Computer-based software named the Tuning Perception Test (TPT) was devel- ... software for measuring orchestral string players' instrument tuning skills.
JMTE 7 (1) pp. 5–21 Intellect Limited 2014
Journal of Music, Technology & Education Volume 7 Number 1 © 2014 Intellect Ltd Article. English language. doi: 10.1386/jmte.7.1.5_1
Michael T. Hopkins University of Michigan
Pilot-testing of new software for measuring string players’ instrument tuning skills Abstract
Keywords
Computer-based software named the Tuning Perception Test (TPT) was developed using Processing, a free, open-source programming language. The specific pitch perception skills examined by the software included unison pitch-matching and harmonic P5 interval tuning. A pilot-test established reliability for the TPT and gathered preliminary data on string instrumentalists’ tuning accuracy at varied school levels (fifth, seventh, ninth, eleventh-grade, university music majors). Reliability was very strong for pitch-matching items (α=0.90) and for the perfect fifth tuning items (α=0.91). Pitch-matching and P5 tuning accuracy improved consistently as school level increased, suggesting that refinement of pitch perception occurs gradually over time, with beginning and intermediate string instrumentalists requiring training in pitch-matching and interval tuning to develop the pitch perception skills necessary to accurately tune a stringed instrument. Participants demonstrated a tendency towards tuning flat, with tuning accuracy decreasing at lower fundamental frequencies.
software development measurement pitch matching interval pitch perception tuning stringed instrument
Introduction The purpose of this study was to develop and pilot-test computer-based software for measuring orchestral string players’ instrument tuning skills. Within the field of music education, very little attention has been devoted 5
Michael T. Hopkins
to understanding string players’ acquisition of tuning skills. Tuning has been described as a fundamental, important and serious skill that string players must master (Fischbach 2003), and teaching young string players independent tuning skills is critical to the success of an orchestra (Hamann et al. 2006). Due to the complex nature of tuning string instruments in an ensemble setting, the development of independent tuning skills in youth ensembles is a process that slowly unfolds over time in several stages (Alexander 2008). There are many factors that affect students’ ability to tune their instruments accurately and confidently, including instructional setting, classroom procedures and student ability levels (Hamann et al. 2002). Among these factors is the ability to accurately perceive unisons and P5 intervals. The tuning of a stringed instrument is considered a rudimentary skill (Platt and Racine 1985), and yet close examination reveals a complex process that involves several distinct pitch perception tasks. The first step involves tuning one string to a reference pitch, typically A440. This procedure is either a unison pitch-matching task (violinists, violists, cellists using harmonic) or the tuning of an octave interval (cellists using open A string, bassists using harmonic). For violinists, violists and cellists, step two typically involves checking the D string to the A string to determine whether the two strings are close enough in tune to fit within the ‘category’ of a perfect fifth (P5). Categorical perception is said to occur when signals that vary continuously are assigned to a few discrete categories by a perceiver (Zatorre and Halpern 1979). The pitch is then adjusted if necessary and verified to be within the category of a P5. The third step is to engage in a fine pitch discrimination task to determine whether the P5 is mistuned. Mistuned intervals are characterized by small frequency differences between those harmonics that coincide completely in pure intervals (Vos 1982). The interference of these non-coinciding harmonics gives rise to the perception of beats or roughness (Helmholtz 1912). String instrumentalists often listen for the disappearance of the beats as they manipulate a peg or fine tuner, then repeat steps two and three for the other strings (e.g., tuning the G string to the D string, E string to the A string, the C string to the G string) (Alexander 2008). Despite the apparent rudimentary nature of stringed instrument tuning, primary and lower secondary classroom string teachers in the United States reported that the average amount of time required for their students to develop tuning independence was 4.5 years (Hopkins 2013). The majority of the teachers (62.5%) reported that they did not believe their youngest string students (most commonly fourth or fifth-graders) had yet developed the aural skills necessary for tuning a stringed instrument, but they also reported they did not formally assess pitch matching or P5 perception skills in their classes. Intrigued by these findings, this author decided to develop a software assessment tool designed to measure the aural skills necessary for tuning a stringed instrument. A review of literature revealed that researchers in the varied disciplines of psychology, psychoacoustics and music education have examined human perception of isolated musical intervals for over 100 years using available technological tools. An interesting aspect of this cross-disciplinary body of research is the variety of devices and methodological approaches used to better understand pitch perception. Researchers in psychology and psychoacoustics have examined perception of musical intervals with professional musicians and musically untrained adults using the ‘method of adjustment’ (MOA) system (Burns and Ward 1978). Experiments of this type present participants with a fixed reference tone and a second tone that is manually adjusted to form an interval with the fixed tone. The adjustment is typically made using a lever,
