Abstract
The purpose of this study was to investigate the effect of playing position, fingers used, and level of training on vibrato rate and width, and possible pitch differences between non-vibrated and vibrated tones of cellists. Participants (N = 30) were volunteers from a high school orchestra program (n = 15) and a large public university (n = 15). Cellists performed three ascending pitch sets in first, fourth, and thumb position. Each pitch set included whole notes performed initially without vibrato, then vibrato was added to the second half of each note. Analysis showed that playing position significantly influenced cellists’ vibrato rates, widths, and pitch of non-vibrated versus vibrated tones. Comparisons revealed a slower mean vibrato rate in first position than the fourth and thumb positions. Cellists’ vibrato became wider in higher playing positions (closer to the bridge). Participants’ vibrated tones occurred slightly above the non-vibrated tones in first position, but slightly below the non-vibrated tones in thumb position. The fingers used or level of training did not affect vibrato rate, width, or pitch.
Performers and pedagogues consider vibrato a vital element in string instrument performance. The inclusion of vibrato enhances the music and helps provide an expressive performance. Balance, evenness, consistency, and a lack of tension are accepted characteristics of a good vibrato (Applebaum, 1986; Fischbach, 1998; Galamian, 1962; Hamann & Gillespie, 2004; Lucktenberg, 1994; Potter, 1980; Rolland, Mutchler, & Hellebrandt, 2000). While pedagogues agree on the traits of a characteristic vibrato, qualities such as rate, width, pitch center, and initial movement are not agreed upon (Fischbach, 1998; Gillespie, 1996). A multitude of contextual variables such as ability level, instrument choice, pitch register, playing position on the fingerboard, finger employed, dynamic level, note duration, and phrase direction can affect a string players’ vibrato (Geringer, Allen, & MacLeod, 2010). Research that investigates those contextual variables is important as music educators determine effective instructional sequences of vibrato. This study attempts to investigate the contextual effects of level of training, playing position on the fingerboard, and finger used on vibrato rate, vibrato width, and possible pitch differences between non-vibrated and vibrated tones by cellists.
Performing artists and pedagogues recommend that vibrato rates should range from 5.0 Hz to 8.0 Hz (Applebaum, 1986; Doschek, 1968; Fischbach, 1998; Joelson, 1964; Kazez, 1984; Oppelt, 1981; Potter, 1980; Rolland, 2000; Rolland et al., 2000; Stoelzing, 1950; Winnick, 1992). To compare recommendations of pedagogues to how musicians actually perform, multiple empirical investigations have focused on vibrato rates of both students and virtuoso string performers. In studies prior to 1970, results revealed that violinists’ vibrato rates varied: 5.0 Hz to 6.0 Hz (Fletcher & Sanders, 1967), 6.0 Hz to 7.0 Hz (Small, 1937), 5.5 Hz to 7.0 Hz (Cheslock, 1931), 6.0 Hz (Seashore, 1967), 6.9 Hz (Reger, 1932), and 7.0 Hz (Hollinshead, 1932). Cheslock (1931) found that the vibrato rates of adult (6.4 Hz) and professional (6.5 Hz) violinists were approximately the same. The inclusion of high school and university level violinists, violists, cellists, and double bassists during more recent investigations have noted slower vibrato rates than earlier studies: 5.6 Hz to 6.5 Hz for violin (Geringer & Allen, 2004; MacLeod, 2008; Papich & Rainbow, 1974), 5.5 Hz for viola (MacLeod, 2008); 5.0 Hz to 5.4 Hz for cello (Geringer & Allen, 2004; Papich & Rainbow, 1974), and 4.0 Hz to 5.1 Hz for double bass (Allen, 2010; Mick, 2011; Papich & Rainbow, 1974). Differences between early and more recent investigations may exist for several reasons, including: 1) The introduction of computer software for sound analysis may provide more accurate examinations; 2) Recent investigations examined the vibrato rate of student performers while past studies investigated virtuoso artists; and 3) Investigators examined performers’ rates of vibrato in various musical contexts and playing positions. Additional investigation is needed to understand why the different rates of vibrato were found.
