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May 1988

Volume 83, Issue S1, pp. S1-S122

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back to top Session BBB. Musical Acoustics V: General Topics in Musical Acoustics
Contributed Papers
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Dependence of vibrational modes of a handbell on thickness and added mass (A)

H. John Sathoff, Jiang Zhiqing, and Thomas D. Rossing

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S119-S119 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The vibrational modes of a large tuned handbell (G2) are compared with those of an untuned bell casting having the same shape but with twice the thickness. Doubling the wall thickness is found to raise the frequencies of the various modes by factors ranging from 1.4 to 2.4 (flat plate theory predicts a factor of 2 for all modes). Unlike the tuned G2 handbell, whose pitch coincides with the frequency of the fundamental mode of vibration, the thick bell has two prominent strike notes, depending upon where it is struck. These subjective tones appear to be created by groups of three nearly harmonic partials radiated by the (m,l) and (m,l#) families of modes, respectively. The acoustical effects of attacking up to twelve 35‐g brass cylinders have also been observed, both in a symmetrical pattern and in clusters similar to the clusters of mei found on ancient Chinese bells [Rossing et al., J. Acoust. Soc. Am. Suppl. 1 77, S102 (1985)]. The additional masses lower the frequencies of certain modes but have relatively little effect on modal decay rates.
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Sound radiation and frequency response of classical and folk guitars (A)

Eric T. Watson and Thomas D. Rossing

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S119-S119 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The sound radiation has been measured as a function of angle in an anechoic room when the guitar is driven with a sinusoidal force. Classical guitars radiate more strongly than folk guitars when the same force is applied to the bridge [J. Popp and T. D. Rossing, International Symposium on Musical Acoustics, Hartford, July 1986]. Radiation constants are large as 2.7 Pa/N are observed at guitar resonances. Near certain resonances, dipolar or quadrupolar radiation predominates. The radiated sound field is compared to the calculated and measured force on the bridge when the string is plucked.
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On the structural‐acoustic design of guitars (A)

Evan B. Davis

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S119-S119 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A structural‐acoustic model of a guitar top plate backed by a rigid cavity has been built. Acoustic coupling between the interior and exterior acoustic fields is accomplished with a simple model of the soundhole. Acoustic power spectra are calculated in 1/12 octave intervals from 55 to 440 Hz. The soundboard is modeled as an orthotropic damped plate with reinforcing beams and a circular cutout forced by harmonic point loads representing the strings. The model requires the plate outline to be axisymmetric. There are no limitations on the number or orientation of the reinforcing beams. Material property variations, brace cross section, brace pattern layouts, individual brace tapers, plate thickness, and varnish and glue line effects can be studied with this model. A suitable database of material properties and guitar geometry parameters, string lengths, bridge placements, etc. has been built to support the model.
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A model analysis of force‐deformation characteristics of a piano hammer (A)

Hideo Suzuki

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S119-S120 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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Effects of a geometry and a Young's modulus profile of a piano hammer on its static force‐deformation characteristics are studied using a finite element mode. The material properties of the model are assumed to be linear as well as isotropic. Therefore, only a geometric nonlinearity is considered. A hammer model with a representative geometry and Young's modulus profile of an actual bass hammer has a force (f)‐deformation (d) relationship approximated by a function, f = AdB , with approximately B = 1.7. On the other hand, the degree of nonlinearity (B) of a particular hammer obtained from a dynamic measurement is approximately 2.3 or larger. A hammer with a larger increase of Young's modulus in the inward direction has a larger degree of nonlinearity. The geometry of a hammer has a large effect on the value A in the formula shown above. A hammer with a shorter height (distance from the top of the hammer to the top of the wood piece) or with a larger width has a larger value of A (in other words, a larger stiffness).
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An alternate fairy tale for brass instruments (A)

R. Dean Ayers

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Arthur Benade's well‐known paperback Horns, Strings, and Harmony includes a didactic fairy tale about a bugler forced to play on a uniform pipe and stay in tune with ordinary bugles. With a bit of sawing and some impressive lipping, he manages to succeed. This story fits nicely with the prevailing view that the bell on a brass instrument causes a considerable variation in the effective length of a (singly) closed pipe, thus making the performer's job much easier. Another possible ending for this fairy tale is that the bugler solves his tuning problems with the hand‐stopping technique of natural horn players, rather than with his embouchure. One day he accidentally closes the pipe completely and discovers that he now has a perfectly good harmonic series. A slight lengthening of the pipe puts him in tune with his colleagues. This ending is consistent with a view just emerging from time‐domain studies that, in terms of reflection back to the driver, the bell of a brass instrument mimics the closed end of a uniform pipe. Demonstrations will be included.
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Influence of bore shape on the resonant frequencies and spectral envelope of a French horn (A)

J. Duane Dudley and William J. Strong

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The harmonicity of the resonant frequencies, and the shape of the spectral envelope of the input impedance curve, are two important indicators that might be used in predicting the usefulness of a given air column as a brass wind instrument. These can be determined by approximating the air column as a large number of concatenated lossy cylindrical increments, and computing and plotting the input impedance of the configuration as a function of frequency. In this paper the results of such calculations are described for a number of bore shapes related to the French horn, and the effects of changing various dimensional parameters are illustrated. The contributions of the bell, the leadpipe, and the mouthpiece of a typical open B‐flat horn are first examined. Then the horn is idealized and represented by 14 dimensional parameters, so that each can be varied independently to study its effects on harmonicity and spectral envelope, and an optimum configuration is determined. Finally, the effects of inserting the hand into the bell are examined.
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Wind instrument transfer responses (A)

