Florida State University Libraries

Electronic Theses, Treatises and Dissertations The Graduate School

2012 An Analysis of Double Bass Vibrato: Rates, Widths, and Pitches as Influenced by Pitch Height, Fingers Used, and Tempo James Paul Mick

Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY

COLLEGE OF MUSIC

AN ANALYSIS OF DOUBLE BASS VIBRATO:

RATES, WIDTHS, AND PITCHES AS INFLUENCED BY

PITCH HEIGHT, FINGERS USED, AND TEMPO

By

JAMES PAUL MICK

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

Degree Awarded: Spring Semester, 2012

James Mick defended this dissertation on March 13, 2012.

The members of the supervisory committee were:

Alice-Ann Darrow Professor Directing Dissertation

Melanie Punter University Representative

John Geringer Committee Member

Steven Kelly Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.

ii

I dedicate this dissertation to Dr. Michael Allen.

iii

ACKNOWLEDGEMENTS

I would like to extend my sincerest appreciation to Alice-Ann Darrow, my major professor. I honestly do not know how I would have finished if not for your continued guidance, encouragement, and dedication. Thank you for taking me as your fourth (!) doctoral student this year, and for providing the parameters that have helped me grow as a researcher, student, teacher, and person. To each of my other committee members: thank you, thank you, and thank you. Your help and guidance throughout my tenure at FSU has been invaluable. Dr. Geringer, your research classes paved the way for me to undertake this dissertation topic, and I wish I knew how to express my appreciation for your guidance after my first year of classes. Dr. Kelly, my committee would not be complete without you. I appreciate your time, feedback, expertise, and kindness of heart for joining my committee. Prof. Punter, your acceptance of me as an “honorary” student was crucial in my continued growth as both a performer and teacher. Thank you for providing a performance perspective throughout this process and for laying the groundwork for my lecture recital. It would have been impossible to collect data without the help of the following professors who graciously opened their double bass studios to my study: Harry Jacobson, Tod Leavitt, Melanie Punter, James VanDemark, and Nicholas Walker. Finally, I would like to thank my family for instilling in me the work ethic and dedication needed to complete such a massive undertaking; David Pope, my friend and colleague whose support, dedication, and loyalty was crucial to my continued growth as a teacher and person, especially after our first year of classes; Ed Kawakami, for your laughter and place to sleep when in town; Dr. Jimenez, for your musical inspiration, laughter, and open-door policy; Dr. Madsen, for your teaching inspiration and for making it possible for me to attend FSU; Lauren Smith, for patiently answering all of my questions; Keith Kaiser, for your mentorship and belief in me; and most importantly, Dr. Michael Allen, the only string pedagogue I have had as a teacher.

iv

TABLE OF CONTENTS

List of Tables ...... viii List of Figures...... ix Abstract...... x 1. INTRODUCTION...... 1 Functions of String Vibrato...... 1 Characteristics of String Vibrato...... 2 Historical Perspectives of String Vibrato...... 3 Need for the Study...... 5 Purpose Statement ...... 7 2. REVIEW OF LITERATURE...... 8 Development and Pedagogical Evolution of the Double Bass...... 8 Double Bass Instrument Development ...... 9 Double Bass Pedagogical Evolution...... 10 String Instrument Vibrato Mechanics ...... 13 Double Bass (and Cello) Vibrato...... 13 Violin and Viola Vibrato ...... 15 Double Bass Vibrato Teaching Methods...... 16 String Instrument Vibrato...... 18 Vibrato Rate...... 18 Pedagogical Views...... 18 Empirical Research ...... 19 Perception Research...... 20 Vibrato Width ...... 20 Pedagogical Views...... 20 Empirical Research ...... 21 Perception Research...... 23 Effect of Individual Fingers on Vibrato Rate and Width...... 23 Pedagogical Views...... 23 Empirical Research ...... 24 Effect of Pitch Height (Register) on Vibrato Rate and Width...... 25 Pedagogical Views...... 25 Empirical Research ...... 26 Effect of Tempo on Vibrato Rate and Width...... 27 Pedagogical Views...... 27 Empirical Research ...... 28

v Pitch Center...... 28 Pedagogical Views...... 28 Empirical Research ...... 29 Perception Research...... 31 Rationale and Research Questions ...... 31 3. METHOD...... 33 Participants ...... 33 Musical Stimuli ...... 34 Procedure...... 35 4. RESULTS...... 39 Data Analysis...... 39 Reliability ...... 41 Analysis Results ...... 41 Research Question #1: Totals ...... 41 Rate ...... 42 Width...... 44 Research Question #2: Individual Finger ...... 46 Rate ...... 46 Width...... 48 Summary Response...... 48 Research Question #3: Pitch Height ...... 49 Rate ...... 50 Width...... 51 Summary Response...... 51 Research Question #4: Tempo...... 52 Rate ...... 52 Width...... 52 Summary Response...... 55 Research Question #5: Pitch ...... 56 Summary Response...... 56 5. DISCUSSION...... 58 Limitations of the Present Study ...... 58 Relationship of Findings to Extant Literature ...... 59 Research Question #1: Totals ...... 59 Research Question #2: Finger...... 60 Research Question #3: Pitch Height ...... 61 Research Question #4: Tempo...... 61 Research Question #5: Pitch ...... 62 Discussion...... 63 Implications for Practice...... 65 Suggestions for Future Research...... 67 Conclusions ...... 68

vi APPENDICES ...... 70 A. Musical Exercises...... 70 B. Participants’ Raw Data ...... 72 C. Human Subjects Approval Memorandum ...... 113 D. Consent Form ...... 116 REFERENCES ...... 119 BIOGRAPHICAL SKETCH ...... 127

vii

LIST OF TABLES

Table 1 Mean Vibrato Rates for each Pitch Register and Finger from Exercises #1, #2, and #3...... 43

Table 2 Mean Vibrato Widths for each Pitch Register and Finger from Exercises #1, #2, and #3...... 45

Table 3 Mean Vibrato Rates of Individual Fingers (1st and 2nd) from Exercises #2 and #3...... 47

Table 4 Mean Vibrato Widths of Individual Fingers (1st and 2nd) from Exercises #2 and #3...... 49

Table 5 Mean Vibrato Rates for Pitch Registers from Exercises #2 and #3...... 50

Table 6 Mean Vibrato Widths for Pitch Registers from Exercises #2 and #3...... 51

Table 7 Mean Vibrato Rates for Slow and Fast Tempi according to Pitch Register and Individual Finger from Exercises #2 and #3...... 53

Table 8 Mean Vibrato Widths for Slow and Fast Tempi according to Pitch Register and Individual Finger from Exercises #2 and #3...... 55

Table 9 Mean Pitch Differences for Identical Vibrated and Non-Vibrated Half- Notes from Exercise #1...... 57

viii

LIST OF FIGURES

Figure 1 Vibrato Exercise #1, Excerpt #1—first position...... 35

Figure 2 Vibrato Exercise #1, Excerpt #2—fourth position ...... 35

Figure 3 Vibrato Exercise #1, Excerpt #3—thumb position...... 36

Figure 4 Vibrato Exercise #2, Excerpt #1—first position...... 37

Figure 5 Vibrato Exercise #3, Excerpt #1—first position...... 37

Figure 6 Vibrato Exercises #2 and #3, Excerpt #2—fourth position ...... 38

Figure 7 Vibrato Exercises #2 and #3, Excerpt #3—thumb position...... 38

Figure 8 Mean vibrato rates of double bassists according to pitch register and individual finger...... 42

Figure 9 Mean vibrato widths according to pitch register and individual finger...... 44

Figure 10 Mean vibrato rates of individual fingers according to pitch register...... 47

Figure 11 Mean vibrato widths of individual fingers according to pitch register...... 48

Figure 12 Mean vibrato rates of slow and fast tempi according to pitch register and individual finger...... 54

Figure 13 Mean vibrato widths of slow and fast tempi according to pitch register and finger...... 54

ix

ABSTRACT

The purpose of this study was to investigate the rates, widths, and pitches of university double bass players’ vibrato in relation to pitch height, fingers used, and tempo. Forty (N = 40) undergraduate and graduate double bass players were individually recorded performing three music exercises that were used for analyses. Each exercise was comprised of three identical excerpts that were transposed for first, fourth, and thumb positions. Excerpts in first and fourth positions utilized fingers 1, 2, and 4, while excerpts in thumb position utilized fingers 1, 2, and 3. The overall mean vibrato rate and width of university double bass students in this study was 5.17 Hz and 19 cents. A comparison of the vibrato rates and widths of participants’ 1st and 2nd fingers revealed that the 2nd finger (5.22 Hz, 21 cents) used both significantly faster and wider vibrato than the 1st finger (5.07 Hz, 18 cents). Additionally, the descriptive data from this study revealed that the 3rd and 4th fingers vibrated faster than both the 1st and 2nd fingers, and they had a wider vibrato width than the 1st finger, but a narrower width than the 2nd finger. The 3rd finger had the overall fastest recorded vibrato rate for any finger in any position. Analysis of vibrato data also indicated that university double bassists use significantly faster vibrato rates as they perform in progressively higher registers. When comparing the combined mean vibrato rates of the 1st and 2nd fingers, participants vibrated at 4.88 Hz in first position, 5.06 Hz in fourth position, and 5.50 Hz in thumb position. Vibrato widths also increased with pitch register. Mean vibrato widths in first position (16 cents) were significantly narrower than mean vibrato widths in both fourth position (21 cents) and thumb position (22 cents). Tempo also significantly affected mean vibrato rates and width. Musical examples played with a fast tempo were faster and wider (5.35 Hz, 20 cents) than musical examples played with a slow tempo (4.94 Hz, 19 cents). Additionally, analysis indicated that university double bassists vibrate almost equally above and below the in- tune pitch. Using the descriptive data for all fingers in all position, the total difference found between mean pitches of vibrated and non-vibrated tones was 1 cent. Music educators can use these results to create more consistent descriptions of double bass vibrato, and potentially, more efficient methods for teaching vibrato.

x

CHAPTER 1

INTRODUCTION

Vibrato is a vital component of string music performances that enhances the performer’s ability to convey musical meaning. Although each player possesses a unique and individualized vibrato sound, many acoustical characteristics of string vibrato are similar among all string performers. Some vibrato characteristics are instrument specific. By objectively analyzing various aspects of string vibrato, an accurate description of vibrato can be made for young and aspiring musicians. Two of the most commonly studied aspects of string vibrato are rate and width; however, few researchers have analyzed these vibrato aspects for double bassists, and consequently, little empirical research exists to shape a thorough description of double bass vibrato.

Functions of String Vibrato Contemporary string pedagogues often agree on the importance of vibrato in performances, suggesting that vibrato gives string instruments warmth and color. “Without vibrato, the sound of a string instrument would be cold and dead” (Morton, 1991, p. 83). Carl Flesch (1930) likened violin tone-quality without vibrato as “cold” and “arid” (p. 66). For these reasons, François Rabbath (1984), a contemporary double bass artist and pedagogue, cited vibrato as one of the most important aspects of double bass performance: “It has been said that the bow is the soul of the double bass; I would add that the vibrato gives it life” (p. xi). By mechanically vibrating tones, string instrumentalists alter the notes to become “warm” (Mantel, 1975). In turn, these vibrated notes help performers express their innermost feelings (Goilav, 1976; Guettler, 1992). Jeff Bradetich (2009), another contemporary double bass artist and pedagogue, stated that vibrato provides “a window into the soul of a performer” (p. 124). This freedom to convey emotions through the use of vibrato allows string musicians to “change”

1 music and thus make it personal, modifying it to ever-changing emotional states. Consequently, no two performances will ever be exactly the same for performers or listeners. Many artists and pedagogues have cited that vibrato creates the individuality of a performance. Eberhardt (1911) proclaimed, “On the open strings, the tone of one artist is not distinguishable from that of another. Individuality of tone can arise only when the fingers of the left hand are placed upon the strings. These fingers vibrate. They vibrate differently” (p. 16). This difference in performer vibrato “becomes a personal stamp, an artistic fingerprint, unique and inimitable through which one can distinguish one instrumentalist from another” (Goilav, 1976, p. 207). Differences in vibrato have even been compared to snowflakes (Morton, 1991): Like the slight differences between every snowflake, each player has a slightly different vibrato in the rate, extent, and waveform of pitch, intensity, and timbre, and the variability of its use and waveform. (p. 83). Beyond personal expression, vibrato has also been credited with a variety of other musical functions. In Viva Vibrato, a heterogeneous string instrument method book dedicated to the development of vibrato, Fischbach and Frost (1997) stated that vibrato enhances sound projection. Another musical function sometimes accredited to the use of vibrato is the ability of vibrato to cover slight intonation errors (Barber, 1990; Johnson, 1994). This function of covering slight intonation errors can be both positive and negative. Young musicians may use vibrato to mask slight intonation errors; however, the use of vibrato can also inhibit playing the exact pitch. For this reason, coupled with individual differences in vibrato tone, Robert Zimmerman— longtime principal double bassist of the Rochester Philharmonic Orchestra—demanded his sections use minimal vibrato, “the preference being improved, matched intonation over individually expressive sounds that cause disruption in unified section sound” (Griffin, 2008, p. 207).

Characteristics of String Vibrato Carl Seashore (1936), an early researcher of string instrument vibrato, defined a good vibrato as: “A pulsation of pitch, usually accompanied with synchronous pulsations of loudness and timbre, of such extent and rate as to give a pleasing flexibility, tenderness, and richness to the tone” (p. 7). In this definition, Seashore outlined four components of vibrato that provided a foundation for the pioneering vibrato research he led at the University of Iowa during the 1920s

2 and 1930s: pitch, intensity, timbre, and time. Pitch and intensity were subsequently shown to both fluctuate in violin performance (Cheslock, 1931; Fletcher, Blackham, & Geersten 1965; Seashore, 1936; C. Seashore, 1932). Metfessel (1932) also provided evidence that timbre fluctuated along with the pitch and intensity; however, this discovery was documented while studying vocal vibrato characteristics. Researchers were later able to corroborate these timbre fluctuation findings with string instruments (Fletcher & Sanders, 1967; Mellody & Wakefield, 2000). The study of time, or duration, in vibrato has generally consisted of pitch fluctuation rates; however, in recent years, researchers have begun to include more minute details of vibrato duration. Most notably, several investigators have recently analyzed vibrato absences between notes that were supposedly being performed with continuous vibrato (Allen, Geringer, & MacLeod, 2009; Geringer, Allen, & MacLeod, 2005). The researchers found that musicians generally stop vibrato between notes and that there is a brief period of “warming” that occurs at the beginning of each new note. Other aspects of string instrument vibrato have been investigated over the years, but in general, the research has continued to be shaped by the four components Seashore outlined during his original studies.

Historical Aspects of String Vibrato The use of string instrument vibrato has been discussed for centuries. Many sources cite Minimis Marin Mersenne, a monk from the early 17th century, as the first person to discuss string instrument vibrato, and in particular, violin vibrato (Clark, 1989; Hauck, 1975; Reger, 1932a). Scott Reger (1932a) quotes Marsenne’s Harmonie Universelle (1636): Now, the beautiful and charming harmonies which may be evoked from [the violin] are so numerous, that one may well prefer it to all other instruments; for the strokes of its bow, are sometimes so ravishing that one can think of no greater dissatisfaction than to hear the end of them, especially when they are mingled with quiverings [sic] and gentle motions of the left hand. (p. 291) In the 18th century, two contrasting opinions emerged as to how often vibrato should be used when performing music on string instruments. These opinions are still cited widely in the vibrato literature. The first opinion, and probably most commonly cited historical reference to string instrument vibrato, came from Leopold Mozart, a violin artist, pedagogue, and father of

3 Wolfgang Amadeus Mozart. In his book on violin playing, Mozart complained about the overuse of vibrato, comparing it to “palsy” of the hand (Mozart, 1948, originally published in 1756, p. 203). In contrast, Francesco Geminiani (1751), a contemporary of Mozart, provided a competing opinion by encouraging string players to use vibrato as often as possible. These contrasting views on the use of vibrato persisted throughout the following 150 years. In the early 1900s, opinions were still commonly split on how often to use vibrato. A few well-known violin pedagogues carried-on the opinion of Mozart and were adamantly against the continuous use of vibrato (Auer, 1980, originally published in 1921; Eberhardt, 1911). Auer (1980) complained vigorously about it: This curious habit of oscillating and vibrating on each and every tone amounts to an actual physical defect, whose existences those who are cursed with it do not in most cases even suspect. The source of this physical evil generally may be traced to a group of sick or ailing nerves, hitherto undiscovered. (p. 23) Yet, during this time, several violin virtuosi became known for their constant use of vibrato. Josef Joachim, Fritz Kreisler, and Carl Flesch all used vibrato extensively (Clark, 1989; Fischbach & Frost, 1997). These artists were some of the first to be recorded with newly invented phonographic audio machines, allowing many people to be exposed to the artists’ playing who otherwise would not have heard it. This exposure helped influence a gradual change in attitudes towards, and acceptance of, the constant use of vibrato. Today, vibrato is generally considered a vital component of a good string instrument sound (Boyden, 1990; Neumann, 1969). William Primrose said that no one should ever “practice anything without vibrato” (Applebaum & Applebaum, 1955, p. 167), and one researcher found evidence that both musicians and non-musicians prefer performances using more vibrato than performances with less vibrato (McDonald, 1998). Some pedagogues still say that vibrato is overused (Clark, 1989; Johnson, 1994), but generally, most pedagogues endorse the continuous use of vibrato except for specific instances. Since the continuous use of vibrato for all performance was not a common practice until recent times, some pedagogues and artists argue that older music should use vibrato sparingly, or even no vibrato at all. The other exception to the use of continuous vibrato occurs with the planned use of non-vibrated notes to enhance the dramatic effect of vibrated notes (Bradetich, 2009; Galamian, 1985; Johnson, 1994; Morton,

4 1991; Rabbath, 1984; Thierbach, 1999); however, if this practice is used too often, it can lose its effect and become monotonous. Outside of these instances when non-vibrato is accepted as a normal performance standard, modern pedagogues agree that when vibrato is used on a tone, it should begin at the beginning of the note and last the entire duration (Applebaum, 1986; Benfield & Dean, 1973; Bradetich, 2009; Fischbach & Frost, 1997; Galamian, 1985; Krakenberger, 2000; Young, 1978). The one exception being that vibrato can purposefully be delayed at the start of the note to heighten expression (Bradetich, 2009; Flesch, 1924; Rabbath, 1984).

Need for the Study For young string instrument players, learning vibrato signals that they have begun to “move out of the beginning student category onto the path that leads to artistry” (Lamb, 1984, p. 55). This transition is often an exciting time for young students, one that may be highly anticipated because “the introduction of vibrato is the high point of an early player allowing them [sic] to personalize their [sic] playing” (Young, 1978, p. 89). Through individualization of sound, students begin to personalize their expression and create a more intimate connection to the music they are performing. String instrument pedagogues, however, often disagree on how to teach vibrato and how to achieve an artistic level of vibrato. Due to the way the instruments are held and performed, upper strings (violin and viola) differ from lower strings (cello and bass) in the mechanics of performing vibrato. Upper string players typically use one, or a combination of three different types of vibrato: arm, wrist, and finger (Applebaum, 1986; Fischbach & Frost, 1997; Galamian, 1985; Hauck, 1975). In contrast, lower string players use similar motions formed by pivoting the lower arm at the elbow (Applebaum, 1986; Hamann & Gillespie, 2004; Klotman, 1996). Regardless of these differences in performing vibrato, pedagogues often apply similar vibrato principles to all of the string instruments. Pedagogues and artists have typically suggested that mean vibrato rates for string instruments should range between 5.0 Hz and 7.0 Hz (Applebaum, 1986; Kazez, 1987; Oppelt, 1981; Potter, 1980; Rolland, 2000; Stoelzing, 1950; Winnick, 1992) and that mean vibrato widths (extent) should range between 25 cents to 50 cents (Doschek, 1958; Fischbach & Frost, 1997; Kazez, 1987; Rolland & Mutschler, 2000); however, it is commonly suggested that double

5 bass vibrato rates and widths should generally be slower and wider than those of upper string players. Several suggestions have been made concerning proper vibrato rates for double bassists (Benfield & Dean, 1973; Bradetich, 2009; Morton, 1991), but no specific suggestions have been made regarding vibrato extent. Only a few researchers have investigated double bass vibrato rates and extent. The resulting double bass vibrato rates typically coincide with pedagogical suggestions that double bass vibrato should be slower than upper string players; however, observed vibrato extent of double bass players tends to be narrower than the suggested mean range for string instruments, not wider as some pedagogues have suggested (Fischbach & Frost, 1997; Gillespie, 1996; Stanton, 1965). It is widely believed that string instrument artists vary vibrato width and range depending on a variety of factors (Bradetich, 2009; Fischbach & Frost, 1997; Galamian, 1985; Guettler, 1992; Kuhn, 1967; Morton, 1991; Potter, 1980). Pitch register is one factor cited often as influencing string players’ vibrato. Pedagogues generally claim that higher notes should have a faster vibrato rate (Benfield & Dean, 1973; Fischbach & Frost, 1997; Goilav, 1976; Hamman & Gillespie, 2004; Lucktenberg, 1994; Mantel, 1975) and a narrower vibrato extent (Applebaum, 1986; Casals, 1922; Goilav, 1976; Hammann & Gillespie, 2004; Lucktenberg, 1994; Mantel, 1975). Researchers have provided mixed results regarding the effects of pitch register on vibrato rates and widths. Some string instrument vibrato investigators have not found a relationship between pitch register and vibrato rate (Fletcher et al., 1965; MacLeod, 2010; Papich & Rainbow, 1975; Thibeault, 1997) or between pitch register and vibrato width (Papich & Rainbow, 1975); however, some researchers have found pitch register to affect both vibrato rates (Allen et al., 2009; Geringer, MacLeod et al., 2010; MacLeod, 2008) and vibrato widths (Allen et al., 2009; MacLeod, 2008, 2010; Papich & Rainbow, 1974). Individual finger employment in vibrato is another factor artists and pedagogues have suggested contributes to varying vibrato rates and widths (Bradetich, 1995; Goilav, 1976; Mantel 1975). Partially because of the finger differences, double bass pedagogues typically recommend first learning vibrato with the 2nd finger, or whichever finger is “easiest” (Bradetich, 2009; Karr, 1988; Kjelland, 2008). Very few researchers have investigated the differences in vibrato characteristics of varying fingers among double bassists.

6 Tempo is cited less often as a factor commonly influencing vibrato rates and widths. Only a few pedagogues and researchers have even discussed tempo in relation to vibrato. Further inquiry is needed to determine the effects of tempo on vibrato rates and widths. The pitch center of vibrated tones is yet another topic commonly discussed by artists and pedagogues. Some pedagogues recommend that the mean vibrato extent should exist below the pitch being performed (Applebaum, 1986; Barber, 1990; Benham et al, 2011; Bradetich, 2009; Fischbach, 1998; Galamian, 1985; Hamann & Gillespie, 2004; Karr, 1988; Klotman, 1996; Lucktenberg, 1994; Miller, 2008). Others state that it should exist above the pitch (Blum, 1977) or centered on the pitch (Eberhardt, 1911; Goilav, 1976; Kazez, 1987; Kuhn, 1967; Mantel, 1975; Skoldberg, 1983). Interestingly, one double bass artist claims that all three beliefs are valid and each can be used to convey different musical intentions (Karr, 1996). Few empirical studies have been conducted concerning the pitch of double bass vibrato. Vibrato is a complicated skill influenced by many factors. Its complexity makes vibrato difficult to describe. Artists and pedagogues often disagree in their descriptions of vibrato, leading Jonas Starker (1979), noted cello artist and pedagogue, to partially blame researchers for the lack of agreement in describing vibrato: “Researchers… have not yet come up with an agreed-upon analysis of the acoustical properties of vibrato. Therefore, we have to rely on our own audio mechanism, which is developed through individual experiences” (p. 147).

Purpose Statement In recent years, researchers have begun to provide a more comprehensive understanding of string instrument vibrato, though more inquiry is needed to explore the different characteristics and factors influencing vibrato—particularly for the double bass. By analyzing the components and influencing variables of vibrato, researchers provide pedagogues with a more complete description of vibrato, and one that can potentially be used to assist young musicians in refining their vibrato performances. The purpose of this study was to investigate the rates, widths, and pitches of university double bass players’ vibrato in relation to pitch height, fingers used, and tempo.

7

CHAPTER 2

REVIEW OF LITERATURE

This chapter includes a review of literature in the following areas: development and pedagogical evolution of the double bass, vibrato mechanics, double bass vibrato teaching methods, and string instrument vibrato. These topics provide the framework and rationale for the research questions of this study.

Development and Pedagogical Evolution of the Double Bass Although a member of the violin family, the double bass has taken a unique path of development that is separate from other string family instruments; consequently, a variety of pedagogical and physical issues exist in teaching and learning to play the instrument. These issues have come about because the double bass, more than any other string instrument, has differences in instrument size, holding techniques, and teaching methodologies. As a member of the violin family, the double bass shares fully in its history, development and technique. Its uniqueness, however, stems from its evolving musical function in the orchestra which has brought about a number of significant changes. Each successive stage in the history of the double bass has required the instrument to adapt to new musical and technical demands; playing techniques and even quality of sound have varied accordingly. The fruit of three centuries of technical progress, the double bass has progressively been subjected to modifications in shape and fittings which differentiate it from its model and point of departure, the violin. (Brun, 1989, p.9) Because of physical differences between the double bass and the other string family instruments, double bassists must often adapt general performance concepts so that they can be successfully transferred to the double bass from the other string instruments. By understanding the unique history and development of the double bass, its differences and subsequent pedagogical evolution can be more fully understood.

8 Double Bass Instrument Development In the early years of development, the double bass was not a standardized instrument and contained many physical variations between instruments. These variations make it difficult to pinpoint the exact date the double bass was first created. Some of the early instruments closely resembled modern instruments while others did not; however, the basic concept and design of the modern double bass was initially introduced and developed during the 16th century (Elgar, 1965) or 17th century (Brun, 1989, 2001). Most of the early double basses were converted to modern variations in the subsequent years and no longer exist in their original form, also making it difficult to trace the development of the double bass as it evolved into its current designs (Brun, 2001). During the 18th century, Leopold Mozart (1948, originally published in 1756) commented on the various sizes and number of strings double basses: “The Great-Bass (il Contra Basso) [sic]…is also made in various sizes…. Usually it has four strings (at times only three), but the larger ones may have five” (p. 11). These differences between instrument attributes continued to be prominent throughout the 19th century with various schools of performance preferring different numbers of strings and tunings. Hector Berlioz and Richard Strauss even preferred their double bass sections to consist of instruments containing varying numbers of strings because of the mixed timbre they provided (Brun, 1989). By the end of the 19th century though, double basses became more standardized, and the modern variation of the double bass began to emerge. In particular, the influential German school of performance began to prefer double basses that contained four strings tuned EADG (Brun, 1989). This tuning system spread throughout Europe and North America during the ensuing years. Today, double basses have relatively standardized sizes, tunings, and number of strings; however, differences between instruments still persist. Probably the most notable difference is instrument size. Double basses can vary widely in their proportions, which can make it either easier or more difficult to maneuver around certain registers of the instrument. These size differences also provide various timbres for diverse styles of performing “depending whether a deep tone or virtuoso playing is to be favored” (Brun, 1989, p.81). Bigger instruments usually contain a deeper range of pitches that is often preferred by orchestral players, but the size can make it more difficult to maneuver in higher registers. Smaller instruments are generally easier

9 to maneuver in the higher registers and are typically associated with virtuosi playing, but they typically do not contain the same deep tone range as the larger instruments (Brun, 1989). By the early 20th century, most double bassists had adopted the German school of performance use of four strings tuned EADG; however, differences in number of strings and tuning persist today depending on the type of performance and personal preferences of the musican. The most commonly used tuning variation is employed by orchestral concerto soloists who often tune their strings a major second higher (F#BEA) than the typical EADG tuning. This type of tuning allows solo instruments to be heard more easily when performing with an orchestra (Brun, 1989). In addition to solo tuning, some double bassists continue to advocate tuning their instruments in perfect fifths (Masuzzo, 2003; McDougal, 1998). And while it is rare to find a three-string double bass today, five-string double basses can be found for sale in various string instrument catalogues. Partially because of the physical differences between instruments, double bassists use various methods for holding the instrument. Pedagogues and artists often discuss the merits of either standing or sitting while playing. Both methods are considered acceptable techniques for teaching young double bassists, and the decision regarding player position is typically left to individual teacher and student preferences (Allen, Gillespie, & Hayes, 2002; Bradetich, 2009; Hamann & Gillespie, 2004; Klotman, 1996). Recently, a new endpin was invented that rebalances the instrument weight for double bassists who stand while playing. This new “bent” endpin is accredited to Francois Rabbath and is encouraged in the “new school,” or Rabbath Method, of double bass methodology (Green & Neighbor, 1999; Rabbath, 1984; Vance & Costanzi, 2000). Nicholas Walker, a Rabbath student, also introduced a variation of the bent endpin. This variation requires drilling an angled endpin hole behind the traditional endpin hole and uses a wooden endpin that is claimed to improve tone quality and sound projection (Laborie, 2006). Ultimately, bent endpins were created to facilitate easier movement around the entire length of the fingerboard. The increased mobility has encouraged more virtuosic solo performances and has come to define the Rabbath Method.

