19, 16-19.

Reel, J. (2005). Strings 101: Music & musicians - drone on: Your inner sense of pitch? it all comes down to one note. Strings, 20, 26-29.

Rizzolo, R. (1969). An experimental taped program to improve sensitivity to intonation.

Robinson, R. L. (1988). The development and evaluation of a computer-assisted music instruction program for the improvement of tonal memory. Computers in the Schools, 5(1-2), 129-140.

Ross, B. (2002). A violist's guide for exquisite intonation. American String Teacher, 52(3), 37.

Ross, B., & American String Teachers Association. (2004). A violinist's guide for exquisite intonation. Fairfax, Va.: American String Teachers Association.

Salzberg, R. S. (1977). The effects of visual stimulus and instruction on intonation accuracy of string instrumentalists. (Ph.D., The Florida State University). ProQuest Dissertations and Theses.

Salzberg, R. S. (1980). The effects of visual stimulus and instruction on intonation accuracy of string instrumentalists. Psychology of Music, 8(2), 42-49.

Sariti, D. (2009). Intonation demystified. American String Teacher, 59(1), 40-44.

140

Schlacks, W. F. (1981). The effect of vocalization through an interval training program upon the pitch accuracy of high school band students. (Ph.D., University of Miami). ProQuest Dissertations and Theses.

Schleuter, S. L. (1984). A sound approach to teaching instrumentalists : An application of content and learning sequences. Kent, Ohio: Kent State University Press.

Schwartz, R. (2010). The tuning C.D. [MP3 download]

Seashore, C. E. (1936). Objective analysis of musical performance. Iowa City, Ia.: The University press.

Seashore, C. E. (1967). Psychology of music. New York: Dover Publ.

Seashore, C. E. (1938). Psychology of music. New York; London: McGraw-Hill Book Company, Inc.

Selby, C. (2012). Advancing strategies for teaching orchestras to tune themselves. American String Teacher, 62(1), 88-89.

Sergeant, D. (1973). Measurement of pitch discrimination. Journal of Research in Music Education, 21(1), 3-19.

Shackford, C. R.,. (1956). Intonation in ensemble string performance. Journal of the Acoustical Society of America, 28(1), 150.

Shade, T., Woolstenhulme, J., & Barden, W. (2010). String basics: Steps to success for string orchestra.

Slayman, H. H. (1965). Problems in teaching and learning the violin: An exploratory study. (Educat.D., University of Cincinnati). ProQuest Dissertations and Theses.

Sloane, M. (2003). Cello drones for tuning and improvisation . Mendocio, CA: Navarro River Music.

Smith, D. A. (2006). The effectiveness of real-time visual feedback to improve seventh and eighth grade saxophone and trombone students' intonation accuracy. (Ph.D., Purdue University). ProQuest Dissertations and Theses.

Smith, C. (1994). Improving the intonation accuracy of string students. American String Teacher, 44(3), 77.

Smith, C. M. (1995). Development of performance pitch accuracy of string students. Bulletin of the Council for Research in Music Education, 124(124), 13-23. 141

Smith, C. M. (1985). The effect of finger placement markers on the development of intonation accuracy in beginning string students. Dialogue in Instrumental Music Education, 9(2).

Smith, C. M. (1987). The effect of finger placement markers on the development of intonation accuracy in fourth- and fifth-grade beginning string students. Dialogue in Instrumental Music Education, 11(2).

Smith, C. M., & Brick, J. S. (1990). Effects of the pitch master on beginning violin students' aural pitch discrimination and performance pitch accuracy, Dialogue in Instrumental Music Education, 14.

Sogin, D. W. (1989). An analysis of string instrumentalists' performed intonational adjustments within an ascending and descending pitch set. Journal of Research in Music Education, 37(2).

Spiegel, M. F. (1984). Performance on frequency-discrimination tasks by musicians and nonmusicians. Journal of the Acoustical Society of America, 76(6)

Spohn, C. L.,. (1959). An exploration in the use of recorded teaching material to develop aural comprehension in college music classes.

Stauffer, D. W. (1954). Intonation deficiencies of wind instruments in ensemble. Catholic University of America Press).

Stauffer, S. L. (1985). An investigation of the effects of melodic and harmonic context on the development of singing ability in primary grade children (aural, discrimination). (Ph.D., University of Michigan). ProQuest Dissertations and Theses.

Stegeman, W. (1967). Poor intonation? No excuse. Music Journal, 25(9), 42.

Sterling, P. A. (1984). A developmental study of the effects of accompanying harmonic context on children's vocal pitch accuracy of familiar melodies. (Ph.D., University of Miami). ProQuest Dissertations and Theses.

Sterling, P. (1985). The effects of accompanying harmonic context on vocal pitch accuracy of a melody. Psychology of Music, 13(2), 72-80.

Sterling, P. A. (1986). A developmental study of the effects of accompanying harmonic context on children's vocal pitch accuracy of familiar melodies.

142

Swaffield, W. R. (1974). Effect of melodic parameters on ability to make fine-tuning responses in context. Journal of Research in Music Education Journal of Research in Music Education, 22(4).

Swift, D. G. (2003). Improving harmonic intonation skills of high school band students using coda music technology's "intonation trainer". (M.M.E., University of Louisville). ProQuest Dissertations and Theses.

Thomsen, L. (2012, Oct 2012). How to improve violin & viola intonation in high positions. Strings, 27, 25-26.

Thomsen, L. (2012, Sep 2012). Improve your violin or viola intonation in 5 simple steps. Strings, 27, 23-24.

Timm, E. (1943). Intonation facts. Music Educators Journal, 29(3), 19-20.

Tromblee, M. R. (1972). An investigation of the effectiveness of programed drill training in teaching intonation discrimination skills. (Educat.D., University of Illinois at Urbana-Champaign). ProQuest Dissertations and Theses.

Turnbull, W. W. (1944). Pitch discrimination as a function of tonal duration. Journal of Experimental Psychology, 34(4), 302-316.

Vaughn, K. (1993). The influence of the tambura drone on the perception of proximity among scale types in north indian classical music. Contemporary Music Review, 9, 21.

Vincent, M. C., & Merrion, M. (1996). Teaching music in the year 2050. Music Educators Journal, 82(6), 38-42.

Wapnick, J., & Freeman, P. (1980). Effects of dark-bright timbral variation on the perception of flatness and sharpness. Journal of Research in Music Education, 28(3).

Ward, W. D. (1954). Subjective musical pitch. The Journal of the Acoustical Society of America, 26(3), 369-380.

Ward, W. D. (1961). Psychophysical comparison of just tuning and equal temperament in sequences of individual tones. Journal of the Acoustical Society of America, 33(5).

Watkins, C. (2004). Advanced intonation skills: Helping students understand what they hear. American String Teacher, 54(1), 86-90.

143

Whitcomb, B. (2007). Improving intonation. American String Teacher, 57(4), 42-45.

Whitman, C. F. (1970). The effects of piano instruction on vocal pitch accuracy in fourth, fifth, and sixth grade students. (Educat.D., University of Florida). ProQuest Dissertations and Theses.

Williams, M. (2009). WV public school music teachers' use of digital audio technologies for teaching and learning. (Ed.D., West Virginia University). , 168.

Wolbers, M. (2002). Singing in the band rehearsal. Music Educators Journal, 89(2), 37- 41.

Worthy, M. D. (2000). Effects of tone-quality conditions on perception and performance of pitch among selected wind instrumentalists. Journal of Research in Music Education, 48(3), 222-236.

Yarbrough, C., Karrick, B., & Morrison, S. J. (1995). Effect of knowledge of directional mistunings on the tuning accuracy of beginning and intermediate wind players. Journal of Research in Music Education, 43(3), 232-241.

Yarbrough, C., & Ballard, D. L. (Spring-Summer 1990). The effect of accidentals, scale degrees, direction, and performer opinions on intonation. Update: Applications of Research in Music Education, 8(2), 19-22.

Yarbrough, C., Green, G., Benson, W., & Bowers, J. (1991). Inaccurate singers: An exploratory study of variables affecting pitch-matching. Bulletin of the Council for Research in Music Education, (107), 23-34.

Yarbrough, C., Morrison, S. J., & Karrick, B. (1997). The effect of experience, private instruction, and knowledge of directional mistunings on the tuning performance and perception of high school wind players. Bulletin of the Council for Research in Music Education, (134), 31-42.

Zdzinski, S. F., & Barnes, G. V. (2002). Development and validation of a string performance rating scale. Journal of Research in Music Education, 50(3).

Zurcher, Z. W. (1972). The effect of model-supportive practice on beginning brass instrumentalists.

144

Appendix A: Student Questionnaire

145

Student Questionnaire

(Please print)

Student’s First and Last Name ______

Directions: Please circle the appropriate answer for each question.

School Name: School 1 School 2 School 3

Current Grade: 6th 7th 8th

Current Age: 9 10 11 12 13

1. What instrument do you play in orchestra class?

Violin Viola Cello Bass None of these

2. When did you start playing a stringed instrument? (violin, viola, cello, bass)

th th th th Before 5 grade 5 grade 6 grade (last school year) 7 grade (this school year)

3. Do you currently take private lessons on the instrument chosen above?

Yes No

4. Have you ever taken private lessons on the instrument chosen above?

Yes No

146

Appendix B: Student Assent Form

147

The Ohio State University Assent to Participate in Research

The effect of a tonic drone accompaniment on the pitch Study Title: accuracy of scales played by beginner violin and viola students. Researchers: Dr. Robert Gillespie and Mr. Charles Laux

• You are being asked to be in a research study. Studies are done to find better ways to treat people or to understand things better. • This form will tell you about the study to help you decide whether or not you want to participate. • You should ask any questions you have before making up your mind. You can think about it and discuss it with your family or friends before you decide. • It is okay to say “No” if you don’t want to be in the study. If you say “Yes” you can change your mind and quit being in the study at any time without getting in trouble. • If you decide you want to be in the study, an adult (usually a parent) will also need to give permission for you to be in the study.

1. What is this study about?

The purpose of this study will be to determine the effectiveness of a pre-recorded harmonic audio accompaniment track in the study of scales on a student’s ability to play with accurate intonation (pitch accuracy).

2. What will I need to do if I am in this study?

First you will be audio‐recorded playing the D Major and C Major scales on your instrument (a pre‐test). Next, for approximately eight class period warm‐ups (about 5-‐8 minutes per class), your teacher will use a special audio accompaniment while you practice the scales along with your class. Your class will be randomly assigned into an experimental treatment group based on the particular accompaniment. The three groups are (a) pitch-matching, (b) pitch-matching with a tonic drone, and (c) tonic drone only. Finally, after you have practiced with the accompaniments in class, you will be tested again (a post-test) to see if there are any differences in your pitch accuracy (intonation).