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slider or knob controller. MOA perception tasks involving pitch-matching and P5 intervals can be considered analogous to the tuning of a stringed instrument. The findings from MOA studies have revealed considerable subjectivity regarding the tuning of isolated unison, octave and P5 intervals among professional musicians. In an early study, H. Moran and C. C. Pratt (1926) used a pair of tone variators developed by Stern to measure interval perception. The three musical experts they studied tuned harmonic P5s with a mean error of 14.8 cents. W. D. Ward (1954) examined professional musicians’ interval perception using a testing circuit consisting of two oscillators, a two-channel electronic switch, amplifiers, attenuators, impedance-matching networks, on-off switches and a pair of earphones. The professional musicians tuned octave intervals composed of sinusoidal tones with a mean error of 10 cents. J. Elliot et al. (1987) generated intervals of simple and complex tones using a Yamaha CX5M Music Computer (Duesenberry 1985). They found that musically experienced participants tuned harmonic P5s with a mean error of 11.6 cents, while inexperienced participants tuned with a mean error of 20.2 cents. Within the field of music education, researchers have used synthesizers to examine wind instrumentalists’ and singers’ pitch-matching of unison intervals using MOA tasks. C. Yarbrough et al. (1995) asked elementary and middle school wind instrumentalists to match a reference tone by turning a pitch control knob on a Casio MT-31 keyboard and found that research participants tuned with a mean error ranging from 22.90 cents for students in their first year of instruction to 13.67 cents for students in their fourth year of instruction. They also found that when pitch-matching, approaching the reference pitch from above resulted in more sharp responses and approaching it from below resulted in more flat responses. In a later study, Yarbrough et al. (1997) found that high school wind instrumentalists tuned with a mean error of 6.86 when completing a similar task. S. M. Demorest (2001) examined the pitchmatching perception and production of seventh, eighth and ninth-grade male singers using a pitch perception task very similar to that of Yarbrough et al. Demorest found that singers who consistently matched pitch correctly with their voices tuned with a mean error of 32.12 cents on a synthesizer MOA task. Inconsistent pitch-matching singers tuned with a mean error of 58.50 cents when pitch-matching by adjusting the synthesizer. Over the past decade researchers have developed MOA perception tasks using computer software. S. M. Demorest and A. Clements (2007) developed a Pitch-Matching Perception Test (PMPT) to examine the pitch-matching perception skills of adolescent boys in grades 6–9. The PMPT was a method of adjustment test that was designed to ‘replicate as closely as possible the act of “matching” a pitch perceptually rather than discriminating between pitches or fine-tuning to a pitch’ (2007: 195). The PMPT played a continuously sounding reference pitch, followed one second later by a comparison pitch randomly set a tritone above or below the reference pitch. Students were asked to match pitch by moving an on-screen slider. The comparison tone moved only by semitones, and so there was no need to fine-tune the pitches. They found a significant difference in perceptual ability among adolescent boys based on vocal pitch-matching ability, with uncertain singers scoring significantly lower on a pitch perception test than inconsistent or certain singers. Using currently available technology, computer-based MOA tests can be developed to assess a variety of pitch perception skills. The MOA approach seems particularly well suited for understanding the perceptual processes used while tuning a stringed instrument. While a considerable amount of
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research in string education has focused on intonation accuracy in instrumental performance (Geringer 1978; Kantorski 1986; Salzberg 1980; Salzberg and Salzberg 1981; Smith 1995; Sogin 1989; Yarbrough and Ballard 1990), very few studies have examined the development of the pitch perception skills needed for accurate instrument tuning. Researchers have compared students’ perceived tuning ability to actual tuning ability (Hamann et al. 2006), and compared tuning accuracy using a variety of reference pitch stimuli (Alexander 2011; Geringer and Witt 1985; Hamann et al. 2006). No studies could be found, however, that examined the pitch perception of string instrumentalists at varied school levels using an MOA task. A better understanding of string instrumentalists’ tuning perception development could lead to improved pedagogy and tools for facilitating student growth in pitch perception, reducing the amount of time required to acquire tuning independence, and ultimately reducing the amount of instructional time that classroom string teachers devote to the tuning process at the beginning of rehearsals. The software-based test developed in this study was named the Tuning Perception Test (TPT). The TPT was developed based on previous research (Demorest 2001; Demorest and Clements 2007; Yarbrough et al. 1995; Yarbrough et al. 1997) to be an ‘active’ measure of perception, analogous in precision to the tuning of a stringed instrument. The specific pitch perception skills examined by the software included unison pitch-matching and harmonic P5 interval tuning. A pilot test was designed to provide reliability data for the TPT and to gather preliminary data for answering the following four questions: (1) How accurately can string instrumentalists at varied school levels (fifth, seventh, ninth, eleventh-grade, university music majors) perceive unisons and P5 intervals using the TPT? (2) Are there tendencies towards sharpness or flatness when matching pitches or tuning P5 intervals with the TPT and do these tendencies change with school level? (3) How is perceptual accuracy affected by the fundamental frequency of the reference tone and does this accuracy change based on school level when using the TPT? (4) Is there a relationship between tuning accuracy as measured by the TPT and the amount of time spent tuning?