Double Bass Pedagogical Evolution Despite the recent rise in virtuosic playing due to improved design and methodological teaching approaches, double bass performance standards have traditionally lagged behind the

10 other string instruments: “The double bass long remained the ‘lame duck’ [sic] of the music schools” (Brun, 1989, p. 42). This lag is the result of various related circumstances. First, in the past there were not many student-sized instruments available, so double bassists generally had to wait until they were older to begin study on the instrument (Neher, 1995). This postponement in initiating bass lessons created a development delay that placed double bassists behind other instrumentalists who were able to begin their study at younger ages. Second, there has been a habitual lack of quality double bass performance repertoire: It has taken the bass longer than the other strings [sic] to develop to a level of performance standards equal to theirs. Our poverty of literature, lack of attention paid to the bass outside the orchestral ensemble, and the archaic and unscientific methods books written by probably very talented but unscientific teachers of the late 19th and early 20th centuries have resulted in our second- and third-class citizenship with the string family. (Grodner, 1979, p. 28) Over the past 40 years though, a psychological shift in attitudes toward the double bass as a solo instrument coupled with improvements in double bass performance standards has occurred. Student-sized instruments have become readily available, more quality literature has been written, and subsequently, performance standards have risen. In the words of François Rabbath: “I am proud because the bass has become respectable. We are not just bass players. We are like violins” (Fanelli, 2009, p. 32). Accordingly, there have been many methods of teaching the double bass throughout its existence. Today, two primary pedagogical models dominate teaching trends in the United States—the “Traditional” Method and the Rabbath Method. Many current pedagogues credit the Traditional approach of teaching the double bass to Franz Simandl (Aaron, 1997). His method “’summarized’ 19th century double bass technique” (Simandl, 1984, p. V) and outlined a fixed- hand positional fingering chart that became the standard for most double bassists and music editors of the 20th century. Traditional Method books based on Simandl principles typically begin instruction in lower positions and registers of the double bass, using fingers 1, 2, and 4. As students become familiar with the lower positions, they progress towards higher positions. Once a player reaches the middle harmonic on the instrument, the thumb is repositioned behind the 1st finger and used as a performance finger in what is known as “thumb position,” first introduced by the Viennese

11 in the years 1766-1768 (Brun, 1989). Additionally, in thumb position, the 3rd finger is substituted for the 4th finger, which typically is not used in thumb position (Manoly, 1923); however, like many other aspects of double bass performance, variations of this fingering system exist. Some pedagogues and performers advocate the use of the 3rd finger below thumb position (Bille, 1922; Bradetich, 2009; Guettler, 1992; Neubert, 1988), others advocate the use of the thumb as a performance finger below thumb position (Bradetich, 2009; Rabbath, 1984), and one pedagogue even advocates the continued use of the 4th finger in thumb position (Guettler, 1992). One pedagogue summed up the various use of fingering systems: [The] choice of fingering is highly personal. It would be hard to find any two players who consistently choose the same fingering in any one piece of music. Choices differ for many reasons: schooling, physical factors determined by variations in bodily proportions, physical condition at any given time and, by no means least, differing musical approach. (Guettler, 1992, p. 82) The Rabbath Method, a newer pedagogical approach to teaching the double bass, has developed out of the more recent emergence of the double bass as a solo performance instrument. This newer approach does not begin in the lower positions and registers of the double bass as the Traditional Method does, but rather, it begins in “block” position—the Traditional Method fourth position where the thumb is placed in the block of the neck. The Rabbath Method then uses the harmonic structure of the instrument to introduce beginning students to the entire length of the fingerboard across all of its registers. The Rabbath Method differs from the Traditional Method in that it does not progressively teach from low registers to high registers, and additionally, it does not require a “fixed-hand” position, but rather, a hand that can pivot. To better facilitate these concepts, a new positional fingering chart was created that is centered on the natural harmonic structure of the instrument (Green & Neighbor, 1999; Rabbath, 1984; Vance & Costanzi, 2000). In the Rabbath Method positional system, the individual fingers used below and above thumb position are relatively the same as the Traditional Method approach (fingers 1, 2, & 4 below thumb position; fingers 1, 2, and 3 in thumb position); however, the hand pivots in the lower registers to reach more notes, thus reducing the number of shifts and hand positions needed in the traditional fixed-hand approach to perform the same notes. Subsequently, the Rabbath Method positional chart consists of six hand positions, or placements, for the entire

12 length of the fingerboard, whereas the Traditional Method only contains six hand positions for the first half of the fingerboard. To draw a more direct comparison between the methods, the Traditional Method fourth position is equal to the third position in the Rabbath Method, whereas the Rabbath Method fourth position is the beginning of thumb position in the Traditional Method, which is located beyond sixth position. While the Rabbath Method approach has become influential in the solo double bass community, the Traditional Method appears to still be the most commonly used fingering positional chart in heterogeneous string classes.

String Instrument Vibrato Mechanics Lower string (cello and double bass) and upper string (violin and viola) instruments use separate mechanics to produce vibrato. The following two sections explain traditional models used to teach the proper mechanics required to produce vibrato on the respective instruments.

Double Bass (and Cello) Vibrato Double bass vibrato is a complex skill, and when used effectively, it has been said to be unique among the string instruments. Longtime Chicago Symphony Orchestra double bassist and Northwestern University professor, Warren Benfield, said that vibrato on the double bass is the most effective of the string instruments: “The bass, more so than the other stringed instruments, is especially effective with its vibrato because of its wider range and longer string length” (Benfield & Dean, 1973, p. 26). All string instrument vibrato is generated by “slightly changing the string length by rolling the left hand on the string” (Hamann & Gillespie, 2004, p. 85); however, each instrument has different string lengths, and subsequently, “greater physical distances [are] required on the larger instruments to produce audible pitch fluctuations” (Fischbach & Frost, 1997, p. 12). This longer string length means that double bassists generally require the largest movements to create pitch fluctuations that are similar to other string instrumentalists. Double bassists must “exaggerate the vibrato for the audience to perceive a vibrato of comparable width to the other stringed instruments” (Morton, 1991, p.85). Cello players also have relatively long string lengths, and although cellists’ vibrato motions are generally not quite as large as double bassists’ motions, cellists and double bassists use a similar motion (Hamann & Gillespie, 2004; Potter, 1980).

13 Cello and double bass vibrato movement should be initiated from muscles in the back (Guettler, 1992; Nestler & Karr, 1981). Phyllis Young (1978), a well-known cello pedagogue, describes it as a “flow of energy from the player’s back” (p. 89). This “energy” transfers through the arm to the fingertip, which remains fixed to one place on the string. A slight changing of the string length then occurs when the fingertip rolls back-and-forth. To achieve this motion, the arm should act as a single unit from the elbow to the fingertip (Hamann & Gillespie, 2004; Klotman, 1996; Morton, 1991; Young, 1978). This unit should remain relaxed (Fischbach & Frost, 1997; Guettler, 1992; Young, 1978) and pivot at the elbow (Hamann & Gillespie, 2004; Morton, 1991). Additionally, when pivoting, the elbow should not move up and down (Hamann & Gillespie, 2004), and the forearm, wrist, and hand should subsequently rotate, or move, in an arc (Guettler, 1992; Hamann & Gillespie, 2004; Klotman, 1996). This arc movement is transferred to the finger, which rolls on the string creating the proper vibrato motion. In lower positions, the arms and fingers of cello and double bass players are fairly perpendicular to the string, creating a vibrato motion that is up and down along the string (Hamann & Gillespie, 2004; Kjelland, 2008; Morton, 1991). The thumb also performs an important role in eliminating hand tension by remaining relaxed, not squeezing the neck of the instrument. To remain relaxed, some pedagogues have suggested that the thumb does not necessarily have to touch the neck (Hamann & Gillespie, 2004). In the higher positions, particularly in thumb position, the left hand strays from being set at a right angle to the fingerboard. Consequently, the vibrato motion becomes more of a side-to-side movement meaning the vibrato motion becomes “less efficient” (Morton, 1991). Fortunately, this inefficiency coincides with a shorter string length where less vibrato extent is needed to cover a similar percentage of the total string length as vibrato in lower positions (Morton, 1991; Rabbath, 1984; P. Neher, in Shimek, 1993). During the initial phases of learning how to vibrate, cello and double bass players often learn beginning technique faster than upper string players (Brungard et al., 2006; Fischbach & Frost, 1997; Hamann & Gillespie, 2004); however, it has been argued that artistic use of vibrato is the most complicated for the double bass: The artistic practice of the vibrato is one of the most complicated problems of the instrumental aesthetic. It is complicated mostly for the strings, particularly for the double

14 bass, for any other string instrument does not require such a noticeably different vibrato between the high and low registers of the instrument. (Goilav, 1976, p. 207) Bradetich (1995) agrees that double bass vibrato is difficult to master. He states that playing the double bass inherently has bigger issues to overcome than the other string instruments: “From holding the bass to manipulating the notes, bass players have larger problems to overcome in strength, flexibility and coordination than any other instrumentalist” (p. 61).

Violin and Viola Vibrato Just as cello and double bass vibrato motions are similar, violin and viola vibrato motions are similar. Compared to the lower strings single type of vibrato motion, there are three different types of vibrato motions typically associated with upper string instruments: arm, wrist (or hand), and finger (Applebaum, 1986; Fischbach & Frost, 1997; Galamian, 1985; Klose, 1989; Klotman, 1996; Rolland & Mutschler, 2000). Each type is named according to the physical impulse needed to produce the vibrato motion, and like the lower strings, requires the fingertip to remain stationary on the fingerboard. Rolling the fingertip on the string by allowing the first knuckle joint of the finger to bend changes the string length, thus creating a vibrato sound. In order for this to happen, all three knuckle joints of the finger being employed must remain relaxed and flexible. Arm vibrato is initiated from the forearm and requires the wrist to remain straight while the vibrato motion is transferred to the fingertip. Wrist vibrato, also known as hand vibrato, requires the forearm to remain still while the vibrato motion is initiated at the wrist joint. The resulting motion is similar to waving, or fanning of the hand, which is transferred to the fingertip the same way as arm vibrato. Finger vibrato is initiated in the base knuckle of the finger and requires the hand to “yield” to the motion (Galamian, 1985). While many pedagogues share similar definitions of the different types of vibrato, they often differ in which type to teach first and whether the different kinds can even be taught independently of the others. In fact, some pedagogues believe the best vibrato motion is a combination of all three different types of vibrato (Applebaum, 1986; Fischbach & Frost, 1997; Flesch, 1924; Galamian, 1985; Klotman, 1996; Rolland & Mutschler, 2000).

15 Double Bass Vibrato Teaching Methods Pedagogues often disagree on when to begin teaching double bass vibrato; however, they generally agree that vibrato needs to be taught earlier in a student’s learning sequence than later (Fischbach, 1998; Karr, 1988; Kjelland, 2008; Klose, 1989; Young, 1978). Some pedagogues suggest teaching beginning vibrato movements almost from the beginning of learning to play the instrument (Karr, 1988; Kjelland, 2008; Klose, 1989). Others advocate waiting until a basic set of performance skills has been mastered (Brungard et al., 2006; Hamann & Gillespie, 2004; Klotman, 1996; Lamb, 1984; Stanton, 1965; Young, 1978). These differences may partially be explained by the fact that some students will almost immediately be capable of producing proper vibrato motions without previous training, but for many students, the act of learning vibrato can be a difficult process (Klotman, 1996). In reference to this debate of when to begin teaching vibrato and the difficulty many students experience while learning vibrato, Marvin Rabin, a well- known string pedagogue, once said: “Do you delay [teaching vibrato] because it’s difficult, or is it difficult because you delay [teaching vibrato]?” (Fischbach, 1998, p. 28). Methods for teaching double bass vibrato differ between pedagogues. During the beginning stages of learning vibrato, the general difference between pedagogical suggestions is whether to teach initial arm motions with a fixed or unfixed fingertip on the fingerboard. Methods that initially teach motions with an unfixed fingertip typically begin with movements that require the fingertip and thumb to slide along the string and instrument neck, a skill sometimes known as “polishing” (Allen et al., 2002; Fischbach & Frost, 1997; Hamann & Gillespie, 2004; Kjelland, 2008). The polishing motion is slowly decreased in extent until the thumb and finger become fixed on the string and neck while the arm continues to pivot with the proper motion. Some pedagogues suggest that initial movements should be practiced away from the instrument first (Benfield & Dean, 1973; Karr, 1988). Peculiarly, one pedagogue even advocates practicing vibrato motions with the right hand before learning to do them with the left hand (Benfield & Dean, 1973). When students reach the phase that the fingertip becomes fixed in place on the string, most pedagogues suggest it should be placed around the middle of the neck, generally between third and fourth positions (Bradetich, 1987, 2009; Guettler, 1992; Kjelland, 2008; Skoldberg, 1983); however, suggested beginning positions also include first position (Allen et al., 2002) and thumb position (Miller, 2008). In addition to the initial neck position, most pedagogues agree

16 that vibrato should initially be taught using the 2nd finger (Benham et al., 2011; Kjelland, 2008; Morton, 1991; Skoldberg, 1983). “On the bass, the most expressive vibrato finger is almost always the second finger because it is well balanced and strong” (Bradetich, 1995, p.62). Still, differences exist among pedagogues with recommendations including the 1st or 2nd fingers (Nestler & Karr, 1981), 3rd finger (Miller, 2008), or whatever finger the student picks as “easiest” for them (Bradetich, 1987, 2009; Karr, 1988). No pedagogical suggestion has been found that recommends beginning vibrato with the 4th finger. And although the thumb can also vibrate, it is not used as often as the other fingers and is generally taught at a more advanced stage (Bradetich, 2009; Guettler, 1992). Once vibrato it learned with the initial finger, it is then transferred to the other fingers. Kjelland (2008) recommends starting with the 2nd finger, then using the 1st finger before finally learning the 4th finger. Allen et al. (2002) also recommend starting with the 2nd finger, but then suggest moving to the 4th finger followed by the 1st finger. Brungard et al. (2006) use a different order: 2nd, 3rd, 4th, 1st. This sequence includes the 3rd finger, which allows double bassists to be taught simultaneously with other string instrumentalists. It is not uncommon in heterogeneous settings for the learning orders to be dictated by the other instruments to maintain consistency across the classroom. Learning the proper rates and widths of vibrato generally requires training because many initial vibrato rates are too fast and narrow (Bradetich, 2009). “Nothing is more discouraging than the feeling that the vibrato is either too fast or too slow, monochrome or monotonous, inappropriate to a certain register of the instrument, irregular, delayed or incomplete” (Goilav, 1976, p. 207). To help develop the motions required to control vibrato rates and widths, most pedagogues recommend beginning with slow, metered vibrato rates that progressively become faster with skill mastery (Allen et al., 2002; Benham et al., 2011; Bradetich, 1987, 2009; Brungard et al., 2006; Fischbach & Frost, 1997; Goilav, 1976; Hamann & Gillespie, 2004; Miller, 2008; Shimek, 1983; Skoldberg, 1983; Stevenson, 1994). As vibrato skill is mastered, it is important to remember that vibrato is a means to enhance music, not an end unto itself. Rabbath provides a vital remark about relating the technique of playing to the process of making music: “I put all my love into what I’m doing. I forget technique. Everything is how I can catch and find the note and express the note to let them feel it; let the public take the feeling with them” (Fanelli, 2008, p. 32). Yet, an objective picture of what is considered expressive vibrato technique may be a helpful guide for aspiring

17 performers. By creating a more detailed description of vibrato characteristics relating to many of the variables pedagogues disagree upon, it seems that teaching and learning vibrato can become more efficient, effective, and consistent.

String Instrument Vibrato String instrument vibrato researchers have primarily focused on characteristics of violin, viola, and cello vibrato, but few have incorporated the double bass in their studies. Further analysis of double bass vibrato may help clarify some of the discrepancies in pedagogical literature while also helping to establish a more comprehensive understanding of its properties and characteristics. The following six vibrato categories will be discussed in relation to the double bass: (1) rate, (2) width, (3) individual finger rate and width characteristics, (4) pitch height (register) differences, (5) tempo influences, and (6) purported pitch centers. Both pedagogical recommendations and empirical observations will be used to outline the issues pertaining to these six categories in double bass vibrato. Perception research, when appropriate, has also been included for several categories.

Vibrato Rate Pedagogical Views on Vibrato Rate Pedagogues and artists have typically suggested that mean vibrato rates for string instruments should range between 5.0 Hz and 7.0 Hz (Applebaum, 1986; Kazez, 1987; Oppelt, 1981; Potter, 1980; Rolland, 2000; Stoelzing, 1950; Winnick, 1992); however, double bass vibrato rates are generally suggested to be slower than the other string players (Fischbach & Frost, 1997; Gillespie, 1996; Morton, 1991; Stanton, 1965). Additionally, compared to the number of suggestions for upper string players, only a few specific mean vibrato rates have been provided for the double bass. Morton (1991) recommended a mean vibrato rate of 4.8 Hz, but also stated that players should be comfortable performing vibrato as slow as 3.3 Hz and as fast as 5.8 Hz. Bradetich (2009) has encouraged students to become comfortable performing vibrato at 4.0 Hz with proper technique before performing a range of vibrato rates between 3.3 Hz and 6.0 Hz. Benfield and Dean (1973) recommended a slower mean rate of approximately 2.5 Hz.

18 Empirical Research on Vibrato Rate Researchers have revealed that student level vibrato rates of double bassists are typically slower than vibrato rates of other string instrumentalists. Allen (2010) measured the vibrato rates of ten middle school and high school double bass students playing in first position and found they averaged 4.1 Hz. Papich & Rainbow (1974) investigated five university students playing in first and fourth positions and found that they commonly ranged between 4.0 Hz and 5.0 Hz. In another study of university students, Mick (2011) found the average vibrato rate of ten participants performing in thumb position to be 5.1 Hz. These rates resemble the recommendations made by Bradetich (2009) and Morton (1991). Mean vibrato rates for student level violin, viola, and cello players have generally been found to range between 5.0 Hz and 6.5 Hz (Fletcher & Sanders, 1967; Geringer & Allen, 2004; MacLeod, 2008; Papich & Rainbow, 1974). Not only are double bass vibrato rates slower than the other string instruments, but there is also evidence to support the notion that vibrato rates progressively increase for all string instruments as the size becomes smaller. Geringer and Allen (2004) investigated the vibrato rates of forty high school and university violin and cello students. Although rates between the instruments were not significantly different, violinists vibrated at a slightly faster rate (5.63 Hz) than the cellists (5.43 Hz). In another study containing forty high school and university violin and viola students, MacLeod (2008) also found that violinists vibrated slightly faster (5.71 Hz) than violists (5.49 Hz). Furthermore, in a study which contained four university violinists, four university cellists, and five university double bassists, mean vibrato rates increased successively with smaller instrument sizes: 4.0 Hz for double bass, 5.0 Hz for cello, and 6.5 Hz for violin (Papich & Rainbow, 1974). Artist level vibrato rates may be more consistent across instrument sizes and have not been found to be slower for double bassists. Thibeault (1997) analyzed 26 recordings of artist level double bassists and found mean vibrato rates to most frequently fall between 6.5 Hz and 7.0 Hz, but contained a total range of 4.0 Hz to 7.2 Hz. Thibeault’s findings closely resembled the mean rates (6.0 Hz to 7.0 Hz) reported for other artist-level string instrument performers (Allen et al., 2009; Cheslock, 1931; Hollinshead, 1932; MacLeod, 2010; Reger, 1932b; Seashore, 1938; Small, 1937).

19 Perception Research on Vibrato Rates In addition to pedagogical views on and empirical observations of vibrato rates, researchers have investigated listener preferences for vibrato rates. Corso and Lewis (1950) evaluated the preferences of musicians and non-musicians who heard pair-wise comparisons of vibrating complex wave tones. The tones were placed into twelve sets and manipulated to contain different combinations of rates (5.5 Hz, 6.0 Hz, 6.5 Hz, 7.0 Hz) and widths (0, 20 cents, 50 cents, 80 cents). Analysis revealed that both musician and non-musician participants preferred a rate of 6.5 Hz. In another study, McDonald (1998) used seventeen professional cello recordings to evaluate the perceived musicality of each performance by string performers, music majors, and non-music majors. Results indicated that participants rated performances using faster vibrato rates as more musical than slower vibrato rates. On average, the highest rated performances contained a mean vibrato rate of 7.5 Hz while the lowest rated were 6.9 Hz.

Vibrato Width Pedagogical Views on Vibrato Width Vibrato width (extent) is another commonly discussed characteristic of vibrato that plays an important role in both performing and learning proper vibrato. Paul Rolland (1960) believed that vibrato width was the most varied aspect of vibrato and was largely responsible for expressiveness in music performances. Reportedly, Yo-yo Ma uses a two-finger technique to occasionally widen his vibrato because it creates a “warmer” and “richer” sound (Harper, 1992, p. 65). A few double bass pedagogues have also discussed the importance of vibrato width and its variation. Bradetich (2009) states, “a great vibrato will be used at many different speeds and widths to bring out the mood and expression of the music” (p. 123). Guettler (1992) said increased expression can occur on individual notes, making each one characteristically distinctive: “It is therefore very important to master different kinds of vibrato; narrow/wide, quick/slow, etc., each of which can give a distinct character to a note, according to the musical context” (Guettler, 1992, p. 61). Pedagogues and artists have suggested a variety of appropriate mean vibrato widths for string instruments, but they generally fall between 25 and 50 cents (Doschek, 1968; Fischbach & Frost, 1997; Kazez, 1987; Lucktenberg, 1994; Rolland & Mutschler, 2000). In addition to mean vibrato widths, a few pedagogues have provided acceptable ranges for varying the vibrato extent:

20 0 cents to 50 cents (Fischbach & Frost, 1997) and 10 cents to 60 cents (Doscheck, 1968). Fischbach and Frost (1997) noted that ensemble performers typically use a smaller mean width (50 cents) than solo performers, who frequently reach 100 cents; anything wider than 100 cents is a “special effect, or a problem” (p. 10). If vibrato becomes too wide, it can sound out of tune (Barber, 1990) or “unpleasant” to the ear (Harper, 1996). It is commonly mentioned that vibrato widths should vary according to instrument size, with larger instruments using a larger extent (Applebaum, 1986; Fischbach & Frost, 1997; Gillespie, 1996; Stanton, 1965). No specific suggestions have been found regarding vibrato extent for double bassists, but because a larger motion is needed to create similar widths as smaller instruments, double bass players will sometimes use two fingers together (Fischbach & Frost, 1997; Hamann & Gillespie, 2004; Harper, 1996; Morton, 1991). There are several methods for implementing two-finger vibrato. The most common method is to press the 3rd and 4th fingers down together, side-by-side to provide more surface area and strength to 4th finger notes (Fischbach & Frost, 1997; Hamann & Gillespie, 2004; Miller, 2008). The other method is a more specialized and advanced skill that is particularly beneficial for performers with thin fingers when performing in the middle and lower registers of the double bass. Morton (1991) explained how to properly execute the method in his double bass teaching manual: [P]lace the next highest finger right next to the one stopping the string so that they are ‘locked’ together as one big finger…. The higher finger is situated so that it will just touch or press the string during the upward oscillation of the vibrato, and lift away from the string during the downward oscillation of the string. (p. 89) Gary Karr used this method of two-finger vibrato in his early years of performing, but stopped using it because his fingers became bigger. He also felt that the resulting sound of two-finger vibrato did not go well with the more “delicate” sound of the harpsichord, which became his primary accompanying instrument later in his career (Harper, 1996, p. 68). It has been mentioned that two-finger vibrato can border on 100 cents or more beginning in thumb position and become “unpleasant” (Harper, 1996).

Empirical Research on Vibrato Widths Research has shown mean vibrato widths generally align with pedagogical suggestions of 25 to 50 cents (30 cents, Cheslock, 1931; 30 cents, Geringer & Allen, 2004; 42 cents, MacLeod,

21 2008; 30 cents, Mellody & Wakefield, 2000; 25 to 50 cents, Papich & Rainbow, 1974; 42 cents, Reger, 1932b; 50 cents, Seashore, 1936; 44 cents, Small, 1937); however, artist musicians have also been found to have larger mean widths than students (74 cents, Allen et al., 2009; 52 cents, Hollinshead, 1932; 63 cents, MacLeod, 2010). Similar to vibrato rates, instrument size and level of training seem to have an effect on vibrato widths. No studies have investigated vibrato widths of double bass artists, but three studies have investigated student performers. The results indicate an increase of vibrato extent with experience. Middle school and high school double bassists were measured performing vibrato in first position and had a mean width of 19 cents (Allen, 2010). The other two studies measured vibrato widths of university students and found them to be slightly wider than secondary school students. Papich and Rainbow (1974) reported a finding of “slightly less than 1/8 step,” or 25 cents, for five participants performing in first and fourth positions, and similarly, Mick (2011) reported a mean width of 24 cents for ten participants performing in thumb position. These results are at the lower end or slightly below the pedagogically suggested mean vibrato extent of 25 to 50 cents. Other instrumentalists have also shown that their level of experience affects their vibrato extent. In Reger’s (1932b) study of violin, viola, and cello performers, each instrument showed an increase in width according to experience. Violin participants included four students (38 cents), two teachers (42 cents), and three artists (48 cents); viola participants included two teachers (34 cents) and one artist (56 cents); and, cello participants included one teacher (34 cents) and one artist (44 cents). Two more recent studies have also shown differences according to level of experience, but both were small. Geringer & Allen (2004) measured vibrato widths of forty high school and university violin and cello players. Mean high school student widths (29 cents) were slightly narrower than university student widths (31 cents). Similar results were found in MacLeod’s (2008) investigation of forty high school and university violin and viola performers. High school students on both the violin and viola had slightly narrower widths than their university counterparts. Some pedagogues have suggested that vibrato widths of larger instruments should be wider than smaller instruments (Applebaum, 1986; Fischbach & Frost, 1997; Gillespie, 1996; Primrose in Applebaum & Applebaum, 1955; Stanton, 1965), but researchers have typically indicated that either the opposite is true or that there is not much difference between the

22 instruments. Reger (1932b) reported only a minimal difference of vibrato widths across instruments: 42 cents for violinists (3 artists, 3 teachers, 4 students), 41 cents for violists (1 artist, 2 teachers), and 39 cents for cellists (1 artist, 1 teacher). Researchers in more recent studies have found even bigger differences in vibrato width according to instrument size. Geringer and Allen’s (2004) investigation of high school and university performers found mean violin widths (34 cents) were larger than cello widths (26 cents). MacLeod (2008) also reported wider widths for violins (46.5 cents) than the larger-sized violas (37.5 cents). Only one study could be found of multiple string instruments that showed a larger instrument containing the widest vibrato. Papich and Rainbow (1974) measured vibrato widths of four violinists, four cellists, and five bassists. The cello players reportedly had the widest vibrato (“slightly less than ¼ step,” or 50 cents). Violinists had “slightly greater than 1/8 step,” or 25 cents, while double bassists, had “slightly less than 1/8 step,” or 25 cents.

Perception Research on Vibrato Widths Seashore (1932) investigated perceptions of vibrato width and found participants generally perceived only 25% to 50% of the actual width, and vibrato extent and rate were found to influence perceptions. Listeners increased their accuracy of perceived vibrato width when actual extent was narrower and rates were slower. In a preference survey of vibrato widths, Corso and Lewis (1950) presented musicians and non-musicians with pair-wise comparisons of various vibrato widths (0, 20 cents, 50 cents, and 80 cents) and rates (5.5 Hz, 6.0 Hz, 6.5 Hz, 7.0 Hz). As stated above, both musicians and non-musicians preferred a vibrato rate of 6.5 Hz; however, musicians preferred a narrower vibrato width (20 cents) than non-musicians (50 cents). Both of these fall in the “acceptable” range of vibrato extent extremes suggested by pedagogues (Doschek, 1968; Fischbach & Frost, 1997) and researchers (Fletcher & Sanders, 1967).

Effect of Individual Fingers on Vibrato Rate and Width Pedagogical Views on the Effect of Individual Fingers on Vibrato Rate and Width Individual finger employment in vibrato is a factor both artists and pedagogues have suggested contribute to varying vibrato rates and widths (Bradetich, 1995; Goilav, 1976; Mantel 1975; Young, 1978). In an attempt to explain these differences, Bradetich (1995) outlined his opinion of vibrato characteristics for each finger on the double bass:

23 [First finger] vibrato is best in lower positions, weakest in the break area, usually producing a pointed focused sound. Pitch is often sharp in first position and flat in middle positions. The second finger is the most expressive vibrato finger and the most balanced – that is, the easiest to shift either direction. It is also the strongest finger with no innate weaknesses. The 3rd finger is used primarily as the speed finger… however, the 3rd finger is a weak vibrato finger and causes the most intonation problems in the lowest positions. The 4th finger produces the softest vibrato tone and usually causes the most problems when learning vibrato…. Pitch tends to be flat when a note is played with the 4th finger. [The thumb] is a weak vibrato finger, and students should avoid playing long and important notes with the thumb. (p. 62) To help compensate for the differences of each finger, Young (1978) has recommended teaching vibrato sound to be identical for all fingers: “In the beginning stages the goal is to keep the sound produced by each finger identical” (p. 91). But it has also been implied that individual finger differences may be a desired musical benefit for performers: “We must be reminded also of the artistic choice of the finger. Each finger can imprint on the vibrato a noticeably different character according to the specific physio-anatomy [sic] of the instrumentalist” (Goilav, 1976, p. 207).

Empirical Research on the Effect of Individual Fingers on Vibrato Rate and Width Research has shown that individual fingers generally have distinctive vibrato characteristics. Allen (2010) investigated individual finger vibrato rates and widths of middle school and high school double bass players performing in first position. Results indicated that the 2nd finger had the fastest mean vibrato rate (4.7 Hz), followed by the 4th finger (4.2 Hz) and 1st finger (3.5 Hz). Mean vibrato widths increased with successively higher fingers: 1st finger (13 cents), 2nd finger (20 cents) and 4th finger (24 cents). Papich and Rainbow (1975) analyzed sound wave diagrams for vibrato evenness of five university double bass students performing in first and fourth positions. Results indicated that 1st and 2nd finger vibrato was more even than 4th finger vibrato; however, all fingers used a more even vibrato in fourth position than first position. The researchers theorized that “the fourth finger has less strength and is shorter than the other fingers and thus may be more difficult to consistently control” (p. 6). Interestingly, mean vibrato rates and widths were similar for all

24 fingers in both positions. The study also included the violin, viola, and cello. Violin and viola players had a more even vibrato with the 2nd and 3rd fingers and a less even vibrato with 1st and 4th fingers. Additionally, vibrato rates and widths were more consistent when playing on the upper two strings than on the lower two strings. Cello players produced relatively similar vibrato evenness in fourth position, regardless of finger, but in the first position, the 1st finger was more uneven than the other three fingers. Geringer and Allen (2004) reported that high school and university violin and cello players did not have significantly different mean vibrato rates or widths for individual fingers; however, the 3rd and 4th fingers (5.6 Hz) were slightly faster than the 1st and 2nd fingers (5.46 Hz), and fingers 2-4 had a slightly wider vibrato (30 cents) than the 1st finger. Allen et al. (2009) investigated individual finger differences of a professional violinist in first and fifth position. The 2nd finger vibrated slightly faster than the other three fingers in both positions, but the 4th finger vibrated the widest (58 cents) in first position and the 3rd finger vibrated the widest (138 cents) in fifth position.