Although pedagogues’ recommendations also differ for the rate of vibrato, most advise that vibrato width should be approximately 25 cents to 50 cents (Doschek, 1968; Fischbach, 1998; Fischbach & Frost, 1997; Kazez, 1987; Lucktenberg, 1994; Rolland, 2000). An examination of systematic research shows that most performers’ vibrato falls within pedagogues’ suggested width range: 25 cents to 50 cents for violin (Cheslock, 1931; Geringer & Allen, 2004; MacLeod, 2008; Mellody & Wakefield, 2000; Papich & Rainbow, 1974; Reger, 1932; Seashore, 1936; Small, 1937), 38 cents for viola (MacLeod, 2008), 30 cents to 50 cents for cello (Geringer & Allen, 2004; Papich & Rainbow, 1974), and approximately 25 cents for double bass (Mick, 2011; Papich & Rainbow, 1974). Similar to vibrato rate, the performers’ ability level seemed to influence vibrato width. Student musicians’ (Geringer & Allen, 2004; MacLeod, 2008; Mick, 2011) vibrato width was smaller than virtuoso performers (Hollinshead, 1932; Reger, 1932; Small, 1937). A comparison of previous results indicates that student musicians’ vibrato width may decrease with increases in instrument size: 34 cents to 47 cents for violin (Geringer & Allen, 2004; MacLeod, 2008; Reger, 1932), 38 cents for viola (MacLeod, 2008); 26 cents for cello (Geringer & Allen, 2004); and 24 cents for double bass (Mick, 2011). However, Papich and Rainbow's (1974) investigation on the vibrato widths of violinists (25 cents), cellists (50 cents), and double bassists (25 cents) did not support that trend. Additional investigation is needed to understand the effect of instrument size on vibrato width.
Pitch register appears to be an important contextual variable when examining vibrato rate and width. On string instruments, the physical distances between intervals decrease as a performer's hand moves toward the bridge. Some pedagogues claim that vibrato width should decrease as the notes ascend in pitch register (Applebaum, 1986; Carroll, 1997; Flesch, 1924; Lucktenberg, 1994; Mantel, 1972). Carroll (1997), Lucktenberg (1994), and Mantel (1972) assert that rate of vibrato should increase as notes climb in pitch register. Empirical research does not provide clear evidence of pitch register's influence on vibrato width and rate. When comparing university level violinists’ vibrato in both first and third positions, Papich and Rainbow (1974) found that performers used a wider vibrato in third position than first. Similarly, MacLeod (2008) revealed that vibrato rates and widths of student violinists and violists were significantly different in first position (5.47 Hz, 34 cents) than seventh position (5.74 Hz, 58 cents). During a case study of an artist-level performer, Allen, Geringer, and MacLeod (2009) found that vibrato rate and width increased during performance in high pitch registers. However, in a subsequent investigation of four professional violinists, MacLeod (2010) found that vibrato became wider in high registers, but rate did not change. No significant differences in vibrato rate and width were revealed during Papich and Rainbow's (1975) investigation on double bass vibrato in first and fourth positions. Fletcher, Blackman, and Geertsen (1965) examined violinists’ vibrato rate and width in four different octaves, and no differences between vibrato widths and rates were revealed. Further research is needed to investigate the inconsistent findings of those studies.
Perception studies on vibrato reveal that listeners’ hear the vibrated pitch near the mean frequency of the vibrato (Brown & Vaughn, 1996; Geringer, MacLeod, & Allen, 2010; Shonle & Horan, 1980; Small, 1937). Those results support empirical research that showed performed vibrato oscillations occurred both above and below conceived pitch (Allen et al., 2009; Brown & Vaughn, 1996; Geringer & Allen, 2004; Geringer, Allen, & MacLeod, 2005; Geringer, MacLeod et al., 2010; C. Seashore, 1967; H. Seashore, 1932; Shackford, 1960; Shonle & Horan, 1980; Small, 1937). In contrast, three studies indicated that vibrated tones tend to oscillate primarily above the conceived pitch (Fletcher, Blackham, & Geertsen, 1965; Papich & Rainbow, 1974, 1975), and one study showed oscillation below the pitch (Fletcher & Sanders, 1967).
