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Analysis of Viola Vibrato Waveforms Katherine Hagen 1,3, Kathleen Horvath 2, and Gary Chottiner 1 1 Department of Physics, 2 Department of Music, Case.

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Presentation on theme: "Analysis of Viola Vibrato Waveforms Katherine Hagen 1,3, Kathleen Horvath 2, and Gary Chottiner 1 1 Department of Physics, 2 Department of Music, Case."— Presentation transcript:

1 Analysis of Viola Vibrato Waveforms Katherine Hagen 1,3, Kathleen Horvath 2, and Gary Chottiner 1 1 Department of Physics, 2 Department of Music, Case Western Reserve University; 3 Department of Viola, Cleveland Institute of Music METHODS Several (n = 14) CIM viola students were recorded using a Marantz CDR300 digital recorder, two Rode microphones, and three Canon video cameras in CIM’s Kulas Center for International Music Education studio, which is soundproof and nonresonant (S/N  50 dB). Each subject played a seven-note sequence nine times with prescribed fingerings and bowings. Instructions were given each time regarding vibrato speed (slow or fast) and width (wide or narrow) or an emotion to convey (happiness, sadness, tenderness, or anger). Each subject also completed a survey about his or her musical history, instrument make and size, and vibrato ideals. Later, audio recordings were made of selected subjects (n = 4) playing vibrato with selected speeds/widths and emotions on each other’s instruments and bows; for this session, an Edirol R-09 digital recorder was used in a nonresonant CIM practice studio (S/N  25 dB ). Single-note vibrato samples, each about 2-3 seconds long, were analyzed in MATLAB. A Discrete Fourier Transform algorithm with frequency interpolation was used to calculate and plot the power spectral density (PSD) vs. frequency vs. time of each sample (see three-dimensional plot above). The frequencies associated with PSD peaks near the fundamental and first few harmonics were then determined and plotted vs. time in Origin. RESULTS AND CONCLUSIONS Peak-frequency plots generated of a representative sample of single-note tracks fell into one or more of the three categories described above. Category 1 waveforms (and, in general, waveforms free from resonance effects) were often observed when subjects were instructed to play with narrow vibrato or to communicate sadness. In these contexts, a small range of frequencies—and likely a soft dynamic and a bow contact point far from the bridge—ensured that resonances in subjects’ instruments were not easily excited and that symmetric finger rolls were directly translated into pitch oscillations. Category 2’s sharp extrema were attributed in [3] to resonance effects in instruments which caused sudden phase shifts at specific frequencies near the fundamental. However, the absence of corresponding resonances near the harmonics “smoothed” the vibrato sound a bit, as illustrated in Fig. 4 [3]. These waveforms were seen in subjects’ wide, happy, and angry vibratos—ones with large frequency ranges, loud dynamics, and bow contact points near the bridge, all of which provided ample opportunity for resonances to be excited. Category 3’s asymmetries frequently appeared in combination with Category 2’s resonance effects and occurred often on naturally resonant notes (those with a matching open string). Vibrato exercises described by some viola pedagogues suggest asymmetrical finger movements [5], but the relative effects of finger movements and instrument resonances are still unclear. References [1]Courtesy commons.wikimedia.org. [2]Geringer, J.M. and M.L. Allen. “An analysis of vibrato among high school and university violin and cello students.” J. Res. Mus. Ed. 52, 167-178 (2004). [3]Mellody, M. and G.H. Wakefield. “The Time-Frequency Characteristics of Violin Vibrato: Modal Distribution Analysis and Synthesis.” J. Acoust. Soc. Am. 107, 598 611 (2000). [4]Brown, J., and K. Vaughn. “Pitch Center of String Instrument Vibrato Tones.” J. Acoust. Soc. Am. 100, 1728-1735 (1996). [5]Castleman, H. “Flexibility of Vibrato: Controlling Width and Speed.” J. Am. Viola Soc. 17, 21-27 (2001). Acknowledgements Thanks to my advisors for their expertise and guidance; to Greg Howe and the CIM Distance Learning/Kulas Center for International Music Education staff for the use of their studio; to CIM Marketing for logo assistance; to my viola teachers, Jeffrey Irvine and Lynne Ramsey, for their inspiration and patience; and especially to my CIM colleagues who generously donated their time as research subjects. For Further Information