Effect of Pitch Height (Register) on Vibrato Rate and Width Pedagogical Views on the Effect of Pitch Height on Vibrato Rate and Width Pitch height (register) is a commonly mentioned factor that influences vibrato widths and rates. Pitch height refers to the location of a note on the fingerboard of a string instrument and the resulting string length. A performer’s hand location is referred to as a playing position, and higher positions (registers) have shorter string lengths. Consequently, if a musician desires to maintain a consistent vibrato extent across registers, higher registers require a smaller vibrato motion. To avoid creating different vibrato widths across registers, pedagogues commonly recommend making vibrato motions narrower in higher registers (Applebaum, 1986; Casals, 1922; Goilav, 1976; Hamann & Gillespie, 2004; Kjelland, 2008; Lucktenberg, 1994; Mantel, 1975; Morton, 1991; Rabbath, 1984; Shimek, 1993). Paul Neher, a double bass pedagogue, related the concept directly to performing in thumb position: “In thumb position, it is important that the width of the oscillations become more narrow with the rise in pitch to maintain a consistent vibrato sound throughout the register” (Shimek, 1993, p. 65). One pedagogue even claimed that by the nature of performing vibrato in higher registers of the double bass, vibrato width will naturally and “fortunately” decrease in size:

25 The frequency and amplitude of the vibrato should simulate the frequency and amplitude of the pitch being vibrated. A low pitch has a slower frequency and tends to have a wider amplitude than a higher one. Therefore, lower pitches should have a slower and wider vibrato, and higher pitches should have a faster and narrower vibrato. This explains why it is acceptable, even preferable [sic] to have, on the average, a slower vibrato on the double bass than with the other stringed instruments. It is a fortunate coincidence that the vibrato, due to the somewhat side to side [sic] vibrato movement in the thumb register, will automatically become more and more narrow as the hand progresses up the fingerboard. (Morton, 1991, p. 89) The effect of pitch height on vibrato rate is another commonly discussed topic among pedagogues who have typically stated that notes in higher registers require a faster vibrato than notes in lower registers (Benfield & Dean, 1973; Fischbach & Frost, 1997; Goilav, 1976; Hamann & Gillespie, 2004; Kjelland, 2008; Lucktenberg, 1994; Mantel, 1975; Morton, 1991); however, Francois Rabbath (1984) maintained that low register notes do not necessarily mean slow vibrato rates should be used: With low notes on the double bass, the vibrato must be very wide in order to become audible although the speed of it is not diminished; on the other hand, the more you play in the treble register, the more the wrist oscillation must decrease. (p. XI)

Empirical Research on the Effect of Pitch Height (Register) on Vibrato Rate and Width Few early researchers investigated the influence of pitch height on vibrato rates and widths. Fletcher et al. (1965) measured vibrato rates and widths of a violinist performing a note in four different octaves (G2, G3, G4, and G5) and did not find differences in vibrato rates and widths. In another study, Papich and Rainbow (1974) found that four university violinists used a wider vibrato in third position than in first position; however, during a follow-up study, Papich and Rainbow (1975) did not find differences between first and fourth positions for university double bassists or cellists. No results regarding pitch height were provided for the violin and viola participants in the follow-up study. More recent vibrato researchers have examined the influence of pitch height, but their findings have produced conflicting results. Thibeault (1997) studied professional double bass vibrato and did not find a strong correlation between pitch height and vibrato rates, r = .20. In

26 another study which included four professional violinists, a non-significant correlation was found between pitch height and vibrato rate, r = -.08; however, a relationship was found between pitch height and vibrato width, r = .42 (MacLeod, 2010). Several studies are in contrast to these reports. Allen et al. (2009) measured vibrato rates and widths of one professional violinist performing in first and fifth positions. Both mean rates and widths increased between first position (5.7 Hz, 40 cents) and fifth position (6.3 Hz, 108 cents). MacLeod (2008) investigated high school and university violin and viola students performing in first and seventh positions. Both vibrato rates and widths were significantly different between first position (5.47 Hz, 34 cents) and seventh position (5.74 Hz, 58 cents). Geringer, MacLeod et al. (2010) recorded an artist violinist and artist cellist playing a vibrated tone on each of their four strings and also found differences between registers. The violin and cello tones were both performed with smaller widths on the lower strings, and additionally, the cellist had a slightly slower vibrato rate on the C and G strings (4.9 Hz) than the D and A strings (5.0 Hz.)

Effect of Tempo on Vibrato Rate and Width Pedagogical Views on the Effect of Tempo on Vibrato Rate and Width As mentioned above, good vibrato contains varying rates and widths that are guided by a number of characteristics. Pedagogues have mentioned several musical characteristics as being influential on vibrato rates and widths, but one of the most commonly mentioned characteristics is dynamics. Probably the earliest mention of the influence of dynamics on vibrato was made by Leopold Mozart (1948, originally published in 1757): “The finger must move forward towards the bridge and backward again towards the scroll: in soft tone quite slowly, but in loud rather faster” (p. 98). More recent pedagogues and artists have also mentioned the influence of dynamics on vibrato rates (Casals, 1922; Fishbach & Frost, 1997; Galamian, 1985, Skoldberg, 1983) and vibrato widths (Fischbach & Frost, 1997; Galamian, 1985; Mantel, 1975; Rolland & Mutschler, 2000; Skoldberg, 1983). Pedagogues have less commonly mentioned tempo as a factor for influencing vibrato rates and widths. Skoldberg (1983) stated that slow, lyric passages should generally use slower vibrato rates, while quicker passages should contain faster vibrato rates. Conversely, Krakenberger (2000) stated that young students have a tendency to speed up their vibrato rates as

27 tempo decreases. No specific references of tempo were found pertaining to double bass vibrato performance.

Empirical Research on the Effect of Tempo on Vibrato Rate and Width Similar to the pedagogical literature, few researchers have addressed the effect of tempo on vibrato rate and width. Only one study could be found in which the researcher specifically investigated the effect of tempo on vibrato, and it was a study of professional double bassists. Thibeault (1997) measured vibrato rates of 26 double bass recordings and found a positive correlation between tempo and vibrato rate (r = .30). In a study of four professional violinists, MacLeod (2010) analyzed the effects of pitch register and dynamics on vibrato rates and widths. Results indicated faster vibrato rates and larger widths while performing loud passages, and slower rates and smaller widths while performing softer passages. In the discussion however, tempo was listed as a possible factor for producing variability among the performances of each artist. Geringer, Allen et al. (2010) also referenced tempo as a possible contributing factor influencing vibrato rates and widths in studies of artist-level performers since musical examples of artists are generally “based on material within a music performance context” (p. 13).

Pitch Center Pedagogical Views on Pitch Center Purported pitch center of vibrated tones is a popular and widely discussed topic among artists and pedagogues. It is generally asserted that vibrato oscillations (extent) either exist: (1) from the in-tune pitch to below the pitch (Applebaum, 1986; Barber, 1990; Benham et al., 2011; Bradetich, 2009; Fischbach, 1998; Galamian, 1985; Hamann & Gillespie, 2004; Karr, 1988; Klotman, 1996; Lucktenberg, 1994; Miller, 2008), (2) from the in-tune pitch to above the pitch (Blum, 1977), or (3) equally above and below the in-tune pitch (Eberhardt, 1911; Goilav, 1976; Kazez, 1987; Kuhn, 1967; Mantel, 1975; Skoldberg, 1983). The double bass literature mirrors the larger debate among string instruments and contains various opinions and beliefs of where the oscillation should occur in relation to the in- tune pitch center. Bradetich (2009) stated:

28 The pitch of the vibrato goes below the written note, then up to the note but not above the note. The ear hears the upper edge of the vibrato and vibrating above the exact pitch of the note will sound sharp. (p. 122) Other double bass pedagogues have disagreed. Morton (1991) and Goilav (1976) both stated that vibrato oscillations should exist above and below the in-tune pitch, something Morton contended has “irrefutable proof” (p. 85). Interestingly, one double bass artist claimed that all three beliefs are valid and each can be used to convey different musical intentions: The actual pitch desired might be at the top, middle, or bottom of the vibrato note…. The manner in which it colors pitch can convey great intensity (pitch on bottom of fast, narrow vibrato), aggressiveness (pitch in the middle of fast, wide vibrato), or lyrical poeticism (pitch on the top of a relaxed, vibrated note). When a player is moody and deliberate, the center of the vibrated pitch often drops below the note with the weight of the vibrated pitch actually beneath the desired intonation. There is no limit to the variations of the vibrato as it affects an intended pitch. (Karr, 1996, p. 85)

Empirical Research on Pitch Center The majority of empirical research has indicated that the mean vibrato extent is centered on the in-tune pitch (Allen et al., 2009; Brown & Vaughn, 1996; Geringer & Allen, 2004; Geringer et al., 2005; Geringer, MacLeod et al., 2010; C. Seashore, 1967; H. Seashore, 1932; Shackford, 1960; Shonle & Horan, 1980; Small, 1937). In an early pitch center study, Shackford

(1960) measured the pitch of three Boston Symphony Orchestra violinists performing an A4 with and without vibrato. In one component of the study, participants performed a vibrated A4 tone and matched it to a straight electronic tone. In another component, participants performed a non- vibrated A4 tone and matched it to a vibrated electronic tone. In both cases, analysis showed the pitch center to be at the middle of the vibrato extent. In more recent studies, Geringer and Allen (2004) investigated identical tones performed with and without vibrato by 40 high school and university violin and cello players. Mean pitches of both the vibrated and non-vibrated tones for all four fingers were then compared. Overall results showed less than a 1-cent difference between vibrated and non-vibrated tones. In one of two ensuing studies, Geringer et al. (2005) again analyzed 40 high school and university violin and cello players performing notes with and without vibrato. This time, whole notes were played

29 without vibrato for the first two beats and with vibrato for the last two beats. Overall mean pitches of vibrated notes for all fingers were not different from non-vibrated notes. Additionally, it was noted that violinists were more consistent in pitch across all four fingers than cellists. In the other ensuing study, Allen et al. (2009) compared tones performed with and without vibrato for all fingers of a violin artist performer. Mean pitches of vibrated and non-vibrated tones were almost exactly identical in first position. In fifth position, mean pitches were also not significant from each other, but the participant had a tendency to vibrate slightly above the non-vibrated tone (about 5 cents). In contrast to the bulk of empirical research supporting the view that perceived pitch is the mean of the vibrato extent, several researchers have found conflicting data. Fletcher and Sanders (1967) examined vibrated violin tones performed by a university concertmaster in order to create synthetic duplications. Vibrato extent and pitch were several characteristics that were closely analyzed. It was found that the vibrato extent ranged primarily from the intended pitch to below the intended pitch; however, as Geringer, Allen, and MacLeod (2010) mention, the violin pitches were compared to an equal tempered tuning expectation and no reference was made of the tuning procedure used by the violinist before performing. In addition to one study showing vibrato extent extending from the in-tune pitch to below the pitch (Fletcher & Sanders, 1967), three studies reported that vibrato extent existed from the in-tune pitch to above the pitch (Fletcher et al., 1965; Papich & Rainbow, 1974, 1975). Fletcher et al. (1965) analyzed violin, viola, cello, and bass students performing four vibrated tones in different registers of their instruments. The extent of vibrated tones was found to exist from the intended pitch and above the intended pitch; however, again, no reference was made of tuning procedures and it has been suggested that the instruments were tuned sharp (Geringer, Allen et al., 2010). Papich and Rainbow (1974) analyzed vibrato tones performed by four violin, four cello, and five double bass university student participants. Vibrated tones were found to exist from the intended pitch to above the intended pitch, but as in other studies, it has been noted that no reference is made to the source of the tuning ‘A’ (Geringer, Allen et al., 2010). A follow-up study by Papich and Rainbow (1975) found similar results of vibrato existing from the intended pitch to above the intended pitch. Their study included four violin, four viola, four cello, and four double bass university students performing tones partially without vibrato and partially with

30 vibrato. Vibrated portions of tones were found to contain vibrato oscillations ranging from the non-vibrato portion pitch and above it.

Perception Research on Pitch Center The findings of several perceptual studies have indicated that pitch is perceived as the mean of the vibrato extent. In an early study of nine professional violinists, Small (1937) analyzed mean vibrato pitches in relation to equal-tempered tuning. Results showed that the mean pitch level and perceived pitch were almost identical; however, deviations were commonly sharp on the fourth and seventh scales degrees. In another study, Brown and Vaughn (1996) recorded a professional violist performing tones with and without vibrato and paired them together in a comparison format. Musician and non-musician participants then heard the pairs of vibrated and non-vibrated tones and indicated whether the non-vibrated pitch was higher, lower, or the same as the vibrated pitch. Analysis revealed that both musicians and non-musicians perceived pitch as the mean extent of the vibrated tones. Geringer, MacLeod et al. (2010) used tones performed on acoustic instruments to measure pitch center perceptions of string music majors and non-string music majors. Recordings were made of an artist violinist and artist cellist performing vibrated and non- vibrated tones on each of their four strings. The vibrated tones were individually presented to participants who manipulated the pitch of the non-vibrated tones with a Continuous Response Dial Interface (CRDI) dial until the pitches of both tones matched. Results showed mean perceived pitches of violin and cello tones were less than 2 cents from the middle of the vibrato extents. No differences were found between string and non-string players; however, string players demonstrated less deviation in their responses than non-string players.

Rationale and Research Questions String instrument pedagogues have made conflicting suggestions for vibrato rates, widths, and pitch center. Additionally, it is common to find disagreement regarding possible characteristics that influence vibrato such as pitch height and tempo. Seashore (1936) blamed teachers and artists alike for the inconsistencies regarding the perception of vibrato: The true nature of the vibrato has not been understood by musicians. The best of artists, theorists, and teachers have remained at the mercy of mere fickle opinion, have been

31 misguided by the ear, and have presented erroneous and conflicting conceptions of the nature of vibrato. (p. 8) Researchers have also provided conflicting results in their investigations of vibrato characteristics. Unfortunately, the double bass has been included in few empirical studies of string instrument vibrato leaving its description to individual musicians, whose “sense of the vibrato determines what shall be good or bad for him. This introduces a most serious obstacle to the efforts towards establishing norms for a vibrato” (Seashore, 1936, p. 101). In addition to a need for more information regarding general double bass vibrato characteristics, more research is needed to determine the effect of tempo on vibrato rates and widths of string players. The purpose of this study was to investigate the rates, widths, and pitch of university double bass players’ vibrato in relation to pitch height, fingers used, and tempo. The following research questions were asked: (1) What are the rates and widths of university double bass students’ vibrato? (2) Do participants’ individual fingers differ in vibrato rates and widths? (3) Does pitch register affect participants’ vibrato rates and widths? (4) Does tempo affect participants’ vibrato rates and widths? (5) Is there a difference between participants’ mean pitches of vibrated and non-vibrated tones?

32

CHAPTER 3

METHOD

Participants Forty-eight undergraduate and graduate double bass students volunteered to participate in this study. All volunteers were enrolled as university music majors and came from a large university in the Southeastern United States (n = 14), a medium-size public university in the Southeastern United States (n = 2), a medium-size private college in the Northeastern United States (n = 14), a medium-size public university in the Northeastern United States (n = 13), or a large music conservatory in the Northeastern United States (n = 5). The volunteers ranged from 18 to 32 years of age (M = 20.4 years old), possessed 3 to 19 years of playing experience (M = 8.3 years), and had 2 to 15 years of private lesson training (M = 6.0 years). It was pre-determined that this study would include forty participants for analyses; however, not all volunteers met the performance criteria for inclusion in this study. Forty-eight volunteers were recorded before the qualified participant pool reached 40. The following definitions and criteria were followed when selecting recordings to be included in the study. Vibrato was defined as a pitch variation that contained at least two complete pitch oscillation cycles (2 Hz) at a minimum width of 7 cents—approximately 0.5 Hz in first position, 0.7 Hz in fourth position, and 1.0 Hz in thumb position. All vibrated and non-vibrated pitches in Exercise #1 needed to be measureable according to the selection criteria. At least 90% of all vibrated tones needed to contain measureable data that met the selection criteria. Excerpts in first and fourth positions utilized fingers 1, 2, and 4, while excerpts in thumb position utilized fingers 1, 2, and 3. Participants were asked to perform three musical exercises on their own instruments. There was a variety of playing differences among the participants. Seventeen participants sat while performing the exercises and 23 stood. Five participants used a German bow and 35 used a French bow. Additionally, a variety of G-string make and models were represented including 18

33 participants who used Thomastik Belcanto; five participants who used Thomastik Spirocore; three participants each who used Pirastro Permanent, D’Addario Helicore, and D’Addario Helicore Hybrid; two participants each who used Pirastro Obligato and Pirastro Flexocore; and one participant each who used Corelli 370 Medium, Thomastik Hybrid, Kolstein VariCor, and Pirastro Evah Pirazzi. All strings were medium gauge except one that was light gauge. All strings were tuned using the common EADG orchestral tuning.

Musical Stimuli Three music exercises were created for this study to measure vibrato rates and widths of university double bass students performing in first, fourth, and thumb positions (see Appendix A). The first exercise was also used to measure and compare the mean pitch center of vibrated and non-vibrated tones. Each exercise was comprised of three identical excerpts that were accordingly transposed for first, fourth, and thumb positions allowing comparative data to be collected from each of the three positions. Additionally, three commonly used fingers from each position were selected and used for data comparison. Excerpts in first and fourth positions utilized fingers 1, 2, and 4, while excerpts in thumb position utilized fingers 1, 2, and 3. All exercises included bowing, fingering, and tempo markings indicating how the exercises should be performed. Three university faculty members from a large university in the Southeastern United States verified the appropriateness and consistency of the markings. Additionally, participants were given time to review the exercises and ask questions before the study begun. A metronome was used to provide participants the marked tempi, which consisted of two measures worth of quarter note “clicks.” To maintain consistency, the tempo for each exercise was given between excerpts. After the metronome was turned off, participants were instructed to perform each excerpt. Digital audio recordings of each participant’s performance were made in either a university practice room or small studio-office used for teaching individual and chamber music lessons. The sound files were made at 24-bit with a 96KHz sampling rate and were analyzed using the software program Praat (Boersma & Weenink, 2009).

34 Procedure Upon entering the room, participants were given time to tune their instrument, review the musical exercises, and ask questions pertaining to the musical markings. Exercise #1 consisted of three identical excerpts that contained five-measure passages written in 4/4 meter. Each excerpt consisted of three measures of half-notes—two for each finger—interspersed with two measures of whole-rests. The excerpts were marked to be performed at 80-bpm on the G-string in first, fourth, and thumb positions.

The first excerpt in Exercise #1 was written for first position and contained two 1st finger nd th (A2) half-notes, followed by a whole-rest, two 2 finger (B♭2) half-notes, rest, and two 4 finger

(B2) half-notes (see Figure 1). The first half-note was marked to be performed non-vibrato with a down-bow while the second half-note was marked to be performed with vibrato using an up- bow. The half-notes in each measure were the same pitch and were marked to be performed with the same finger, thus allowing for a measurement to be made of the mean pitches of non-vibrated and vibrated tones.

Figure 1. Vibrato Exercise #1, Excerpt #1—first position.

The second excerpt of Exercise #1 was identical to the first excerpt except that it was st nd transposed for fourth position. The notes consisted of two 1 finger (D3) half-notes, two 2 th finger (E♭3) half-notes, and two 4 finger (E3) half-notes (see Figure 2).

Figure 2. Vibrato Exercise #1, Excerpt #2—fourth position.

35 Similarly, the third excerpt was identical to the first two excerpts, except that it was transposed for thumb position, which commonly replaces the 4th finger with the 3rd finger. The st nd rd notes consisted of two 1 finger (A3) half-notes, two 2 finger (B♭3) half-notes, and two 3

finger (B3) half-notes (see Figure 3).

Figure 3. Vibrato Exercise #1, Excerpt #3—thumb position.

The second and third exercises were identical to each other except for their tempo markings—Exercise #2 was marked 60-bpm and Exercise #3 was marked 120-bpm (see Figures 4 and 5). Similar to Exercise #1, Exercises #2 and #3 consisted of three identical excerpts that contained six-measure passages written in 4/4 meter. Each excerpt consisted of a two-measure rhythm—one half-note, four quarter-notes, one half-note—repeated three times. The excerpts for Exercises #2 and #3 were marked to be performed on the G-string in first, fourth, and thumb positions. The first excerpt in Exercises #2 and #3 was written for first position (see Figures 4 and st 5). The first excerpt began with a 1 finger (A2) half-note marked to be performed with vibrato and a down-bow. The vibrated half-note was followed by four quarter-notes marked to begin with an up-bow. The quarter-notes—in sequential order—were A2, B♭2, B2, and B♭2, and contained finger markings that indicated all of the notes were to be performed in first position. st Following the quarter-notes, a 1 finger (A2) half-note was marked to be performed with vibrato and an up-bow. The next two measures of the first excerpt were rhythmically identical to the first two nd measures, but began and ended with 2 finger (B♭2) half-notes marked to be performed with vibrato. The first half-note was marked to be performed with a down-bow and the last half-note was marked to be performed with an up-bow. The middle four quarter-notes were marked to begin with an up-bow and contained fingering markings that indicated all notes were to be

36 performed in the first position. The quarter-notes—in sequential order—were B♭2, B2, B♭2, and

A2. The final two measures of the first excerpt were rhythmically identical to the previous th two-measure segments, but began and ended with 4 finger (B2) half-notes marked to be performed with vibrato. The first half-note was marked to be performed with a down-bow and the last half-note was marked to be performed with an up-bow. The middle four quarter-notes were marked to begin with an up-bow and contained finger markings that indicated all notes were to be performed in the first position. The quarter-notes—in sequential order—were B♭2, B2,

B♭2, and A2. See Figures #4 and #5 for examples of the first excerpt for Exercises #2 and #3.

Figure 4. Vibrato Exercise #2, Excerpt #1—first position.

Figure 5. Vibrato Exercise #3, Excerpt #1—first position.

The second excerpt of Exercises #2 and #3 was identical to the first excerpt, but was transposed for fourth position (see Figure 6). The first two measures consisted of two 1st finger

(D3) half-notes on either side of four quarter-notes—D3, E♭3, E3, and E♭3. The next two measures nd consisted of two 2 finger (E♭3) half-notes on either side of four quarter-notes—E♭3, E3, E♭3, and th D3. And the final two measures consisted of two 4 finger (E3) half-notes on either side of four

quarter notes—E3, E♭3, D3, and E♭3.

37

Figure 6. Vibrato Exercises #2 and #3, Excerpt #2—fourth position.

The third excerpt of Exercises #2 and #3 was identical to the first two excerpts, but was transposed for thumb position, which commonly replaces the 4th finger with the 3rd finger (see st Figure 7). The first two measures consisted of two 1 finger (A3) half-notes on either side of four nd quarter-notes—A3, B♭3, B3, and B♭3. The next two measures consisted of two 2 finger (B♭3) half-notes on either side of four quarter-notes—B♭3, B3, B♭3, and A3. And the final two measures rd consisted of two 3 finger (B3) half-notes on either side of four quarter notes—B3, B♭3, A3, and

B♭3.

Figure 7. Vibrato Exercises #2 and #3, Excerpt #3—thumb position.

38

CHAPTER 4

RESULTS

Data Analysis Data were collected from 40 university double bass participants performing in first position (fingers 1, 2, & 4), fourth position (fingers 1, 2, & 4), and thumb position (fingers 1, 2, & 3). Measurements consisted of vibrato rates (expressed in Hz) and vibrato extent valleys and peaks (expressed in Hz) for half-notes performed in three musical examples. Nine vibrated tones from Exercise #1 were isolated for comparison along with 18 vibrated tones from each Exercise #2 and Exercise #3, creating a total of 45 vibrated tones and 135 measurements for each participant. Additionally, mean pitch levels (expressed in Hz) of both vibrated and non-vibrated tones were collected from half-notes in Exercise #1, adding another 18 measurements collected per participant. In all, a sum total of 54 tones were isolated and analyzed from each participant’s performance creating a grand total of 153 measurements per participant. All measurements were made using the software program Praat (Boersma & Weenink, 2009). Specific vibrato characteristics varied both within and between subjects. For instance, some participants had very consistent vibrato pitch oscillation cycles that began almost at the beginning of the tone while others took longer to establish a consistent vibrato pitch oscillation pattern, providing fewer complete vibrato pitch oscillation cycles that could be used for analysis. Additionally, some participants did not vibrate on all tones or had immeasurable data for some tones. For this reason, Exercises #2 and #3 were written to contain two tones for each independent variable (finger, position, and tempo) that were averaged together. If one tone was immeasurable, data could still be used from the corresponding tone; however, if both tones for a specific independent variable were immeasurable, all of the data for that particular participant were excluded from the study. Of the 48 original volunteers for this study, data from eight participants were excluded because of immeasurable tones.

39 All measurements of vibrated tones were taken from the middle of the tones. Irregular pitch oscillation cycles often found at the beginning and ending of notes were excluded. Non- vibrated tones also contained irregular consistencies at the beginning and ending of each tone that were excluded from analysis. Participants’ data often varied in the number of regular pitch oscillation cycles for each tone. For instance, in Exercise #2, which employed a slow tempo, it was common for each tone to contain five or six regular pitch oscillation cycles; however, in Exercise #3, which employed a fast tempo, it was uncommon for a participant to have more than three regular pitch oscillation cycles. For this reason, each vibrated tone had to contain a minimum of two regular pitch oscillation cycles to be measured. If the tone did not contain at least two regular pitch oscillation cycles, it was not measured. Previous vibrato researchers established a minimum of three regular pitch oscillation cycles to be considered acceptable for measurement, but either tempo was not isolated as a variable in the study (Mick, 2011) or the study included violins and violas, which generally vibrate at a faster rate providing more time to establish regular pitch oscillation cycles (MacLeod, 2008). Additionally, since two measurements were taken from each tone, an average was used for analysis that generally consisted of four or more regular pitch oscillation cycles spread between the two tones. Vibrato rates were calculated by measuring the frequency of regular pitch oscillation cycles. This calculation required counting the number of regular pitch oscillation cycles and dividing it by the elapsed time in which they occurred, thus providing a rate in Hertz. Vibrato widths were calculated by measuring the frequency range of one regular pitch oscillation cycle. These measurements of vibrato width required observer judgment to select which oscillation cycle best represented the width of all of the cycles. A measurement was then taken of both the vibrato extent valley and peak pitches (in Hz) for the specified regular pitch oscillation cycle. These two measurements were then compared to provide a cent difference that could be used to compare vibrato widths across pitch registers. It was predetermined that each vibrated tone needed to consist of at least a 7 cent range to be included in the study, which corresponded to approximately 0.5 Hz in first position, 0.7 Hz in fourth position, and 1.0 Hz in thumb position. All statistical analyses employed the average of both tones’ vibrato rate and width measurements taken for each independent variable. If only one tone of an independent variable was measurable, then that tone’s characteristics were used for statistical analyses instead of an average.

40 Research Question #5 also required that mean pitches of both vibrated and non-vibrated tones from Exercise #1 be compared. Mean pitches of vibrated tones were taken from the regular pitch oscillation cycles that were included in the measurements of vibrato rate for the selected tone. Mean pitches of non-vibrated tones consisted of the middle portion of the tone that did not include irregular pitch consistencies often found at the beginning and ending of tones. Similar to the other measurements of vibrato rate and width, it required observer judgment to select the part of the tone that was consistent.

Reliability Observer judgment was required to establish tone characteristics that excluded irregular characteristics often found at the beginning and ending of tones. To calculate reliability, two independent observers measured 10% of the isolated tones for a combined total of 20% of all tones. Their measurements were then compared with the principal investigator’s measurements. Agreement criteria among the independent observers and principal investigator consisted of vibrato rate (± 0.1 Hz), vibrato width (± 0.1 Hz for both the valley and peak pitches of the selected pitch oscillation cycle), and mean pitches of vibrated and non-vibrated tones (± 0.1 Hz). Agreement indices for each criterion were: 80% for vibrato rate (287 agreements out of 360 measurements), 89% for vibrato width (644 agreements out of 720 measurements), and 94% for mean pitches of vibrated and non-vibrated tones (136 agreements out of 144 measurements). Total reliability was 87%.

Results Research Question #1 What are the rates and widths of university double bass students’ vibrato? Data consisted of the vibrato rates and widths of 45 selected tones collected from participants performing Exercises #1, #2, and #3. Exercise #1 contained a single vibrated half- note for each finger (1st, 2nd, and 3rd or 4th) in each pitch register (first, fourth, and thumb positions) for a total of nine vibrato rate measurements and nine vibrato width measurements. Exercises #2 and #3 each contained two vibrated half-notes for each finger in each pitch register for a total of 18 vibrato rate measurements and 18 vibrato width measurements per participant; however, corresponding half-note measurements for both vibrato rates and widths were averaged

41 together to provide a total of nine vibrato rate and nine vibrato width measurements per participant that were used for data analyses. In total, nine data points existed for each of the three exercises creating a grand total of 27 data points per participant. Means and standard deviations were calculated for each pitch register, each individual finger, and overall totals.

Vibrato Rate Totals The overall mean vibrato rate for all positions and fingers was 5.17 Hz (SD = 0.67). Table 1 lists all of the mean vibrato rates and standard deviations for each position and each finger. Mean vibrato rates increased between positions as they became successively higher and within positions as successively higher fingers were utilized (see Figure 8). First position contained the slowest vibrato rate with M = 4.90 Hz (SD = 0.71), followed by fourth position with M = 5.13 Hz (SD = 0.64), and thumb position with M = 5.48 Hz (SD = 0.69). The total difference of mean vibrato rates between the slowest mean rate in first position and the fastest mean rate in thumb position was 0.58 Hz. Within each position, fourth position

5.6

5.4

5.2 in Hz in Hz 5 Vibrato Rate Rate Vibrato

4.8

4.6 1st 2nd 4th 1st 2nd 4th 1st 2nd 3rd

First Position Fourth Position Thumb Position

Pitch Register and Individual Finger

Figure 8. Mean vibrato rates of double bassists according to pitch register and individual finger.