3. How long will I be in the study?

The study will last approximately two weeks. 148

4. Can I stop being in the study?

You may stop being in the study at any time.

5. What bad things might happen to me if I am in the study? There are no foreseeable inconveniences or risks involved in participating in the study.

6. What good things might happen to me if I am in the study?

Potential benefits of participating in the study are: 1. Improved aural (listening) skills 2. Improved perception of intervallic relationships in ascending and descending major scale patterns 3. Improved intonation and increased awareness of one’s pitch accuracy 4. Increased awareness of the ability to adjust pitch (finger placement on the fingerboard)

7. Will I be given anything for being in this study?

No, there are no incentives to participate.

8. Who can I talk to about the study?

For questions about the study you may contact Charles Laux via email at [email protected] or via phone at (770) 423-6553.

To discuss other study-related questions with someone who is not part of the research team, you may contact Ms. Sandra Meadows in the Office of Responsible Research Practices at 1-800-678-6251.

149

Signing the assent form

I have read (or someone has read to me) this form. I have had a chance to ask questions before making up my mind. I want to be in this research study.

AM/PM Signature or printed name of subject Date and time (student)

Investigator/Research Staff

I have explained the research to the participant before requesting the signature above. There are no blanks in this document. A copy of this form has been given to the participant or his/her representative.

Charles Laux Printed name of person obtaining Signature of person obtaining assent assent

AM/PM Date and time

This form must be accompanied by an IRB approved parental permission form signed by a parent/guardian.

150

Appendix C: Parent Permission Form

151

The Ohio State University Parental Permission For Child’s Participation in Research

The effect of a tonic drone accompaniment on the pitch Study Title: accuracy of scales played by beginner violin and viola students. Researcher: Dr. Robert Gillespie and Mr. Charles Laux

This is a parental permission form for research participation. It contains important information about this study and what to expect if you permit your child to participate. Your child’s participation is voluntary. Please consider the information carefully. Feel free to discuss the study with your friends and family and to ask questions before making your decision whether or not to permit your child to participate. If you permit your child to participate, you will be asked to sign this form and will receive a copy of the form.

Purpose: The purpose of this study will be to determine the effectiveness of a pre-recorded harmonic audio accompaniment track in the study of scales on a student’s ability to play with accurate intonation (pitch accuracy).

Procedures/Tasks: Students will first be audio‐recorded individually playing the D Major and C Major scales on their instrument (a pre‐test). Next, for approximately eight class period warm‐ups (about 5‐8 minutes per class), the child’s orchestra teacher will use a special audio accompaniment while students practice the scales along with their class. Each class will be randomly assigned into one of three groups based on the audio accompaniment used. The groups are (a) pitch-matching, (b) pitch-matching with a tonic drone, and (c) tonic drone only. Finally, after students have practiced with the accompaniments in class, they will be individually recorded again (a post-test) to see if there are any differences in your pitch accuracy (intonation).

Duration: The study will last approximately two weeks.

Your child may leave the study at any time. If you or your child decides to stop participation in the study, there will be no penalty and neither you nor your child will lose any benefits to which you are otherwise entitled. Your decision will not affect your future relationship with The Ohio State University.

152

Risks and Benefits: There are no foreseeable inconveniences or risks involved in participating in the study.

Potential benefits of participating in the study are: 5. Improved aural (listening) skills 6. Improved perception of intervallic relationships in ascending and descending major scale patterns 7. Improved intonation and increased awareness of one’s pitch accuracy 8. Increased awareness of the ability to adjust pitch (finger placement on the fingerboard)

Confidentiality: Efforts will be made to keep your child’s study-related information confidential. However, there may be circumstances where this information must be released. For example, personal information regarding your child’s participation in this study may be disclosed if required by state law. Also, your child’s records may be reviewed by the following groups (as applicable to the research): • Office for Human Research Protections or other federal, state, or international regulatory agencies; • The Ohio State University Institutional Review Board or Office of Responsible Research Practices;

Incentives: There are no incentives to participate in this study.

Participant Rights: You or your child may refuse to participate in this study without penalty or loss of benefits to which you are otherwise entitled. If you or your child is a student or employee at Ohio State, your decision will not affect your grades or employment status.

If you and your child choose to participate in the study, you may discontinue participation at any time without penalty or loss of benefits. By signing this form, you do not give up any personal legal rights your child may have as a participant in this study.

An Institutional Review Board responsible for human subjects research at The Ohio State University reviewed this research project and found it to be acceptable, according to applicable state and federal regulations and University policies designed to protect the rights and welfare of participants in research.

Contacts and Questions: For questions, concerns, or complaints about the study, or you feel your child has been harmed as a result of study participation, you may contact Charles Laux via email at [email protected] or via phone at (770) 423-6553.

For questions about your child’s rights as a participant in this study or to discuss other study-related concerns or complaints with someone who is not part of the research team, you may contact Ms. Sandra Meadows in the Office of Responsible Research Practices at 1-800-678-6251.

153

Signing the parental permission form

I have read (or someone has read to me) this form and I am aware that I am being asked to provide permission for my child to participate in a research study. I have had the opportunity to ask questions and have had them answered to my satisfaction. I voluntarily agree to permit my child to participate in this study.

I am not giving up any legal rights by signing this form. I will be given a copy of this form.

Printed name of subject (student)

Printed name of person Signature of person authorized authorized to provide permission to provide permission for for subject subject

AM/PM Relationship to the subject Date and time

Investigator/Research Staff

I have explained the research to the participant or his/her representative before requesting the signature(s) above. There are no blanks in this document. A copy of this form has been given to the participant or his/her representative.

Charles Laux Printed name of person Signature of person obtaining obtaining consent consent

AM/PM Date and time

154

Appendix D: Scale Sheet Music for Violin and Viola

155

Violin Scales

0 1 2 3 0 1 2 3

2 1 0 3 2 1 0

3 0 1 low 2 3 0 1 low 2

1 0 3 low 2 1 0 3

156

Viola Scales

2 3 0 1 2 3 0 1

2 1 0 3 2 1 0

low 2 3 0 1 low 2 3 0 1

1 0 3 low 2 1 0 3

157

Appendix E: Teacher Script

158

Directions:

Please follow the script closely. The dates and approximate time are marked so it should be fairly easy to follow.

Anything marked in italics is what you are to say to students.

Anything marked in [brackets] are action items for you to do, or directions to follow.

Notes:

* Be sure that the volume of your CD player/audio system is loud enough for all students to hear it well. You will check this by using the provided 5 seconds of white noise.

* For each class period, be sure that you are using the correct accompaniment CD. Here are the accompaniments assigned to each class. The CD is clearly labeled with the type of accompaniment.

• [list of classes in the drone group] – Drone only (D) • [list of classes in the pitch-matching group] – Pitch-matching (PM) • [list of classes in the pitch-matching plus drone group] – Pitch matching plus drone (PMD)

159

Day 1 – Wednesday, August 13

Objective: Students will gain familiarity in playing scales with an accompaniment track.

Time: 6-7 minutes

[Class begins. Please be sure instruments are accurately tuned.]

Today are going to begin a new way of practicing our scales. I know we have practiced the D major and C major scales in the past, but today we will start using an audio accompaniment track that will help us play our scales more in tune or with better intonation.

The first thing I will ask you to do is to watch and listen to me perform the scales with the accompaniment track. The track will provide a count off and a metronome click so that we can play together. In addition to this, you will hear:

• [list of classes in the drone group] – a drone, which is a sustained drone pitch, which is the first note of the scale. • [list of classes in the pitch-matching group] – the pitches that exactly match the notes you are playing. • [list of classes in the drone group] - a sustained drone pitch, which is the first note of the scale, along with pitches that exactly match the ones you are playing.

Our goal will be to match our pitches as best we can to the accompaniment. Let’s start with the D Major scale. First, you will listen and watch as I play the scale. When I am playing, notice how I try to blend my sound and match my pitch to the accompaniment. Notice also how I use full bows and produce a large, full sound. I keep my bow in between the bridge and fingerboard with a good amount of weight into the stick.

[NOTE: Be sure that you are using the appropriate CD that has been assigned to that particular class. The accompaniments are different on each CD.

[Start the accompaniment, and perform the D major scale with the selected treatment track.]

Now, let’s play the D major scale together. Please get your instruments in proper playing position. [Students get ready].

Start the CD and have the students play the D major scale along with you.

160

Excellent work! Let’s do that one more time with big, full bows so that we can make a large, full sound. Be sure to keep your bow placed centered between the bridge and fingerboard and keep a good amount of weight into the stick. [Start the CD and have the students play the D major scale again.]

Now let’s practice our C Major scale. [Repeat the procedure with the C major scale, playing it only twice.]

161

Day 2 – Thursday, August 14

Objective: Students will learn to or be reminded to adjust their pitch by sliding their fingers on their fingerboard.

Time: 6-7 minutes

[Class begins. Please be sure instruments are accurately tuned.]

[Note: For each class period, be sure that you are using the correct accompaniment CD.]

Today we are going to continue practice our scales with an accompaniment track, and I would like to show you a strategy that will help you to play better in tune.

When we first learned our scales, we learned about which fingers to put down on the fingerboard in order to play certain notes. Your instrument might have finger tapes that help you see and feel where the notes are. While these tapes are great to get you started, they do not show you exactly where the notes are. The only way you can play with good pitch accuracy is to listen and carefully adjust each pitch you play. In order to do this, you should listen to the pitch in the accompaniment track, and if your pitch is not accurate, you will need to slide your fingers, just slightly, on the fingerboard to make the pitch blend to sound more accurate.

Watch as I demonstrate how to do this. [Pick up violin, play the note E (1st finger on the D string) for several seconds, then slide your finger slightly back toward nut to lower the pitch. While continuing to sustain the pitch, the teacher brings the note back to E, and then slides finger up to make the pitch a bit too sharp. Finally, bring it back to E.]

Now we are going to play an intonation game together. [Put down your violin.] When I put my hands together, you will play an E, first finger on the D string. [Put your hands together in front of them, as if they were clapping.] I will hold my hands together until I feel that we have matched our sound so that we sound the same. Then, when I pull my hands apart, I would like you to slide your finger up or down a bit on the fingerboard to make it sound out of tune. When I bring my hands back together, you should slide your finger back to the position so that your E is in tune again.

162

Let’s try it! [Start with hands closed.] Play your E, first finger on the D string. [Allow students time to play E, and solidify the intonation. Then bring your hands apart.] Now, slide your fingers to play out of tune. [Bring hands back together. Repeat]

Now, let’s use F-sharp. [Repeat procedure above].