The purpose of the present study was to investigate the effects of playing position on the fingerboard, finger used, and level of training on vibrato rate, vibrato width, and possible pitch differences between non-vibrated and vibrated tones of cellists. Pedagogues’ recommendations and results from past empirical studies do not always align, and a better understanding of musicians’ performance tendencies is needed. Numerous researchers have focused on the vibrato of violinists and violists, but limited research has been conducted on the cellists’ vibrato characteristics. The current study compared cellists’ vibrato rate, width, and pitch center to previous investigations of string instrument vibrato. The following research questions were investigated: Are there differences between the vibrato rates, widths, and frequencies of non-vibrated versus vibrated tones of 1) high school and university level cellists, 2) different playing positions, and 3) different fingers?
Method
Participants (N = 30) in this study were cellists at the high school level (n = 15) or university level (n = 15) in the southeastern United States. High school participants were volunteers recruited from string orchestra classes at a suburban public secondary school. All high school participants attended a single middle school and studied under the same orchestra director for two years. The mean age of high school participants was 15.60 years, and they averaged 6.60 years of playing cello with 3.87 years of private study. University level participants were undergraduate and graduate student volunteers enrolled in a music education or performance degree program. The university students’ mean age was 23.53, and they averaged 13.40 years of playing cello with 10.67 years of private cello study. All participants were informed that their performance was being recorded to analyze the performance practices of string players.
Based on the excerpts created by Geringer and Allen (2004), I created music stimuli consisting of three ascending pitch sets to address the purposes of this study. To control for individual player preferences, playing position and finger numbers were clearly indicated on each pitch set (shown in Figure 1). Directions for the use and non-use of vibrato were also clearly indicated on the pitch sets. The three pitch sets varied from five to seven measures in 4/4 meter, and each contained whole-notes with nonvibrato indicated over the first half of each note and the addition of vibrato above the third beat of each note. The whole-notes were composed in an ascending pattern that alternated each whole-note with a whole-note rest. Participants performed the first pitch set in first position. The first pitch set began on the bass clef's third-space E (E3) and included the notes E3, F3, F#3 and G3. The second pitch set began on the second ledger line above the staff in bass clef on the note E (E4). Participants performed the second pitch set in fourth position, and it included the notes E4, F4 F#4 and G4. The final set was performed in thumb position. That pitch set began on the treble clef's third-line B (B4) and included the notes B4, C#5, and D5. That pattern allowed performers to use the three fingers that are commonly employed in a standard thumb position passage for cello.
Music stimulus performed by participants.
All performances were recorded in one of two studios that were commonly used to make audio recordings of solo performers and small ensembles. Participants were individually brought into the recording studio and provided time to warm-up, tune, practice the excerpt, and get accommodated to the room's acoustics. A metronome was used to provide the indicated tempo for the excerpt to be performed (72 beats per minute), but was turned off during the actual recording session. Recording equipment included a Samson O1U digital microphone and a computer. Digital recordings were made with16-bit resolution and a 44.1 KHz sampling rate. Each digital recording was analyzed with the software program Praat (Boersma & Weenink, 2010).
Results
The following dependent variables were examined: rate of vibrato (expressed in Hz), width of vibrato (expressed in cents), and the difference between non-vibrated versus vibrated tones (expressed in cents). Reliability analysis based on 20 percent of total observations showed an agreement rate of 91 percent. Reliability criteria for agreement between observers were the following: rate of vibrato (± 0.1 Hz), width of vibrato (± 0.5 cents for all positions), and pitch levels of both non-vibrated and vibrated tones (± 0.5 cents). Independent variables included the level of training (high school and university level cellists), playing position of the vibrato (first position, fourth position, and thumb position), and the finger used to vibrate (first finger, second finger, third finger, and fourth finger). Mixed-design repeated-measures analysis of variance tests were used to examine the rate of vibrato, width of vibrato, and the difference between non-vibrated versus vibrated tones. Since common cello technique does not use the fourth finger in thumb position, only the first finger, second finger, and third finger were compared in the statistical analysis. Descriptive statistics were provided for the fourth finger.