42 Table 1 Mean Vibrato Rates for each Pitch Register and Finger from Exercises #1, #2, and #3

Position Finger Mean SD

First 1st 4.79 (Hz) .71 (Hz) 2nd 4.91 .65 4th 5.00 .65 Total (n = 360) 4.90 .67

Fourth 1st 4.93 .64 2nd 5.16 .65 4th 5.30 .63 Total (n = 360) 5.13 .64

Thumb 1st 5.40 .68 2nd 5.51 .70 3rd 5.54 .68 Total (n = 360) 5.48 .69

Total 1st (n = 360) 5.04 .68 2nd (n = 360) 5.19 .67 *3rd (n = 120) 5.54 .68 *4th (n = 240) 5.15 .64 Total (N = 1080) 5.17 .67

Note. (*) denotes data differences that may occur with the replacement of the 3rd finger for the 4th finger in thumb position.

contained the largest difference in mean vibrato rates with 0.37 Hz, followed by first position with 0.21 Hz, and thumb position with 0.14 Hz. The 2nd finger within each pitch register had the

43 smallest difference with the 4th or 3rd finger, and a larger difference with the 1st finger. In first position, the 2nd finger was 0.09 Hz slower than the 4th finger, but 0.12 Hz faster than the 1st finger. In fourth position, the 2nd finger was 0.14 Hz slower than the 4th finger, but 0.23 Hz faster than the 1st finger. And in thumb position, the 2nd finger was 0.03 Hz slower than the 3rd finger, but 0.11 Hz faster than the 1st finger.

Vibrato Width Totals The overall mean vibrato width for all positions and fingers was 19 cents (SD = 5). Table 2 lists all of the mean vibrato widths and standard deviations for each position and each finger. Mean vibrato widths increased between positions, but within each position, the 2nd finger always had the widest vibrato width and the 1st finger always had the narrowest vibrato width (see Figure 9).

24

22

20

in Cents 18 Vibrato Width

16

14 1st 2nd 4th 1st 2nd 4th 1st 2nd 3rd

First Position Fourth Position Thumb Position

Pitch Register and Individual Finger

Figure 9. Mean vibrato widths according to pitch register and individual finger.

44 Table 2 Mean Vibrato Widths for each Pitch Register and Finger from Exercises #1, #2, and #3

Position Finger Mean SD

First 1st 15 (cents) 4 (cents) 2nd 17 5 4th 16 5 Total (n = 360) 16 4

Fourth 1st 18 4 2nd 21 6 4th 19 6 Total (n = 360) 20 5

Thumb 1st 20 5 2nd 22 7 3rd 21 6 Total (n = 360) 21 6

Total 1st (n = 360) 17 5 2nd (n = 360) 20 6 *3rd (n = 120) 21 6 *4th (n = 240) 18 5 Total (N = 1080) 19 5

Note. (*) denotes data differences that may occur with the replacement of the 3rd finger for the 4th finger in thumb position.

First position contained the narrowest vibrato width with M = 16 cents (SD = 4), followed by fourth position with M = 20 cents (SD = 5), and thumb position with M = 21 cents (SD = 6).

45 The total difference of mean vibrato widths between the narrowest mean width in first position and the widest mean width in thumb position was 5 cents. Within each position, fourth position contained the largest change of mean vibrato widths between individual fingers with 3 cents, followed by both first position and thumb, each containing a variability of 2 cents between individual fingers.

Research Question #2 Do participants’ individual fingers differ in vibrato rates and widths? Data consisted of the vibrato rates and widths of 24 selected tones collected from participants performing Exercises #2 (slow tempo) and #3 (fast tempo). Both exercises contained two vibrated half-notes for each finger (1st and 2nd) in each pitch register (first, fourth, and thumb positions) for a total of 12 vibrato rate measurements and 12 vibrato width measurements per participant; however, corresponding half-note measurements for both vibrato rates and widths were averaged together to provide a total of six vibrato rate measurements and six vibrato width measurements per participant that were used for data analyses. In total, six data points existed for each of the two exercises creating a grand total of 12 data points per participant. Both the 3rd and 4th fingers were excluded from analysis because they were not employed uniformly across all playing positions. An alpha of .01 was used for all statistical analyses.

Vibrato Rate according to Individual Finger A three-way within-subjects ANOVA was used to compare vibrato rates according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast). Results showed a significant difference between the 1st finger (M = 5.07 Hz, SD = 0.66) and 2nd 2 st finger (M = 5.22 Hz, SD = 0.64), F(1, 39) = 20.90, p < .001, ηp = .35. The 1 finger always vibrated with a slower rate than the 2nd finger (see Figure 10), and the largest difference in vibrato rates between fingers occurred in fourth position with 0.21 Hz, followed by first position with 0.13 Hz and thumb position with 0.10 Hz (see Table 3 for means and standard deviations of each finger). No significant interactions were found for finger, pitch register, or tempo.

46 5.6

5.4

5.2 in Hz 1st Finger

Vibrato Rate 5 2nd Finger

4.8 First Position Fourth Position Thumb Position Pitch Register

Figure 10. Mean vibrato rates of individual fingers according to pitch register.

Table 3 Mean Vibrato Rates of Individual Fingers (1st and 2nd) from Exercises #2 and #3

Independent Variable Mean SD

First Position 1st Finger 4.81 (Hz) .71 (Hz) 2nd Finger 4.94 .61 Fourth Position 1st Finger 4.95 .61 2nd Finger 5.16 .63 Thumb Position 1st Finger 5.45 .65 2nd Finger 5.55 .68 Total 1st Finger 5.07 .66 2nd Finger 5.22 .64

Note. Underlined total means are significantly different from each other.

47 Vibrato Width according to Individual Finger A three-way within-subjects ANOVA was used to compare vibrato widths according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast). Results showed a significant difference between the 1st finger (M = 18 cents, SD = 5) and 2nd 2 st finger (M = 21 cents, SD = 6), F(1, 39) = 40.53, p < .001, ηp = .51. The 1 finger always vibrated with a narrower width than the 2nd finger (see Figure 11), and the largest difference in vibrato widths between fingers occurred in fourth position with 5 cents, followed by first position with 3 cents and thumb position with 2 cents (see Table 4). No significant interactions were found for finger, pitch register, or tempo.

24

22

20

in Cents 18 1st Finger

Vibrato Width 2nd Finger 16

14 First Position Fourth Position Thumb Position Pitch Register

Figure 11. Mean vibrato widths of individual fingers according to pitch register.

Summary Response to Research Question #2: Vibrato Rates and Widths according to Finger These analyses indicate that both vibrato rates and widths are significantly affected by individual finger usage. Mean vibrato rates and widths of the 1st finger were always slower and narrower than mean vibrato rates and widths of the 2nd finger. Descriptive data indicate that the 3rd and 4th fingers always vibrated faster than both the 1st and 2nd fingers, and that the 3rd and 4th fingers always vibrated wider than the 1st finger, but narrower than the 2nd finger.

48 Table 4 Mean Vibrato Widths of Individual Fingers (1st and 2nd) from Exercises #2 and #3

Independent Variable Mean SD

First Position 1st Finger 15 (cents) 4 (cents) 2nd Finger 18 4 Fourth Position 1st Finger 18 4 2nd Finger 23 6 Thumb Position 1st Finger 21 5 2nd Finger 23 7 Total 1st Finger 18 5 2nd Finger 21 6

Note. Underlined total means are significantly different from each other.

Research Question #3 Does pitch register affect participants’ vibrato rates and widths? Data consisted of the vibrato rates and widths of 24 selected tones collected from participants performing Exercises #2 (slow tempo) and #3 (fast tempo). Both exercises contained two vibrated half-notes for each finger (1st and 2nd) in each pitch register (first, fourth, and thumb positions) for a total of 12 vibrato rate measurements and 12 vibrato width measurements per participant; however, corresponding half-note measurements for both vibrato rates and widths were averaged together to provide a total of six vibrato rate measurements and six vibrato width measurements per participant that were used for data analyses. In total, six data points existed for each of the two exercises creating a grand total of 12 data points per participant. Both the 3rd and

49 4th fingers were excluded from analysis because they were not employed uniformly across all playing positions. An alpha of .01 was used for all statistical analyses.

Vibrato Rate according to Pitch Register A three-way within-subjects ANOVA was used to compare vibrato rates according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast). Analysis indicated a violation of sphericity for data pertaining to pitch register, therefore a Greenhouse-Geiser adjustment for a within-subjects ANOVA was used. Results showed a 2 significant difference for pitch register, F(1.42, 55.34) = 39.57, p < .001, ηp = .50. The Bonferroni test for multiple comparisons showed that vibrato rates in first position (M = 4.88 Hz, SD = 0.66) were significantly different than vibrato rates in fourth position (M = 5.06 Hz, SD = 0.62), p < .01, and thumb position (M = 5.50 Hz, SD = 0.66), p < .001, and that vibrato rates in fourth position were significantly different that vibrato rates in thumb position, p < .001 (see Table 5). The difference in means between first and fourth positions was 0.18 Hz, between fourth and thumb positions was 0.44 Hz, and between first and thumb positions was 0.62 Hz. No significant interactions were found for finger, pitch register, or tempo.

Table 5 Mean Vibrato Rates for Pitch Registers from Exercises #2 and #3

Independent Variable Mean SD

First Position 4.88 (Hz) .66 (Hz) Fourth Position 5.06 .62 Thumb Position 5.50 .66

Note. All means are significantly different from each other, p < .01.

50 Vibrato Width according to Pitch Register A three-way within-subjects ANOVA was used to compare vibrato widths according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast). Analysis indicated a violation of sphericity for data pertaining to pitch register, therefore a Greenhouse-Geiser adjustment for a within-subjects ANOVA was used. Results showed a 2 significant difference for pitch register, F(1.57, 61.40) = 38.60, p < .001, ηp = .50. The Bonferroni test for multiple comparisons showed that vibrato rates in first position (M = 16 cents, SD = 4) were significantly different than vibrato rates in fourth position (M = 21 cents, SD = 5), p < .006, and thumb position (M = 22 cents, SD = 6), p < .001; however, no significant differences for vibrato rates existed between fourth position and thumb position, p > .33 (see Table 6). The difference in means between first and fourth positions was 5 cents, between first and thumb positions was 6 cents, and between fourth and thumb positions was 1 cent. No significant interactions were found for finger, pitch register, or tempo.

Table 6 Mean Vibrato Rates for Pitch Registers from Exercises #2 and #3

Independent Variable Mean SD

First Position 16 (cents) 4 (cents) Fourth Position 21 5 Thumb Position 22 6

Note. Underlined means are significantly different from the other mean (p < .01), but are not significantly different from each other.

Summary Response to Research Question #3:Vibrato Rates and Widths according to Register These analyses indicate that both vibrato rates and widths are significantly affected by pitch register. Mean vibrato rates for each pitch register were significantly different from each

51 other, and mean vibrato rates increased as pitch register increased. Mean vibrato widths in first position were significantly different from both fourth and thumb position mean vibrato rates, but fourth and thumb position vibrato rates were not significantly different from each other.

Research Question #4 Does tempo affect participants’ vibrato rates and widths? Data consisted of the vibrato rates and widths of 24 selected tones collected from participants performing Exercises #2 (slow tempo) and #3 (fast tempo). Both exercises contained two vibrated half-notes for each finger (1st and 2nd) in each pitch register (first, fourth, and thumb positions) for a total of 12 vibrato rate measurements and 12 vibrato width measurements per participant; however, corresponding half-note measurements for both vibrato rates and widths were averaged together to provide a total of six vibrato rate measurements and six vibrato width measurements per participant that were used for data analyses. In total, six data points existed for each of the two exercises creating a grand total of 12 data points per participant. Both the 3rd and 4th fingers were excluded from analysis because they were not employed uniformly across all playing positions. An alpha of .01 was used for all statistical analyses.

Vibrato Rate according to Tempo A three-way within-subjects ANOVA was used to compare vibrato rates according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast). Results showed a significant difference between the vibrato rates of slow (M = 4.94 Hz, SD = 2 0.64) and fast tempi (M = 5.35 Hz, SD = 0.65), F(1, 39) = 107.12, p < .001, ηp = .73. Participants vibrated slower during the slow tempi than they vibrated during the fast tempi (see Figure 12). The largest difference in vibrato rates between tempos occurred in fourth position with 0.47 Hz, followed by thumb position with 0.40 Hz and first position with 0.35 Hz (see Table 7 for means and standard deviations according to pitch height and individual finger). No significant interactions were found for finger, pitch register, or tempo.

Vibrato Width according to Tempo A three-way within-subjects ANOVA was used to compare vibrato rates according to finger (1st and 2nd), pitch register (first, fourth, and thumb positions), and tempo (slow and fast).

52 Table 7 Mean Vibrato Rates for Slow and Fast Tempi according to Pitch Register and Individual Finger from Exercises #2 and #3

Slow Tempo Fast Tempo Position Finger Mean SD Mean SD

First 1st 4.65 (Hz) .71 (Hz) 4.98 (Hz) .70 (Hz) 2nd 4.76 .65 5.11 .57 Total 4.70 .68 5.05 .64

Fourth 1st 4.72 .61 5.18 .61 2nd 4.93 .60 5.40 .65 Total 4.82 .61 5.29 .63

Thumb 1st 5.24 .64 5.67 .67 2nd 5.36 .64 5.74 .72 Total 5.30 .64 5.70 .69

Total 1st 4.87 .65 5.28 .66 2nd 5.02 .63 5.42 .65 Total 4.94 .64 5.35 .65

Note. Underlined total means are significantly different from each other, p < .01.

Results showed a significant difference between the vibrato widths of slow (M = 19 cents, SD = 2 6) and fast tempi (M = 20 cents, SD = 5), F(1, 39) = 9.03, p < .01, ηp = .19. Participants used a narrower vibrato during the slow tempi than during the fast tempi (see Figure 13). All positions (first, fourth, and thumb) contained a 1-cent difference in vibrato widths according to tempo (see

53 5.8 5.6 5.4 5.2 in Hz 5 Vibrato Rate 4.8 Slow Tempo 4.6 Fast Tempo 1st 2nd 1st 2nd 1st 2nd

First Position Fourth Thumb Position Position

Pitch Register and Individual Finger

Figure 12. Mean vibrato rates of slow and fast tempi according to pitch register and individual finger.

26 24 22 20 18 in Cents 16 Vibrato Width 14 Slow Tempo 12 Fast Tempo 1st 2nd 1st 2nd 1st 2nd

First Position Fourth Position Thumb Position

Pitch Register and Individual Finger

Figure 13. Mean vibrato widths of slow and fast tempi according to pitch register and finger.

Table 8 for means and standard deviations according to pitch height and individual finger). No significant interactions were found for finger, pitch register, or tempo.

54 Table 8 Mean Vibrato Widths for Slow and Fast Tempi according to Pitch Register and Individual Finger from Exercises #2 and #3

Slow Tempo Fast Tempo Position Finger Mean SD Mean SD

First 1st 14 (cents) 4 (cents) 15 (cents) 5 (cents) 2nd 17 4 18 5 Total 16 4 17 4

Fourth 1st 18 4 19 5 2nd 22 6 24 7 Total 20 5 21 6

Thumb 1st 20 5 21 6 2nd 22 8 23 7 Total 21 6 22 7

Total 1st 18 4 18 5 2nd 21 6 22 6 Total 19 6 20 5

Note. Underlined total means are significantly different from each other, p < .01.

Summary Response to Research Question #4: Vibrato Rates and Widths according to Tempo These analyses indicate that both vibrato rates and widths are significantly affected by tempo. Mean vibrato rates and widths of tones played with a slow tempo were always slower and narrower than mean vibrato rates and widths of tones played with a faster tempo.

55 Research Question #5 Is there a difference between participants’ mean pitches of vibrated and non-vibrated tones? Data consisted of mean pitches of vibrated and non-vibrated half-notes in Exercise #1. Measurements were taken of each finger (1st, 2nd, and 3rd or 4th) performing identical non- vibrated and vibrated half-notes in each pitch register (first, fourth, and thumb positions) for a grand total of nine data points per participant. Mean pitches were then compared to provide descriptive data (see Table 9); however, for statistical analysis, only 1st and 2nd finger data were included since the 3rd and 4th fingers were not uniformly employed across all pitch registers. All vibrated pitches were compared to the non-vibrated counterpart pitches. A negative value indicates that the mean vibrated pitch was lower than the mean non-vibrated pitch. A positive value indicates that the mean vibrated pitch was higher than the mean non-vibrated pitch. An alpha of .01 was used for all statistical analyses. A two-way within-subjects ANOVA was used to compare pitch center differences according to individual finger (1st and 2nd) and pitch register (first, fourth, and thumb positions). Results showed no significant difference for pitch register, p > .95, but there was a significant difference between the 1st (M = 0 cents, SD = 5) and 2nd (M = -2 cents, SD = 5) fingers, F(1, 39) 2 nd = 20.43, p < .001, ηp = .34. This indicates that for the 2 finger, the mean vibrated pitch was 2 cents lower than the mean non-vibrated pitch. No significant interactions were found for pitch register and individual finger.

Summary Response to Research Question #5: Pitches of Vibrated and Non-Vibrated Tones These analyses indicate that mean pitches of vibrated and non-vibrato tones are affected by individual finger usage, but not by pitch register. The first finger contained 0 cent differences between vibrated and non-vibrated tones while the second finger vibrated 2 cents lower than the non-vibrated tone counterparts. Descriptive data indicate that the 3rd and 4th fingers combined vibrated 1-cent lower than the non-vibrated tone counterpart.

56 Table 9 Mean Pitch Differences for Identical Vibrated and Non-Vibrated Half-Notes from Exercise #1

Position Finger Mean SD

First 1st 1 (cent) 5 (cents) 2nd -2 5 4th -2 5 Total -1 5

Fourth 1st 1 4 2nd -3 5 4th -2 5 Total -1 5

Thumb 1st 0 6 2nd -2 5 3rd -1 6 Total -1 6

Total 1st (n = 120) 0 5 2nd (n = 120) -2 5 3rd (n = 40) -1 6 4th (n = 80) -2 5 Total -1 5

Note. Bracketed total means are significantly different from each other, p < .01. Positive values indicate that the mean vibrated pitches were higher than the mean non-vibrated pitches. Negative values indicate that the mean vibrated pitches were lower than the mean non-vibrated pitches.

57

CHAPTER 5

DISCUSSION

The purpose of this study was to investigate the rates, widths, and pitch of university double bass players’ vibrato in relation to pitch height, fingers used, and tempo. Results revealed that participants had an overall mean vibrato rate of 5.17 Hz and a mean vibrato width of 19 cents. Mean vibrato rates increased significantly as pitch register became higher and tempo increased, while mean vibrato widths were significantly wider for excerpts performed with a fast tempo than excerpts performed with a slow tempo. Mean vibrato widths in thumb position were significantly wider than mean vibrato widths in first position. Tones performed with vibrato were significantly lower in pitch than tones performed without vibrato; however, the overall difference between vibrated and non-vibrated pitches was only -1 cent. This chapter includes a discussion of these findings’ relevance to the existing literature, limitations of the findings, as well as suggestions for future research, implications for future practice, and research conclusions.

Limitations of the Present Study One possible limitation of the current study involves the measurement of vibrato. For analysis purposes, vibrato was defined as two complete pitch oscillation cycles. Previous researchers defined vibrato as a minimum of three complete pitch oscillation cycles (MacLeod, 2008; Mick, 2011); however, double bass participants in this study often had only two pitch oscillation cycles for notes performed under the fast tempo condition (Exercise #3). Additionally, of the 36 measured notes in Exercises #2 and #3, 24 participants had at least one note that could not be measured due to inconsistencies in the tone and oscillation cycles, or lack of vibrato. If a particular note could not be measured, the recorded data for that tone consisted of the other identical note performed under the same conditions. If both notes for a particular tone and set of conditions could not be measured, all data for that participant were excluded from analyses. No discernible patterns were apparent for notes that could not be measured.

58 Another possible limitation of the present study may be the various preferences and methods of teaching vibrato that were represented among the participants in this study. Participants were drawn from five different institutions in the Northeast and Southeast United States, and results may be idiosyncratic to the vibrato preferences of the professors and double bass studios represented at these institutions. This study was also limited to double bassists performing alone. Other instrumentalists were not included and no measurements were taken of participants performing in a group setting. Additionally, several performance variables were controlled for the purposes of this study and to eliminate possible confounding variables. The controlled variables included shifting, bowings, tempo, and fingerings. Generally, performers have some degree of freedom in manipulating these variables during typical performance situations. Finally, double bass playing techniques and instrument set-ups varied among participants. Issues such as participants standing versus sitting, using a French bow versus a German bow, using a bent endpin versus a straight endpin, or participants’ instrument set-up, such as string make and model, were not controlled for in the present study.

Relationship of Findings to Extant Literature Research Question #1 What are the rates and widths of university double bass students’ vibrato? The total mean vibrato rate of university double bass students in this study was 5.17 Hz. The findings from this study included measurements of vibrato rates in first, fourth, and thumb positions, and they indicate that a slightly faster total mean vibrato rate than those reported for other university double bassists (Mick, 2011; Rapick & Rainbow, 1974). Mick (2011) reported a mean vibrato rate of 5.1 Hz when double bassists performed in thumb position, while Papich and Rainbow (1974) reported a mean vibrato rate range of 4.0 Hz to 5.0 Hz when playing in first and fourth positions. All of these reported mean vibrato rates lie within the suggested ranges made by double bass pedagogues: 3.3 Hz to 6.0 Hz (Bradetich, 2009) and 3.3 Hz to 5.8 Hz (Morton, 1991); however, the total range of measured vibrato rates in this study was 3.38 Hz to 7.96 Hz, which is broader than both Bradetich (2009) and Morton (1991) recommend. Participants in this study had a total mean vibrato width of 19 cents. This finding corroborates other empirical measurements of double bass vibrato widths, which range between

59 19 and 25 cents (Allen, 2010; Mick, 2011; Papich & Rianbow, 1974). Interestingly, these mean vibrato widths are all less than the mean vibrato width suggestions that pedagogues generally recommend for string players, which usually fall between 25 and 50 cents (Doschek, 1968; Fischbach & Frost, 1997; Kazez, 1987; Lucktenberg, 1994; Rolland & Mutschler, 2000); however, it should be noted that a total vibrato width range of 7 cents (the defined minimum width for data inclusion in this study) to 40 cents was found for participants in this study.

Research Question #2 Do participants’ individual fingers differ in vibrato rates and widths? A comparison of the vibrato rates of participants’ 1st and 2nd fingers revealed that the 2nd finger (5.22 Hz) used a significantly faster vibrato rate than the 1st finger (5.07 Hz). Additionally, the descriptive data from this study also revealed that the 3rd and 4th fingers vibrated faster than both the 1st and 2nd fingers. The 3rd finger had the overall fastest vibrato rate for any finger in any position. This finding corroborates Mick’s (2011) finding that the 3rd finger had the fastest vibrato rate, and seemingly supports Bradetich’s (1995) assertion that the 3rd finger is the “speed finger” (p.62). The 3rd finger vibrato rate may have been influenced by pitch register since it was only employed in thumb position, which resulted in significantly faster vibrato rates than both the first or fourth positions. In the first and fourth positions, the 3rd finger was not used, but the highest finger employed (4th finger) still resulted in a faster vibrato rate than the other fingers. These findings corroborate those of Allen et al. (2009), Geringer and Allen (2004), and MacLeod (2008) who found that 3rd and 4th finger data resulted in faster vibrato rates than the 1st and 2nd fingers on the other string instruments. A comparison of participants’ 1st and 2nd finger vibrato widths revealed that the 2nd finger (21 cents) used a significantly wider vibrato width than the 1st finger (18 cents). The descriptive data also revealed that the 3rd and 4th fingers vibrated wider than the 1st finger, but narrower than the 2nd finger. This finding indicates that double bassists use the narrowest vibrato with their 1st finger, corroborating other reports of double bass individual finger vibrato characteristics (Allen, 2010; Mick, 2011). Results of the present study indicate participants’ 2nd finger used the widest vibrato, which seemingly corroborates Mick’s (2011) findings; however, Mick also reported that the 3rd finger used the same vibrato width as the 2nd finger. In contrast, Allen (2010) reported the 4th finger as using a wider vibrato than the 2nd finger. When comparing results to other string

60 instruments, results of this study corroborate the findings of other researchers who also found the 1st finger used the narrowest vibrato (Geringer & Allen, 2004; MacLeod, 2008).

Research Question #3 Does pitch register affect participants’ vibrato rates and widths? Results of the present study indicate that university double bassists use significantly faster vibrato rates as they perform in progressively higher pitch registers. When comparing the mean vibrato rates of the 1st and 2nd fingers, participants vibrated at 4.88 Hz in first position, 5.06 Hz in fourth position, and 5.50 Hz in thumb position. This finding is counter to the report of Papich and Rainbow’s (1975) who found no differences in vibrato rates when comparing four university double bassists’ performances in first and fourth positions; however, it corroborates Thibeault’s (1997) finding that a small correlation (r = .20) existed between pitch height and vibrato rates of professional double bassists. Other investigations of the relationship between pitch height and vibrato rate for other string instruments were also inconclusive (Allen et al., 2009; MacLeod, 2008, 2010). Results from the present study indicate that vibrato widths increase as the pitch register becomes higher. The mean vibrato width in first position (16 cents) was significantly narrower than the mean vibrato widths in both fourth position (21 cents) and thumb position (22 cents). These findings are not consistent with Papich and Rainbow’s (1975) second study of university double bassists where no differences in vibrato width were reported between first and fourth positions; however, when describing the vibrato width of participants on various instruments, the authors listed their results as “slightly less than 1/8 step,” “slightly greater than a 1/8 step,” and “slightly less than ¼ step,” which raises questions as to the precision of the measurements. Specific pitch cent differences are not provided for post-hoc comparisons. In contrast, the findings of this study corroborate reports of vibrato widths increasing with pitch height for other string instrumentalists (Allen et al., 2009; MacLeod, 2008, 2010).

Research Question #4 Does tempo affect participants’ vibrato rates and widths? Few pedagogues have made suggestions concerning the influence of tempo on vibrato rates. Krakenberger (2000) stated that young students have a tendency to speed up their vibrato

61 rate for slower tempi, while Skoldberg (1983) suggested that vibrato rates should increase with tempo. Results from the present study indicate that tempo significantly affected participants’ mean vibrato rates—mean vibrato rates of musical examples played with a fast tempo were faster (5.35 Hz) than musical examples played with a slow tempo (4.94 Hz). In another study of 26 artist double bass recordings, Thibeault (1997) reported a correlation (r = .30) between tempo and vibrato rate. No other empirical data could be found regarding tempo effects on string instrument vibrato rate; however, several other researchers have suggested tempo as a possible factor affecting vibrato characteristics (Geringer, Allen et al., 2010; MacLeod, 2010). No pedagogical comments or empirical data were found concerning the influence of tempo on vibrato widths of string players. Results from the present study indicated that tempo significantly affected participants’ mean vibrato widths. Mean vibrato widths for musical examples performed with a fast tempo were wider (20 cents) than for musical examples played with a slow tempo (19 cents). This difference of one cent between slow and fast tempi is obviously negligible, and likely means that in practice, vibrato widths are imperceptibly affected by tempo. Perception researchers may want to provide further information concerning characteristics of vibrato rates and widths in relation to tempo.

Research Question #5 Is there a difference between participants’ mean pitches of vibrated and non-vibrated tones? Results from the present study suggest that university double bassists vibrate almost equally above and below the in-tune pitch, which corroborates with most other findings of string instrument vibrato pitch centers (Allen et al., 2009; Brown & Vaughn, 1996; Geringer & Allen, 2004; Geringer et al., 2005; Geringer, MacLeod et al., 2010; C. Seashore, 1967; H. Seashore, 1932; Shackford, 1960; Shonle & Horan, 1980; Small, 1937). Using the descriptive data for all fingers in all position, the total difference found in mean pitches of vibrated and non-vibrated tones was one cent. A significant difference was found between the mean differences of vibrated and non-vibrated tones performed by the 1st finger (0 cents) and 2nd finger (-2 cents); however, a two-cent difference is below the threshold for discrimination of pitch differences (Geringer, MacLeod et al., 2010). Interestingly, data for the 1st finger were the only finger-related data that resulted in the mean vibrated pitch being higher than the non-vibrated mean pitches (1 cent in first position; 1 cent in fourth position; 0 cents in thumb position). The 3rd and 4th fingers

62 combined contained mean vibrated pitches that were slightly lower than the mean non-vibrated pitches (-1 cent in each of the three positions). The 2nd finger also vibrated slightly below non- vibrated pitches (-2 cents in first position; -3 cents in fourth position; -2 cents in thumb position).