Method Development of the tuning perception test The TPT was designed by the researcher and developed with the help of a research assistant using Processing, a free, open-source programming language, development environment and online community (processing.org). The TPT was designed to run as a stand-alone application on Windows 7 and Macintosh 10.5 operating systems. The TPT was a two-part test. Part One contained 24 pitch-matching items that represented the twelve open string pitches of the four orchestral stringed instruments (E5, A4, D4, A3, G3, D3, C3, G2, D2, C2, A1, E1). For each item, participants were aurally presented with a reference tone (e.g., A4, with a fundamental frequency of 440.0 Hz). After three seconds, a mistuned tone was aurally presented to participants, while the reference tone continued to play, forming a harmonic microtonal interval similar to that typically heard when tuning a stringed instrument to a reference tone. Each of the aforementioned twelve open string pitches was presented sharp and each was presented flat, comprising the 24 items. Part Two contained fourteen P5 items that represented all of the P5 open string combinations of the violin, viola and cello (E5-A4, A4-D4, D4-G3,
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A3-D3, G3-C3, D3-G2, G2-C2). Items representing double bass strings were not included because the bass is tuned in perfect fourths and bassists most commonly tune using unison pitch-matching of harmonics. For P5 items participants were presented with the higher frequency tone of the P5 interval as the reference tone (the exception to this was E5-A4, in which the A4 was the reference tone, because the violin E string is typically tuned to the A string). After three seconds, the other tone of the P5 interval was aurally presented as the tuning tone to participants, while the reference tone continued to play. Each of the aforementioned seven P5 intervals was presented with the mistuned tone tuned sharp, and each was presented with the mistuned tone tuned flat, comprising the fourteen items. For each item, the computer screen displayed a horizontal slider. The initial position of the slider on the screen was centred. The participants’ task was to use a computer mouse to manipulate the slider through the action of clicking and dragging, and match the mistuned tone to the reference tone in items 1–24, or to tune the P5 interval in items 25–38. Moving the slider to the left lowered the frequency of the mistuned tone and moving the slider to the right raised the frequency of the tone. The presentation sequence of the items within parts one and two was randomized by the researcher to reduce the possibility of an order effect. The mistuned tones were randomized by the researcher in the range of ± 18 to 50 cents from their nominal fundamental frequencies and so participants could not use visual cues from the software interface as to when each item was in tune (i.e., the slider needed to be moved to a different on-screen location for each item). The range of adjustment of the slider was limited to ± ½ semitone from the starting fundamental frequency for each item so that participants’ ‘categorical’ perception would not be affected (i.e., it was not possible for participants to tune P5 intervals to a tritone or minor 6th). A screenshot of the TPT is presented in Figure 1. All items were presented using a sawtooth wave timbre. The sawtooth waveform was chosen because it contains all harmonic overtones and closely
Figure 1: TPT screenshot.