Vibrato rate
Using a repeated-measures ANOVA with the Greenhouse-Geisser adjustment because of a violation of sphericity, a significant main effect was found for playing position, F (1.35, 37.86) = 7.74, p < .01, partial η2 = .22. The slowest mean rate of vibrato occurred in first position. Post hoc comparisons with the Bonferroni correction revealed significant differences for vibrato rates between the first and fourth positions (p < .001) and the first and thumb positions (p < .05). No significant difference was revealed between rates in fourth and thumb positions. Playing position mean vibrato rates ranged from 5.07 Hz (first position) to 5.33 Hz (fourth and thumb positions). Standard deviations for vibrato rate in each playing position were similar and ranged from .71 Hz (fourth position) to .78 Hz (first position).
No significant differences in rates were revealed for vibrato finger and level of training. Vibrato rates of university (M = 5.36 Hz, SD = .46 Hz) and high school (M = 5.11 Hz, SD = .94 Hz) cellists were similar. The mean vibrato rate for each finger ranged from 5.20 Hz to 5.32 Hz with standard deviations between .72 Hz and .79 Hz. All mean vibrato rates and standard deviations are shown in Table 1. All two- and three-way interactions were not significant.
Means (in Hz) and Standard Deviations of Vibrato Rates
Note: The fourth finger was not included in statistical analysis due to its lack of use in standard thumb position. Only the first, second, and third fingers were used for statistical comparisons.
Vibrato width
Vibrato widths were analyzed with a repeated-measures ANOVA using the Greenhouse-Geisser adjustment due to a violation of sphericity. A significant main effect was found for playing position, F (1.34, 37.56) = 66.45, p < .001, partial η2 = .70. Participants’ vibrato width increased as they moved down the fingerboard (closer to the bridge) to perform in higher playing positions. Mean vibrato widths ranged from 23.13 cents in first position to 43.09 cents in thumb position. Standard deviations for vibrato widths also increased as participants performed in higher sounding playing positions. Post hoc comparisons with the Bonferroni correction revealed significant differences between all positions for vibrato width: first and fourth positions (p < .001), first and thumb positions (p < .001), and fourth and thumb positions (p < .001).
No significant main effects were revealed for vibrato finger and level of training. High school cellists (33.13 cents) had a slightly larger mean vibrato width than university performers (31.90 cents). Analysis revealed that the first finger, second finger, and third finger had similar mean vibrato widths that ranged from 32.70 cents to 34.30 cents. Although not used in thumb position, the fourth finger had the smallest mean vibrato width at 27.01 cents. All two- and three-way interactions were not significant. Mean vibrato widths and standard deviations are reported in Table 2.
Means (in cents) and Standard Deviations of Vibrato Widths
Note: The fourth finger was not included in statistical analysis due to its lack of use in standard thumb position. Only the first, second, and third fingers were used for statistical comparisons.
Non-vibrated versus vibrated tones
Due to a violation of sphericity, a repeated measures ANOVA with the Greenhouse-Geisser adjustment was used to analyze non-vibrated versus vibrated tones. The ANOVA revealed a significant two-way interaction between vibrato finger and level of training, F (1.83, 51.10) = 6.33, p < .01, partial η2 = .18. That interaction is shown in Figure 2. University level cellists’ vibrated tones with the first (-.74 cents) and third (-.05 cents) fingers sounded lower (flat) than the non-vibrated tones, but the second (1.84 cents) finger's vibrated tones were higher (sharp) than the non-vibrated. The opposite trends were found for high school cellists. Vibrated pitches with the first (1.79 cents) and third (.71 cents) fingers sounded higher (sharp) than the non-vibrated pitches, but the second finger's vibrated tones (-1.54 cents) were lower (flat) than the non-vibrated pitches. All other interactions were not significant.