Discussion Playing experience is one variable that other researchers have investigated when comparing vibrato rates and widths of string instrumentalists. Participants in this study included only university level players, but when comparing results from this study to those of other studies of double bass players, they are consistent with the idea that playing experience affects vibrato rates. The total mean vibrato rate of 5.17 Hz from this study fell between reported mean vibrato rates for both less experienced and more experienced double bass players. Allen (2010) reported a total mean vibrato rate of 4.1 Hz for middle school and high school double bass players, and Thibeault (1997) reported an average mean vibrato rate range of 6.5 Hz to 7.0 Hz for artist-level double bassists. Together, these findings suggest that performance experience affects the vibrato rates of double bassists. This possible relationship between vibrato rate and playing experience raises the following questions: Is there an “ideal” mean vibrato rate that double bassists should strive to attain? Should pedagogues establish recommended norms according to experience level? Previous research indicates performers’ playing experience affects vibrato widths of string instrumentalists (Geringer & Allen, 2004; MacLeod, 2008; Reger, 1932b); however, more research is warranted to draw conclusions regarding the effect of playing experience on vibrato widths of double bassists. Analysis of the present data resulted in a mean vibrato width of 16 cents in first position. This is narrower than Allen’s (2010) reported mean vibrato width of 19 cents in his study of middle school and high school double bassists performing in first position, and narrower than other reports of university double bassists (Mick, 2011; Papich & Rainbow, 1974). No other reports could be found of a possible relationship between double bassists’ vibrato width and their performance experience. The total mean vibrato rate of 5.17 Hz for participants in this study was slower than the reported mean vibrato rates of other university string instrumentalists (Geringer & Allen, 2004; MacLeod, 2008; Papich & Rainbow, 1974). This finding corroborates pedagogical suggestions that instrument size affects vibrato rates and widths (Applebaum, 1986; Applebaum &

63 Applebaum, 1955; Fischbach & Frost, 1997; Gillespie, 1996; Stanton, 1965), and that double bassists use the slowest vibrato rates of the string instrument family (Fischbach & Frost, 1997; Gillespie, 1996; Morton, 1991; Stanton, 1965); however, in contrast to university participants, studies of artist-level performers generally indicate that mean vibrato rates are relatively similar regardless of instrument (Allen et al., 2009; Cheslock, 1931; Hollinshead, 1932; MacLeod, 2010; Reger, 1932b; Seashore, 1938; Small, 1937; Thibeault, 1997). Differences in university players’ vibrato rates according to instrument size were not found among artist level performers; thus, raising the questions: Is there an “ideal” mean vibrato rate that all string instrumentalists should strive to attain? If so, what differentiations occur, or should occur, in teaching the various instruments to help aspiring musicians achieve the ideal vibrato rate? Should this mean rate be different for orchestral and solo playing? The total mean vibrato width of 19 cents found in this study is smaller than the total mean vibrato widths reported for other string instruments in studies that share similar sample sizes and participant experience levels (Geringer & Allen, 2004; MacLeod, 2008). Additionally, in a study with relatively few participants, Reger found vibrato widths decreased as instrument size increased from violin to viola to cello (1932b). Subsequently, it appears that vibrato width, regardless of instrument, may be more related to the general pitch height spectrum than to differences between instruments; thus, in contrast to suggestions that as instrument size increases, so should vibrato widths (Applebaum, 1986; Applebaum & Applebaum, 1955; Fischbach & Frost, 1997; Gillespie, 1996; Stanton, 1965). Perhaps, instead of suggesting that double bassists should have larger widths than the other string instruments, pedagogues might say that double bassists should use a larger motion than the other instrumentalists to create an appropriate vibrato width. Further clarification is needed to establish teaching practices that may differentiate vibrato widths according to instrument size. The finding in this study—that participants’ vibrato rates and widths varied depending on the finger used—corroborates Bradetich’s (1995) assertion that performers should plan their performances according to individual finger vibrato characteristics; however, it seems pertinent to know if the differences in vibrato characteristics between fingers are a practiced skill or a natural occurrence. Subsequently, should young musicians strive to have similar vibrato for all fingers, or should differences between fingers be encouraged? Perceptually, how much difference is discernible to the average listener? If differences between fingers are easily

64 perceptible to listeners, it may be prudent to account for these differences when planning fingerings for the music being played; however, if differences between fingers are not easily perceptible, specific fingerings according to vibrato characteristics may not be an important factor to consider beyond personal preference. Vibrato rates and widths of participants in this study were also affected by tempo. A 0.41 Hz difference existed between mean vibrato rates of excerpts performed with a fast and slow tempo, along with a one cent difference in mean vibrato widths. Are these differences perceptible to listeners? Are they aesthetically pleasing or desirable? Do professional musicians also alter their vibrato rates and widths according to tempo? Other contextual elements such as dynamics have also been shown to affect vibrato rates and widths. Do these musical elements of tempo and dynamics work in tandem, or are they mutually exclusive from each other? Vibrato pitch center results from this study and others predominantly show vibrato extent is centered on the in-tune pitch. Paradoxically, string pedagogues continue to debate the topic, and many continue to state that vibrato extent extends from the in-tune pitch to below the pitch. With the increasing data that support vibrato extent as being centered on the in-tune pitch, perhaps this pedagogical disagreement will soon be resolved. Finally, it should be noted that mean pitch differences of 1 or 2 cents cannot be perceived by the human ear (Geringer, MacLeod et al., 2010). Consequently, discussion of pitch tendencies and differences between fingers may not even be relevant since means for fingers existed within a several cent range. Additionally, some of the pitch differences between measurements of mean vibrated and non-vibrated pitches may lie within the range of error associated with analysis.

Implications for Practice It seems prudent that pedagogues and aspiring double bassists be aware of variables that affect vibrato characteristics. As double bassists gain more experience, their vibrato rates become faster. During the developmental years, vibrato rates and widths of double bassists are slower and narrower than other string instrumentalists; however, the vibrato rate gap appears to close for professional musicians, who appear to vibrate at approximately similar rates regardless of instrument. Additionally, empirical evidence predominantly shows that as instrument size increases, vibrato width decreases. Subsequently, pedagogues and teachers should be careful when suggesting that lower string players should be using a wider vibrato than their upper string

65 counterparts. It seems prudent to differentiate between the size of the motion used when vibrating and the actual acoustical vibrato extent that is produced. Perhaps one of the biggest vibrato characteristic debates among string pedagogues is the issue of pitch center. The findings of this study indicate that vibrato extent is centered on the in- tune pitch for university double bass performers; yet, the strong belief among pedagogues that vibrato exists from the in-tune pitch to below the pitch persists. Why does this belief continue in string pedagogical literature, particularly among upper string teachers? One possible explanation is the manner in which upper string players are taught to vibrate, which consists of the fingertip rolling from its starting point backwards, or lower in pitch, and then back up to the starting point. This motion of rolling away from and back to the starting finger placement may occur because the fingernail and finger shape prevent a rolling motion that goes from the starting point to above the pitch. Perhaps, this pedagogical teaching method of only rolling away from and back up to the starting point then became construed with how we perceive the pitch; however, in actuality, upper string players may learn to set their finger above the in-tune pitch, and while pulling back, rock equally below the in-tune pitch before returning to the initial starting position. Alternatively, wrist vibrato may enable motion in both directions from the pitch center. Interestingly, many lower string teachers have adopted this belief that vibrato extent exits below the in-tune pitch, even though cellists and double bassists use a rocking motion uninhibited by the fingernail or finger posture. In other words, lower string players should be able to equally rock their finger above and below the initial starting position pending that the finger is set perpendicular to the string and is balanced by the thumb and arm. Interestingly, the finding in this study of pitch differences between participants’ individual fingers corroborates Bradetich’s (1995) pedagogical summations for each finger: the 1st finger has a tendency to be sharp when performing vibrato in first and fourth positions, while the 4th finger has a tendency to be flat. This difference in fingers may be caused by the shape of the left hand while performing, which generally consists of fingers 2-4 being perpendicular to the string in the first and fourth positions, and the 1st finger stretching back, touching the string at a slight angle. Since the thumb is also generally placed behind the 2nd finger, the weight and balance of the hand may naturally influence the intonation of specific fingers. For instance, the 1st finger may have a sharp vibrato tendency in relation to the other fingers as the hand may have a tendency to be drawn to its center of balance—thumb and 2nd finger—while in the same

66 manner, the 4th finger may have a flat vibrato tendency. Contradictory to this argument of hand balance affecting pitch of individual fingers though, is the present study findings that revealed similar vibrato pitch differences in both lower positions and thumb position, which generally employs a different shape and center of balance. Additionally, possible issues related to hand balance do not explain the 2nd finger’s tendency to vibrate slightly below the pitch center when it is seemingly the most balanced finger in first and fourth positions, and should be the most capable finger for vibrating equally above and below the pitch.

Suggestions for Future Research Few investigators have studied double bass vibrato and findings from this study indicate that additional research is warranted. While some trends in vibrato research are emerging, many aspects of vibrato need more empirical data to establish a broader understanding of how vibrato is utilized and manipulated. In particular, further exploration is warranted to establish whether relationships exist between vibrato rates and widths and performers’ playing experience. Only one study was found that reported the vibrato rate characteristics of artist-level double bassists (Thibeault, 1997), and no studies were found that reported vibrato widths of artist-level double bassists. Researchers who include double bassists in their vibrato studies may be able to provide data that can be used to compare artist-level vibrato rates and widths with results of artist-level performers on the other string instruments. Additionally, vibrato width data collected from artist- level double bassists may be used to examine vibrato widths based on pitch height and performers’ degree of experience. Future researchers studying differences in vibrato widths according to instrument size may also want to design a single study to compare vibrato widths among all the string instrument family members. Only one vibrato study could be found that included all of the string instrument family members (Papich & Rainbow, 1975). Future researchers who include all of the instruments may be able to discern trends within the string family as a whole. Additionally, it may be pertinent to study why artists’ vibrato rates are seemingly unaffected by instrument size, while university-level performers’ vibrato rates are affected by instrument size. Among string performers, double bass players, due to the size of the instrument, have perhaps the greatest challenge changing between low and high registers. Consequently, research on the impact of pitch height is particularly pertinent for double bassists. In this study, pitch

67 height was found to affect both vibrato rates and widths. Future investigators may wish to ask: Are differences in vibrato rates and widths according to pitch height intentional? Are these differences aesthetically pleasing or desirable? Does experience level affect how fast and wide double bassists perform vibrato according to pitch height? Future researchers may also want to compare mean vibrato rate and width differences of orchestra players, who generally play in the lower registers of the instrument, and solo players, who generally play in the upper registers of their instruments. Is there a difference according to whether musicians are playing orchestral or solo music? Do musicians consciously or unconsciously change their vibrato according to the style of music they are playing, like jazz and popular music styles? Future investigators may wish to further explore vibrato characteristic differences between double bassists’ individual fingers in relation to various fingering choices. Specifically, it may be interesting to investigate the concept of a “speed finger” and measure 3rd finger vibrato rates in lower positions so that they may be statistically compared to the other fingers. Future investigators may also wish to further study perceived pitch differences of vibrated and non-vibrated tones. Small mean pitch differences of 1 or 2 cents between vibrated pitches performed on string instruments are not perceptible, and may have little relevance to actual practice. Additionally, it may be pertinent for future researchers to investigate the specific pitch perceptions of double bass vibrato. Is perception of double bass pitches similarly accurate as perception of pitches performed on the other, higher sounding string instruments? Similarly, future perception researchers may also find it interesting to continue investigating pitch perceptions of string instrumentalists’ vibrato by varying the vibrato rates and widths of performances. Finally, the length of vibrated notes that string players perform may also be a factor that future researchers wish to investigate. It may be interesting to examine possible differences in vibrato characteristics that occur on “short” notes of a musical example played with a slow tempo that are identical time-wise in length to “long” notes of another musical example played with a fast tempo.

Conclusions Opinions of beauty and aesthetically pleasing musical products vary amongst people, cultures, and time periods. Today, string instrumentalists commonly use vibrato when

68 performing to individualize their tone and convey musical meaning, and subsequently, learning to vibrate is often a monumental and exciting process for many young students. Unfortunately, it often takes many years for aspiring musicians to develop a musical vibrato because vibrato is a complex skill with many varying components that require patience and dedication to develop and control. Some of these vibrato components may potentially be perceived by the human ear and can be explained; however, most vibrato components cannot be accurately perceived by the human ear and are difficult to explain, often resulting in confusing and conflicting pedagogical suggestions. It is important that professional performers, pedagogues, and researchers work together to provide aspiring musicians with the descriptions and skills they need to succeed in mastering vibrato. Professional performers and pedagogues both provide crucial perspectives in developing vibrato descriptions for young musicians, but it seems imperative that vibrato researchers also contribute to the discussion. Vibrato researchers are able to explore various components that comprise vibrato and can provide pedagogues and teachers with objective information that can be used to create clearer descriptions of what exactly is happening when a string player uses vibrato in their performances. These descriptions can then be used to help develop potentially more efficient, more effective, and more consistent methods and approaches for teaching vibrato. Through evidence-based vibrato teaching practices, aspiring musicians will better be able to create their own individualized and expressive vibrato sound.

69

APPENDIX A

MUSICAL EXERCISES

70 Exercise #1 ( 80) q » non-vib. non-vib. non-vib.! vib. ! vib. ~~~~~~~ ! vib. ~~~~~~~ 1 " ~~~~~~~ 2 " 4 " ? 4 ˙ ˙ # ˙b ˙ # ˙n ˙ 4 non-vib. non-vib.! vib. ! vib. ~~~~~~~ non-vib.! vib. ~~~~~~~ 1 " ~~~~~~~ 2 " 4 " ˙ ˙ ˙b ˙ ˙n ˙ ? 4 # # 4 non-vib. vib. ! ~~~~~~~ non-vib. vib. non-vib. vib. 1 " ! ! 2 " ~~~~~~~ 3 " ~~~~~~~ 4 # # & 4 ˙ ˙ ˙b ˙ ˙n ˙

Exercise #2 ( 60) q » vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ 1 " 2 4 1 2 " 4 2 1 2 4 " 2 1 4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n ? 4 vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ 1 " 2 4 1 2 " 4 2 1 2 4 " 2 1 4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n ? 4 4

vib. vib. ! ~~~~ " ~~~~ vib. vib. vib. vib. 1 " 1 ! ~~~~ 1 " ~~~~ ! ~~~~ 1 " ~~~~ 2 3 2 " 3 2 2 3 " 2 3 &4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n

Exercise #3 ( 120) q » vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ vib.! ~~~~ vib." ~~~~ 1 " 2 4 1 2 " 4 2 1 2 4 " 2 1 4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n ? 4

vib. vib. vib.! ~~~~ vib." ~~~~ vib.! ~~~~ " ~~~~ vib.! ~~~~ " ~~~~ 1 " 2 4 1 2 " 4 2 1 2 4 " 2 1 4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n ? 4

vib. vib. ! ~~~~ " ~~~~ vib. vib. vib. vib.~~~~ 1 " 1 ! ~~~~ 1 " ~~~~ ! ~~~~ 1 " 2 3 2 " 3 2 2 3 " 2 3 4 ˙ œ œb œn œb ˙ ˙b œ œn œb œ ˙b ˙n œ œb œ œb ˙n & 4

71

APPENDIX B

PARTICIPANTS’ RAW DATA

72 Participant #1 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.65 108.88 110.07 19 109.77 109.51 -4 B♭2 4.49 115.29 116.41 17 116.08 115.82 -4 B2 4.30 122.36 123.39 15 122.97 122.84 -2 D3 4.76 145.03 147.20 26 146.10 146.18 1 E♭3 5.10 152.63 154.29 19 153.71 153.55 -2 E3 5.05 163.39 164.74 14 163.71 163.99 3 A3 5.15 217.14 219.01 15 218.51 217.98 -4 B♭3 5.00 228.88 231.31 18 230.31 230.05 -2 B3 5.05 242.37 245.15 20 244.49 243.86 -4

Example #2 A2 4.72 109.04 110.43 22 Slow Tempo A2 4.63 109.27 110.56 20 B♭2 4.46 114.97 116.22 19 B♭2 4.60 115.73 116.73 15 B2 4.63 121.63 122.69 15 B2 4.71 122.27 123.30 15 D3 4.80 144.75 146.88 25 D3 4.92 145.73 147.39 20 E♭3 4.90 151.68 154.06 27 E♭3 4.85 152.55 154.77 25 E3 5.26 162.18 164.24 22 E3 4.81 162.52 164.26 18 A3 5.00 215.44 218.36 23 A3 5.17 216.24 218.34 17 B♭3 5.22 228.11 231.85 28 B♭3 5.10 228.64 232.41 28 B3 4.47 239.11 243.37 31 B3 5.04 241.03 244.49 25

Example #3 A2 4.76 109.02 110.39 22 Fast Tempo A2 5.08 109.51 110.71 19 B♭2 4.55 115.45 116.63 18 B♭2 5.17 115.83 117.03 18 B2 5.26 122.15 123.42 18 B2 5.08 122.02 123.31 18 D3 4.92 144.46 146.73 27 D3 5.36 144.42 146.78 28 E♭3 5.17 150.96 153.56 30 E♭3 4.92 152.07 154.90 32 E3 5.17 162.51 164.30 19 E3 5.17 163.14 164.94 19 A3 5.00 215.99 219.52 28 A3 5.36 217.09 220.65 28 B♭3 5.17 231.32 235.91 34 B♭3 5.26 230.29 233.58 25 B3 5.36 240.43 245.33 32 B3 5.45 242.27 246.39 29

73 Participant #2 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.59 112.01 112.97 15 111.59 112.48 14 B♭2 4.90 118.36 119.96 23 118.81 119.19 6 B2 4.90 126.34 127.46 15 126.93 126.95 0 D3 5.04 146.38 147.54 14 146.23 146.97 8 E♭3 5.26 154.66 156.26 18 155.62 155.38 -3 E3 5.23 164.02 165.53 16 164.91 164.80 -1 A3 5.00 218.12 219.85 14 219.50 221.58 16 B♭3 5.09 232.63 235.23 19 233.07 234.07 7 B3 5.09 246.61 249.22 18 248.67 248.11 -4

Example #2 A2 4.59 112.59 113.15 9 Slow Tempo A2 4.42 111.06 111.88 13 B♭2 5.02 116.63 117.66 15 B♭2 4.99 116.56 118.11 23 B2 5.04 123.64 124.68 15 B2 4.92 123.35 124.52 16 D3 4.94 145.64 147.11 17 D3 5.04 145.68 147.15 17 E♭3 5.13 152.45 154.62 24 E♭3 4.95 153.08 155.47 27 E3 5.05 162.85 164.64 19 E3 5.18 161.59 163.76 23 A3 5.12 219.09 221.74 21 A3 5.24 219.35 221.99 21 B♭3 5.32 228.32 231.39 23 B♭3 4.99 227.25 229.65 18 B3 5.25 238.41 241.70 24 B3 4.94 236.27 239.13 21

Example #3 A2 4.55 112.46 113.42 15 Fast Tempo A2 4.55 111.13 112.50 21 B♭2 4.60 117.11 118.06 14 B♭2 4.60 117.08 118.47 20 B2 4.87 124.36 125.39 14 B2 4.84 123.78 124.92 16 D3 5.05 147.03 148.64 19 D3 5.44 146.33 147.76 17 E♭3 5.35 152.24 154.19 22 E♭3 4.90 151.83 154.27 28 E3 5.37 161.73 163.81 22 E3 5.41 162.72 164.70 21 A3 5.25 216.43 219.11 21 A3 5.19 215.01 217.04 16 B♭3 5.24 227.70 230.45 21 B♭3 4.90 225.84 229.29 26 B3 5.56 240.09 242.93 20 B3 5.40 239.49 242.72 23

74 Participant #3 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.62 108.59 109.33 12 109.05 108.93 -2 B♭2 4.60 115.10 116.85 26 116.63 116.00 -9 B2 4.72 122.64 124.55 27 123.87 123.57 -4 D3 5.22 145.00 146.58 19 146.31 146.07 -3 E♭3 5.26 152.28 154.21 22 154.09 153.34 -8 E3 5.33 163.56 166.28 29 165.30 165.02 -3 A3 5.13 214.56 216.93 19 217.05 216.78 -2 B♭3 5.38 228.81 232.13 25 231.68 230.80 -7 B3 5.38 241.97 246.66 33 245.65 245.64 0

Example #2 A2 4.59 109.49 110.56 17 Slow Tempo A2 4.40 109.96 111.06 17 B♭2 4.21 114.54 116.01 22 B♭2 4.72 113.67 115.28 24 B2 4.35 122.91 124.26 19 B2 4.50 122.12 124.09 28 D3 4.64 144.81 146.52 20 D3 4.80 146.04 147.30 15 E♭3 4.69 151.49 154.72 37 E♭3 4.63 151.76 154.01 26 E3 4.46 163.88 166.28 25 E3 4.80 163.32 166.48 33 A3 5.05 215.14 219.02 31 A3 5.06 219.16 221.70 20 B♭3 5.26 229.34 233.17 29 B♭3 5.22 229.05 231.95 22 B3 5.07 243.76 246.27 18 B3 5.04 243.83 247.31 25

Example #3 A2 4.62 109.20 110.50 20 Fast Tempo A2 4.84 109.33 110.42 17 B♭2 4.00 113.95 115.55 24 B♭2 4.35 114.55 116.43 28 B2 4.61 123.62 124.99 19 B2 4.69 122.86 124.71 26 D3 4.92 146.19 147.45 15 D3 5.00 146.07 147.84 21 E♭3 4.76 151.51 155.04 40 E♭3 4.92 152.90 155.45 29 E3 4.76 164.00 166.77 29 E3 4.92 163.46 167.34 41 A3 5.36 218.01 222.02 32 A3 5.00 217.76 222.13 34 B♭3 5.08 227.93 232.91 37 B♭3 5.00 230.47 234.57 31 B3 5.48 244.77 247.42 19 B3 5.36 247.32 250.59 23

75 Participant #4 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.33 108.95 109.95 16 109.80 109.50 -5 B♭2 5.72 115.44 116.54 16 116.28 115.98 -4 B2 5.58 123.23 124.29 15 123.97 123.93 -1 D3 5.34 144.03 145.41 17 144.57 144.72 2 E♭3 5.82 151.62 152.92 15 152.76 152.33 -5 E3 6.18 160.76 162.62 20 162.64 161.73 -10 A3 5.87 220.90 222.52 13 222.27 221.64 -5 B♭3 6.00 234.69 236.21 11 235.43 235.53 1 B3 6.12 247.25 249.42 15 247.99 248.27 2

Example #2 A2 4.74 108.40 109.32 15 Slow Tempo A2 4.86 107.88 109.09 19 B♭2 5.05 114.15 115.24 16 B♭2 4.95 114.56 115.86 21 B2 5.54 121.07 122.26 17 B2 5.38 122.86 124.00 16 D3 5.04 143.22 144.66 17 D3 4.89 143.78 145.64 22 E♭3 5.36 152.15 153.17 12 E♭3 5.83 152.64 153.90 14 E3 5.97 163.20 165.01 19 E3 6.18 159.86 161.99 23 A3 5.47 219.58 221.96 19 A3 5.83 221.16 222.65 12 B♭3 6.44 236.36 238.39 15 B♭3 6.44 234.57 236.62 15 B3 6.61 247.26 248.94 12 B3 6.28 247.70 249.15 10

Example #3 A2 4.69 109.31 110.21 14 Fast Tempo A2 5.14 109.65 110.45 13 B♭2 5.33 115.05 116.60 23 B♭2 5.24 116.14 117.41 19 B2 6.16 121.90 122.95 15 B2 5.68 123.32 124.35 14 D3 5.89 142.54 144.25 21 D3 6.07 143.24 144.81 19 E♭3 6.46 149.22 150.90 19 E♭3 6.04 150.29 151.50 14 E3 No Vibrato E3 6.07 160.90 162.46 17 A3 6.07 216.45 218.21 14 A3 6.07 217.31 218.86 12 B♭3 7.25 228.24 230.13 14 B♭3 7.25 227.94 229.45 11 B3 No Vibrato B3 7.01 239.34 240.83 11

76 Participant #5 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.64 109.39 110.58 19 110.11 110.08 0 B♭2 3.57 114.43 115.74 20 115.41 114.90 -8 B2 4.17 122.10 123.26 16 122.93 122.62 -4 D3 3.60 146.52 147.83 15 147.01 147.14 2 E♭3 3.88 153.39 155.40 23 154.31 154.21 -1 E3 4.26 161.04 163.26 24 162.79 162.22 -6 A3 3.91 217.57 220.78 25 218.66 218.52 -1 B♭3 3.74 226.25 229.88 28 229.19 228.37 -6 B3 4.07 239.56 242.85 24 242.52 240.93 -11

Example #2 A2 3.73 109.87 111.15 20 Slow Tempo A2 3.85 109.29 110.52 19 B♭2 4.27 114.92 116.21 19 B♭2 4.04 113.80 115.39 24 B2 3.96 121.60 122.90 18 B2 4.24 122.13 123.21 15 D3 3.57 145.94 147.61 20 D3 3.75 146.68 148.34 19 E♭3 3.70 153.15 154.21 12 E♭3 3.75 153.44 155.50 23 E3 4.46 162.44 164.43 21 E3 4.35 162.41 164.16 19 A3 3.91 216.18 219.25 24 A3 4.29 214.27 217.05 22 B♭3 4.21 227.44 230.52 23 B♭3 4.08 225.15 228.56 26 B3 4.65 237.38 241.33 29 B3 4.29 238.50 243.10 33

Example #3 A2 5.00 109.83 110.76 15 Fast Tempo A2 5.08 109.10 110.47 22 B♭2 4.69 115.00 116.34 20 B♭2 4.69 114.39 116.09 25 B2 4.62 122.36 123.64 18 B2 4.92 122.21 123.47 18 D3 4.17 146.22 148.03 21 D3 4.00 146.11 147.63 18 E♭3 4.48 153.34 155.57 25 E♭3 4.76 152.71 155.66 33 E3 5.08 162.58 164.75 23 E3 4.76 161.47 164.55 33 A3 4.55 216.13 219.95 30 A3 4.62 218.62 221.65 24 B♭3 4.35 228.47 232.00 27 B♭3 5.00 228.09 231.81 28 B3 4.92 241.14 245.80 33 B3 4.92 242.80 245.66 20

77 Participant #6 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.41 111.39 112.11 11 111.79 111.73 -1 B♭2 4.23 117.62 118.27 10 117.87 117.95 1 B2 4.86 125.43 125.97 7 125.39 125.70 4 D3 4.84 144.68 145.31 8 144.81 145.01 2 E♭3 4.84 151.37 151.95 7 151.84 151.63 -2 E3 4.98 163.27 163.99 8 163.05 163.27 2 A3 5.60 219.43 221.06 13 220.37 220.24 -1 B♭3 5.35 229.84 231.60 13 231.28 230.81 -4 B3 5.42 242.89 244.62 12 243.82 243.74 -1

Example #2 A2 4.59 111.06 111.60 8 Slow Tempo A2 4.60 110.37 111.08 11 B♭2 4.73 115.52 116.49 15 B♭2 No Vibrato B2 4.88 122.83 123.46 9 B2 No Vibrato D3 4.42 146.03 147.07 12 D3 4.44 145.18 146.23 12 E♭3 4.65 151.65 153.03 16 E♭3 4.58 151.33 152.65 15 E3 4.54 163.59 164.64 11 E3 4.54 162.74 163.78 11 A3 5.27 220.12 222.34 17 A3 5.03 220.43 222.50 16 B♭3 4.93 229.70 232.14 18 B♭3 4.89 230.94 233.09 16 B3 4.97 243.41 245.95 18 B3 5.00 242.53 244.88 17

Example #3 A2 No Vibrato Fast Tempo A2 4.52 111.42 112.08 10 B♭2 4.92 116.86 117.63 11 B♭2 4.74 117.14 118.10 14 B2 4.87 116.72 117.67 14 B2 4.72 117.11 118.12 15 D3 4.47 145.30 146.29 12 D3 No Vibrato E♭3 4.84 152.19 153.42 14 E♭3 5.02 153.49 154.46 11 E3 4.91 164.56 165.85 14 E3 4.71 165.57 166.85 13 A3 5.03 216.19 218.57 19 A3 5.33 216.11 217.93 15 B♭3 5.19 226.52 228.28 13 B♭3 4.85 227.32 229.08 13 B3 5.31 238.28 240.65 17 B3 5.61 240.17 242.78 19

78 Participant #7 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.73 110.80 111.93 18 111.00 111.34 5 B♭2 3.79 118.27 119.91 24 118.91 119.00 1 B2 4.08 124.25 126.27 28 125.51 125.18 -5 D3 4.00 146.80 148.54 20 147.75 147.72 0 E♭3 4.07 154.35 157.49 35 156.38 156.03 -4 E3 4.44 163.83 165.98 23 165.60 165.00 -6 A3 4.17 220.19 222.87 21 221.20 221.64 3 B♭3 4.76 233.06 236.80 28 235.52 235.48 0 B3 4.62 249.00 252.54 24 251.03 250.65 -3

Example #2 A2 4.17 109.61 110.78 18 Slow Tempo A2 3.85 109.22 110.53 21 B♭2 3.94 115.05 116.74 25 B♭2 3.88 115.49 116.77 19 B2 4.03 121.72 123.25 22 B2 4.26 122.28 123.51 17 D3 3.91 146.58 148.85 27 D3 3.74 147.06 149.14 24 E♭3 4.04 154.01 157.30 37 E♭3 3.92 154.61 157.63 33 E3 4.17 162.63 164.78 23 E3 4.29 163.96 166.37 25 A3 4.49 215.66 219.47 30 A3 4.76 215.42 219.92 36 B♭3 4.62 230.83 234.99 31 B♭3 4.71 230.77 235.57 36 B3 4.49 244.45 248.80 31 B3 4.44 248.73 252.52 26

Example #3 A2 4.05 110.18 111.87 26 Fast Tempo A2 4.23 111.03 112.30 20 B♭2 4.00 116.52 117.86 20 B♭2 4.17 116.73 118.13 21 B2 4.26 122.52 124.43 27 B2 4.17 122.62 124.67 29 D3 4.05 145.92 148.45 30 D3 3.95 147.34 149.56 26 E♭3 4.17 154.33 157.52 35 E♭3 4.48 153.61 157.10 39 E3 4.62 163.44 165.64 23 E3 4.29 163.87 166.71 30 A3 4.69 217.05 221.20 33 A3 5.19 218.71 222.93 33 B♭3 5.17 232.46 236.42 29 B♭3 5.08 232.82 236.96 31 B3 4.48 245.73 249.58 27 B3 4.76 248.64 252.10 24

79 Participant #8 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.03 110.94 111.88 15 111.18 111.45 4 B♭2 4.92 117.85 118.68 12 117.89 118.27 6 B2 5.06 124.07 125.21 16 124.90 124.70 -3 D3 4.90 146.05 147.77 20 146.40 146.84 5 E♭3 4.91 155.95 157.51 17 156.86 156.77 -1 E3 4.97 164.15 165.81 17 165.55 165.05 -5 A3 5.22 218.07 220.09 16 218.40 219.51 9 B♭3 5.29 228.84 233.27 33 231.33 230.83 -4 B3 5.03 243.20 245.98 20 244.00 244.91 6

Example #2 A2 5.22 110.45 111.12 11 Slow Tempo A2 5.20 109.75 110.83 17 B♭2 4.98 116.20 117.34 17 B♭2 5.26 116.06 117.25 18 B2 4.97 123.26 124.13 12 B2 5.21 123.11 124.03 13 D3 4.93 146.85 148.83 23 D3 4.69 146.52 148.14 19 E♭3 4.72 154.04 155.05 27 E♭3 4.83 154.18 156.60 27 E3 4.88 164.88 166.73 19 E3 5.02 164.24 165.91 18 A3 4.94 218.84 220.78 15 A3 5.13 216.60 219.44 23 B♭3 5.01 229.76 234.27 34 B♭3 4.88 228.36 232.86 34 B3 4.92 244.82 247.42 18 B3 5.13 242.38 245.62 23