Now, we will play our D major and C major scales. As we play, really keep your ears open. Listen carefully to yourself and the accompaniment. If you hear that you are not blending or matching the accompaniment, you should try to slide your fingers a bit to make your pitch blend or match. The reason we are playing the scales slowly is so that we have time to listen and adjust our pitch. Every time you play, you should be listening and making adjustments if necessary so that you can play with good intonation.

Please get your instruments in proper playing position. [Students get ready].

[Start the CD and have the students play the D major scale along with you. After the first performance, remind them about playing with full bows, good weight, and

Let’s do that one more time with full bows so that we can make a large, full sound. Be sure to keep your bow placed centered between the bridge and fingerboard and keep a good amount of weight into the stick.

[Start the CD and have the students play the D major scale again.]

[Repeat the procedure with the C major scale, playing it twice.]

163

Days 3 to 7 – Friday, August 15 to Thursday, August 21

Objective: Scale practice and reinforcement to refine listening skills and the adjustment of pitch.

Time: 5-6 minutes

[Class begins. Please be sure instruments are accurately tuned.]

[Note: For each class period, be sure that you are using the correct accompaniment CD.]

Let’s practice our C and D major scales. Before we begin, here are some reminders: • Be sure to listen carefully to the accompaniment track. • Always be willing to adjust your pitch so that it matches or blends with the accompaniment. • Sit with your best posture. Use long bows, good weight, and a centered contact point so that you get a big, full sound.

Let’s begin. Be sure to listen and adjust.

[Teacher starts the playback of the accompaniment tracks. The class performs each scale a total of 3 times. Teacher provides guidance and feedback as necessary.]

[Alternate the delivery/order each day.]

Day 3 – DDD, CCC Day 4 – CCC, DDD Day 5 – DCD, CDC Day 6 – CDC, DCD Day 7 – DDD, CCC

164

Appendix F: Directions for Research Assistants

165

Directions for research assistants

Equipment: Each recording station kit comes with… • CD player boom box • Clip-on lapel microphone with long cable • Tascam Digital audio recorder • Folder containing: 1. Scale sheet for violin and viola; 2. These directions and verbal script • 8 C-size batteries for CD player (will be pre-installed in boom box) • Power cord for CD player (use only if batteries die) • Extra Batteries (use only if needed) • Button-style battery for lavalier microphone • AA batteries for audio recorder

Preparation checklist: • Load CD into CD player. Be sure to use the CD Marked “P1” for the first class and “P2” for the second class. • Plug the microphone into the front of the recorder (MIC/EXT IN). Make sure that the microphone is switched “ON.” • Place CD player on a chair or desk. Check volume of CD player. It should be set so that the blue tape lines approximately meet. You may need to turn it up or down slightly so that the participant can hear it while they play, but it’s not too loud that they can’t hear themselves play.

Procedures for recording: 1. Welcome the student, collect their participant ID card/paper. 2. Affix microphone on to instrument so that the microphone clips to the strings, just above the tailpiece (see photo). Try to make sure it doesn’t rattle around. You can place it near the fine tuners or even on a fine tuner if that will help 3. Read the script with directions for the participant 4. Make sure there are no questions. 5. Start the audio recorder (and leave it recording for the duration of the test) 6. Announce the student’s Participant ID clearly so that it gets recorded. 7. Begin playback of the specified CD (CD marked for 1st or 2nd class period) and specified track number. Refer to the student’s sheet 8. Allow student to play first scale. During white noise, quickly let them know what they will do next. (Every student plays two D major scales, and two C major scales). 9. Stop the recorder. 10. Remove the lapel microphone and thank the student for playing. 11. REPEAT!

Tips for working with subjects: • Be friendly and relaxed. Make it seem easy. • Speak clearly and slowly.

166

• Make sure participants understand what they will do before they start. There isn’t time to allow them to stop. Once they start playing, the CD will prompt them to play 4 scales with only a short pause in between. • If a participant wants to quit at any time, you must allow them to stop.

[Student enters the room. His/her instrument has been tuned.]

Say: Hello, may I please have your card? [Take card from student]

Say: Hello [insert student name]. Thank you for agreeing to participate. Is it okay if I clip this microphone to your instrument? [Clip microphone to strings behind bridge]

Say: Ok, let’s begin. This is an experiment concerned with scales and intonation, or playing in tune. You will be recorded performing two different scales - the D Major scale, and the C Major scale, two times each. If you need them, the scales are printed on the sheet music on the stand in front of you. [Point to the correct sheet (violin or viola)]

Say: Between each of the scales you will hear some white noise, and will have a short time to prepare for the next scale. Before we begin, do you have any questions?

[Start the audio recorder and ensure that recording is taking place by looking at the display. You should see: 1.) the recording timer counting up and 2.) activity on the audio level meters.

While recording audio, announce the students name and their participant ID.

Say: This is participant # [Insert student participation ID number]. Then begin the CD player, advancing to the track number that is marked on his/her sheet: #1, 2, 3, or 4.]

[Student will follow prompts on audio recording to perform D major scales two times, and C major scale two times. Feel free to remind them what scale they are playing

167 between takes (during the white noise). Once they have completed, remove the microphone from their instrument.]

Say: Thank you for playing today! [Put the student’s card in your folder.]

Troubleshooting:

No recording levels? 1.) Microphone is OFF. Switch on. 2.) Recorder is not is “record ready” mode. Push the record button.

Not recording? 1.) The record button needs to be pushed twice.

168

Appendix G: Institutional Review Board Approval Letter

169

Behavioral and Social Sciences Institutional Review Board

Office of Responsible Research Practices 300 Research Administration Building 1960 Kenny Road Columbus, OH 43210-1063

Phone (614) 688-8457 May 2, 2014 Fax (614) 688-0366 www.orrp.osu.edu Protocol Number: 2014B0109 Protocol Title: THE EFFECT OF A TONIC DRONE ACCOMPANIMENT ON THE PITCH ACCURACY OF SCALES PLAYED BY BEGINNER VIOLIN AND VIOLA STUDENTS, Robert Gillespie, Charles Laux, School of Music Type of Review: Initial Review—Expedited – expedited IRB Staff Contact: Jacob R. Stoddard Phone: 614-292-0526 Email: [email protected]

Dear Gillespie,

The Behavioral and Social Sciences IRB APPROVED BY EXPEDITED REVIEW the above referenced research. The Board was able to provide expedited approval under 45 CFR 46.110(b)(1) because the research meets the applicability criteria and one or more categories of research eligible for expedited review, as indicated below.

Date of IRB Approval: May 2, 2014 Date of IRB Approval Expiration: May 2, 2015 Expedited Review Category: 6, 7

In addition; the research was approved for the inclusion of children (permission of one parent sufficient).

If applicable, informed consent (and HIPAA research authorization) must be obtained from subjects or their legally authorized representatives and documented prior to research involvement. The IRB-approved consent form and process must be used. Changes in the research (e.g., recruitment procedures, advertisements, enrollment numbers, etc.) or informed consent process must be approved by the IRB before they are implemented (except where necessary to eliminate apparent immediate hazards to subjects).

This approval is valid for one year from the date of IRB review when approval is granted or modifications are required. The approval will no longer be in effect on the date listed above as the IRB expiration date. A Continuing Review application must be approved within this interval to avoid expiration of IRB approval and cessation of all research activities. A final report must be provided to the IRB and all records relating to the research (including signed consent forms) must be retained and available for audit for at least 3 years after the research has ended.

It is the responsibility of all investigators and research staff to promptly report to the IRB any serious, unexpected and related adverse events and potential unanticipated problems involving risks to subjects or others.

This approval is issued under The Ohio State University’s OHRP Federalwide Assurance #00006378. All forms and procedures can be found on the ORRP website – www.orrp.osu.edu. Please feel free to contact the IRB staff contact listed above with any questions or concerns.

Michael Edwards, PhD, Chair Behavioral and Social Sciences Institutional Review Board

hs-017-06 Exp Approval New CR Version 05/18/10

170

Appendix H: Raw cent deviation scores for each participant

171

Participant ID: DCN103_232 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -41.8 -17 -29.5 -17.5 F# -16.4 4.6 6.2 -0.6 G 26.8 28.5 14.5 3.7 B -36 -44.7 -26.5 -16.9

Ascending C# -27.4 -22.9 8.6 3.8 D 5.7 19 0.9 28.3

C# -30.1 -24.2 -10.4 -5.9 B -31.2 -40 -39.3 -13.4 G 0.6 17.5 17.7 17.6 F# -30.6 -14.1 -4.7 8.7

Descending E -18.8 -20.6 -6.7 -14.1 172

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 26 61.5 26.3 12.4 E -38.2 -41.2 -24 -20.5 F 88.2 -84.5 -38.2 -28.8 G 33.6 7.6 4.9 4.8

Ascending B -45 -59.7 -18.2 -30 C -17.2 -61.2 -17.2 14.7

B -47.8 -56.5 -19.7 -21.8 G 2.4 10.5 11.3 8.9 F 47.5 -74.4 -39.9 -10.7 E -37.9 -39.5 -19.6 -18.5

Descending C -9.3 23.2 8 27.6

172

Participant ID: DCN104_241 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -21.6 -40.4 -18.2 6.4 F# -32 22.9 -36.3 -14.4 G -26.2 -61.5 -16.5 -20.4 B -27.2 -35.7 -9.6 8.4

Ascending C# 35.4 4.8 -19.6 -16.2 D -36.1 -24 -10.8 -1.9

C# 29.9 -37.4 -22.2 -19.7 B -32.9 -42.6 -0.67 13.9 G -72.2 -63 -20.7 -28 F# -47.4 -12.6 -34.7 -31.6 Descending

173 E -29.8 -45.3 -25.2 -15.7

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 50.4 -39.7 -24.1 -6.1 E -13.1 -5.2 -19.7 -29.3 F 56.2 -12.8 -40 -39.9 G -33.6 -45.1 -31.8 -7.3

Ascending B -27.1 -14.9 -14.9 -9.3 C 85.5 14.1 -35.9 -20.1

B -25.2 -17.2 -6.7 6.4 G 41.6 -42.3 -39.4 -43.2 F 55.2 42 -32 -26.8 E -27.9 -30.7 -21.6 -15.3

Descending C -46.6 -80 -0.1 -37.5

173

Participant ID: DCN105_211 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -15.2 2.8 -21.1 -7.8 F# -22.5 -17.3 -43.1 -32.4 G 7.4 17.2 -17.5 -29.8 B 7.3 4.1 8.6 -6.7