Please contact Katherine Hagen at katherine.hagen@case.edu. ABSTRACT Vibrato is a series of expressive pitch oscillations produced by left hand and arm movements on the viola. In this project, the characteristics of viola vibrato waveforms in various technical and musical contexts were investigated. Several viola majors at the Cleveland Institute of Music were audio- and video- recorded; plots of selected notes’ peak frequencies vs. time near their fundamentals and harmonics were generated and characterized. After additional recording of selected subjects playing on each other’s instruments, it was determined that vibrato waveforms are affected by resonance patterns in particular instruments as well as subjects’ physical vibrato motions. Figure 3. A plot of a violist playing G6 with vibrato (dotted line) and without (solid line) from Brown and Vaughn (1996) [4]. The waveform’s upswings are slightly slower than its downswings. Figure 2. Plot of a cellist playing E3 vibrato and nonvibrato from Geringer and Allen (2004) [2]. The vibrato waveform is approximately symmetric and resembles a sine wave. Figure 4. A plot of a violinist’s vibrato on D5 from Mellody and Wakefield (2000) [3], including peak frequencies near the fundamental (dotted line) and a scaled average of the harmonics (solid line). The fundamental-frequency waveform resembles a sine wave but has sharp discontinuities at its minima. Vibrato is one of the least standardized techniques in string playing. Neglected for centuries by pedagogues who felt it must come straight from the soul, vibrato is taught through exercises today, but teachers’ ideas regarding its execution and musical role vary widely. Scientists have discovered that viola vibrato has an amplitude of about one quarter tone and a frequency of about 5-7 Hz, but other characteristics remain ambiguous. Plots of vibrato waveforms in published studies indicate a wide range of shapes are possible: Figs. 2-4 illustrate three of them. None of these studies were explicitly investigating the characteristics of waveform shap- INTRODUCTION CATEGORY 1. The peak-frequency waveform near the fundamental resembled a symmetric sine or triangle wave. Left plot: scaled peak frequencies near the first four partials (in black, red, green, and blue, respectively) of Subject 14 playing B4 “with vibrato” follow a single waveform closely. Right plot: the peak frequencies near the fundamental with a sine wave fit. The waveform’s slopes generally match the sine wave’s; small inconsistencies at extrema varied with window size and were attributed to noise. CATEGORY 2. The peak-frequency waveform near the fundamental had large spikes in the positive and/or negative direction. Left plot: scaled peak frequencies near the first four partials (black, red, green, and blue, respectively) of Subject 6 playing A4 “with narrow, slow vibrato.” Right plot: Subject 5 playing A4 “with vibrato” on Subject 6’s viola. The spikes in both plots originate near 440 and 445 Hz, indicating that they are a result of the resonance characteristics of Subject 6’s viola body and/or strings. CATEGORY 3. The peak-frequency waveform near the fundamental was asymmetric. Some samples also had resonance effects (see Category 2). Left plot: the first four partials (black, red, green, and blue, respectively) of Subject 9 playing B4 “with vibrato.” The vibrato upswings (pitch-raising motions) appear to be faster than the downswings (pitch- lowering motions). Right plot: the first four partials of Subject 4 playing B4 “with vibrato;” the upswings are slower than the downswings. INITIAL PLOTTING. A three-dimensional plot of Subject 4 playing B4 “with vibrato.” The first four partials are shown. The frequencies associated with power spectral density (PSD) peaks at each time were saved, scaled, and plotted on two-dimensional plots. es, and it is unclear whether the differences in the plots are a result of subjects’ technical skills, instrument characteristics, the acoustics of the room in which Figure 1. The viola (bottom) is slightly larger than its better-known cousin, the violin (top) [1]. recordings were made, or differences in pitch-detection algorithms. Goals of this project are: - To quantify the differences between CIM violists’ vibrato waveforms, with respect to instruments, given instructions, and vibrato techniques and ideals. - To explain the observed waveforms by comparing them to those published in scientific studies and/or described by pedagogues. Time (sec) Frequency (Hz) Magnitude of PSD (Volts 2 )


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