Example #3 A2 5.32 110.72 111.75 16 Fast Tempo A2 5.68 110.46 111.43 15 B♭2 4.85 115.80 116.67 13 B♭2 5.14 115.51 116.54 15 B2 4.90 122.57 123.62 15 B2 5.26 122.71 123.71 14 D3 4.98 146.54 148.61 24 D3 5.04 145.69 147.55 22 E♭3 4.76 153.43 156.53 25 E♭3 5.13 153.98 156.45 28 E3 5.08 165.39 167.53 22 E3 5.08 165.15 167.39 23 A3 5.54 221.16 223.44 18 A3 5.40 219.19 222.22 24 B♭3 5.00 230.18 234.96 36 B♭3 No Vibrato B3 5.04 248.19 250.62 17 B3 5.07 245.93 247.94 14

80 Participant #9 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.69 108.21 109.48 20 109.22 108.86 -6 B♭2 5.83 115.21 116.08 13 116.15 115.62 -8 B2 5.50 122.15 123.71 22 123.61 122.92 -10 D3 5.79 145.67 146.91 15 146.74 146.26 -6 E♭3 5.75 153.78 155.15 15 155.52 154.56 -11 E3 5.50 164.90 166.49 17 165.66 165.72 1 A3 5.56 216.90 219.54 21 218.10 218.31 2 B♭3 5.59 228.63 231.27 20 230.08 229.87 -2 B3 6.02 241.85 244.85 21 244.43 243.52 -6

Example #2 A2 5.56 109.18 110.15 15 Slow Tempo A2 5.88 108.84 109.62 12 B♭2 5.41 114.45 115.46 15 B♭2 5.66 114.72 115.65 14 B2 5.56 121.25 122.59 19 B2 5.74 121.97 123.30 19 D3 5.47 145.97 147.61 19 D3 5.68 145.39 147.36 23 E♭3 5.76 152.98 154.96 22 E♭3 5.61 154.32 156.25 22 E3 5.34 162.84 164.64 19 E3 5.67 161.86 164.41 27 A3 5.38 217.46 219.66 17 A3 5.56 216.88 219.41 20 B♭3 5.47 230.29 233.85 27 B♭3 5.56 230.59 233.81 24 B3 5.65 243.65 247.11 24 B3 5.97 243.79 247.28 25

Example #3 A2 5.56 108.05 109.08 16 Fast Tempo A2 6.00 108.26 108.94 11 B♭2 5.77 113.15 114.46 20 B♭2 5.77 114.12 115.39 19 B2 5.56 120.65 121.88 18 B2 6.00 122.68 123.97 18 D3 5.56 145.48 146.87 16 D3 5.66 145.90 147.36 17 E♭3 5.77 151.64 153.90 26 E♭3 6.00 151.20 153.38 25 E3 5.56 160.48 162.85 25 E3 5.80 161.73 164.38 28 A3 5.56 217.03 219.19 17 A3 5.88 218.42 220.68 18 B♭3 5.66 229.61 233.49 29 B♭3 5.88 230.55 234.11 27 B3 6.00 244.21 247.57 24 B3 6.38 246.03 249.69 26

81 Participant #10 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.32 109.33 110.07 12 109.52 109.74 3 B♭2 4.55 115.11 115.83 11 115.80 115.53 -4 B2 4.50 122.77 123.58 11 123.57 123.17 -6 D3 4.41 146.88 148.20 16 147.22 147.59 4 E♭3 4.72 154.92 156.02 12 155.04 155.40 4 E3 4.58 164.93 165.86 10 165.94 165.32 -6 A3 5.28 218.07 220.42 19 218.31 219.39 9 B♭3 5.36 232.31 234.03 13 232.52 233.23 5 B3 5.17 247.01 249.05 14 247.79 248.20 3

Example #2 A2 4.30 109.57 110.18 10 Slow Tempo A2 4.52 110.36 110.81 7 B♭2 4.52 116.33 116.84 8 B♭2 4.27 115.56 116.07 8 B2 4.38 122.91 123.42 7 B2 4.44 122.03 122.49 7 D3 4.25 146.48 147.68 14 D3 4.06 146.72 147.72 12 E♭3 4.25 153.78 155.02 14 E♭3 4.11 155.05 156.33 14 E3 4.69 164.72 165.94 13 E3 4.44 164.45 165.46 11 A3 4.66 217.66 219.34 13 A3 4.92 218.01 219.34 11 B♭3 4.80 230.54 233.31 21 B♭3 4.83 231.49 233.57 15 B3 5.22 246.93 249.27 16 B3 4.89 246.04 249.10 21

Example #3 A2 4.52 109.21 109.85 10 Fast Tempo A2 4.67 109.95 110.46 8 B♭2 4.71 114.98 115.51 8 B♭2 No Vibrato B2 4.95 122.76 123.28 7 B2 No Vibrato D3 4.14 146.97 147.73 9 D3 4.44 147.63 148.44 9 E♭3 4.73 154.82 155.71 10 E♭3 4.42 153.97 155.36 16 E3 5.39 164.92 166.10 12 E3 5.39 165.06 166.05 10 A3 5.29 218.16 219.77 13 A3 5.59 218.56 220.01 11 B♭3 5.78 229.78 232.27 19 B♭3 5.58 231.60 234.15 19 B3 6.21 245.21 248.95 26 B3 6.32 245.94 248.86 20

82 Participant #11 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.63 108.87 110.43 25 109.57 109.67 2 B♭2 5.00 115.41 116.13 11 115.76 115.72 -1 B2 5.31 122.85 123.87 14 123.25 123.35 1 D3 4.80 147.32 148.29 11 147.25 147.80 6 E♭3 5.38 152.74 154.89 24 153.96 153.86 -1 E3 5.15 161.53 164.22 29 163.72 163.23 -5 A3 5.17 217.95 220.83 23 220.60 219.52 -8 B♭3 4.96 226.22 230.51 33 229.13 228.53 -5 B3 4.86 237.82 242.45 33 242.76 240.86 -14

Example #2 A2 5.43 108.85 110.44 25 Slow Tempo A2 4.71 109.64 110.96 21 B♭2 4.82 114.33 115.86 23 B♭2 No Vibrato B2 5.06 122.52 123.77 18 B2 4.88 121.88 123.10 17 D3 4.17 144.94 146.21 15 D3 No Vibrato E♭3 5.00 151.88 154.62 31 E♭3 5.26 152.39 155.23 32 E3 5.43 162.76 165.40 28 E3 5.43 163.93 165.93 21 A3 4.92 216.29 220.23 31 A3 5.05 219.78 223.18 27 B♭3 5.26 230.01 233.82 28 B♭3 5.15 231.21 234.64 25 B3 5.43 239.54 244.68 37 B3 5.34 241.79 245.98 30

Example #3 A2 5.56 109.08 110.86 28 Fast Tempo A2 4.84 109.20 110.85 26 B♭2 5.17 114.09 115.76 25 B♭2 No Vibrato B2 5.08 119.91 121.03 16 B2 5.36 121.52 122.57 15 D3 5.45 145.59 146.98 16 D3 No Vibrato E♭3 5.66 152.41 155.13 31 E♭3 5.56 153.87 156.34 28 E3 6.10 162.99 166.35 35 E3 6.25 160.68 163.98 35 A3 5.26 216.67 220.14 28 A3 5.26 217.40 220.64 26 B♭3 5.56 231.31 235.99 35 B♭3 5.36 230.33 234.31 30 B3 5.77 242.10 247.60 39 B3 6.00 244.35 248.72 31

83 Participant #12 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.50 108.26 109.28 16 108.88 108.77 -2 B♭2 5.03 113.64 115.05 21 114.36 114.50 2 B2 5.47 121.23 122.66 20 121.78 122.04 4 D3 5.62 145.39 147.31 23 146.65 146.04 -7 E♭3 5.46 154.30 155.75 16 154.52 155.10 6 E3 5.32 166.34 168.68 24 169.01 168.27 -8 A3 5.50 216.79 219.19 19 218.06 217.77 -2 B♭3 5.70 228.22 230.49 17 227.76 229.31 12 B3 5.73 255.12 258.24 21 255.91 256.18 2

Example #2 A2 5.12 108.75 110.16 22 Slow Tempo A2 4.67 108.52 109.74 19 B♭2 4.65 115.34 116.63 19 B♭2 4.78 115.89 117.17 19 B2 5.15 122.83 124.24 20 B2 5.38 121.24 122.54 18 D3 5.15 146.34 148.76 28 D3 5.34 148.25 150.16 22 E♭3 5.43 157.56 159.54 22 E♭3 5.53 160.88 162.53 18 E3 5.26 170.41 172.69 23 E3 5.18 171.92 174.04 21 A3 5.25 213.75 216.25 20 A3 5.29 217.34 220.69 26 B♭3 5.78 227.73 231.26 27 B♭3 5.50 229.29 233.17 29 B3 5.75 254.05 256.68 18 B3 5.45 256.16 259.40 22

Example #3 A2 5.25 108.76 109.91 18 Fast Tempo A2 5.04 108.93 110.31 22 B♭2 No Vibrato B♭2 5.08 115.69 117.05 20 B2 5.68 124.08 125.38 18 B2 5.59 122.34 123.44 16 D3 5.62 145.76 148.34 30 D3 5.55 147.36 149.34 23 E♭3 5.97 155.80 157.82 22 E♭3 5.93 157.67 159.97 25 E3 6.01 166.61 169.01 25 E3 5.98 168.91 170.98 21 A3 5.67 215.74 218.85 25 A3 5.86 218.21 221.55 26 B♭3 5.98 228.34 231.79 26 B♭3 No Vibrato B3 5.74 256.44 259.92 23 B3 5.78 256.73 260.40 25

84 Participant #13 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.40 108.91 109.98 17 109.48 109.45 0 B♭2 4.42 114.36 115.95 24 115.60 115.08 -8 B2 4.63 121.52 122.40 12 122.14 121.98 -2 D3 4.69 145.14 146.67 18 145.97 145.75 -3 E♭3 4.72 152.00 154.10 24 153.35 153.05 -3 E3 4.72 162.86 164.92 22 164.72 163.83 -9 A3 4.81 214.83 217.45 21 217.22 215.96 -10 B♭3 4.76 226.07 229.54 26 228.67 228.10 -4 B3 4.81 241.32 244.08 20 242.85 242.81 0

Example #2 A2 4.11 108.62 109.86 20 Slow Tempo A2 4.48 108.69 109.69 16 B♭2 4.38 113.78 115.31 23 B♭2 4.42 113.81 115.42 24 B2 4.58 121.02 122.14 16 B2 4.44 121.92 122.76 12 D3 4.35 145.45 147.00 18 D3 4.31 146.53 147.94 17 E♭3 4.65 153.34 155.95 29 E♭3 4.50 152.03 154.36 26 E3 4.50 161.72 163.26 16 E3 4.35 161.89 163.84 21 A3 4.55 214.87 216.97 17 A3 4.65 214.48 217.04 21 B♭3 4.60 226.25 229.96 28 B♭3 4.76 226.29 230.02 28 B3 4.48 236.43 239.95 26 B3 4.49 238.14 241.65 25

Example #3 A2 4.35 108.64 109.71 17 Fast Tempo A2 4.31 108.78 110.19 22 B♭2 5.00 114.29 115.86 24 B♭2 4.84 114.04 115.79 26 B2 4.76 120.70 121.91 17 B2 4.69 121.30 122.22 13 D3 4.69 144.09 146.34 27 D3 5.03 144.52 147.12 31 E♭3 4.62 149.53 152.85 38 E♭3 5.00 149.03 152.35 38 E3 4.76 160.14 161.55 15 E3 5.08 160.98 162.86 20 A3 4.92 213.77 216.54 22 A3 5.08 213.80 216.09 18 B♭3 4.55 222.02 226.48 34 B♭3 5.08 224.47 228.18 28 B3 4.76 235.93 239.67 27 B3 4.41 235.38 239.48 30

85 Participant #14 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.29 108.33 109.50 19 108.96 108.96 0 B♭2 5.17 114.85 116.22 21 115.69 115.50 -3 B2 5.36 121.83 123.22 20 123.13 122.58 -8 D3 5.49 145.08 146.81 21 146.15 145.97 -2 E♭3 5.91 154.53 156.20 19 155.10 155.42 4 E3 5.77 163.85 165.77 20 165.29 164.95 -4 A3 6.07 216.98 220.22 26 218.03 218.73 6 B♭3 5.86 223.21 226.24 23 223.91 224.82 7 B3 5.47 235.31 238.61 24 237.68 237.18 -4

Example #2 A2 4.84 109.44 110.79 21 Slow Tempo A2 4.76 109.33 110.24 14 B♭2 4.81 115.82 117.11 19 B♭2 5.03 117.03 118.41 20 B2 5.47 124.88 126.25 19 B2 5.44 125.71 127.70 27 D3 No Vibrato D3 5.03 144.96 146.85 22 E♭3 6.08 154.54 156.28 19 E♭3 5.45 155.53 157.49 22 E3 5.08 164.74 167.30 27 E3 5.35 165.02 167.25 23 A3 4.62 218.06 220.45 19 A3 4.92 214.29 218.36 33 B♭3 5.56 223.41 226.75 26 B♭3 5.50 222.15 225.60 27 B3 5.06 232.85 237.02 31 B3 4.95 234.85 239.54 34

Example #3 A2 5.24 109.78 110.90 19 Fast Tempo A2 5.12 109.54 110.37 13 B♭2 5.66 115.51 116.78 19 B♭2 5.36 116.92 118.49 23 B2 5.77 123.79 125.32 21 B2 5.29 125.68 126.97 18 D3 5.75 145.62 147.17 18 D3 5.84 145.01 147.05 24 E♭3 6.21 153.12 154.90 20 E♭3 6.25 155.05 156.36 15 E3 6.13 164.12 166.00 20 E3 5.76 164.12 166.39 24 A3 6.19 215.94 218.25 18 A3 5.80 215.08 217.61 20 B♭3 6.47 224.20 228.13 30 B♭3 6.52 222.10 225.50 26 B3 5.63 236.38 239.12 20 B3 6.09 237.98 241.24 24

86 Participant #15 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.64 109.19 110.06 14 109.56 109.62 1 B♭2 4.94 116.06 117.36 19 116.53 116.62 1 B2 5.19 123.66 124.93 18 124.18 124.29 2 D3 5.05 146.75 147.92 14 147.40 147.38 0 E♭3 5.15 154.35 156.58 15 155.34 155.70 4 E3 5.19 166.13 167.96 19 166.52 166.60 1 A3 5.00 217.09 219.93 23 218.60 218.39 -2 B♭3 5.50 229.94 232.54 19 232.66 231.25 -11 B3 5.41 247.85 250.26 17 246.78 248.72 14

Example #2 A2 4.08 110.57 111.89 21 Slow Tempo A2 4.62 111.36 112.61 19 B♭2 4.21 116.68 118.03 20 B♭2 4.62 117.85 118.91 16 B2 4.55 125.95 126.67 10 B2 4.62 126.71 127.90 16 D3 4.29 146.72 148.24 18 D3 5.00 147.28 149.23 23 E♭3 4.76 155.07 157.10 23 E♭3 4.76 155.44 157.44 22 E3 4.76 165.65 167.79 22 E3 4.84 165.36 167.56 23 A3 5.22 216.09 218.59 20 A3 5.10 215.12 217.22 17 B♭3 5.19 229.21 232.49 25 B♭3 5.33 226.89 229.54 20 B3 5.50 240.81 244.86 29 B3 4.76 240.72 243.63 21

Example #3 A2 4.55 110.86 111.97 17 Fast Tempo A2 4.69 111.91 112.91 15 B♭2 4.55 117.64 118.74 16 B♭2 4.55 117.68 118.98 19 B2 4.76 124.61 125.39 11 B2 4.92 125.31 126.20 12 D3 5.00 146.05 147.67 19 D3 5.36 146.49 148.37 22 E♭3 5.36 153.85 155.84 22 E♭3 5.66 154.50 155.88 15 E3 5.17 165.36 167.36 21 E3 5.45 163.98 165.95 21 A3 5.70 211.14 213.77 21 A3 5.48 217.10 219.47 19 B♭3 5.48 228.38 231.73 25 B♭3 5.88 228.18 230.63 18 B3 5.26 241.27 244.29 22 B3 5.56 240.41 243.81 24

87 Participant #16 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.76 109.94 111.13 19 110.43 110.59 3 B♭2 4.97 115.90 117.13 17 116.87 116.54 -5 B2 4.97 122.75 123.87 16 123.45 123.31 -2 D3 4.60 145.32 146.84 18 146.19 146.15 0 E♭3 4.64 152.68 154.70 23 154.30 153.70 -7 E3 4.80 163.24 165.08 19 164.63 164.12 -5 A3 4.66 217.28 218.52 10 218.00 218.00 0 B♭3 5.19 228.63 230.66 15 229.78 229.56 -2 B3 5.33 243.18 245.18 14 244.31 244.12 -1

Example #2 A2 4.41 110.11 111.16 16 Slow Tempo A2 4.75 109.95 111.48 24 B♭2 4.60 116.42 117.21 12 B♭2 4.69 116.21 117.53 20 B2 4.41 123.52 124.35 12 B2 4.82 122.50 123.70 17 D3 4.36 145.38 146.69 16 D3 4.56 145.34 146.56 15 E♭3 4.58 151.47 153.45 22 E♭3 4.52 151.38 153.22 21 E3 4.67 162.46 164.08 17 E3 4.83 162.01 163.96 21 A3 4.88 217.12 218.47 11 A3 5.03 215.51 216.96 12 B♭3 4.98 225.40 227.99 20 B♭3 5.05 229.72 231.58 14 B3 5.08 244.18 246.66 18 B3 5.10 241.26 243.72 18

Example #3 A2 4.89 109.95 110.82 14 Fast Tempo A2 No Vibrato B♭2 5.08 115.11 115.98 13 B♭2 5.13 113.76 115.26 23 B2 4.67 121.29 122.32 15 B2 4.91 121.87 123.02 16 D3 4.35 146.07 147.01 11 D3 4.82 144.78 146.02 15 E♭3 4.91 151.78 153.58 20 E♭3 4.83 151.69 153.63 22 E3 4.54 161.73 163.07 14 E3 5.11 162.42 164.44 21 A3 5.39 216.24 217.46 10 A3 5.39 217.11 218.22 9 B♭3 5.25 227.77 229.44 13 B♭3 5.67 227.48 229.19 13 B3 5.49 240.04 241.74 12 B3 5.38 240.76 242.38 12

88 Participant #17 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.76 108.87 109.97 17 109.83 109.38 -7 B♭2 4.42 114.24 115.52 19 115.07 114.89 -3 B2 4.26 120.90 122.32 20 121.82 121.63 -3 D3 4.42 141.31 143.44 26 142.65 142.30 -4 E♭3 4.69 147.75 149.49 20 149.74 148.63 -13 E3 4.05 158.09 159.76 18 159.74 159.04 -8 A3 4.63 210.54 213.39 23 212.32 212.10 -2 B♭3 4.81 221.15 224.00 22 224.20 223.41 -6 B3 4.42 234.44 237.22 20 237.45 235.03 -18

Example #2 A2 3.80 107.65 108.47 13 Slow Tempo A2 4.17 107.57 108.43 14 B♭2 4.60 111.92 113.24 20 B♭2 4.76 112.02 113.63 25 B2 4.62 118.92 120.31 20 B2 4.13 119.91 121.31 20 D3 4.55 141.22 143.38 26 D3 4.29 141.60 143.36 21 E♭3 4.81 147.30 149.64 27 E♭3 4.48 150.61 152.45 21 E3 4.88 160.27 162.13 20 E3 4.40 160.11 161.98 20 A3 4.85 213.11 216.48 27 A3 4.67 212.60 215.34 22 B♭3 5.31 223.57 227.66 31 B♭3 4.55 225.38 228.27 22 B3 5.21 240.43 242.77 17 B3 4.65 238.87 242.52 26

Example #3 A2 5.26 109.51 110.74 19 Fast Tempo A2 5.56 109.37 110.34 15 B♭2 5.08 114.12 115.42 20 B♭2 4.92 114.16 115.82 25 B2 5.17 120.15 121.67 22 B2 4.76 120.93 122.29 19 D3 5.45 140.25 142.31 25 D3 5.36 140.48 142.52 25 E♭3 6.06 147.57 149.91 27 E♭3 5.77 148.73 151.15 28 E3 5.26 158.78 160.77 22 E3 5.36 160.34 162.29 21 A3 5.97 219.55 223.46 31 A3 5.56 219.08 222.22 25 B♭3 5.97 232.74 236.75 30 B♭3 5.88 232.65 236.11 26 B3 6.15 246.99 250.83 27 B3 6.00 243.15 246.96 27

89 Participant #18 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.05 109.18 110.00 13 109.36 109.47 2 B♭2 4.89 113.73 114.57 13 113.95 114.09 2 B2 4.89 120.70 121.90 17 121.17 121.34 2 D3 4.59 146.65 148.02 16 147.12 147.34 3 E♭3 5.07 153.87 155.56 19 154.66 154.78 1 E3 5.12 163.44 165.34 20 164.32 164.26 -1 A3 5.21 218.57 221.01 19 219.43 219.77 3 B♭3 5.43 228.85 231.39 19 230.40 230.38 0 B3 5.69 239.71 243.65 28 242.38 242.48 1

Example #2 A2 4.89 109.02 109.78 12 Slow Tempo A2 4.82 109.11 109.89 12 B♭2 4.65 113.44 114.32 13 B♭2 4.99 113.92 114.56 10 B2 4.80 120.62 121.56 13 B2 4.89 121.16 122.06 13 D3 4.47 146.12 147.40 15 D3 4.49 145.79 146.98 14 E♭3 4.90 152.81 154.10 15 E♭3 4.82 153.07 154.62 17 E3 5.07 162.36 163.60 13 E3 5.04 162.54 163.96 15 A3 5.26 216.60 218.86 18 A3 5.30 217.24 219.07 15 B♭3 5.49 227.05 230.94 29 B♭3 5.70 227.32 230.87 27 B3 5.62 238.87 243.03 30 B3 5.70 239.82 243.39 26

Example #3 A2 5.10 107.71 108.74 16 Fast Tempo A2 4.83 108.03 108.94 15 B♭2 5.15 112.14 113.08 14 B♭2 4.81 112.12 112.93 12 B2 5.20 119.40 120.75 19 B2 5.26 119.91 120.92 15 D3 4.42 146.17 147.51 16 D3 4.84 144.97 146.75 21 E♭3 5.03 152.90 154.29 16 E♭3 4.99 153.80 155.49 19 E3 5.23 163.29 165.02 18 E3 5.12 163.62 165.37 18 A3 5.06 218.09 221.72 29 A3 5.46 216.81 219.45 21 B♭3 5.46 225.50 230.33 37 B♭3 5.59 226.27 230.83 35 B3 5.65 238.14 241.96 28 B3 5.57 238.73 242.38 26

90 Participant #19 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.97 108.38 109.25 14 109.07 108.74 -5 B♭2 3.98 114.03 114.79 12 114.56 114.43 -2 B2 4.07 121.91 122.86 13 122.50 122.34 -2 D3 3.92 144.24 145.73 18 144.93 144.87 -1 E♭3 3.82 149.94 151.49 18 151.38 150.76 -7 E3 4.49 160.97 162.13 12 161.57 161.51 -1 A3 4.21 220.90 223.26 18 222.16 222.15 0 B♭3 4.58 230.72 232.78 15 231.56 231.73 1 B3 4.93 240.83 244.00 23 242.97 242.40 -3

Example #2 A2 4.26 108.90 109.50 10 Slow Tempo A2 4.00 107.90 108.70 13 B♭2 3.80 113.96 115.01 16 B♭2 3.80 114.85 115.70 13 B2 4.44 120.86 121.72 12 B2 4.10 122.42 123.79 19 D3 3.85 145.10 146.69 19 D3 4.20 143.75 145.29 18 E♭3 3.62 151.97 154.01 23 E♭3 3.80 150.58 153.07 28 E3 4.41 160.18 161.99 19 E3 4.60 162.14 163.36 13 A3 4.50 219.85 222.23 19 A3 4.40 218.43 220.65 18 B♭3 4.55 232.39 235.18 21 B♭3 4.55 232.83 235.10 17 B3 5.03 246.83 249.68 20 B3 5.00 244.95 247.87 21

Example #3 A2 4.41 109.47 110.73 20 Fast Tempo A2 4.05 107.68 108.72 17 B♭2 5.36 114.03 114.83 12 B♭2 5.00 114.89 115.74 13 B2 4.36 121.40 122.27 12 B2 4.23 122.72 123.79 15 D3 4.35 143.00 144.42 17 D3 4.69 143.54 144.71 14 E♭3 4.55 152.21 154.39 25 E♭3 4.55 151.37 153.28 22 E3 4.48 160.85 162.54 18 E3 4.76 163.15 165.18 21 A3 4.41 218.84 221.44 20 A3 4.23 215.13 217.46 19 B♭3 5.08 232.08 235.20 23 B♭3 5.17 231.29 234.00 20 B3 5.63 244.37 247.21 20 B3 5.48 246.25 249.91 26

91 Participant #20 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.68 108.30 109.62 21 108.74 108.99 4 B♭2 3.82 113.26 114.82 24 114.43 113.94 -7 B2 3.86 120.77 121.96 17 121.63 121.73 1 D3 4.14 146.38 148.18 21 146.89 147.24 3 E♭3 4.66 155.76 158.41 29 158.31 157.44 -10 E3 4.93 165.71 167.90 23 166.95 166.90 -1 A3 5.77 220.66 223.15 19 222.51 221.92 -5 B♭3 5.81 233.23 236.65 25 235.92 235.24 -5 B3 5.81 249.59 252.44 20 251.22 250.78 -3

Example #2 A2 3.50 110.93 112.04 17 Slow Tempo A2 3.48 110.36 111.64 20 B♭2 3.71 115.77 117.52 26 B♭2 3.68 116.52 117.74 18 B2 4.07 122.65 124.17 21 B2 4.01 123.47 124.83 19 D3 4.20 146.45 148.39 23 D3 4.09 147.51 149.05 18 E♭3 3.99 157.19 159.63 27 E♭3 4.09 154.74 157.30 28 E3 4.92 163.32 166.02 28 E3 4.25 165.28 167.73 26 A3 5.85 210.34 213.30 24 A3 5.61 215.23 217.52 18 B♭3 5.44 226.42 229.39 23 B♭3 5.54 222.98 226.51 27 B3 5.51 238.60 241.68 22 B3 5.70 237.10 239.36 16

Example #3 A2 3.78 110.80 111.92 17 Fast Tempo A2 No Vibrato B♭2 4.47 115.15 116.97 27 B♭2 4.51 114.24 115.50 19 B2 4.21 120.88 122.27 20 B2 4.08 120.92 122.33 20 D3 4.93 145.65 148.12 29 D3 4.62 146.86 148.72 22 E♭3 4.59 155.83 159.03 35 E♭3 4.67 155.16 158.45 36 E3 5.02 164.07 166.61 27 E3 5.06 163.12 165.72 27 A3 6.33 219.32 223.03 29 A3 6.37 216.15 220.67 36 B♭3 6.37 229.35 233.41 30 B♭3 No Vibrato B3 6.22 237.27 240.64 24 B3 6.17 239.74 243.09 24

92 Participant #21 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.23 110.85 111.72 14 111.51 111.27 -4 B♭2 4.29 116.48 117.45 14 117.76 116.98 -12 B2 4.55 124.10 124.86 11 124.85 124.48 -5 D3 4.76 145.98 147.01 12 146.46 146.53 1 E♭3 4.94 154.40 155.75 15 155.17 155.10 -1 E3 4.96 163.88 165.45 17 165.06 164.49 -6 A3 4.88 218.91 221.32 19 220.19 220.31 1 B♭3 4.96 230.74 232.84 16 232.37 231.69 -5 B3 4.72 245.46 248.09 18 247.10 247.74 4

Example #2 A2 4.29 110.66 111.32 10 Slow Tempo A2 4.29 111.94 112.78 13 B♭2 4.60 117.43 118.60 17 B♭2 4.92 117.94 118.99 15 B2 4.71 124.56 125.58 14 B2 4.95 123.56 124.88 18 D3 4.55 144.60 146.28 20 D3 4.76 145.34 146.88 18 E♭3 4.90 153.08 154.53 16 E♭3 4.55 152.93 154.63 19 E3 5.13 162.85 164.62 19 E3 5.26 162.02 163.83 19 A3 4.92 217.52 221.20 29 A3 4.76 214.09 217.62 28 B♭3 4.29 226.57 228.97 18 B♭3 5.08 228.01 230.40 18 B3 4.55 242.00 245.03 22 B3 5.08 246.18 249.04 20

Example #3 A2 4.59 110.32 111.08 12 Fast Tempo A2 4.71 110.69 111.50 13 B♭2 4.29 115.47 116.86 21 B♭2 5.00 115.56 117.12 23 B2 4.62 122.50 123.43 13 B2 4.41 123.38 124.22 12 D3 4.55 145.61 147.08 17 D3 4.76 146.00 147.29 15 E♭3 4.48 151.78 153.44 19 E♭3 No Vibrato E3 5.08 162.55 164.57 21 E3 4.92 162.57 164.17 17 A3 5.00 217.36 220.55 25 A3 4.92 217.48 220.72 26 B♭3 5.26 227.65 229.73 16 B♭3 5.00 226.91 229.56 20 B3 5.00 243.35 246.02 19 B3 5.00 245.97 248.51 18

93 Participant #22 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.63 109.60 110.43 13 109.75 110.01 4 B♭2 5.84 115.11 115.96 13 115.28 115.47 3 B2 5.88 122.75 123.71 13 122.76 123.06 4 D3 5.73 146.29 147.37 13 146.91 146.72 -4 E♭3 6.21 154.44 156.03 18 154.76 155.40 -9 E3 6.30 164.31 166.37 22 164.37 165.35 10 A3 6.57 219.39 221.47 16 221.42 221.00 -3 B♭3 6.81 230.27 234.04 28 231.99 231.80 -1 B3 6.80 243.11 245.28 15 245.98 244.52 -10

Example #2 A2 5.67 108.81 109.66 13 Slow Tempo A2 5.33 109.41 110.44 16 B♭2 5.64 114.97 115.57 9 B♭2 5.54 114.89 115.76 13 B2 6.11 122.43 123.75 19 B2 5.62 122.82 124.06 17 D3 5.41 146.82 147.88 12 D3 5.67 145.50 146.70 14 E♭3 5.69 153.55 155.36 20 E♭3 5.75 153.51 154.98 17 E3 6.33 164.20 166.49 24 E3 5.66 163.34 165.55 23 A3 6.59 216.52 219.39 23 A3 6.41 217.87 220.65 22 B♭3 6.55 229.95 233.04 23 B♭3 6.69 231.22 234.11 22 B3 6.75 245.34 248.08 19 B3 6.16 242.98 245.90 21