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resembles the overtone content of a bowed string. Previous research has shown pitch discrimination and tuning accuracy to be better for complex than for pure tones (Spiegel and Watson 1984; Platt and Racine 1985). The sawtooth tones were generated by Minim, an audio library developed for the Processing environment (code.compartmental.net/tools/minim/). A complete list of TPT items for Part One items, including the presentation order and the amount of mistuning, is presented in Table 1. A list of Part Two P5 tuning items is presented in Table 2. The TPT was designed to track the amount of time the user spent on each item and to record the fundamental frequency (Hz) of a user’s response to each item. Before the pilot test the TPT was debugged by the researcher and research assistant on a variety of computers to ensure consistency of users’ interaction with the software and to check that the software was writing the data file correctly. The content validity of the TPT for measuring students’ perceptual ability to match pitch and tune P5 intervals was established by asking a panel of three experts in music education to use the software and answer questions on
Pitch Matching Item E5 E5 A4 A4 D4 D4 A3 A3 G3 G3 D3 D3 C3 C3 G2 G2 D2 D2 C2 C2 A1 A1 E1 E1
Direction of mistuning
Amount of mistuning in cents
Frequency of mistuned pitch* (Hz)
Frequency of reference pitch* (Hz)
TPT Item Presentation Order
sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat
+ 47 – 28 + 23 – 48 + 27 – 21 + 37 – 30 + 39 – 36 + 26 – 20 + 34 – 46 + 36 – 22 + 22 – 43 + 42 – 40 + 28 – 24 + 33 – 49
677.4 648.6 445.8 428.0 298.3 290.1 224.7 216.2 200.5 192.0 149.1 145.1 133.4 127.4 100.1 95.8 74.3 71.6 67.0 63.9 55.9 54.2 42.0 40.05
659.3 659.3 440.0 440.0 293.7 293.7 220.0 220.0 196.0 196.0 146.8 146.8 130.8 130.8 98.0 98.0 73.4 73.4 65.4 65.4 55.0 55.0 41.2 41.2
6 16 9 1 8 5 4 15 7 19 14 20 17 12 11 3 21 23 22 10 18 2 24 13
Note: *All items presented using sawtooth waveform. Frequency number listed is the fundamental frequency of the complex tone.
Table 1: TPT Part One Pitch-Matching Items.
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P5 Interval Item
Mistuned pitch name
A4 – E5 A4 – E5 A4 – D4 A4 – D4 D4 – G3 D4 – G3 A3 – D3 A3 – D3 G3 – C3 G3 – C3 D3 – G2 D3 – G2 G2 – C2 G2 – C2
E5 E5 D4 D4 G3 G3 D3 D3 C3 C3 G2 G2 C2 C2
Direction of mistuning
Amount of mistuning in cents
Frequency of mistuned pitch* (Hz)
sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat sharp flat
+ 45 – 30 + 29 – 19 + 41 – 34 + 28 – 18 + 36 – 44 + 38 – 20 + 44 – 38
677.4 648.6 298.3 290.1 200.5 192.0 149.1 145.1 133.4 127.4 100.1 95.8 67.0 63.9
Frequency TPT Item of reference Presentation pitch* (Hz) Order 440.0 440.0 440.0 440.0 293.7 293.7 220.0 220.0 196.0 196.0 146.8 146.8 98.0 98.0
27 33 29 25 37 32 34 35 30 31 26 38 36 28
Note: *All items presented using sawtooth waveform. Frequency number listed is the fundamental frequency of the complex tone.
Table 2: TPT Part Two P5 Tuning Items. the efficacy of the instrument. All of the panellists were experienced researchers with strong backgrounds in the measurement of musical skills. The panel agreed that the TPT software was easy to use, the task was perceptually analogous to what string students are expected to do when tuning and was a useful measure of the aural skills needed to tune a string instrument.
Pilot-test participants The participants for the pilot test (N=130) were string instrumentalists as follows: fifth-grade students (n=48) enrolled in string classes at two elementary schools, seventh-grade students (n=32) enrolled at one middle school, ninth-grade students (n=23) and eleventh-grade students (n=13) enrolled in orchestra at one high school, and music majors (n=14) enrolled at one university. All participants lived in a medium-sized city in the Midwestern United States. The fifth, seventh, ninth and eleventh-graders were all from the same school district. The fifth-grade students had been learning to play stringed instruments in heterogeneous string classes for approximately four months, with 60 minutes of instructional time per week. The fifth-grade teacher had not begun teaching the fifth-grade students how to tune their own instruments. The teacher was responsible for tuning all the fifth-graders’ instruments at the beginning of class. The seventh-grade students were in the process of learning to tune their own instruments, but still required considerable assistance from their teacher. The high school orchestra director reported that some of the ninth-graders needed assistance in problematic tuning situations (e.g., if the pegs have all slipped due to changes in temperature or humidity) but the eleventh-graders
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never required any assistance. The university music majors had assumed complete responsibility for tuning their own instruments, and for the purposes of this study, were considered tuning ‘experts’. The sample was 66% female and 34% male. Participants were 50% White, 13% Black or African American, 34% Asian and 3% Hispanic or Latino. The instruments played by the participants were violin (n=67), viola (n=25), violoncello (n=33) and contrabass (n=5). Data were collected to determine whether any of the elementary, middle or high school participants had begun instruction before the fifth grade or received private instruction. A small number of participants had received private instruction on their instruments before fifth grade – two eleventhgraders, four ninth-graders, four seventh-graders and one fifth-grader. The dataset was analysed including and excluding those participants and no significant differences were found on within-group or between-group comparisons. Therefore, the data from those participants were included in the analysis to increase the size of the sample and to reflect the diversity of musical backgrounds typically found in American public school orchestra programmes.