James W. Beauchamp

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Mouthpiece and output pressure signals from several instruments (e.g., trombone, clarinet, saxophone) have been recorded, harmonic spectra have been computed, and transfer responses have been estimated by taking ratios of corresponding harmonic amplitudes. Each transfer response appears to be a series of points on a smooth high pass filter function, even though it actually corresponds to points on (tending toward the minima of) a multiresonant response curve. According to simplified assumptions the measured responses would be independent of amplitude and fundamental frequency. However, there is, in fact, a considerable degree of variation. Results will be presented and reasons for the variations will be discussed.
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On the bore‐to‐driver feedback in double‐reed conical woodwinds (A)

J. Agulló, A. Barjau, J. Martínez, and S. Cardona

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The nonlinear behavior of double‐reed drivers makes advisable the use of time domain to study bore‐to‐driver feedback. The characteristic trends of the impulse response of a conical woodwind are revised. The low intensity of the reflection coming from the first open hole shows the essential role that Bernoulli pressure plays in the reed self‐sustained oscillation (also proved by the reed squeaks that players produce to check reed readiness). Time‐domain study of these instruments leads to the convolution product relating pressure and velocity at the bore input section. The use of the impulse response h(t), the plane‐wave and the spherical‐wave reflection functions, Rp(t) and Rs(t) respectively, as kernel functions in this product is revised. The sharp fluctuations of Bernoulli pressure may impair the use of Rp(t) while R s(t) is unsuitable due to the usual taper discontinuity in the staple‐main body junction of these instruments. Computed and experimental initial transients are given for the case of a “tenora” (Catalan tenor shawm).
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Woodwind instrument simulation in real‐time (A)

Michael Park and Douglas H. Keefe

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A real‐time implementation of the McIntyre‐Schumacher‐Woodhouse time‐domain description of musical oscillators (1983) has been developed using digital signal processing (DSP) hardware. The system is comprised of a microcomputer with installed DSP board including a digital‐to‐analog converter. The task is to perform a convolution and solve two simultaneous equations with nonlinearities for the unknown pressure and volume flow at successive instants of time. A table lookup with linear interpolation simplifies the original formulation. The reflection functions used in the convolution are calculated based upon analytical models of woodwinds, but the nonlinear valving mechanism is somewhat idealized. One can “play” the instrument via an MIDI keyboard controller. Each MIDI note‐on message loads a different reflection function into the DSP board memory, while the pitch wheel controls “blowing pressure.” Recorded examples will be presented.
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Patterns of expressive timing in performances of a Beethoven Minuet by nineteen famous pianists and one computer (A)

Bruno H. Repp

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S120-S120 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Onset‐to‐onset durations of quarter notes and sixteenth notes were ‘measured in nineteen complete performances of the third movement of Beethoven's Piano Sonata op. 31, No. 3. These measurements were compared to those from a computer performance incorporating the “Beethoven pulse” expressive microstructure devised by Manfred Clynes [U.S. Patent No. 4,704,682 (1987)]. This pulse is a particular pattern of relative note durations (and amplitudes) within successive time units, and it is designed to be invariant except for occasional larger deviations at structurally salient points. Although patterns resembling the Beethoven pulse could be found locally in the human performances, on the whole there was little evidence for a fixed, pulselike pattern of timing deviations. Rather, the measurements suggest that great artists change the patterns of relative note durations continuously to meet the local expressive requirements of the composition, and that, despite considerable individual differences, there is some consensus about what these requirements are. If the invariant Beethoven pulse enhances the expressiveness of the computer performance, as it seems to do [B. H. Repp, J. Acoust. Soc. Am. Suppl. 181, S92 (1987)], this is apparently not because it captures aspects of human performance. [Work supported by NIH.]
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The role of tambura spectra in drone tunings of North Indian ragas (A)

Edward C. Carterette, Nazir Jairazbhoy, and Kathryn Vaughn

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S121-S121 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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As part of a program on the role of drone interactions with North Indian ragas played on the sitar, the waveforms of the tambura for the most common drone tuning of the four strings [pa, sa1, sa2, sa′ (low sa)] were analyzed. Each of the strings was played with and without juari threads that have the effect of separating the string slightly from the bridge. The resulting sound is referred to by Indian musicians as a buzz. Without juari the pitch heard is very close to the string fundamental and the partials fall linearly in decibels. With juari the pitch is heard at one or even two octaves above the base pitch and the partials have great power as far as the 20th partial. With juari the 4th, 7th, 11th, or 12th, and the 17th partials have more amplitude than the fundamental. Total harmonic distortion is on the order of 1 to 19 dB without juari but ranges from 12 to 44 dB with juari. The upward spread of energy into higher partials imparts richness to tambura tones, and underlies the use of different drone tunings for different ragas. The pitch and timbre changes with tambura are discussed in terms of the psychoacoustics of complex tones.
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