Example #3 A2 5.84 110.62 111.51 14 Fast Tempo A2 6.28 110.53 111.36 13 B♭2 5.88 116.10 117.16 16 B♭2 5.88 116.83 117.96 17 B2 6.26 123.64 125.57 27 B2 6.04 124.08 125.77 23 D3 5.81 144.97 146.78 22 D3 6.12 144.45 145.96 18 E♭3 5.75 152.34 154.23 21 E♭3 5.90 153.25 155.18 22 E3 5.96 163.78 166.05 24 E3 6.04 164.03 165.72 18 A3 6.38 216.29 219.17 23 A3 6.71 217.26 219.70 19 B♭3 6.55 227.99 231.29 25 B♭3 6.67 228.45 231.37 22 B3 6.87 241.97 244.59 19 B3 6.82 244.64 248.39 26

94 Participant #23 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.88 109.23 109.87 10 109.60 109.52 -1 B♭2 6.03 115.19 116.20 15 115.87 115.69 -3 B2 6.25 124.40 125.35 13 125.06 124.94 -2 D3 5.79 144.71 146.10 17 145.00 145.27 3 E♭3 5.67 152.75 154.51 20 153.76 153.69 -1 E3 6.02 162.58 163.93 14 163.43 163.34 -1 A3 5.31 218.61 221.97 26 219.74 220.17 3 B♭3 5.04 234.62 237.92 24 235.99 236.30 2 B3 5.41 248.97 251.90 20 250.35 250.65 2

Example #2 A2 5.62 109.85 110.41 9 Slow Tempo A2 5.60 109.69 110.30 10 B♭2 5.56 115.48 116.74 19 B♭2 5.49 116.41 117.35 14 B2 6.10 124.65 125.20 8 B2 5.83 124.37 125.09 10 D3 5.16 143.97 145.50 18 D3 5.47 143.94 145.76 22 E♭3 5.30 152.63 154.11 17 E♭3 5.32 152.93 154.56 18 E3 5.56 161.84 162.93 12 E3 5.98 163.35 164.66 14 A3 5.17 215.31 217.98 21 A3 5.19 217.21 219.46 18 B♭3 4.48 230.86 234.11 24 B♭3 5.00 224.47 227.66 24 B3 4.73 245.98 248.41 17 B3 5.37 246.47 248.75 16

Example #3 A2 6.25 109.70 110.24 9 Fast Tempo A2 6.00 110.02 110.81 12 B♭2 6.00 115.55 116.49 14 B♭2 6.15 115.76 116.82 16 B2 6.52 122.25 123.09 12 B2 6.17 122.92 123.76 12 D3 5.48 144.24 145.77 18 D3 5.66 144.42 146.07 20 E♭3 5.66 152.60 154.06 16 E♭3 6.06 152.67 154.74 23 E3 6.25 161.96 163.48 16 E3 6.25 163.17 165.06 20 A3 5.56 219.39 222.22 22 A3 5.56 219.10 222.29 25 B♭3 No Vibrato B♭3 5.00 228.84 231.04 17 B3 No Vibrato B3 5.21 254.45 257.01 17

95 Participant #24 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 6.01 108.86 109.84 16 109.56 109.37 -3 B♭2 5.63 116.65 117.38 11 116.85 117.10 4 B2 6.17 123.09 124.96 26 124.01 124.03 0 D3 5.73 145.74 147.30 18 146.45 146.71 3 E♭3 5.76 154.40 156.67 25 155.69 155.51 -2 E3 6.80 164.67 167.69 31 166.73 166.38 -4 A3 6.54 217.16 218.70 12 218.35 219.39 8 B♭3 6.96 227.59 229.58 15 228.97 229.15 1 B3 6.83 242.20 246.32 29 243.42 244.37 7

Example #2 A2 4.71 108.12 108.94 13 Slow Tempo A2 5.11 109.41 110.21 13 B♭2 4.75 116.75 117.52 11 B♭2 4.72 117.24 118.06 12 B2 5.37 124.11 125.93 25 B2 5.66 124.07 125.87 25 D3 4.91 144.20 145.82 19 D3 4.83 145.51 147.11 19 E♭3 5.29 154.00 155.52 17 E♭3 5.77 155.15 156.70 17 E3 6.42 167.57 169.57 21 E3 6.66 166.77 170.25 36 A3 5.69 217.63 219.96 18 A3 No Vibrato B♭3 5.87 226.58 229.10 19 B♭3 5.84 231.44 233.52 16 B3 5.83 243.20 247.54 31 B3 6.31 239.19 244.03 35

Example #3 A2 5.55 109.69 110.76 17 Fast Tempo A2 5.83 110.31 111.50 19 B♭2 5.76 117.03 117.71 10 B♭2 5.36 117.27 118.14 13 B2 5.57 124.20 125.83 23 B2 5.71 124.39 125.99 22 D3 5.42 145.79 147.45 20 D3 5.70 145.89 147.71 21 E♭3 5.73 154.59 155.85 14 E♭3 5.73 153.01 154.62 18 E3 6.08 163.68 165.27 17 E3 6.74 162.40 164.68 24 A3 6.83 219.26 222.43 25 A3 6.47 215.87 217.64 14 B♭3 6.97 228.34 230.75 18 B♭3 6.73 229.03 231.03 15 B3 7.17 244.67 247.54 20 B3 7.07 244.60 248.81 30

96 Participant #25 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.26 109.13 109.89 12 109.19 109.53 5 B♭2 5.26 114.64 115.47 13 115.22 115.04 -3 B2 5.22 121.60 122.73 16 122.55 122.16 -6 D3 5.36 145.84 147.23 16 145.98 146.50 6 E♭3 5.38 153.39 154.61 14 154.04 154.02 0 E3 5.15 161.75 163.54 19 162.94 162.61 -4 A3 5.66 216.53 218.19 13 218.37 217.43 -7 B♭3 5.83 226.88 228.91 15 229.57 228.14 -11 B3 6.03 242.86 244.60 12 243.61 243.71 1

Example #2 A2 5.30 111.14 111.97 13 Slow Tempo A2 5.21 112.05 112.89 13 B♭2 5.19 117.50 118.54 15 B♭2 5.10 118.20 119.27 16 B2 4.84 123.82 125.29 20 B2 5.04 124.57 125.90 18 D3 5.08 145.96 147.52 18 D3 5.07 146.84 148.50 19 E♭3 5.15 151.05 153.02 22 E♭3 5.04 151.52 153.55 23 E3 5.00 161.86 163.70 20 E3 5.07 160.86 162.79 21 A3 5.66 218.01 220.17 17 A3 5.77 222.55 224.22 13 B♭3 5.56 235.43 238.21 20 B♭3 5.45 238.40 240.97 19 B3 6.10 251.82 253.27 10 B3 5.74 253.98 256.25 15

Example #3 A2 5.17 109.38 110.22 13 Fast Tempo A2 5.36 109.92 111.12 19 B♭2 5.00 114.64 116.18 23 B♭2 5.26 116.35 117.63 19 B2 5.00 123.03 124.29 18 B2 5.13 123.75 125.16 20 D3 5.36 146.38 148.19 21 D3 5.36 146.87 148.37 18 E♭3 5.45 153.61 155.63 23 E♭3 5.17 153.74 155.74 22 E3 5.36 162.77 165.09 25 E3 5.26 162.83 165.36 27 A3 6.12 217.68 220.17 20 A3 6.00 221.55 223.41 15 B♭3 6.12 233.97 237.45 26 B♭3 6.25 235.71 238.43 20 B3 No Vibrato B3 6.36 253.84 256.04 15

97 Participant #26 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.24 109.63 110.76 18 110.18 110.19 0 B♭2 4.52 114.47 116.30 27 115.55 115.40 -2 B2 4.77 123.76 124.82 15 124.44 124.29 -2 D3 5.03 144.83 146.28 17 146.02 145.68 -4 E♭3 5.45 150.91 152.69 20 152.49 152.28 -2 E3 6.14 162.96 163.80 9 164.14 164.09 -1 A3 5.13 221.51 222.67 9 223.42 222.30 -9 B♭3 4.94 230.05 231.77 13 232.35 231.61 -6 B3 5.06 243.76 246.08 16 246.34 244.89 -10

Example #2 A2 3.99 108.48 109.27 13 Slow Tempo A2 4.27 109.49 110.29 13 B♭2 4.57 113.97 115.11 17 B♭2 4.73 114.57 115.84 19 B2 4.66 121.66 122.78 16 B2 4.47 123.42 124.49 15 D3 4.54 146.37 147.97 19 D3 4.78 145.21 146.83 19 E♭3 4.65 149.20 151.41 25 E♭3 4.71 149.18 150.94 20 E3 5.57 159.07 160.53 16 E3 5.95 159.79 160.78 11 A3 5.09 217.31 219.23 15 A3 5.00 219.02 221.05 16 B♭3 5.00 228.39 230.74 18 B♭3 5.04 228.40 230.78 18 B3 5.32 239.87 242.85 21 B3 5.14 242.84 245.06 16

Example #3 A2 4.43 109.65 110.44 12 Fast Tempo A2 4.71 110.75 112.18 22 B♭2 4.73 115.34 116.70 20 B♭2 No Vibrato B2 5.18 123.76 125.00 23 B2 5.15 124.02 125.26 17 D3 5.74 144.52 145.77 15 D3 5.38 143.70 145.45 21 E♭3 5.28 149.33 151.19 21 E♭3 5.13 148.81 150.81 23 E3 6.19 159.26 160.72 16 E3 6.85 159.40 160.90 16 A3 5.45 218.13 219.70 12 A3 5.29 216.94 219.15 18 B♭3 5.13 226.09 227.68 12 B♭3 5.54 225.11 227.06 15 B3 5.73 233.19 235.33 16 B3 5.46 238.22 239.89 12

98 Participant #27 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.76 109.35 110.06 11 109.46 109.73 4 B♭2 4.35 114.80 115.69 13 115.53 115.20 -5 B2 4.63 123.18 124.15 14 124.00 123.60 -6 D3 5.00 148.20 149.04 10 148.34 148.68 4 E♭3 5.30 155.77 157.05 14 156.93 156.29 -7 E3 5.38 166.78 168.22 15 167.25 167.64 4 A3 5.56 218.06 220.58 20 221.81 219.44 -19 B♭3 5.94 230.40 232.43 15 233.41 231.59 -14 B3 6.07 246.70 248.82 15 247.53 247.99 3

Example #2 A2 4.12 109.69 110.40 11 Slow Tempo A2 4.35 110.13 111.03 14 B♭2 4.49 115.67 116.52 13 B♭2 4.55 115.92 116.78 13 B2 4.51 123.58 124.47 12 B2 4.50 124.68 125.53 12 D3 4.62 147.86 149.28 17 D3 4.76 148.36 149.66 15 E♭3 4.84 155.94 157.35 16 E♭3 4.88 156.20 157.56 15 E3 5.00 165.73 167.36 17 E3 4.94 166.62 167.98 14 A3 5.45 216.24 218.25 16 A3 5.83 210.68 212.82 17 B♭3 5.69 221.66 224.03 18 B♭3 5.83 220.09 221.87 14 B3 5.95 234.97 237.21 16 B3 5.97 235.28 237.73 18

Example #3 A2 4.62 109.57 110.32 12 Fast Tempo A2 4.88 109.70 110.49 12 B♭2 5.17 114.83 115.65 12 B♭2 4.88 115.27 116.44 18 B2 4.44 122.76 123.82 15 B2 4.69 123.88 124.68 11 D3 5.08 147.75 149.24 17 D3 5.13 148.33 149.51 14 E♭3 4.92 156.47 157.85 15 E♭3 5.13 156.20 157.70 17 E3 5.44 166.63 167.90 13 E3 5.66 168.29 169.77 15 A3 6.00 218.73 221.15 19 A3 5.91 218.06 219.97 15 B♭3 5.60 230.43 232.84 18 B♭3 5.38 232.27 234.03 13 B3 6.18 245.09 248.62 25 B3 6.17 245.82 248.68 20

99 Participant #28 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 6.36 108.33 109.39 17 109.13 108.79 -5 B♭2 6.98 112.36 113.41 16 113.47 112.99 -7 B2 6.43 119.51 120.39 13 121.01 119.69 -20 D3 6.35 143.20 145.02 22 144.06 144.11 1 E♭3 6.75 149.55 150.74 14 149.94 150.15 2 E3 6.41 161.09 162.32 13 163.23 162.76 -5 A3 6.02 214.62 217.01 19 215.08 215.63 4 B♭3 5.80 227.26 229.54 17 228.93 228.53 -3 B3 6.05 251.64 254.22 18 253.34 252.94 -3

Example #2 A2 6.24 107.57 108.28 11 Slow Tempo A2 6.49 109.08 109.75 11 B♭2 6.41 113.57 114.49 14 B♭2 7.14 114.52 115.38 13 B2 7.01 122.28 122.92 9 B2 6.67 121.77 122.67 13 D3 6.25 142.73 143.95 15 D3 6.49 143.26 144.62 16 E♭3 6.31 149.46 150.41 13 E♭3 6.27 148.75 149.65 10 E3 6.23 160.28 161.52 13 E3 5.92 162.21 163.22 11 A3 6.74 215.46 217.68 18 A3 6.84 214.82 216.90 17 B♭3 6.41 224.00 226.29 18 B♭3 6.17 226.30 228.75 19 B3 6.13 237.41 240.84 25 B3 6.01 240.04 243.06 22

Example #3 A2 6.75 109.19 110.04 13 Fast Tempo A2 6.67 109.88 110.99 17 B♭2 No Vibrato B♭2 6.84 113.21 114.39 18 B2 No Vibrato B2 6.90 122.64 123.82 17 D3 6.31 142.82 144.19 17 D3 6.91 143.54 145.09 19 E♭3 6.86 149.18 150.24 12 E♭3 6.52 148.86 150.52 20 E3 No Vibrato E3 6.32 161.71 162.64 10 A3 6.17 213.86 217.20 27 A3 5.97 215.17 218.59 27 B♭3 6.96 226.52 229.50 23 B♭3 No Vibrato B3 6.75 242.16 246.78 33 B3 6.18 244.03 247.71 26

100 Participant #29 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.05 109.65 110.72 17 110.25 110.09 -3 B♭2 5.01 116.35 117.49 17 116.91 116.88 0 B2 5.00 123.70 125.18 21 123.76 124.40 9 D3 5.00 147.10 148.93 21 147.43 148.06 7 E♭3 5.17 154.85 156.76 21 155.88 155.77 -1 E3 5.10 163.99 165.90 20 164.40 165.06 7 A3 5.00 219.78 222.44 21 221.14 221.44 2 B♭3 5.12 233.79 235.48 12 234.72 234.62 -1 B3 5.27 247.14 249.55 17 247.97 248.49 4

Example #2 A2 5.06 109.90 110.77 14 Slow Tempo A2 4.76 110.20 111.10 14 B♭2 4.72 116.63 118.04 21 B♭2 4.96 117.36 118.49 17 B2 4.92 123.23 124.67 20 B2 4.87 123.84 125.39 22 D3 4.98 146.78 148.40 19 D3 4.93 147.04 148.89 22 E♭3 4.82 155.41 157.52 23 E♭3 5.00 155.05 157.44 26 E3 4.95 163.71 166.39 28 E3 4.99 163.85 166.43 27 A3 5.15 219.80 223.50 29 A3 4.87 219.76 222.82 24 B♭3 4.88 232.30 234.64 17 B♭3 4.86 230.91 232.92 15 B3 4.88 243.71 246.42 19 B3 5.05 243.12 246.40 23

Example #3 A2 5.37 110.12 111.00 14 Fast Tempo A2 5.26 109.68 110.65 15 B♭2 5.05 115.74 116.98 18 B♭2 5.32 116.64 117.97 20 B2 No Vibrato B2 5.20 122.77 124.51 24 D3 5.37 146.60 148.37 21 D3 5.10 146.90 148.68 21 E♭3 5.24 154.52 156.76 25 E♭3 5.08 154.67 156.85 24 E3 5.69 163.46 165.95 26 E3 5.52 163.33 166.06 29 A3 5.66 221.16 223.61 19 A3 5.08 220.68 223.54 22 B♭3 5.24 232.30 235.20 21 B♭3 5.46 234.71 237.01 17 B3 5.42 246.43 249.41 21 B3 5.37 248.52 251.50 21

101 Participant #30 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.90 108.84 109.64 13 109.02 109.27 4 B♭2 4.66 114.63 115.96 20 114.62 115.33 11 B2 4.41 121.05 122.13 15 121.72 121.75 0 D3 3.87 144.29 145.37 13 144.54 144.81 3 E♭3 5.08 151.29 153.32 23 152.07 152.30 3 E3 4.90 161.90 163.76 20 163.19 162.63 -6 A3 5.24 218.25 219.33 9 218.56 218.80 2 B♭3 5.54 228.46 230.99 19 231.29 229.91 -10 B3 5.43 238.15 239.95 13 239.21 239.29 1

Example #2 A2 No Vibrato Slow Tempo A2 3.38 108.82 109.64 13 B♭2 3.66 113.57 115.24 25 B♭2 3.85 113.34 115.18 28 B2 4.00 123.24 124.67 20 B2 4.07 121.77 122.97 17 D3 3.83 144.15 145.42 15 D3 3.68 146.42 147.64 14 E♭3 4.19 152.79 155.41 29 E♭3 4.48 153.32 155.80 28 E3 No Vibrato E3 5.03 164.52 166.16 17 A3 5.60 218.90 220.51 13 A3 5.04 216.39 218.36 16 B♭3 5.15 227.99 229.83 14 B♭3 5.27 229.71 231.19 11 B3 5.13 240.74 242.74 14 B3 5.39 239.47 241.06 11

Example #3 A2 3.85 108.00 108.68 11 Fast Tempo A2 4.25 108.10 108.89 13 B♭2 4.02 112.41 114.36 30 B♭2 4.38 113.67 115.21 23 B2 4.71 121.67 123.21 22 B2 4.62 121.80 122.95 16 D3 4.42 143.99 145.54 19 D3 No Vibrato E♭3 5.02 151.55 154.06 28 E♭3 5.65 151.94 154.75 32 E3 5.22 163.93 166.04 22 E3 5.59 163.71 165.04 14 A3 6.37 218.41 220.14 14 A3 6.43 217.60 219.46 15 B♭3 6.27 229.03 231.13 16 B♭3 6.11 229.92 231.84 14 B3 6.90 243.92 245.57 12 B3 6.19 244.18 245.72 11

102 Participant #31 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.97 108.52 109.32 13 109.08 109.00 -1 B♭2 3.91 116.07 117.00 14 116.72 116.52 -3 B2 4.08 124.70 125.50 11 125.31 125.14 -2 D3 3.98 145.65 146.73 13 146.30 146.18 -1 E♭3 4.32 155.65 156.50 10 156.00 156.05 1 E3 4.52 165.43 166.33 9 166.38 165.91 -5 A3 4.24 219.03 220.54 12 220.01 219.95 0 B♭3 4.77 230.11 231.66 12 231.21 230.87 -3 B3 4.12 245.00 247.98 21 246.43 246.26 -1

Example #2 A2 4.26 108.89 109.92 16 Slow Tempo A2 4.64 108.86 109.80 15 B♭2 4.86 115.32 116.24 14 B♭2 4.35 116.08 117.22 17 B2 4.74 122.85 123.92 15 B2 4.37 124.84 125.34 7 D3 4.31 145.89 146.87 12 D3 4.31 144.63 145.62 12 E♭3 4.82 155.28 156.30 11 E♭3 4.92 155.34 156.14 9 E3 5.50 165.13 166.12 10 E3 5.07 165.27 166.30 11 A3 4.56 217.58 219.02 11 A3 4.40 216.59 218.30 14 B♭3 4.81 225.99 227.95 15 B♭3 4.85 225.50 227.10 12 B3 5.56 241.74 243.81 15 B3 5.12 245.65 248.33 19

Example #3 A2 4.25 109.72 110.39 11 Fast Tempo A2 No Vibrato B♭2 5.35 115.02 116.46 22 B♭2 5.08 116.25 117.11 13 B2 5.08 122.00 122.93 13 B2 5.15 124.56 125.42 12 D3 4.42 146.37 147.41 12 D3 4.84 146.73 147.55 10 E♭3 5.09 154.29 155.70 16 E♭3 5.36 155.39 156.79 16 E3 5.79 165.73 166.62 9 E3 5.26 165.96 167.25 13 A3 4.71 217.17 218.38 10 A3 5.00 214.31 215.69 11 B♭3 5.19 226.42 228.23 14 B♭3 5.32 226.59 228.32 13 B3 5.36 244.09 246.65 18 B3 5.41 246.55 249.21 19

103 Participant #32 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.16 111.83 112.35 8 112.05 112.08 0 B♭2 4.35 117.19 118.26 16 117.71 117.68 0 B2 4.43 124.97 125.77 11 126.28 125.38 -12 D3 4.38 144.82 145.46 8 145.18 145.21 0 E♭3 4.99 150.98 152.06 12 151.25 151.49 3 E3 4.37 161.51 162.70 13 162.17 162.20 0 A3 4.23 212.51 214.51 16 213.93 213.67 -2 B♭3 4.74 222.27 224.17 15 223.18 223.34 1 B3 5.03 232.57 234.95 18 233.19 233.46 2

Example #2 A2 3.81 110.51 111.06 9 Slow Tempo A2 4.10 109.30 109.78 8 B♭2 4.18 114.73 116.06 20 B♭2 4.06 114.66 115.86 18 B2 4.26 121.52 122.40 13 B2 4.45 120.42 121.48 15 D3 3.98 146.28 147.30 12 D3 4.27 144.70 145.93 15 E♭3 5.16 151.17 152.47 15 E♭3 4.92 151.43 152.44 12 E3 4.79 160.39 161.85 16 E3 4.16 159.95 161.59 18 A3 6.18 210.96 213.27 19 A3 No Vibrato B♭3 6.34 218.42 219.45 8 B♭3 6.39 219.46 220.74 10 B3 6.55 229.89 232.15 17 B3 5.47 230.96 232.81 14

Example #3 A2 4.26 110.90 111.71 13 Fast Tempo A2 4.63 111.06 111.92 13 B♭2 4.81 116.03 117.37 20 B♭2 4.48 116.52 118.17 24 B2 4.89 123.01 124.23 17 B2 4.59 122.54 123.65 16 D3 5.15 143.47 144.86 17 D3 5.54 143.34 145.62 27 E♭3 5.13 149.87 151.36 17 E♭3 5.08 149.75 151.82 24 E3 5.56 160.48 162.37 20 E3 4.74 160.44 162.27 20 A3 6.58 214.28 216.15 15 A3 6.73 213.68 216.46 22 B♭3 6.48 225.31 227.21 15 B♭3 No Vibrato B3 6.51 238.23 240.54 17 B3 6.24 239.77 241.59 13

104 Participant #33 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.28 111.83 112.65 13 112.29 112.18 -2 B♭2 4.38 116.44 117.85 21 117.36 117.05 -5 B2 4.47 124.79 125.94 16 125.42 125.47 1 D3 4.91 146.96 148.27 15 148.10 147.57 -6 E♭3 4.90 154.80 156.86 23 156.73 155.90 -9 E3 4.98 165.61 168.16 26 166.39 166.91 5 A3 5.38 221.46 223.50 16 223.12 222.48 -5 B♭3 5.45 230.35 231.79 11 230.96 231.87 7 B3 5.27 248.26 251.68 24 250.10 250.40 2

Example #2 A2 3.99 110.52 111.22 11 Slow Tempo A2 4.31 112.00 112.90 14 B♭2 4.44 117.77 119.02 18 B♭2 4.37 118.84 120.37 22 B2 5.10 127.13 128.18 14 B2 4.72 126.60 127.88 17 D3 4.41 146.70 147.95 15 D3 4.51 147.30 149.15 22 E♭3 4.88 155.13 157.73 29 E♭3 4.88 152.89 155.39 28 E3 5.05 163.66 166.18 26 E3 5.21 161.73 164.26 27 A3 5.23 219.58 221.76 17 A3 5.69 219.06 221.48 19 B♭3 6.09 230.32 233.19 21 B♭3 5.56 230.50 233.42 22 B3 6.07 241.08 244.21 22 B3 5.86 243.21 245.89 19

Example #3 A2 3.93 109.84 110.56 11 Fast Tempo A2 3.85 110.49 111.24 12 B♭2 4.93 116.06 117.14 16 B♭2 4.72 116.88 118.25 20 B2 5.42 125.18 126.45 17 B2 5.14 125.76 127.08 18 D3 5.00 145.95 147.52 19 D3 5.52 145.99 147.88 22 E♭3 5.79 152.85 155.31 28 E♭3 5.67 152.02 154.11 24 E3 5.95 162.64 164.81 23 E3 5.28 162.54 165.51 31 A3 5.94 219.96 221.29 10 A3 5.88 218.22 220.34 17 B♭3 6.28 229.87 231.76 14 B♭3 No Vibrato B3 6.46 241.53 244.53 21 B3 5.71 241.51 245.73 30

105 Participant #34 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 6.42 109.39 109.92 8 109.98 109.70 -4 B♭2 5.94 114.01 114.54 8 114.84 114.46 -6 B2 5.49 123.84 124.61 11 124.30 124.14 -2 D3 5.41 145.69 146.90 14 145.27 145.99 9 E♭3 5.71 150.78 152.23 17 152.37 151.38 -11 E3 6.06 162.79 164.02 13 163.09 163.62 6 A3 6.08 215.68 217.00 11 215.23 215.64 3 B♭3 7.58 224.56 226.93 18 225.79 225.90 1 B3 7.35 238.19 239.91 12 239.27 239.54 2

Example #2 A2 No Vibrato Slow Tempo A2 6.78 111.86 112.40 8 B♭2 6.52 116.85 117.61 11 B♭2 6.68 116.87 118.05 17 B2 6.56 124.08 124.69 9 B2 5.95 124.14 125.37 17 D3 No Vibrato D3 6.39 145.39 146.65 15 E♭3 6.05 150.03 152.17 25 E♭3 6.15 150.80 153.03 25 E3 5.88 158.07 160.02 21 E3 6.50 161.46 163.04 17 A3 6.82 215.81 216.99 9 A3 6.99 216.44 217.67 10 B♭3 6.96 228.28 230.34 16 B♭3 7.29 229.10 231.76 20 B3 6.77 244.86 246.13 9 B3 7.11 243.04 244.52 11

Example #3 A2 7.08 109.78 110.36 9 Fast Tempo A2 6.83 110.69 111.19 8 B♭2 6.30 116.19 117.23 15 B♭2 6.60 115.88 117.30 21 B2 6.93 123.19 123.95 11 B2 6.72 125.00 126.04 14 D3 6.91 145.62 146.72 13 D3 6.83 144.90 146.53 19 E♭3 6.88 152.04 153.84 20 E♭3 6.73 151.73 154.09 27 E3 7.06 161.44 163.21 19 E3 6.90 162.52 163.87 14 A3 7.38 217.28 218.59 10 A3 7.71 216.76 218.50 14 B♭3 7.96 227.84 230.06 17 B♭3 7.67 227.35 230.25 22 B3 7.52 241.26 243.38 15 B3 7.43 242.68 244.36 12

106 Participant #35 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 3.95 110.42 110.97 9 110.66 110.77 2 B♭2 4.81 116.45 117.87 21 117.07 117.07 0 B2 4.99 122.36 123.22 12 123.27 122.81 -6 D3 4.86 147.80 149.17 16 148.72 148.32 -5 E♭3 5.38 154.55 155.75 13 155.71 155.10 -7 E3 5.59 163.07 165.33 24 165.19 164.44 -8 A3 5.98 222.30 225.14 22 223.25 223.92 5 B♭3 5.61 233.55 236.64 23 235.07 235.23 1 B3 5.80 245.57 248.30 19 245.61 247.36 12

Example #2 A2 4.27 110.45 111.17 11 Slow Tempo A2 4.20 109.00 110.00 16 B♭2 4.55 114.53 115.41 13 B♭2 4.77 114.82 115.68 13 B2 4.90 123.61 124.35 10 B2 4.31 123.37 123.93 8 D3 4.49 146.22 147.38 14 D3 4.28 146.23 147.66 17 E♭3 4.62 153.48 155.36 21 E♭3 5.00 154.15 156.40 25 E3 5.45 162.68 165.01 25 E3 5.46 166.10 168.03 20 A3 5.45 221.67 224.62 23 A3 5.67 220.64 223.37 21 B♭3 5.55 231.51 233.84 17 B♭3 5.71 234.24 237.35 23 B3 5.59 247.09 248.92 13 B3 5.85 247.19 249.85 19

Example #3 A2 4.42 110.94 111.86 14 Fast Tempo A2 4.62 110.30 111.25 15 B♭2 5.42 115.50 117.07 23 B♭2 5.47 116.35 117.77 21 B2 4.24 122.93 123.55 9 B2 4.84 122.68 123.41 10 D3 5.22 148.07 149.36 15 D3 5.15 147.91 149.48 18 E♭3 5.59 154.97 157.14 24 E♭3 5.46 154.21 155.76 17 E3 5.45 164.43 166.26 19 E3 5.65 166.38 168.58 23 A3 6.19 219.97 223.30 26 A3 6.13 222.36 224.74 18 B♭3 5.85 232.67 235.19 19 B♭3 5.65 234.44 237.30 21 B3 6.12 246.78 249.40 18 B3 6.08 247.16 249.79 18

107 Participant #36 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.82 110.38 111.45 17 110.99 110.93 -1 B♭2 5.01 116.77 117.45 10 116.92 117.11 3 B2 4.92 123.69 124.24 8 123.36 123.93 8 D3 5.30 147.71 148.68 11 148.19 148.40 2 E♭3 5.45 155.74 157.18 16 156.15 156.34 2 E3 5.77 166.24 167.85 17 165.91 166.78 9 A3 6.33 221.26 224.10 22 221.72 222.59 7 B♭3 6.12 231.99 234.90 22 232.71 233.57 6 B3 6.00 245.24 246.76 11 245.65 246.41 5