Significant two-way interaction between vibrato finger and level of training for non-vibrated and vibrated tones.
A significant main effect was found for playing position, F (1.76, 49.32) = 9.94, p < .001, partial η2 = .26. Post hoc comparisons revealed a significant difference between first and thumb positions (p < .01) in vibrated and non-vibrated tones. No differences were revealed when comparing the first and fourth positions and the fourth and thumb positions. In the first and fourth positions, performers’ mean vibrated tones were minimally higher (sharp) in pitch than non-vibrated tones: first position (2.10 cents) and fourth position (.84 cents). An examination of the difference between mean non-vibrated versus mean vibrated tones in thumb position revealed that vibrated tones in thumb position occurred 1.94 cents below (flat) the non-vibrated tones.
No significant main effects for vibrato finger and level of training were found between the frequencies of vibrated and non-vibrated tones. Differences were minimal when considering level of training (see Table 3). Both high school (.69 cents) and university cellists’ (.38 cents) vibrated tones occurred only slightly above (sharp) the non-vibrated tones. The difference between non-vibrated versus vibrated tones varied as performers changed playing positions. An analysis of descriptive data for all fingers revealed that vibrated tones occurred slightly higher (sharp) in pitch (between .15 cents and 1.44 cents) than the non-vibrated tones. Mean differences and standard deviations for non-vibrated versus vibrated tones are shown in Table 3.
Mean Differences (in cents) and Standard Deviations between Non-vibrated and Vibrated Tones
Note: The fourth finger was not included in statistical analysis due to its lack of use in standard thumb position. Only the first, second, and third fingers were used for statistical comparisons. Positive numbers represent vibrated tones performed higher (sharp) than the non-vibrated tones. Negative numbers represent vibrated tones performed lower (flat) than the non-vibrated tones.
Discussion
In this study of cellists’ vibrato, the overall mean vibrato rate was 5.24 oscillation cycles per second (Hz). A comparison of these results to previous investigations corroborates that cellists’ vibrato is slower than violinists and violists (Allen, Geringer, & MacLeod, 2009; Cheslock, 1931; Fletcher & Sanders, 1967; Geringer & Allen, 2004; Hollinshead, 1932; MacLeod, 2008, 2010; Mellody & Wakefield, 2000; Seashore, 1967; Small, 1937), but faster than double bassists’ vibrato (Allen, 2010; Mick, 2011; Papich & Rainbow, 1974). Geringer and Allen (2004) found the mean vibrato rate in first position for high school and university level cellists was 5.43 Hz. Cellists’ first position vibrato in the current study was 5.07 Hz. Supporting previous research that found increased vibrato rates in higher positions (closer to the bridge) for an artist-level violinist (Allen, Geringer, & MacLeod, 2009), solo artists (MacLeod, 2010), and high school and university level violinists and violists (MacLeod, 2008), cellists’ mean vibrato rate in the current study increased when performing in fourth and thumb positions.
A comparison of the individual finger's vibrato rates yielded some interesting trends. However, it should be remembered that these differences were not significant. The vibrato rates of the four fingers were similar, but possible trends were identified: first finger 5.21 Hz, second finger 5.23 Hz, third finger 5.20 Hz, and fourth finger 5.32 Hz. Cellists in the current study vibrated their fourth finger at a slightly faster rate than their first, second, and third fingers, and that result also occurred in Geringer and Allen (2004).