Ascending C# -10.7 -19.7 -31.3 -37.6 D 24.9 20 -20.3 -12.2

C# -8.5 -15.2 -21 -34.3 B 4.9 10.9 5.8 -7.8 G -7.1 -27.1 -26.1 -25.8 F# -27 -28.4 -39.9 -41.8

Descending E 1.7 -7.3 -8.5 -25.4 174

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -22.9 17.1 -27.9 -32.9 E -19.2 15.4 -34.4 -38.4 F -37.6 -12.9 -18.2 -41.6 G -37 -20 -36.1 -33.5

Ascending B -10.6 -1.6 -9.8 -13.1 C -30.3 -26.1 -43.1 -32.6

B -2.9 0.2 -9.3 -16.1 G -0.6 -30.3 -33.6 -30.7 F -46.8 -21.5 -37.9 -56.8 E -15.7 0.5 -17.7 -26.1

Descending C -8.1 -9.3 -20.9 -6.3

174

Participant ID: DCN106_221 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -59.9 -20 -69.2 -69.1 F# -29.4 -15.1 -83.5 -44 G 6.9 26.1 -60.4 -4.5 B -35 -12.6 -37.2 -25.2

Ascending C# -81.7 2.3 -94.9 -22.6 D -26.6 -3.1 -45.4 -14.3

C# -78 -59.1 -89.9 -28.3 B -38.3 -7.1 -39.1 -24.5 G 7.4 18.7 -88 -18.6 F# -27.7 -20.5 -86 -43.3 Descending

175 E -16.6 32.6 -43.3 -27.1

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 34.5 -0.2 -30.4 -25.4 E -9.2 -25.1 -26.8 -31.5 F 70 11.6 80 88.6 G 0.2 -26.7 -19.9 17

Ascending B 77 -16.7 -72.9 -27.9 C 71 4.1 8.8 -91.2

B -18.3 -16.3 -66.1 -19.2 G -5.2 -28.9 -46.9 -4 F 74.9 -35.8 45.9 67.1 E -26.3 -23 -32.1 -8.8

Descending C 23.4 -1.7 18.2 13

175

Participant ID: DCN107_231 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 6.4 -11.2 -17.6 -30.5 F# 5.7 -41.6 -42.1 -39.7 G 25 22.7 4.9 -10.2 B -24 -11.2 -15.7 -37.6

Ascending C# -6.8 -7.5 -22 -24.6 D 23 44.1 -0.6 9.9

C# -14.7 -9.3 -24.3 -22.6 B -24.1 -14 -18.3 -38.7

ending G 9.4 -2.2 16.5 18 F# -63.7 -17.4 -28.9 -23.2

Desc E -13.4 -4.1 -5.4 -32 176

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 14 7.7 19.5 24.1 E -8.8 -1.1 -32.8 -36.1 F 1.2 -17.2 -38.9 -40.2 G 8.9 6.9 -10.1 -8.7

Ascending B -19.4 -21.5 -31.4 -19.4 C -38.4 -41.2 -37.2 -34.9

B -28 -21.5 -27.8 -14.3 G -6 -15.7 13.5 -2.7 F -29.4 -32.9 -42.7 -45.4 E -20.9 -10.6 -17.6 -29.2

Descending C -38.4 -32 32.5 38.9

176

Participant ID: DCN109_211 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -26.9 -35.7 -1.6 7.4 F# -21.9 -22.2 -1.7 1 G -23.7 37.1 5.3 -0.1 B -38.8 -33.5 2.5 -12.6

Ascending C# -19.3 -40.9 -7.3 -23.5 D -18.3 -46.5 -1.3 9.6

C# -35.8 -42 -24.7 -15.1 B -20.1 -36.4 9.6 -7.5 G -32.4 -41.3 -4.9 -12.2 F# -33.7 -46.2 -13.9 -31.9

Descending E -7.3 -9.1 -0.6 -2.5 177

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -23.5 1 -6.9 -16.5 E -14.3 -28.5 2 30.5 F 65.5 78.9 24.6 98.3 G -17.4 -20 -6.2 -3

Ascending B -11.2 -7.9 -1.6 -10.2 C 81.9 69.7 -3.2 13.2

B -12.6 -18.8 6.2 -6.4 G -26.9 -0.2 8.1 -17.5 F 62.7 67.2 6.8 -11.8 E 15.7 4.7 15.1 2.1

Descending C -14.5 -1.5 7.7 -6.5

177

Participant ID: DCN110_222 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 8.5 2.9 1.1 -8.4 F# -10.6 4.1 3.9 -17.5 ing G 2 -19.9 -43.5 -18.1 B 9.6 1.1 5.5 -6.4

Ascend C# -2.2 0.4 5.1 25.5 D -3.3 -5.1 24.8 -4.1

C# -6.3 -13.9 -29.5 8.2 B 18.4 8.1 2.7 -10.9 G -41.7 -12.8 -32.3 -59.8 F# -15.6 0.4 -48.2 -29

Descending E 16.9 26.1 -10.4 -37.5 178

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 0.7 -38.8 -17.2 -6.5 E 22 9 0.4 -0.4 F -28.5 -45 -29.5 -65.4 G 3.8 -66.5 -20.6 -41.8

Ascending B 16.2 -31.8 6.8 14.6 C -8.9 -37.5 16.2 -39.8

B 19.7 -1.4 16.9 -7 G 7.6 -30.9 -45.3 -47.1 F -25.1 -34.9 -62.6 -72.6 E -1.7 1.5 -60.7 -48.2

Descending C 0.7 -44 -40.4 -60.6

178

Participant ID: DCN111_231 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 10.9 4.4 0.2 10.9 F# 13.8 -14.7 0.1 15.5 G -9.7 -24.7 18.8 3.4 B 2.2 -4.9 2.3 -0.8

Ascending C# -18.4 0.5 10.4 1.7 D -29.1 -15.7 -34.2 -10

C# -15.3 6.1 11.8 1.5 B -12.2 -7.6 -4.1 -8.2 G 0.7 -0.8 5.9 -4 F# -13.9 -13.1 -34.8 4.3 Descending

179 E 15.5 3.9 8.8 -3.9

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 24.5 18 2.6 17.5 E 10.4 5.8 -2.6 5.1 F -8.2 0.1 -25.5 9 G 19.6 11 24.6 9.5

Ascending B 2.1 12.3 2.2 -0.3 C -5.3 -15.6 -20.3 -0.4

B 3.6 12.8 -2.3 5.5 G -14.6 9.4 -9.6 22 F -6.7 4.2 17.4 20.2 E 1.6 18.4 3.5 14.9

Descending C -12.3 0.8 -20.2 6

179

Participant ID: DCN112_241 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 41.5 35.9 -41.5 25 F# 33.3 22 12.3 4.6 G 24.3 20.9 3.8 14.4 B 28 10.4 30.3 29.5

Ascending C# -3.9 1.7 -4.3 -7.9 D -24.9 1.3 -14.6 -31.1

C# -8.9 -5.4 -13 10.3 B 29.8 9.6 41.1 30.1 G 34 19.5 25.4 30.1 F# 31.1 21.3 18.3 10.2

Descending E 37 38.5 40.9 30.7 180

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 27.5 7.2 6.9 1.9 E 11 18.1 38.9 9.5 F 10.5 10.7 117 -20.5 G 11.7 28 12.8 -28

Ascending B -9.9 13.6 15.3 1 C -45.8 -20.9 -23.8 -28.1

B -21.2 13.2 11.8 5.1 G 14.8 41.4 26.1 10 F 4.3 12.3 -20.6 -12.2 E 38.1 47.7 17.7 27.3

Descending C 20.7 32.8 1.9 9.9

180

Participant ID: DCN113_211 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 12.6 19.5 -9 -4.3 F# 6.8 5.7 -5.8 -5 G 3 1.3 -6.6 -11.4 B 12.8 4.6 -20.4 4.3

Ascending C# -18.6 -21 -37 -27.2 D -17.7 -12.7 -34.5 -28

C# -15 -18.4 -37 -35.5 B 16.5 5.9 -9.4 8.4 G 18.5 41.1 -5.1 -10.8 F# -5.6 -3.4 -19.3 -21.7

Descending E 31.7 34.3 14.1 11.5 181

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -23.6 -25.1 -23.3 -29.6 E -8.3 4.3 -8.9 -15.7 F 13.8 92.6 -3 -4.4 G -37.1 -8.3 -39.3 -29.1

Ascending B 6.5 -8.7 -20.2 -13.8 C 48 16.4 22.8 33.9

B 10.5 0.5 -6.9 -8.4 G 11.2 0.8 -36.1 -16.2 F 23.4 9.6 -14.2 -13.5 E 8.2 5.3 -12.7 -6.6

Descending C 10.9 -16.2 -27.6 -2

181

Participant ID: DCN114_221 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -3.2 -3.8 -45.9 -40.6 F# -4.6 -22.9 -39.7 -27.6 G 23.5 3.7 -7.8 -26.2 B -7.9 -35.7 -37.8 -22.8

Ascending C# -21.9 -32.5 -46.5 -55.8 D -22 -5.9 -8.7 -38.3

C# -24.5 -40.5 -41.1 -57.4 B -7.9 -27.7 -36.1 -34 G 16.5 15.4 -0.7 -9.6 F# -9.3 -14.7 -6.9 -37.9

Descending E 3.4 9.3 -14.1 -17.5 182

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -2.6 -9 -12.7 -27 E 10.9 -27.6 -21.9 -17.3 F -19.1 -13.3 -45.9 -45.1 G -10.4 17.8 -26 -18.1

Ascending B -12 -27.1 -12.1 -31.5 C -27.8 -55.2 -40.5 -46.7

B -3.4 -31.2 -7.2 -17.8 G 2.4 -15.5 11.1 -7.6 F -27.2 -30.8 -29.8 -23.2 E -6.9 -11.4 -3.8 -8.6

Descending C 18 14.6 -6.3 18.9

182

Participant ID: DCN201_311 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -39.9 -9.9 -20.6 -25.3 F# -19.2 -3.1 -13.6 -17.2 G -2.3 -8.5 0.6 -9.5 B -57.1 -30.2 -17 -7.9

Ascending C# -38.3 -27.1 -5.4 -16.8 D -29.7 -26 0.6 2

C# -37.8 -30.9 -5.7 -21.9 B -56.6 -41.8 -24.2 -14.3 G -8.6 -13.6 -12.8 -13.2 F# -22.3 -15.9 -28 -30.5

Descending E -24.7 -14.9 -19.5 -24.9 183

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 14.7 -1.7 -14.4 -19.3 E -23.6 -9.8 -14.1 -6.9 F -38.4 -35.4 -46.6 -37.6 G -16.8 -17 0 -18.6