Example #2 A2 4.98 109.98 111.08 17 Slow Tempo A2 5.12 109.95 110.94 16 B♭2 5.33 116.32 117.19 13 B♭2 5.08 115.96 116.99 15 B2 5.20 123.21 123.75 8 B2 4.95 123.29 123.76 7 D3 5.34 147.95 148.56 7 D3 5.38 147.82 149.00 14 E♭3 5.15 154.40 156.98 29 E♭3 5.34 154.25 156.31 23 E3 5.34 165.47 166.29 9 E3 5.50 165.19 166.22 11 A3 6.45 219.48 222.22 22 A3 6.35 219.31 222.23 23 B♭3 6.28 228.59 231.30 20 B♭3 6.35 228.75 230.76 15 B3 6.28 243.37 245.05 12 B3 6.43 243.90 245.88 14

Example #3 A2 5.47 111.27 112.07 14 Fast Tempo A2 5.12 110.64 111.56 14 B♭2 5.59 116.90 117.43 8 B♭2 5.48 116.49 117.29 12 B2 5.93 123.98 124.80 11 B2 6.04 123.81 124.70 12 D3 5.69 147.60 148.75 13 D3 5.59 147.99 149.53 18 E♭3 6.24 155.36 157.08 19 E♭3 6.06 154.84 157.56 30 E3 5.98 165.67 167.75 22 E3 5.56 165.37 167.22 19 A3 6.72 218.82 222.17 26 A3 6.99 220.23 222.03 14 B♭3 6.45 228.89 231.80 22 B♭3 6.16 229.41 231.62 17 B3 No Vibrato B3 6.20 248.53 250.41 13

108 Participant #37 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.85 110.71 111.54 13 111.48 111.30 -3 B♭2 4.81 116.13 117.27 17 117.00 116.74 -4 B2 4.04 123.04 124.40 19 123.62 123.74 2 D3 4.21 144.65 146.52 22 145.99 145.63 -4 E♭3 4.19 152.43 154.30 21 153.69 153.43 -3 E3 4.18 162.30 164.41 22 163.60 163.39 -2 A3 4.71 221.07 223.73 21 222.34 222.22 -1 B♭3 4.53 231.10 233.87 21 231.86 231.98 1 B3 4.42 240.46 243.50 22 241.99 242.15 1

Example #2 A2 4.76 110.85 111.55 11 Slow Tempo A2 4.58 111.25 111.95 11 B♭2 4.42 117.31 118.40 16 B♭2 4.29 117.54 118.63 16 B2 4.91 123.88 124.74 12 B2 4.35 124.00 125.23 17 D3 4.44 144.90 146.25 16 D3 4.17 144.90 146.22 16 E♭3 4.27 152.71 154.58 21 E♭3 4.03 153.25 154.81 18 E3 4.26 162.64 164.56 20 E3 4.31 161.97 164.12 23 A3 4.42 217.81 221.72 31 A3 4.46 218.11 220.46 19 B♭3 5.13 228.95 231.13 16 B♭3 4.76 227.36 229.75 18 B3 4.64 239.43 242.28 20 B3 4.84 237.10 239.28 16

Example #3 A2 5.37 112.25 112.90 10 Fast Tempo A2 5.57 112.38 113.17 12 B♭2 5.04 118.08 119.21 16 B♭2 5.00 118.36 119.43 16 B2 4.84 123.74 125.14 19 B2 4.94 124.26 125.35 15 D3 5.08 145.59 146.70 13 D3 4.76 144.69 146.08 17 E♭3 4.52 152.49 154.27 20 E♭3 4.37 153.25 155.26 23 E3 4.31 161.83 164.10 24 E3 4.55 163.15 165.06 20 A3 4.85 217.65 220.22 20 A3 5.04 216.34 219.15 22 B♭3 5.00 223.94 227.84 30 B♭3 5.26 222.70 225.92 25 B3 4.98 230.65 234.10 26 B3 5.26 230.08 232.87 21

109 Participant #38 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 5.23 110.78 111.28 8 110.85 111.20 12 B♭2 5.34 116.43 117.83 21 117.13 117.15 0 B2 5.38 124.28 125.44 16 124.80 124.84 1 D3 5.51 145.95 146.91 11 146.25 146.44 2 E♭3 5.59 153.65 155.27 18 155.44 154.90 -6 E3 5.83 164.95 166.39 15 166.27 165.78 -5 A3 5.49 216.27 218.22 16 218.70 217.60 -9 B♭3 5.46 229.69 231.94 17 231.23 230.89 -3 B3 5.70 244.06 246.02 14 245.50 244.88 -4

Example #2 A2 5.25 109.26 109.72 7 Slow Tempo A2 5.36 109.84 110.51 11 B♭2 5.37 115.69 116.53 13 B♭2 5.81 115.75 117.22 22 B2 5.36 122.89 123.45 8 B2 5.53 122.84 123.69 12 D3 5.37 145.51 146.54 12 D3 5.34 145.97 146.75 9 E♭3 5.32 153.48 154.73 14 E♭3 5.41 153.42 155.12 19 E3 5.63 163.57 165.10 16 E3 5.97 163.60 165.30 18 A3 5.47 216.22 218.55 19 A3 5.49 216.14 218.57 19 B♭3 5.40 231.08 233.95 21 B♭3 5.52 231.88 234.04 16 B3 5.53 241.51 243.38 13 B3 5.55 243.51 245.86 17

Example #3 A2 5.28 108.33 108.98 10 Fast Tempo A2 5.39 109.15 109.75 10 B♭2 5.48 114.13 115.16 16 B♭2 No Vibrato B2 5.71 123.26 124.00 10 B2 5.99 122.89 124.02 16 D3 5.54 145.47 146.57 13 D3 5.69 145.91 147.01 13 E♭3 5.64 153.54 155.56 23 E♭3 5.46 153.06 155.58 28 E3 5.91 163.83 165.48 17 E3 6.02 163.65 165.55 20 A3 5.46 214.72 217.85 24 A3 5.59 216.49 218.89 19 B♭3 5.55 228.30 231.82 26 B♭3 5.76 227.21 229.61 18 B3 5.63 242.53 245.26 19 B3 5.67 241.89 244.63 20

110 Participant #39 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.59 110.21 111.05 13 109.98 110.59 10 B♭2 4.79 114.50 115.32 12 115.22 114.89 -5 B2 5.05 121.94 123.30 19 123.03 122.65 -5 D3 4.55 144.61 146.31 20 145.51 145.33 -2 E♭3 5.46 151.61 153.41 20 152.58 152.37 -2 E3 6.09 162.70 163.87 12 163.93 163.23 -7 A3 6.21 213.15 215.30 17 214.34 214.35 0 B♭3 6.18 225.58 227.53 15 225.79 226.01 2 B3 5.23 230.07 232.75 20 232.31 232.17 -1

Example #2 A2 4.03 109.01 109.69 11 Slow Tempo A2 4.13 110.36 111.06 11 B♭2 4.68 115.78 116.71 14 B♭2 4.52 116.14 117.05 14 B2 5.22 121.95 122.71 11 B2 5.26 122.95 123.56 9 D3 4.73 145.49 146.70 14 D3 4.99 146.29 147.93 19 E♭3 5.81 152.76 153.93 13 E♭3 5.64 152.18 153.77 18 E3 5.55 163.55 164.64 12 E3 5.61 163.66 164.62 10 A3 5.64 214.79 217.70 23 A3 5.97 217.68 220.82 25 B♭3 5.73 226.74 229.69 22 B♭3 5.60 228.04 229.88 14 B3 5.96 242.98 245.84 20 B3 6.15 242.33 244.84 18

Example #3 A2 5.18 109.44 110.20 12 Fast Tempo A2 4.76 110.25 111.06 13 B♭2 5.23 115.68 116.85 17 B♭2 5.33 116.46 117.41 14 B2 No Vibrato B2 5.57 123.23 124.09 12 D3 5.09 145.17 146.65 18 D3 No Vibrato E♭3 6.12 152.43 153.88 16 E♭3 6.04 151.97 154.02 23 E3 No Vibrato E3 5.99 162.65 163.93 14 A3 6.17 213.23 215.83 21 A3 No Vibrato B♭3 5.78 230.08 232.06 15 B♭3 5.61 230.83 233.97 23 B3 6.15 241.09 243.77 19 B3 6.23 244.27 246.55 16

111 Participant #40 Characteristics Mean Pitches Rate Valley Peak Width Non-Vib Vib Difference (Hz) (Hz) (Hz) (cents) (Hz) (Hz) (cents)

Example #1 A2 4.17 109.14 109.90 12 109.60 109.75 2 B♭2 4.65 115.11 115.82 11 115.38 115.42 1 B2 4.50 122.83 123.94 16 123.72 123.44 -4 D3 4.87 145.06 146.21 14 144.53 145.54 12 E♭3 4.73 150.53 152.30 20 151.76 151.49 -3 E3 5.02 161.36 162.96 17 162.45 161.89 -6 A3 4.98 215.01 217.20 18 216.23 216.45 2 B♭3 5.20 222.90 225.10 17 224.92 224.33 -5 B3 4.77 241.18 244.50 24 242.94 243.29 2

Example #2 A2 3.84 110.91 111.58 10 Slow Tempo A2 3.89 110.24 111.14 14 B♭2 4.23 115.67 116.50 12 B♭2 4.08 116.33 117.17 12 B2 4.02 122.66 123.75 15 B2 4.12 123.14 124.10 13 D3 4.18 144.78 146.38 19 D3 4.30 145.37 146.43 13 E♭3 4.77 151.29 153.14 21 E♭3 4.88 151.50 153.79 26 E3 5.08 161.78 162.77 11 E3 4.65 161.56 163.18 17 A3 5.01 214.62 217.40 22 A3 5.11 218.68 221.30 21 B♭3 4.97 224.75 230.50 44 B♭3 4.82 229.07 234.13 38 B3 5.15 242.26 246.05 27 B3 4.99 243.94 249.54 39

Example #3 A2 4.11 111.96 112.71 12 Fast Tempo A2 4.85 111.25 112.15 14 B♭2 5.24 116.39 117.09 10 B♭2 5.28 116.40 117.16 11 B2 5.93 122.86 123.83 14 B2 5.56 122.68 123.60 13 D3 5.32 145.14 146.52 16 D3 5.87 145.54 146.45 11 E♭3 6.20 153.32 155.16 21 E♭3 6.46 152.06 154.43 27 E3 6.80 161.87 163.10 13 E3 6.28 160.62 162.58 21 A3 4.94 214.00 216.46 20 A3 5.65 215.95 218.44 20 B♭3 5.23 226.62 230.15 27 B♭3 5.29 228.45 231.43 22 B3 5.04 240.52 243.30 20 B3 4.91 240.19 242.74 18

112

APPENDIX C

HUMAN SUBJECTS APPROVAL MEMORANDUM

113 Office of the Vice President For Research Human Subjects Committee Tallahassee, Florida 32306-2742 (850) 644-8673 · FAX (850) 644-4392

APPROVAL MEMORANDUM

Date: 9/7/2011

To: James Mick Dept.: MUSIC SCHOOL

From: Thomas L. Jacobson, Chair Re: Use of Human Subjects in Research

An Analysis of Double Bass Vibrato: Rates, Widths, and Pitches as Influenced by Pitch Height and Tempo

The application that you submitted to this office in regard to the use of human subjects in the proposal referenced above have been reviewed by the Secretary, the Chair, and one member of the Human Subjects Committee. Your project is determined to be Expedited per per 45 CFR § 46.110(7) and has been approved by an expedited review process.

The Human Subjects Committee has not evaluated your proposal for scientific merit, except to weigh the risk to the human participants and the aspects of the proposal related to potential risk and benefit. This approval does not replace any departmental or other approvals, which may be required.

If you submitted a proposed consent form with your application, the approved stamped consent form is attached to this approval notice. Only the stamped version of the consent form may be used in recruiting research subjects.

If the project has not been completed by 9/4/2012 you must request a renewal of approval for continuation of the project. As a courtesy, a renewal notice will be sent to you prior to your expiration date; however, it is your responsibility as the Principal Investigator to timely request renewal of your approval from the Committee.

You are advised that any change in protocol for this project must be reviewed and approved by the Committee prior to implementation of the proposed change in the protocol. A protocol change/amendment form is required to be submitted for approval by the Committee. In addition, federal regulations require that the Principal Investigator promptly report, in writing any unanticipated problems or adverse events involving risks to research subjects or others.

By copy of this memorandum, the Chair of your department and/or your major professor is reminded that he/she is responsible for being informed concerning research projects involving

114 human subjects in the department, and should review protocols as often as needed to insure that the project is being conducted in compliance with our institution and with DHHS regulations.

This institution has an Assurance on file with the Office for Human Research Protection. The Assurance Number is FWA00000168/IRB number IRB00000446.

Cc: Alice-Ann Darrow, Advisor HSC No. 2011.6747

115

APPENDIX D

CONSENT FORM

116
Double Bass Vibrato Research Study


My name is James Mick and I am PhD student at Florida State University who is conducting a study for my dissertation. I am asking if you would like to take part in a research study named An Analysis of Double Bass Vibrato: Rates, Widths, and Pitches as Influenced by Pitch Height and Tempo, which concerns university double bass players’ vibrato practices.
If you agree to participate in this study, you will play several short music examples in several different pitch registers and at several different tempi. The musical examples are intentionally easy because I am primarily interested in your vibrato on the corresponding whole-notes and half-notes in the musical excerpts. The study will take less than ten (10) minutes to complete and is anonymous, meaning it will be impossible for me or anyone else to know the individual results of each participant.
An audio recording will be made of you playing the examples so that I can analyze them for this study. No one else will listen to the recording, and since the recordings are anonymous, it will be impossible for me to know who is playing while I analyze them.
It is my desire that the results of this study will both provide a better explanation of double bass vibrato characteristics and help teachers better describe and teach proper vibrato characteristics to younger double bass students who are in the early stages of learning how to vibrate.
This study is completely voluntary, which means that you can decide whether or not to participate at any time. You will not receive any compensation for participating in this study and there are no consequences if you choose not to participate.
Please feel free ask any questions that you may have about this study. If you have a question later that you do not think of now, you can reach me The major professor for this study is Dr. Alice-Ann Darrow who can be reached at [email protected] or 850-645-1438. You may also contact the FSU Institutional Review Board (IRB) at 850-644-8633 or through the website: http://www.fsu.research.edu. You will be given a copy of this consent form for your records.
Signing your name at the bottom means that you agree to participate in this study.

Your First and Last Name (please print):


Your Signature: Date:


Gender (circle one): Male Female
Age:

FSU Human Subjects Committee Approved on 9/6/2011. Void after 9/4/2012. HSC# 2011.6747

117

How many total years have you played the double bass?
How many years have you received professional training (private lessons) on the bass?

FSU Human Subjects Committee Approved on 9/6/2011. Void after 9/4/2012. HSC# 2011.6747

118

REFERENCES

Aaron, J. (1997). The state of teaching the double bass. American String Teacher, 46(4), 59-60.

Allen, M. L. (2010, March). A pilot study of vibrato among middle school and high school double bass students. Research poster presented at the American String Teachers Association National Conference, Santa Clara, CA.

Allen, M. L., Geringer, J. M., & MacLeod, R. B. (2009). Performance practice of violin vibrato: An artist-level case study. Journal of String Research, 4, 27-38.

Allen, M. L., Gillespie, R., & Hayes, P. T. (2002). Essential elements 2000 for strings, book 1. Milwaukee, Wisconsin: Hal Leonard.

Applebaum, S. (1986). The art and science of string performance. Sherman Oaks, CA: Alfred Publishing.

Applebaum, S., & Applebaum, S. (1955). With the artists: World famed string players discuss their art. New York: John Market.

Auer, L. (1980). Violin playing as I teach it. Mineola, New York: Dover. (Original work published in 1921).

Barber, B. (1990). Intonation: A sensory experience. American String Teacher, 40(4), 81-85.

Benfield, W. A., & Dean, J. S., Jr. (1973). The art of double bass playing. USA: Summy- Birchard Music.

Benham, S. J., Wagner, M. L., Aten, J. L., Evans, J. P., Odegaard, D., & Lieberman, J. L. (2011). ASTA curriculum: Standards, goals, and learning sequences for essential skills and knowledge in K-12 string programs. Reston, VA: American String Teachers Association.

Bille, I. (1922). New method for double-bass: Part I. Milan, Italy: Ricordi.

Blum, D. (1977). Casals and the art of interpretation. New York: Heinemann Educational Books.

Boersma, P., & Weenink, D. (2009). Praat: Doing phonetics by computer (Version 5.1.20) [computer program]. Retrieved September 3, 2010, from http://www.praat.org/

119 Boyden, D. D. (1990). The history of violin playing from its origins in 1761 and its relationship to the violin and violin music. Oxford, United Kingdom: Claredon Press.

Bradetich, J. (1987). The mythology of bass pedagogy. American String Teacher, 37(2), 60-63.

Bradetich, J. (1995). A practice checklist for bassists. American String Teacher, 45(4), 61-63.

Bradetich, J. (2009). Double bass: The ultimate challenge. Moscow, ID: Music For All To Hear.

Brown, J. C., & Vaughn, K. V. (1996). Pitch center of stringed instrument vibrato tones. Journal of the Acoustical Society of America, 100, 1728-1735.

Brun, P. (1989). A history of the double bass (Trans. by Lynn Moreel & Paul Brun). Chemin de la Flanerie, France: Author.

Brun, P. (2001). A new history of the double bass. American String Teacher, 51(1), 66-70.

Brungard, K. D., Alexander, M. L., Anderson, G. E., & Dackow, S. (2006). Orchestra expressions, book 2: Teacher resource guide. Van Nuys, CA: Alfred.

Casals, P. (1922). The technique of violoncello playing (compiled by D. Alexanian; translated by F. Fairbanks). Paris: Editions Salabert.

Cheslock, L. (1931). An introductory study of the violin vibrato. Research Studies in Music, Baltimore, MD: Peabody Conservatory of Music.

Clark, P. (1989). Vibrato: The right arm dances, the left hand enhances. American String Teacher, 39(3), 38-39.

Corso, J. F., & Lewis, D. (1950). Preferred rate and extent of the frequency vibrato. Journal of Applied Psychology, 34, 206-212.

Doschek, A. (1968). Some physical aspects of the vibrato. American String Teacher, 48(3), 19- 20.

Eberhardt, S. (1911). Violin vibrato: Its mastery and artistic use. (English ed.). New York: Carl Fischer.

Elgar, R. (1965). Introduction to the double bass (Rev. 2nd ed.). St. Leonards-on-Sea, England: Author.

Fanelli, M. (2008). A life of self discovery and passion for the double bass and teaching. American String Teacher, 58(4), 30-35.

Fanelli, M. (2009). A life of self discovery and passion for the double bass and teaching: Part II. American String Teacher, 59(1), 30-33.

120

Fishbach, G. F. (1998). The birth of a vibrato. American String Teacher, 48(4), 28-35.

Fischbach, G. F., & Frost, R. S. (1997). Viva vibrato! San Diego, CA: Neil A Kjos Music Company.

Flesch, C. (1924). The art of violin playing: Applied technique. (F. H. Martens, Trans.). New York: Carl Fischer.

Flesch, C. (1930). The art of playing the violin: Artistic realization and instruction. (F. H. Martens, Trans.). New York: Carl Fischer.

Fletcher, H., Blackham, E. D., & Geertsen, N. O. (1965). Quality of violin, viola, cello, and bass- viol tones. Journal of the Acoustical Society of America, 37, 851-863.

Fletcher, H., & Sanders, L. C. (1967). Quality of violin tones. Journal of the Acoustical Society of America, 41, 1534-1544.

Galamian, I. (1985). Principles of violin playing and teaching (3rd ed.). Ann Arbor, MI: Shar Products.

Geminiani, F. (1751). The art of playing on the violin. Ed. by David Boyden. London: Oxford University Press.

Geringer, J. M., & Allen, M. L. (2004). An analysis of vibrato among high school and university violin and cello students. Journal of Research in Music Education, 52, 167-178.

Geringer, J. M., Allen, M. L., & MacLeod, R. B. (2005). Initial movement and continuity in vibrato among high school and university string players. Journal of Research in Music Education, 53, 248-259.

Geringer, J. M., Allen, M. L., & MacLeod, R. B. (2010). String vibrato: Research related to performance and perception. String Research Journal, 1, 7-24.

Geringer, J. M., MacLeod, R. B., & Allen, M. L. (2010). Perceived pitch of violin and cello vibrato tones among music majors. Journal of Music Education, 57, 351-363.

Gillespie, R. (1996). Vibrato: What do we know from research about this shaking, waving, wobbling thing anyway? American String Teacher, 46(1), 91-93.

Goilav, Y. (1976). The vibrato (Trans. by L. Proto). Bass World, 2(4), 207-208.

Green, B., & Neighbor, J. (1999). The popular bass method: Book 1, 2 & 3. El Cerrito, CA: Author.

121 Griffin, M. (2008). Bob Zimmerman: Living the legacy. Playing it from the heart. International Society of Bassists, 32(1), 23-27.

Grodner, M. (1979). The double bass—A string instrument. In M. Grodner (Ed.), Concepts in string playing: Reflections by artist-teachers at the Indiana University School of Music. (pp. 27-37). Bloomington, IN: Indiana University Press.

Guettler, K. (1992). A guide to advanced modern double bass technique. London, England: Yorke Edition.

Hamann, D. L., & Gillespie, R. (2004). Strategies for teaching strings: Building a successful string and orchestra program. New York: Oxford University Press.

Harper, K. (1996). Two-finger vibrato. American String Teacher, 46(3), 65-68.

Hauck, W. (1975). Vibrato on the violin (3rd ed., Trans. by K. Rokos). London: Bosworth.

Hollinshead, M. T. (1932). A study of the vibrato in artistic violin playing. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 281-288). Iowa City, Iowa: University of Iowa.

Johnson, E. (1994). Good vibrations – without vibrato. The Strad, 105, 554-555.

Karr, G. (1988). The Gary Karr double bass book, book two. Pacific, MO: Amati Productions.

Karr, G. (1996). In tune. American String Teacher, 46(1), 83-85.

Kazez, D. (1987). An objective look at string instrument vibrato. American String Teacher, 37(3), 33-34.

Kjelland, J. (2008). Teaching cello and double bass vibrato. In J. May (Ed.), The string teacher’s cookbook: Creative recipes for a successful program. (pp. 66-68). Galesville, MD: Meredith Music.

Klose, R. (1989). Concepts in teaching vibrato. American String Teacher, 39(3), 36-37.

Klotman, R. H. (1996). Teaching strings: Learning to teach through playing (2nd ed.). Belmont, CA: Schirmer/Thomas Learning.

Krakenberger, J. (2000). Good vibration. The Strad, 45, 372-373.

Kuhn, W. E. (1967). The strings. Boston, MA: Allyn and Bacon, Inc.

Laborie, C. (2006). The Laborie-Rabbath endpin genesis: A successful collaboration between musicians and a luthier. International Society of Bassists, 30(1), 13-15.

122 Lamb, N. (1984). Guide to teaching strings (4th ed.). Dubuque, IA: WM. C. Brown Company.

Lucktenberg, J. (1994). Developing violin vibrato. The Instrumentalist, 48(10), 32-36.

MacLeod, R. B. (2008). Influences of dynamic level and pitch register on the vibrato rates and widths of violin and viola players. Journal of Research in Music Education, 56, 43-54.

MacLeod, R. B. (2010). A pilot study of relationships between pitch register and dynamic level and vibrato rate and width in professional violinists. String Research Journal, 1, 75-83.

Manoly, L. E. (1923). The contrabass and its position. In F. H. Martens, String mastery: Talks with master violinists, viola players and violoncellists. (pp. 279-283). New York: Frederick A. Stokes Company.

Mantel, G. (1975). Cello technique: Principles and forms of movement (Translated by B. H. Thiem). Bloomington, IN: Indiana University Press.

Masuzzo, D. (2003). Taking the fifth: How tuning in fifths changed my experience playing the double bass. Bass World, 27(1), 19-20. (Reprinted from August 2002 ASTA)

McDonald, W. R. (1998). A comparison of perceived musicianship and appropriate use of vibrato in professional cello performances by string performers, music majors, and nonmusic majors. Dissertation Abstracts International, 60(5), 1387. (UMI No. 9931933)

McDougal, B. (1998). Quintessential Quarrington. Double Bassist, 22(2). Retrieved from http://joelquarrington.com/quintessential-quarrington.html#more-95

Mellody, M. & Wakefield, G. H. (2000). The time-frequency characteristics of violin vibrato: Modal distribution analysis and synthesis. Journal of the Acoustical Society of America, 107, 598-611.

Metfessel, M. (1932). The vibrato in artistic voices. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 14-117). Iowa City, Iowa: University of Iowa.

Mick, J. P. (2011, January). An analysis of thumb position vibrato among university double bass students. Research poster presented at the Alabama Music Educators Association Conference, Montgomery, AL.

Miller, P. (2008). Incorporating vibrato into the warm-up routine. In J. May (Ed.), The string teacher’s cookbook: Creative recipes for a successful program. (pp. 78-80). Galesville, MD: Meredith Music.

Morton, M. (1991). Dr. Morton’s double bass technique: Concepts and ideas. Columbus, OH: Basso Profondo.

123 Mozart, L. (1948). A treatise on the fundamental principles of violin playing. (E. Knocker, Trans.). New York: Oxford University Press. (Original work published 1756 & 1787).

Neher, P. (1995). A new pedagogy for the mini-bass. American String Teacher, 45(2), 45-49.

Nestler, D., & Karr, G. (1981). Learning to vibrate. International Society of Bassists, 7, 699-701.

Neubert, D. (1988). An interview with Gary Karr. American String Teacher, 38(3), 52-55.

Neumann, F. (1969). Violin left hand technique. Urbana, Illinois: American String Teachers Association.

Oppelt, R. (1981). Introducing, correcting, and developing vibrato. American String Teacher, 31(3), 42-45.

Papich, G., & Rainbow, E. (1974). A pilot study of the performance practices of twentieth- century musicians. Journal of Research in Music Education, 22, 24-43.

Papich, G., & Rainbow, E. (1975). Research in the performance practices of musicians. Psychology of Music, 22, 4-8.

Potter, L., Jr. (1980). The art of cello playing. Princeton, NJ: Summy-Birchard Music.

Rabbath, F. (1984). A new technique for the double bass: Vol. III. Paris, France: Alphonse Leduc.

Reger, S. N. (1932a). Historical survey of the string instrument vibrato. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 289-304). Iowa City, Iowa: University of Iowa.

Reger, S. N. (1932b). Historical survey of the string instrument vibrato. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 305-343). Iowa City, Iowa: University of Iowa.

Rolland, P. (1960). Basic principles of violin playing (2000 ed.). Reston, VA: ASTA with NSOA.

Rolland, P., & Mutschler, M. (2000). The teaching of action in string playing (3rd ed.). Urbana, Illinois: Illinois String Research.

Seashore, C. E. (1932). Introduction. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 7-13). Iowa City, Iowa: University of Iowa.

Seashore, C. E. (1936). Psychology of the vibrato in voice and instrument. In Studies in the Psychology of Music: Vol. 3. Iowa City, IA: University of Iowa.

124 Seashore, C. E. (1938). Psychology of music. New York: McGraw-Hill.

Seashore, H. G. (1932). The hearing of the pitch and intensity in vibrato. In C. Seashore (Ed.), Studies in the psychology of music, Vol. 1: The vibrato. (pp. 213-235). Iowa City, Iowa: University of Iowa.

Shackford, C. (1960). Pitch range and the actual pitch of vibrato tones. American String Teacher, 10(2), 25, 28.

Shimek, J. B. (1993). Vibrato for the double bassist. American String Teacher, 43(3), 65-66.

Shonle, J. I., & Horan, K. E. (1980). The pitch of vibrato tones. Journal of the Acoustical Society of America, 67, 246-252.

Simandl, F. (1984). New method for the double bass, book I (Rev. by F. Zimmerman, Ed. By L. Drew). New York: Carl Fischer.

Skoldberg, P. (1983). The strings – A comparative view, Vol. II. Bloomington, IN: Tichenor.

Small, A. M. (1937). An objective analysis of artistic violin performance. In C. E. Seashore (Ed.), University of Iowa studies in the psychology of music: Vol. 4. Objective analysis of musical performance. (pp. 172-231). Iowa City, IA: University of Iowa.

Stanton, D. H. (1965). The string (double) bass, M. J. Isaac (Ed.). Evanston, IL: The Instrumentalist.

Starker, J. (1979). An organized method of string playing. In M. Grodner (Ed.), Concepts in string playing: Reflections by artist-teachers at the Indiana University School of Music. (pp. 133-155). Stoelzing, L. L. (1950). Basic vibrato studies for the violin. Rockville Centre, NY: Belwin.

Stevenson, H. (Ed.). (1994). Discussion corner: How do you teach vibrato? International Society of Bassists, 19(2), 27-33.

Stoelzing, L. L. (1950). Basic vibrato studies for the violin. Rockville Centre, NY: Belwin.

Thibeault, M. (1997). The vibrato rate of professional double bass players. American String Teacher, 47(1), 71-73.

Thierbach, S. P. (1999). Vibrato in the violin music of the baroque period. American String Teacher, 49(2), 76-80.

Vance, G., & Costanzi, A. (2000). Progressive repertoire for the double bass, vol. 1. New York: Carl Fischer.

125 Winnick, W. (1992). Tips for the non-professional symphony player. American String Teacher, 42(3), 37-39.

Young, P. (1978). Playing the string game: Strategies for teaching cello and strings. Ann Arbor, MI: Shar Publications.

126

BIOGRAPHICAL SKETCH

Name: James Paul Mick

Date of Birth: August 27, 1979

Birth Place: Salina, Kansas

Home Town: Newton, Kansas

Higher Education: Texas Christian University Fort Worth, Texas Major: Music Education Degree: B. M. E. (2002)

Ithaca College Ithaca, New York Major: Music Education Degree: M. M. (2005)

The Florida State University Tallahassee, Florida Major: Music Education Degree: Ph. D. (2012)

Experience: Frankford Middle School Plano, Texas, 2005-2007 Orchestra (6-8)

Fayetteville-Manlius High School Manlius, New York, 2007-2009 Orchestra (9-10), String Lessons (9-12), Jazz Band (9-12)

Ithaca College Ithaca, New York, 2011-present Assistant Professor of Music Education

127