While vibrato width has been investigated in previous research, results from this study add to the knowledge base. The overall mean vibrato width for participants in this study was 32.51 cents. When considering the mean vibrato width from first position only in this study, participants’ mean vibrato width was only slightly larger than in Geringer and Allen (2004) who found that high school and university level cellists’ mean vibrato width in first position was 26.00 cents. Similarly, Papich and Rainbow (1974, 1975) reported mean vibrato widths that were narrower than the results found in this study. The overall mean vibrato width noted in this study was much smaller than that found in McDonald's (1998) examination of cello artists’ vibrato while performing J.S. Bach's cello suites. Mean vibrato widths revealed in this study were also smaller than those reported for artist level violinists (Hollinshead, 1932; MacLeod, 2010; Reger, 1932; Small, 1937). Individual finger vibrato width was also examined in this study, and mean vibrato widths were similar for the first, second, and third fingers: first finger (32.70 cents), second finger (34.20 cents), and third finger (34.30 cents). The fourth finger's mean vibrato width was slightly narrower at 27.01 cents, and that difference may have occurred since the fourth finger is not used in thumb position. Additional analysis of each finger in the three playing positions examined in this study did not reveal any consistent trends.
The difference in vibrato widths discussed above could be directly related to the variation in the physical distance on the examined instruments. Another factor that could impact the comparison of results was the inclusion of other independent variables (tempo, dynamics, pitch register, and playing position) in prior investigations. Variation in reported vibrato widths may also be influenced by the increased precision of recent computer software.
Many string pedagogues have discussed the physical motion and teaching of vibrato. Some string pedagogues believe that vibrato motions should cause the pitch to oscillate evenly above and below the intended pitch; while others believe that oscillations should occur exclusively above (sharp) or below (flat). In the current study, the mean frequency of non-vibrated and vibrated tones were compared to each other. Cellists’ vibrato oscillation patterns in the current study occurred both above and below the note, and the performers’ overall mean vibrato tone sounded just above (sharper) the non-vibrated tone by less than one cent (0.53 cents), virtually the same. Additional examination of the non-vibrated and vibrated tones in multiple playing positions indicated that participants’ vibrated tones occurred slightly above the non-vibrated tones in the first (2.10 cents) and fourth (0.84 cents) positions, but slightly below (flat) the non-vibrated tones in thumb position (-1.94 cents). That small difference in mean vibrated tone frequency by position may result from necessary left hand techniques for cellists. The proper left hand technique in first position and fourth position keeps fingers in almost a perpendicular angle to the string or at a minimal angle back toward the scroll. In thumb position, cellists’ fingers tend to lean back toward the scroll at a more severe angle than other playing positions. As a result of the various angles used by the left hand, it is possible that cellists’ vibrato in thumb position may tend to occur more below the conceived pitch. An interaction between level of performer and vibrato finger was found in the current study with regard to differences between vibrated and non-vibrated tones. Future researchers may wish to investigate possible reasons for the interaction and possibly include vibrato pitch tendencies of professional cellists.
String pedagogues identify evenness as a characteristic of good vibrato. Music educators should consider the influence of instrument and playing position during the instruction of vibrato in the heterogeneous string class. Empirical findings show that the vibrato rates and widths of violinists, violists, cellists, and double bassists are different. To teach the varying vibrato rates for each instrument, music educators might consider modifying their daily lessons. Rather than teaching vibrato in a heterogeneous setting, string teachers may wish to instruct students in homogeneous groups or individual lessons. Teaching vibrato in homogeneous groups allows instructors to help control the vibrato rate being performed by the students. Future researchers may wish to examine the effects of individual, homogeneous, and heterogeneous vibrato instruction on student learning and performance.
Educators may also improve vibrato consistency by teaching students that vibrato width and rate increase as performers play in higher positions (closer to the bridge). To help students’ produce an even vibrato, instructors can create exercises that focus on the rate and width of vibrato in the various playing positions. Understanding and teaching vibrato idiosyncrasies across positions may improve students’ performance abilities both in the short- and long-term. Similar to previous investigations that compared high school and university musicians’ vibrato (Geringer & Allen, 2004; Geringer et al., 2005; MacLeod, 2008), no consistent differences in vibrato characteristics were revealed in the current study. Since comparable results were found in this study, researchers might consider combining high school and university level populations for future investigations of vibrato. However, future researchers might also include middle school students’ vibrato for comparison. Researchers may also wish to analyze cellists’ vibrato in multiple musical contexts such as scales, etudes, orchestral repertoire, and solo repertoire to identify possible differences.