Ascending B -24.6 -24.2 -14 -19.3 C -24.5 69.4 -41.9 -44.6

B -31.7 -26 -6.8 -12.4 G -28.2 10.4 -3.8 -15.9 F -33.8 -45.8 -44.2 -46.7 E -21.2 -18.5 -21.4 -30.7

Descending C -5.5 1.3 -17.9 2.5

183

Participant ID: DCN202_322 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -11.8 0.1 -7.6 -1.3 F# -3.6 3.6 -3 -3.4 G 30.3 13.4 27 23.4 B -30.7 -21.2 -25.9 -17.1

Ascending C# -4.1 -4.8 -9.8 -9.2 D 60.8 -16.4 23.8 11.5

C# 0.3 -10.5 -11.6 -12.6 B -30.5 -41.9 -32.1 -30.5 G 42.8 17.1 20.8 38.8 F# 2.9 -9.8 -7 -13.5

Descending E 13.8 -21.7 -12.7 -20.1 184

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 30.3 2.6 5.1 0 E -17.1 -0.6 -17.7 -23.6 F -9.1 73.8 15.8 -3.2 G 34 3.2 9.6 19.8

Ascending B -41.5 -30.3 -40.5 -39.8 C -38.7 -3 -25.6 3

B -31.4 -35.4 -45 -44.4 G 17.4 4.4 17.3 11.2 F 6.2 -41.8 -5.8 -9.9 E -14.3 -24.1 -23.5 -21.7

Descending C 29.6 35.3 23.4 4

184

Participant ID: DCN203_331 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 5.9 -5 -36.8 -40.3 F# 8.1 9.4 -14.2 -58.1 G -13 8.8 -11.4 -27 B 8.9 -3.2 -63.1 -16.1

Ascending C# -98.1 -20.3 -65.2 2.8 D -20.6 4.1 -45.8 5

C# -86.4 -10.6 -58.3 0.8 B -3.4 -1.6 -45.8 -10.2 G 21.5 -23.2 -15.5 -8.9 F# -73.5 -40.8 -38.3 -2.5

Descending E -34 -2.2 -12.9 -39.8 185

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 25 74.5 -2.1 -0.8 E 2.6 28 -31.3 -5.8 F 38.9 6.6 -77.2 -22.8 G -18.8 2.8 -88.3 -95

Ascending B 26.4 12.2 -15.4 -7.3 C -23.9 6.9 -38.9 -32.8

B 32.8 19.3 -10.5 -6.1 G 34.6 3.1 15 0.1 F 128 6.8 -11.7 -54.4 E 32.2 35.4 -9.3 -26.9

Descending C 14.2 3 4.2 -7.4

185

Participant ID: DCN204_341 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -13.5 10.9 6.6 -15.1 F# -14 -0.7 12.6 8.3 G 36.7 42.8 40.7 12.3 B -29.5 -15.3 -23.8 -30.1

Ascending C# -33.1 -34 -21 -24.4 D 1 1.9 -9.7 -18.6

C# -38.4 -39.1 -17.6 -29 B -31.5 -14 -22.1 -39.1 G -40 25.1 6.4 -9 F# 15.4 -13.1 -7.1 -7.6

Descending E -33.8 -2.5 -4.6 -23 186

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -20.9 4 -15.4 -17.4 E -27.4 14.9 9.8 -7.1 F 12.2 6.1 -24.4 -33.5 G 11.6 10 7.7 -4.1

Ascending B -30.1 -36.3 -36.1 -25.3 C 41.1 -8.7 -45 -66.5

B -32 -27.9 -33.6 -24.5 G -3.1 -9.5 19.5 23.1 F -36.8 -16.9 -9.3 -5.2 E -32.2 16.2 23 18.4

Descending C 13.9 20.4 -21 -30.8

186

Participant ID: DCN205_311 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 3.4 -2.8 9.7 5.6 F# 11.3 2 4 9 G 31.1 0.4 36.7 42.2 B -15.2 -12.8 2.1 -4.8

Ascending C# -0.4 -11.4 2.9 0.2 D -2.3 5.3 24.2 17.3

C# -16.8 -2.3 8.5 -6.2 B -26 -12.4 -2.7 -3.1 G 20.4 33 25.6 -2 F# 1 0.2 11 8.8

Descending E -6.5 -1.2 -5.8 6 187

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 18 2.5 1.4 7.8 E -25 -2.6 -7.6 -3.6 F -27.7 18.2 -37 -27.2 G 32.9 20.9 18.3 18.4

Ascending B -19 -23.2 -10.4 -27.7 C -12.9 -23.6 -44.7 37.7

B -17.7 -17.5 -21.7 -30.9 G 33.7 33.3 36.1 21.7 F 6.6 9.1 -17.9 -19.5 E -6.7 -9.9 10.2 -10.9

Descending C 4.4 21.3 31.8 8.7

187

Participant ID: DCN208_341 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -21.9 -19.7 17.6 21.6 F# -34.1 -61.3 0.9 3 G 4.3 -28.3 18.5 31.2 B 13.7 -27.9 16 18.6

Ascending C# -9 -47.7 3.8 9 D 28.1 -24.2 8 24.9

C# -12.5 -46.8 3.2 13.3 B 4.2 -27.4 43.7 12.1 G -1.5 -4.7 26.8 24.2 F# -62.9 -59.2 -0.1 -13.2

Descending E -18.6 -14.3 30.3 26.9 188

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 44.3 59.7 36 -20.6 E 22.2 41.4 38.7 23.1 F 88.1 107.6 77.7 68.5 G 11.3 56.5 -12.6 -14.8

Ascending B 7.5 8.3 20.1 4 C 92.2 94.8 66.4 41.1

B -0.4 19.1 33.6 6.8 G -22.6 3.1 24.9 74.1 F 88.5 96.3 111 143 E 21.6 2.9 44.1 103.3

Descending C 44.3 59.7 34.8 55.8

188

Participant ID: DCN209_311 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 5.6 -1.5 11.5 -10.1 F# -24.8 8.7 -3.5 1.7 G 9.4 30.6 -34.9 27.9 B -5.9 -3.3 21.8 44.9

Ascending C# -60.6 6.1 7 47.9 D 6.5 22.2 43.3 102.2

C# 39.2 6.6 8.7 -27.5 B 9.6 3.2 27.4 21.8 G 0 -10.2 34.5 27.7 F# -18.5 -31.2 8.1 3.8

Descending E 21.2 16.8 48.6 45 189

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -6.4 17.2 13.5 33.1 E 28.2 17.6 -1.2 2.9 F 25.9 -15.6 -26.5 5 G 3.6 9.2 -16.6 26.7

Ascending B 35.7 18.7 3.4 24 C 8.1 -16.7 -17.6 12.3

B 31.3 17.1 4.6 23 G 26.5 12.6 28 20.2 F 21.7 -4.6 8.3 -15 E 31.1 16.2 12.5 18.8

Descending C 3.9 2.5 15.6 48.3

189

Participant ID: DCN210_321 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -16.7 -1.3 -8 -1.2 F# -10.2 -0.9 5.5 0.6 G 9.4 8.7 -14.4 12.5 B 1.4 3.7 -25.4 -32.5

Ascending C# 4 -19.6 -23.9 -28.6 D 23.3 -6.5 -32.2 -20

C# -9.8 -12.9 -43.7 -38.1 B 9.6 2.7 -41.8 -30.9 G 3.1 6 0 3.7 F# 23.2 -0.3 -5 -7.6

Descending E 4.4 19.3 -13 -4.1 190

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 38.8 23.3 21.4 3.8 E 14.7 6.4 -1.7 5.4 F 37.5 9.4 17.1 0.3 G 35 34.1 23 8.5

Ascending B -1 -2.5 -22.5 25.4 C 13.1 9.2 -23 -44.7

B 4.3 -9.3 -19.2 -26.7 G 13.6 15.7 28.6 -5.5 F 29.4 7.3 35.2 4.6 E 12.3 11.2 7.3 -2.3

Descending C -2.2 -29.6 12.9 22

190

Participant ID: DCN211_331 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 21.5 25.6 36.1 38.7 F# 23.4 23.3 33.2 20.7 G 17.4 16.6 15.6 11.2 B 38.8 35.6 31.4 33.9

Ascending C# 37.7 20.7 13.5 7.1 D 32.3 10 4.6 4.8

C# 30.5 18 15.3 6.3 B 35.9 36.6 30.1 34.8 G 31.7 22 15.5 20.9 F# 21.1 5.6 19.5 15.1

Descending E 32.2 7.1 26.4 14.8 191

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 23.4 0.1 6.6 -2.1 E 35.6 23.7 35.3 25.8 F 10.5 6.5 19.6 0.4 G 21.6 13.3 31 21.1

Ascending B 38.4 34.8 29.7 29 C 5.7 1.9 1.7 1.8

B 31.1 29.8 29.1 30.2 G 7.4 6.3 -0.2 18.9 F 0.4 -2.2 15 3.5 E 3.9 36.1 40.8 33

Descending C 30.3 28.5 10.3 12.4

191

Participant ID: DCN212_341 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 4.6 7.4 11.2 7.1 F# -23.8 0.7 26.9 15.6 G 43.7 41.5 30.7 17.1 B -38.5 -23.2 -10.5 -11.5

Ascending C# -5.4 -38.9 -38.6 -12.7 D 44.5 -1.3 -40 13.2

C# -20.9 -35.5 -21.8 -5.8 B -38.2 -30.1 -8.6 -15.4 G 8.2 15.1 16.5 19.2 F# -35.9 27.4 -15.7 -30.3

Descending E -6.5 -37.7 19.8 -3.7 192

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 36.3 25 44.1 40.1 E 8.2 -22 41.9 5.1 F -18.9 -45.1 -44.8 -25.3 G 38.4 -0.4 29.6 36.6

Ascending B -10.1 -18.2 -39.8 -18.9 C -28.1 -61.6 -77.5 -61.5

B -22.8 -35.2 -34.7 -18.1 G 13.7 -26.7 26.9 23.9 F 43.1 -60.5 -25.2 -47.4 E 8.3 -16.5 9.4 -2.2

Descending C 11.1 -1.2 19.3 59.4

192

Participant ID: DCN213_311 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -45.3 18.1 -15.9 -8.9 F# -64.2 -33.9 -42.9 -43 G 4.6 40.4 0.4 -0.4 B -13.7 21.7 -41.9 -18.1

Ascending C# -50.6 -29.6 -55.9 -48.8 D -11.7 25.7 5.2 -11.5

C# -23 -34.4 -40.4 -55.5 B -21.6 29.9 -41.5 -15.9 G 23.5 2 3.1 6.4 F# -32.2 33.1 1.8 -25.8

Descending E 6.1 35.6 11.4 7.4 193

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -4.6 -26 -56.9 -24.3 E 12.2 -3.8 -11.7 -9.5 F 6.4 1.7 -23.8 -10.3 G 9.3 15.8 -3.6 -42