Pilot-test procedures Permission to conduct the pilot test was obtained from the university IRB, the district arts supervisor, the building principals and the participants’ parent or guardian. The elementary, middle and high school students were brought in groups to their schools’ computer labs to use the TPT software during their regular orchestra class meeting time. The researcher was present to provide instructions to the participants and troubleshoot any problems that occurred. All participants used headphones while working with the software. Volume output level was set to the computer’s midpoint level (eight on a sixteen-point loudness scale). Participants were instructed to sit alone at a computer and launch the software by double-clicking the TPT icon on the computer desktop. The software displayed an instruction screen containing the following text, ‘Part One: Pitch-matching. You will hear a first and second pitch. The second pitch will be out of tune. Use the computer mouse to drag the slider and make the second pitch match the first pitch. Click on the next button to begin’. Participants completed items 1–24 at their own pace. After completing items 1–24 participants were presented with an instruction screen that displayed the following text: Part 2: Interval Tuning. You will hear the pitches of two different strings. In example one, the first pitch will be the same as the A string. The second pitch will be the same as the D string but will be out of tune. Using your mouse, adjust the slider to make the D in tune with the A. Click on the next button to begin. Following the completion of items 25–38 the software displayed a final screen, thanking the participants for their participation. When participants clicked on the ‘Quit’ button, the software wrote the participants’ response data to a text file on the computer. The file data included the fundamental frequency (Hz) of a participant’s response for each item and the time (in seconds) a participant spent on each item. When participants finished, they were instructed to quietly leave the computer lab and return to their classroom. The university music majors worked with the software following the same procedure during individual appointments
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made with the researcher. The reliability of the TPT was determined using Cronbach’s α. Reliability was computed for the 24 pitch-matching items in Part One (α=0.90) and for the fourteen P5 items in Part Two (α=0.91).
Results Accuracy of pitch-matching and P5 interval tuning Participants’ accuracy in pitch-matching and P5 interval tuning was determined by calculating the cent value of the difference between their response and the reference tone. The cent value was calculated using the formula 1200×3.322038403 log10 (f2 / f1), where f2 is the fundamental frequency (Hz) of the participant’s response and f1 corresponds to the reference tone’s fundamental frequency listed in Table 1 for each item. Participants’ responses were negative (flat) or positive (sharp) values; therefore, absolute values were computed for each item in order to compare participants’ overall accuracy. The accuracy of participants’ P5 responses was computed based on pure P5s (i.e. an exact 3: 2 ratio with reference tone) rather than equal tempered P5s. The mean error in cents for the TPT test items was computed for the 24 pitch-matching items (M=16.3, SD=11.2) and the fourteen P5 items (M=19.3, SD = 18.0). A comparison of means for the five school levels is presented in Table 3.
95% CI* Part One – Pitch-matching (24 items)
n
Mean error† M (SD)
LL
UL
University Eleventh grade Ninth grade Seventh grade Fifth grade
14 13 23 32 48
3.5 (2.7) 6.5 (4.0) 12.2 (5.2) 14.4 (5.6) 25.9 (11.1)
2.0 4.0 10.0 12.4 22.7
5.1 8.9 14.4 16.5 29.2
Total
130
16.3 (11.2)
14.4
18.3
95% CI* Part Two – P5 Tuning (14 items)
Mean error† M (SD)
n
LL
UL
University Eleventh grade Ninth grade Seventh grade Fifth grade
14 13 23 32 48
3.2 (2.5) 6.5 (6.6) 9.0 (5.0) 12.8 (9.1) 36.6 (17.3)
1.8 2.5 6.8 9.5 31.5
4.6 10.5 11.2 16.1 41.6
Total
130
19.3 (18.0)
16.1
22.4
Note. *CI = Confidence Interval, LL = Lower Limit, UL = Upper Limit. † - Absolute values are presented for mean error.
Table 3: Tuning Perception Test (TPT) mean error in cents by school level.
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Pitch-matching
P5 Tuning
School level
n
U
p
n
U
p
University – Eleventh grade University – Ninth grade University – Seventh grade University – Fifth grade Eleventh grade – Ninth grade Eleventh grade – Seventh grade Eleventh grade – Fifth grade Ninth grade – Seventh grade Ninth grade – Fifth grade Seventh grade – Fifth grade
27 37 46 62 36 45 61 55 71 80
44.0 33.0 14.0 5.0 50.0 46.0 22.0 298.0 154.0 287.0
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