Ascending B 8.3 4.3 -21.9 -15 C 26.8 8.4 -23.3 -17

B 2.8 3.7 -15.8 -12.8 G -4.2 -3 1.3 -7.2 F -25.7 -3.5 5.3 12.7 E 17.6 -15.8 -0.9 -5.7

Descending C -11.1 -6.4 -21 -41.6

193

Participant ID: DCN214_321 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -33.1 -35.6 -16.2 -33.8 F# -30.1 -42.9 -27.7 -22.3 G -1.6 -9.7 -8.4 -5.4 B -32.7 -26.6 -24.9 -26.6

Ascending C# -35.7 -39.4 -7.2 -14.4 D -20.4 -23 -16 -14.8

C# -41.4 -40.3 -2.1 -14.3 B -22.8 18.6 -17.3 -27.1 G -14.8 -23.8 0.1 2.9 F# -12.5 -31.5 -14.6 -19.8

Descending E -11.9 -23.1 -18.8 -19.6 194

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -20 -24.7 -26.1 -21.5 E -22.6 -27.6 -43.8 -34 F -45.6 -26 -42.3 -40.5 G -24.7 -40.4 -11.8 -21

Ascending B -29.3 -29.4 -29.2 -30.5 C -42.6 -45.2 -47.2 -60.8

B -19.9 -29.4 -19.1 -29.5 G -31.5 -26.3 -34.9 -22.5 F -45.6 20.9 -57.7 -25.5 E -29.2 -18.4 -21.9 -6.5

Descending C 3.1 -18.8 -1.5 -3

194

Participant ID: DCN215_331 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 0.7 3.9 -17.3 -7.5 F# 2.9 1.8 -19.1 -13.1 G 12.2 13.9 -4 15.6 B -29.4 -9.6 -11.7 -14.5

Ascending C# 34.5 -14.6 -5.1 -27.8 D -23 -12.6 8.2 10

C# 35.5 -18.4 -6 -24.8 B -14.4 -11 -12.7 -15.6 G 12.6 -11.2 -3.2 -5.6 F# -4.1 -3 -21.9 -10.8

Descending E -13.7 -4.6 -20.6 -18 195

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 5.6 1.6 5.6 -1.6 E 2.4 -2.1 -18.9 -18.9 F 36.2 -0.7 -8.6 -22.1 G 4.8 10 -3.4 -2

Ascending B -18.3 -20.7 -22.7 -18.4 C -14.9 -45.5 -38.9 -35.1 B -27.8 -25.1 -24 -15.1

ng G 16.3 11 -17.7 -4.6 F -6.3 -3.1 -11.5 -8.4 E -14.1 -16.5 -24 -24.9

Descendi C -11.6 -6 -11.6 -6

195

Participant ID: DCN217_311 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 15.7 -31.2 -21.8 0.2 F# -35.9 -24.7 1.4 5.8 G -0.7 -19.6 15.2 17.9 B -15 -14 -12.1 -20.8

Ascending C# 23 -17.4 -22.1 -17.6 D 7 -4.1 9 -1.1

C# 25 -12.6 -22 -13.4 B -19.6 -9.9 -23 -12.3 G -21.2 -3.5 20.7 1.6 F# -38.9 -11.7 14.6 40.8

Descending E 37.7 -8.8 -31.6 13.9 196

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 38.1 37.2 3.9 2.4 E -29 -29.1 -27.8 -19.2 F -27 -29 -37.4 -24 G -31.5 -23.3 -6.1 -13.8

Ascending B -22.1 -20 -27.8 31.4 C -21.2 -21.9 -14.2 -16.6

B -7.9 -7.2 -26.7 -37.9 G 22 21.5 20.9 31.4 F 23.8 -42.4 -40.9 -29.8 E -17.6 -18.5 -2.2 -7.1

Descending C -22.7 -2.7 37.7 18.9

196

Participant ID: DCN219_331 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -13.9 -0.8 10.4 17 F# -16.1 -34.6 -14.5 -29.2 G 40.9 36.5 15.2 24 B -38.2 -20.9 -20.6 7.3

Ascending C# 36.2 32.4 -20.2 -28 D 15.3 0.5 16.9 19

C# 3.1 26.7 -19.1 -21.2 B -39 -24 -20.4 -7.5 G -5.6 -5.7 19.9 7.7 F# -30.3 -25.6 -37.7 -2

Descending E -41.8 -12 -17.7 -6.5 197

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 33.9 -15.6 19.5 -2.5 E -18.1 -16.3 -5.3 -8.6 F -34.9 -26.7 -2.7 -29.1 G 16.4 5.5 -3.7 -7.1

Ascending B -18.3 -21.9 -10.3 -31.5 C -21.4 -25.2 -44.4 -41.8

B -28.4 -21.7 -3.4 -33.4 G -1.7 12.9 -16.1 16.7 F -20.2 -17.5 23 -38.3 E -35.1 -20.5 -20.8 -7.8

Descending C 12.7 5.4 -11 8.1

197

Participant ID: DCN220_341 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 30.6 32.6 -26.3 -11.8 F# -2.5 -18.9 -68.1 -34.4 G 13.5 4.1 -37.1 -4.5 B 21.6 10 -21.6 -12.5

Ascending C# 28.5 -2 -10.9 -24 D -19.3 -37.2 -2.8 -12.4

C# -28.5 -6.9 -6.6 -32.5 B 22 12.4 -14.8 -11.4 G 0 -28.6 -22.6 -17.7 F# -8 -40.1 -28.1 -30.6

Descending E 13.8 5.6 -25 -20.5 198

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -45.1 -36.5 -34 -40 E -0.9 -21.7 -27.5 -7.4 F -10.6 -60.9 -42.9 -37.2 G -31.6 -72.3 -40.5 -42.8

Ascending B -1.2 -32.1 -35.4 -21.3 C -25.4 -73 -71 -65.7

B -3.6 -32.1 -33.7 25.9 G -32.2 -31.8 -68.7 -33.8 F -44.1 -60.7 -71.5 -46.3 E -12.6 -32.2 -59.1 -24.4

Descending C -29.7 -48.2 -40.1 30.7

198

Participant ID: DCN222_321 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 5.9 -20.5 -21.3 -2.3 F# -25.1 -17.4 3.2 10.8 G 40.8 -9.6 20.7 34 B 11 -20.8 -36.1 0.7

Ascending C# 39 1.7 -38.2 3.8 D 69.6 42.4 4 23.9

C# 30.7 1.4 -35.9 12.1 B 14.2 -6.5 -34.8 6.4 G 5.3 -14.3 -35.8 22.2 F# -28.9 -41.6 -43.2 -19.2

Descending E -2.5 -25.1 -35.9 -17 199

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -1 17.9 6.8 37.8 E -2.5 -30.5 2.6 -11.9 F -36.3 39.3 11.4 12.4 G 18.1 38.1 4.9 2.7

Ascending B -15.5 -18.5 -35.8 -31.1 C -24.8 3.1 9 4.7

B -7.9 -14.4 -26.5 -27.2 G -15.7 -18.6 -12.7 28.7 F 40.7 -16.8 4.6 1.8 E -6.9 -7.8 -17.5 1.8

Descending C 10.8 0.1 19.8 29.3

199

Participant ID: DCN223_332 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 3.6 8 1.1 3.2 F# 4.6 21 -9.8 1.9 G 11.4 29.9 -7.2 14.7 B -5.6 4.7 -0.8 -30.3

Ascending C# -4.7 9.7 -19.9 -17.2 D 10.1 27.1 -0.4 -12.7

C# 0 8.8 -19.6 -12.3 B -6.5 7 -2.5 -29.8 G 37.1 46.4 14.9 3.7 F# -4 34 -2.9 23.3

Descending E -0.5 32.4 5.9 -15.1 200

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 3.3 15.4 17.7 -10.6 E 0.3 0.5 5.5 -13.3 F -9.6 -19.3 -23.1 -24.4 G 17.1 14 -2.9 -32.7

Ascending B -14.2 -8.9 -19.4 -1.6 C -32.8 -41.1 -48.6 -30.8

B -23.4 -16.2 -28.4 5.3 G 30.8 39.5 -20.5 -4.2 F -3.6 42.6 -47.8 3.4 E -0.7 -12.4 -10.7 -28.6

Descending C 23.1 17.2 -37.2 -20.3

200

Participant ID: DCN224_342 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -16.3 4.2 8.7 -2.8 F# -20.6 8.9 -2 -8.2 G -16.9 15.3 -5.9 -11.4 B 4.9 4.1 -11 -3.4

Ascending C# -1.6 24.1 -17.3 0.6 D -5.3 21.3 12.7 6.6

C# 1.8 19.9 -17.5 -1.5 B 6.2 2.6 -18.6 -8.7 G 8.1 22.8 38.2 17.3 F# -2.3 18.5 1 11.4

Descending E 13.8 7 -7.2 -11.4 201

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -34.4 1 37.8 1.6 E 9.3 14.9 -22 -17.6 F 64.7 8.3 -41.8 -26 G -11.8 13.2 1.4 -26.1

Ascending B -12.7 8.6 -36.7 -34.3 C -42.7 -16.7 -41.6 -54.2

B -12.2 11.1 -23.4 -38.6 G 2.7 10.1 -11.1 -23.3 F -13.5 20.5 -9.5 -31.1 E 3.3 19.4 2.8 14.9

Descending C 19.4 23.8 -16 2

201

Participant ID: DCN225_312 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -10.1 -2.5 -9.4 -14.1 F# 10.8 -1.4 -4.6 -28.3 G -41.7 -27.2 22.1 31.7 B -7.1 5.1 16.2 1.5

Ascending C# 0.6 -11.6 -4.7 -13.1 D -25.9 28.7 15.2 4.1

C# 5.5 -6.7 -7.7 -0.8 B 8.2 1.2 13.3 3 G 15.8 -7.7 5.6 10.6 F# -30.6 -30.1 -30.1 -15.7

Descending E 10.2 -2.4 -19.9 -25 202

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 45.3 83.2 -35.1 -3.6 E 7.1 1.3 -3.6 -4.7 F -1.6 -6.4 -5.9 -5.7 G 41.5 46 -9.2 27.7

Ascending B 9.9 6.1 9.1 2.7 C 13.9 -26.7 8.7 -0.6

B 11.6 6.5 22.4 10.8 G -15.6 -21.7 -42.3 -38.3 F -23 -45.5 -8.6 -22.1 E -26.4 -11.1 -22.7 -4.9

Descending C 3.9 42.6 24.6 1.5

202

Participant ID: DOD102_121 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -24.3 22 15 -17.8 F# -29 -2.2 3.3 -5.5 G -26.9 -2.6 3.1 -9.1 B -28.2 13.4 -5.2 -24.3

Ascending C# 13.8 -5.8 -8.1 -20.3 D -16.9 1.2 -15.6 -21.1

C# -14.7 -7.1 -14.9 -18.7 B -24.5 12.9 2.4 -35.6 G -18.2 3.3 33.9 -11.3 F# -12 1.8 -8.2 5.1

Descending E 12.9 15.7 18.6 0 203

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -11.7 -8.7 -6.4 -19.8 E 7.1 4.8 -15.6 15.8 F -0.5 2.2 -20.9 -1.3 G -0.9 0.3 -7.7 -3.1

Ascending B -32.8 1 -44.3 -19.5 C -39.8 -27.5 -46 -48.6

B -26.7 5.6 -33 -21.1 G 26.3 2.6 -9.3 -2 F -18.3 2.7 -35.9 -26.5 E 6.8 10.4 -14.1 -14.7

Descending C -21.2 8 5.9 15.9

203

Participant ID: DOD103_131 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 6.1 -4.5 0.6 10.7 F# -1.2 -13 10.7 -8.6 G -18.7 -3.7 -3.7 -30.5 B -21.2 6.2 -21.2 0

Ascending C# -12.4 3.6 -9.1 -3.3 D -7.5 -13.6 -5.1 -13.9

C# -0.9 -6.2 -7.4 -0.7 B -10.2 -2.7 -28.5 -2.5 G -8.5 -9.2 -13.4 -15.1 F# -20.5 16.3 -30.3 -10.1

Descending E -12.7 3.4 -9.3 -3.7 204

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -22.8 -0.1 -12.6 -2.4 E -5.2 -1.2 -10.1 -6.5 F -9.4 -16.4 -7.9 -17 G 5.4 -7.4 8.9 4.8

Ascending B -21.1 3.6 -16.5 -3.6 C -34.1 2.7 -20.1 -8

B -14.1 10.5 -16.4 -3.2 G -5.1 2.2 -13.9 -7.3 F -18 10.7 -7.5 -7.4 E -9.7 7.8 -13 -12.1

Descending C -2.4 -1.4 -15.3 -6.3

204

Participant ID: DOD104_141 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 30 3.7 -2.9 -12.5 F# 16.8 -7.8 -40.5 -35.1 G 20.7 2.6 -32.7 -24.9 B 33 17.7 -9.9 -43.4

Ascending C# 26.7 -7.6 -83.9 -69.2 D -44.6 3.2 -61 -55.1

C# 12.2 18.7 6.9 -88.6 B 39.6 30.6 -7.7 -11.9 G 45.2 -28.9 -17.3 29 F# -35.2 -31 -17.8 -5.4

Descending E 63.2 -34.4 15 11.4 205

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 27.6 19 64.7 -72.7 E 9.1 8.7 42.2 -4.2 F -21.9 50.5 92.4 85.4 G 59.6 3.4 5.6 -22.9

Ascending B -27.9 32.9 -6.6 -6.6 C 13.2 -8.2 81.5 84.4

B 33 28.7 18.6 -20.5 G -14.2 -9.2 -0.8 -28.5 F 62.3 80 77.5 87.4 E 61.1 47.8 65.3 -4.9

Descending C -24.5 -28.7 -22.6 -23

205

Participant ID: DOD105_111 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 8.5 40 1.2 -6.8 F# 11.6 71.8 -6.3 7.6 G 35 83.3 1.8 0.2 B 4.4 4.5 -20.1 -27.4

Ascending C# 6.6 10.9 -24.4 -21.7 D 2.1 16.3 -14.8 -10.4

C# -29.5 8 -22.7 -23.2 B 2 -9.7 -24.6 -23.6 G -3.5 0.1 4.1 -14.1 F# 33.5 -7.8 9.7 -3.5

Descending E 24.3 9 8.3 -11.9 206

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -0.5 -8 32.9 10.6 E 31.6 34.2 -22.7 -1.3 F 100.4 113 -12.1 78.7 G 29.8 28.3 -30.8 -6.4

Ascending B 0.1 2.4 -35.3 -25.8 C 69.1 82.8 4.3 76.1

B -10.5 -12.5 -28.8 -23.5 G 4.9 4.9 5.1 25.5 F 111.8 114 13.3 116.2 E 11.7 11.7 6.4 11.5

Descending C 1 0.8 12.2 35.9

206

Participant ID: DOD106_122 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 11.7 13.7 30.8 -65.5 F# 21.9 20 10.1 -46 G 26.6 -15.7 30.4 -5.3 B 10.8 -7 -38.4 -34.1

Ascending C# 4.2 -2.7 -94 -22.3 D -7.9 5.8 -47.8 -14.2

C# 8 -3.7 106.5 62.7 B 3.3 -9.4 -47.5 -24.3 G 34.3 3.8 -77.6 -18.4 F# 39.5 5.8 -84.2 -41.5

Descending E 31.7 10.1 56.6 -26.9 207

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 7.2 1.5 -30.3 -21.9 E 8.4 0.2 -29.6 -31.1 F 606 6.1 67.7 70.1 G 7.5 0.8 -20.2 14.9

Ascending B 10.4 2.3 -82.5 -24.9 C 1.4 11.4 16.3 34.9

B 11.1 1.1 -66 -14.9 G 6 2.3 -47 -10.5 F 26.4 0.3 43.3 67.6 E 23.9 0.8 -32.1 -10

Descending C 6 4.4 -69 13

207

Participant ID: DOD107_132 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 84.4 10.8 6.8 17.3 F# -12.1 -17.2 -42 -10.6 G 15 1.6 -29.2 10.1 B 17.1 -4.4 -0.3 8.9

Ascending C# -12.1 -36.1 -0.9 2.8 D 3.6 -17.1 0.6 -10.9

C# -15.9 -34.8 12.1 9 B 5.4 -7.6 -0.3 7.2 G 3.4 13.5 -23.8 -33 F# -15.9 -7.8 -7.1 2.8

Descending E 29.5 27.9 7.3 23.8 208

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 15.4 12.4 33.9 50.9 E 27.2 13.2 -12.6 15.5 F 14.2 15 -38.9 9.2 G -20.6 -14 -40 -1.5

Ascending B -18.2 -10 -19.7 -5.4 C -42.4 -22.6 -25.9 -21.2

B -22.3 -8.6 -30.1 3.1 G -5.9 -9 -47.7 -27.1 F -7.7 -6.5 -33.1 -18.3 E 11.4 15.6 0.1 -21

Descending C -2.6 -3 37.3 6.2

208

Participant ID: DOD202_121 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 11.3 -5.5 -14 -8.7 F# 1.8 -2.9 0.1 -12.5 G 5.6 -7.4 -6.4 -9.9 B -8.4 -6.2 -9.2 -11.2

Ascending C# -2.4 -3.5 -12.9 -13.9 D -9.9 -1.7 -15.4 -6.5

C# -16.9 -6.3 -29.7 -14.9 B -9.9 -29.4 -18.7 -22.9 G -11.6 -17.9 -7.8 -22.8 F# -29.8 -22.2 -5.8 -11.5

Descending E -11.6 -25.6 3.2 10.7 209

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 3 0.4 8.4 -1.9 E 2.6 -2.7 5.7 14 F 29.8 17.6 0.2 27.5 G -7.7 -1.7 8.5 -10.8

Ascending B -20.9 -17.5 15 10 C 31.6 -2.4 -26.3 -14.2

B -13.5 -34.3 -7.9 -1 G 3.4 -16.2 -5.6 -3.5 F 41.1 -2.6 5.3 -8.1 E -3.4 3.7 8.1 -11.3

Descending C -9.1 -7.9 15.6 -2.7

209

Participant ID: DOD203_131 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -17.2 -15.7 -11.3 6.3 F# -9.4 -47.4 -13.9 -5.7 G 20.9 -46 -46.1 -40.4 B -30.8 -14 -4.1 -31.7

Ascending C# -27.8 -27.7 -7.2 -30.9 D -46.7 -25.6 17.7 -25

C# -17.3 -12.5 -5.7 -32.6 B -13.4 10.1 2.7 -11 G 34.9 30.1 -42.5 -35.6 F# -37.7 -2.1 -2.3 -2.3

Descending E 6 -14.1 13 -31.1 210

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -18.9 -111 -38 -40 E -43.6 -39 -14.4 1.3 F -19.6 51.4 11.8 18.8 G -0.9 2.4 -63.3 -25.8

Ascending B -37.1 -35.4 -21 -5.3 C 56.1 -11.8 10.3 -0.9

B -32.1 -31.1 -17.7 -11.6 G 23.9 -1.9 -32.7 12.6 F 63.7 -12.9 -1 -0.5 E -24 -34.1 -2.5 5.6

Descending C 22.7 -13.1 -18.4 -36.1

210

Participant ID: DOD206_122 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -3.4 -1 -28.6 -15.1 F# 24.6 10.8 12.2 -59.3 G 88.4 68.8 -68.6 -7.1 B -12.2 -6.4 -36 -39.7

Ascending C# -6.1 -1.7 5 -44.1 D 43.5 37.4 -45.8 3.2

C# -21.3 -18.4 16.5 -36.3 B -6.2 -11.2 -63.5 -74.6 G 74.4 16 -46 1.7 F# -11.8 -46.6 -60.9 1.1

Descending E 3.5 -11.2 -7.9 -32.9 211

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 22.5 29.2 26.4 18.6 E 71 33.3 -22.8 -0.8 F -60 9.6 13.1 16.5 G 27.2 26.3 41.9 7.9

Ascending B 15 24.1 -65.9 -31.8 C 74.2 90.1 70 18.6

B 17 29 -62.1 -35 G 26 24.5 9.8 9.3 F 34 -45.5 -2.3 -28.2 E 37 20.4 36.6 -20.8

Descending C 18.6 27.8 19.6 1.3

211

Participant ID: DOD207_131 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 2.4 15.1 12.7 -0.7 F# -9.1 -1.6 -0.9 -15.2 G -16.5 3.2 -3.8 -25.6 B -33.5 -7.4 6.7 -5.9

Ascending C# -26.1 -23 -15.5 -8.1 D -9.4 -6.2 -4.1 -24.1

C# -34.5 -36 -21.3 -16.5 B -41.7 -4.6 -0.4 -10.4 G -13.5 -5.7 -25.8 -35.7 F# -12.9 2.7 -18.4 -38.9

Descending E -12.6 0.6 -4.9 -6.7 212

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -29.3 -1 -22.2 -31.4 E -8 -9.3 -3.2 2.4 F -7.6 -13 -5.6 -12.6 G -15.3 -15 -19.1 -24.5

Ascending B -20.4 -41 2.7 -3.5 C -18.1 -26.9 0.4 -7

B -12.6 -29.3 11 -3.6 G -6.5 15.7 -24.6 -27.4 F 13.4 -8.1 7.1 -14.4 E 11.3 9.2 1.1 1.3

Descending C -13.7 -18.3 -7.3 -22.5

212

Participant ID: DOD208_141 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 14.9 30.9 14 2.9 F# 17.6 14.5 -13.3 -4.4 G 11 38 18.4 16.9 B 1.1 13.6 -7.9 -1.2

Ascending C# -5.8 -11.4 -25.5 -17.7 D 11.9 14.4 11.4 1.5

C# -31.2 -41.3 -27.9 -35.9 B -1.5 17.2 -8.2 -29.6 G 67.8 33.6 0 28.1 F# -37.6 -42.9 -39.4 -17

Descending E 0.6 -1.5 -17.7 -2.5 213

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 76.1 63.3 36.4 34 E 25.4 -19.7 -5.1 -14 F 76.6 72.1 -1.8 -6.4 G 36.3 5.4 15 -2.2

Ascending B 6.7 14.1 -1.2 -21.2 C 34.7 30.7 11.1 13.3

B -9.3 -1.3 -0.4 0.7 G 37.5 3 5.5 -31 F 77.3 25 10.8 12 E 20.3 15 -29 -18.3

Descending C 39.6 68.7 33.5 14.4

213

Participant ID: HTT101_111 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -0.5 7.1 -1.1 -4.9 F# -6.5 5.8 -5.9 -15.2 G -10.7 -1.4 -18.7 -27.9 B -13.5 -1.6 4.7 -15.7

Ascending C# -3.5 -0.1 -5.3 -15.4 D -8.9 -12.1 -12.8 -14.5

C# -10.2 -6.7 -7.4 -17.1 g B -7.6 0.7 -9.5 -14.6 G -39.2 4.6 -0.8 6.1 F# 12.2 40.7 -15.8 4.7

Descendin E 10.5 20.7 2.5 0.5 214

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 40 35.6 -16.7 10.4 E 16 18.2 7.9 16.8 F -9.9 -1.4 3.2 -0.1 G 6.9 11.7 9.9 5.8

Ascending B 16.5 11.1 0.8 -3.1 C 0.9 -13.8 -14.5 -10.8

B 13.6 9.4 -0.8 -0.5 G 7.7 13.9 -2.3 3.1 F -14.7 0.4 -5.5 -10.7 E -1.1 10.5 0.4 -0.5

Descending C -4.8 21.5 12.2 34.9

214

Participant ID: HTT102_122 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -11.4 -12.5 -33.9 -17.7 F# 20 18.5 -18.2 -16.8 G 4.2 22.5 -11.8 -19.4 B -19.4 -23.2 -35.2 -31

Ascending C# 7.2 -2.1 -34.8 -41.1 D 0.5 10.8 -28.5 -45.3

C# 5.5 4.4 -42 -42.8 B -9.9 -21.5 -22.5 -20.3 G -26.1 -13.7 -32.1 -22.1 F# -7.4 -26.9 -67.1 -3.6

Descending E -22 -1.8 -21.3 -5.5 215

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 8.6 3.9 2 5.3 E -17.3 -36.3 -23.6 -15.4 F 6.5 22.7 21.3 10.7 G -41.3 -1.3 -31.5 -4.5

Ascending B -41.6 -24.7 -33.4 -18.1 C -11.1 -11.8 -5.4 21.9

B -35.9 -17.8 -33 -13.3 G -21.5 -9.2 -5 -23.5 F 21.9 32.1 24.4 29.4 E -2.9 -39.5 -3.4 -38.2

Descending C 9 3.3 -2.1 3.7

215

Participant ID: HTT104_141 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 19.3 -1.8 0.3 32.5 F# 18.6 18.9 16.9 9.7 G 9.5 20.3 10.7 24.4 B 7.1 -1.2 0.7 34.2

Ascending C# 3.7 -1.6 2.6 10.4 D 12.6 -8.6 -0.8 -2

C# -1.6 -0.8 10.5 8.6 B 5.9 -2.1 -9.1 32.7 G 31.5 -29.9 -25.1 7.2 F# 11.6 -41.1 9.9 20.4

Descending E 34.2 5.9 15.8 20.8 216

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 58 27.7 38.8 12.5 E 11.2 5.5 18.7 16.1 F -30.9 -29.3 -11.9 -13.6 G 18.2 4.8 11.9 11.7

Ascending B 4.2 -8.9 -2.6 19.1 C -43.8 -64.5 -30.8 -11

B 1 -6.7 5.7 20.7 G -56 -2 2.4 -1.1 F -7.9 -32.3 11.8 -19.7 E 35.3 17.3 55.4 30.7

Descending C 30.9 -0.3 35.5 29.4

216

Participant ID: HTT105_111 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -7.1 -2.2 -4 12.1 F# 8.9 4.7 -9.1 -3.5 G -29.2 -18 -12.3 -1.7 B -27.1 -14.4 -27.9 -14.3

Ascending C# -38.5 -15.1 -35.8 -18.7 D -29.6 -37.4 -18.4 -5.1

C# -26.7 -6.4 -36.3 -21.6 B -26.7 -9.3 -25.9 -13.6 G -10.9 -3.1 -12.3 11.7 F# 8.3 7.3 -23.1 -4.8

Descending E -4.9 -15.4 -35 -7.3 217

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -31 -23.7 -23.5 -8.2 E -9.3 -15.5 -13 -8.6 F -32 -34.4 -27.5 -5.6 G -28.7 -25.6 -35.5 -17.5

Ascending B -27.1 -31.1 -30.4 -27.5 C -36.7 -41 -27.8 -13.4

B -21.4 -31.9 -30.1 -9.4 G -38.2 -38.7 -18.2 -8.3 F -40.1 -26.8 -8.4 -11.5 E -8.7 -3.6 -8 -23.9

Descending C -24 -18.1 -11.3 -5.1

217

Participant ID: HTT201_211 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -7.8 -10.3 8.2 -15.3 F# -17.2 9.1 -34.2 -18.8 G -28.3 -5 -45.3 -15.3 B 7.1 -4.8 -24.9 -17.3

Ascending C# -8.5 -19.3 -59.1 -13.9 D -6.4 -9.4 -22.9 -5

C# -1 -36 -67.8 -18.5 B 2.3 -16.7 -41 -12.7 G -27.8 -12.2 -19 -32 F# -24.1 -21.6 -3.1 -41.3

Descending E -15.1 -6 -12.2 -44.3 218

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C -19.5 -3 -8.1 -1.6 E -12.9 -2.1 -27.1 -12.4 F -13.6 -23.8 -9.2 -14.1 G 5.5 4.4 -11.6 -1.2

Ascending B -6.9 -5.6 -15.8 -15.3 C 0.5 -4.6 -26.3 -16.9

B -2.6 -7.1 -15.5 -12.1 G -16.2 3.3 -24.4 -11.7 F -16.6 10.5 6.8 -13.3 E -8.8 -21.6 -13.5 15.1

Descending C -19.5 -2.2 5.6 -3.8

218

Participant ID: HTT202_221 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 4.1 -0.2 -11.7 5.4 F# 12.4 9 -13 -3.2 G -10.8 13.8 -26.3 -27.6 B -0.6 8.9 -7.1 6.2

Ascending C# -1.8 -1.4 5.3 -1.4 D 1 -7.3 -19.9 -26.7

C# -2.8 -1.7 -2 -9.6 B -7.5 -0.5 -16.7 0.6 G -9.4 -17.5 -20.6 -6 F# 9.8 4 -17.4 19.3

Descending E -0.36 0.2 -19.3 -2.5 219

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 12.7 3.7 -20 -12.7 E 21.2 10.1 -7.6 1.2 F -6.4 6.7 -33.2 -17.7 G -2.4 -0.7 -5.8 -3.7

Ascending B 4.9 -4.2 -8.9 -7.6 C -19.6 -25.3 -29.3 -19.4

B 6.7 -6 -2.8 -4.2 G -4.6 -22 -27.5 -0.8 F -4.1 -2.9 -20.4 -9.7 E 0.2 0.7 -9.3 15.6

Descending C -3.7 -14.2 -8.6 -31.5

219

Participant ID: HTT204_241 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E -34.5 -27.3 -6.2 -22.6 F# -3.3 -7.2 -2 1.2 G 19.7 20.4 13.9 18.5 B -32.2 -21.2 -1.1 -21.7

Ascending C# -2.9 -5.4 10.6 -16.1 D 14.4 0.2 11.5 -30.1

C# -4.4 -9.6 1.9 -17.1 B -28.7 -24.1 -5.6 -21.4 G -8.5 12.3 21.1 8 F# -8.7 -11.8 6 8.1

Descending E -18.8 -18.2 -8.5 12.8 220

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 10.5 11.8 12.7 -16.4 E -18.6 -25.8 -2.5 -10.1 F -3.9 -33.7 -21.1 -20 G 0.1 11.3 28.3 14.9

Ascending B -31 -27.6 -4.6 -26.1 C -35.3 -47.3 -20.1 -47.8

B -31.3 -23.8 8.5 -27.9 G -0.2 14.5 33.6 17.1 F 3.3 -31.3 6.7 -29.2 E -19.5 -23.9 -1.6 7.3

Descending C 32.7 6.7 17.6 5

220

Participant ID: HTT205_212 RAW DIRECTIONAL CENT DEVIATION DATA

D-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied E 12.2 13.3 -7.8 -0.3 F# 9.4 1.2 11.1 2.9 G -7.7 -17.3 -12.7 -14.9 B 2.4 -7.1 -2.9 4.1

Ascending C# 10.4 10.4 -3.1 -10.9 D -8.6 0.6 -8.3 -9

C# 14.5 6.2 10.3 -10.9 B 13.2 16.7 6.2 2.8 G 18.7 19.7 9.6 15.7 F# 17.4 14.1 -2.5 11.1

Descending E 3.2 8 4.9 11.4 221

C-major Scale Pretest Posttest Pitch Unaccompanied Accompanied Unaccompanied Accompanied C 27.3 7 8.1 0.1 E 5.3 -0.9 -2.9 4.8 F -19.9 -14.4 -8.9 37.3 G 5.5 19.9 -25 12.4

Ascending B -5.2 -6.4 -18.3 -17.2 C -17.4 -27.6 -16.2 -6.2

B -2.4 -9.2 2 -5.6 G 3 6.8 6.2 12 F 6.6 5.4 -9.6 12.9 E 14.7 0.7 7.9 8.4

Descending C 8.4 3.3 7.2 -2.8

221