FRIDAY MORNING, 4 JULY 2008

AMPHI MAILLOT, 11:00 A.M. TO 6:20 P.M.
Session 5aMUeMusical Acoustics and Signal Processing in Acoustics: Signal Representations and Models of MusicalSounds II
James W. Beauchamp, Cochair
University of Illinois, 1002 Eliot Drive, Urbana, IL 61801, USA
Bertrand David, Cochair
Télécom Paristech (ENST) ” TSI - CNRS LTCI, 46, rue Barrault, Paris Cedex 13, 75634, France
Contributed Paper
11:00
5aMUe1.
Early use of the Scott-Koenig phonautograph for
documenting performance. George Brock-Nannestad 共Patent Tactics,
Resedavej 40, DK-2820 Gentofte, Denmark, pattac@image.dk兲, Jean-Marc
Fontaine 共Université UPMC - Ministère de la Culture - CNRS - IJRA LAM, 11, rue de Lourmel, F-75015 Paris, France, jmfontai@ccr.jussieu.fr兲
Acoustics in the 1850s combined listening, observation and notation.
This was “real-time”, catching any phenomenon as it appeared. If it was repeatable, one could prepare for it. Continuous data rather than observation
data enabled a very different analysis from observation and notebooks.
Édouard-Léon Scott’s invention of the phonautograph enabled this. A surface moved below a stylus that was vibrated by sound in air. Originally a

blackened glass plate, the scientific instrument maker Rudolph Koenig contributed by devising a very long axis representing time, because now blackened paper was wrapped around a cylinder on a threaded shaft. A twodimensional representation of the individual vibrations was obtained. Scottboth deposited a sealed letter with the Paris Academy of Sciences in January, 1857 and filed a patent application in April, 1857. Later he deposited afurther sealed letter and in 1859 he filed an application for patent ofaddition. Following the thoughts expressed and documented in his manuscripts here analyzed in context and comparing with Koenig’s production itis feasible to see how they were dependent on each other, although they had
different purposes in mind. The paper concentrates on Scott’s interests inperformance, and a number of original tracings are discussed.

Invited Papers
11:20
5aMUe2. Sparse representations of audio: from source separation to wavefield compressed sensing? Remi Gribonval 共INRIA,
IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France, remi.gribonval@irisa.fr兲
Sparse signal representations, which are at the heart of today’s coding standards 共JPEG, MPEG, MP3兲, are known to have had asubstantial impact in signal compression. Their principle is to represent high-dimensional data by a combination of a few elementarybuilding blocks, called atoms, chosen from a large collection called a dictionary. Over the last five years, theoretical advances in sparse
representations have highlighted their potential to impact all fundamental areas of signal processing. We will discuss some current andemerging applications of sparse models in musical sound processing including: signal acquisition 共Compressed Sensing - sampling wave
fields at a dramatically reduced rate兲 and signal manipulation 共e.g., source separation and enhancement for digital remastering兲. We willconclude by discussing the new algorithmic and modeling challenges raised by these approaches.
11:40
5aMUe3. Towards a hierarchically sparse model for audio signals. Laurent Daudet 共UPMC Univ Paris 06, LAM ” IJLRA, 11 rue
de Lourmel, 75015 Paris, France, daudet@lam.jussieu.fr兲
In this paper we discuss a major issue that arises when building sparse atomic models for music signals: in which space 共”
dictionary兲 should we represent the signals? Having extremely redundant dictionaries is very informative for the locally most important
atoms, but is irrelevant for the detail atoms that represent residual signals. Also, what are the advantages of dictionaries composed oflearned atoms 共which brings the issue of representativeness兲 compared to generic dictionaries? We here advocate for non-fixed dictionaries, with a multi-layered hierarchical decomposition: the first layer roughly describes the signal, in an extremely redundant, signaltailored, structured dictionary. This layer is also very sparse, most of the information being carried by the atoms’ parameters, similarly
to parametric representations. Subsequent layers give more and more details, increasing the data amount while reducing overcompleteness and structural model constraints. These techniques have obvious applications for audio coding, but are also useful for scalable
music data mining. This research is supported by the French ANR 共DESAM project兲.
12:00
5aMUe4. Bayesian inference in hierarchical non-negative matrix factorisation models of musical sounds. Ali Taylan Cemgil
共University of Cambridge, Trumpington Street, CB2 1PZ Cambridge, UK, atc27@cam.ac.uk兲, Tuomas Virtanen 共Tampere Universityof Technology, Inst. of Signal Processing, FI-33101 Tampere, Finland, tuomas.virtanen@tut.fi兲
There has been a surge of interest to efficient audio and music modeling using tools from statistical machine learning. One suchtechnique, that has been particularly successful, is non-negative matrix factorisation 共NMF兲. However, a detailed theoretical understanding of this success is missing, as well as links to other modeling strategies such as sinusoidal or harmonic models. To fill this gap,
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we describe NMF in a statistical framework, as a hierarchical generative model consisting of an observation and a prior component. We
show that particular choices lead to standard NMF algorithms as special cases, where parameter estimation is carried out via maximum
likelihood. Starting from this view, we develop extensions that facilitate more realistic acoustic modeling 共such as spectral smoothnessor harmonicity of natural sounds兲 and alternative inference techniques via Gibbs sampling and variational Bayes, which allow us to doprincipled comparisons between alternative models via Bayesian model selection. Our novel construction, where we make use of Markov chains of Gamma random variables, retains conjugacy and enables us to develop models that fit better to real data while retaining
attractive features of standard NMF such as fast convergence and easy implementation. We illustrate our approach on polyphonic pitch
estimation.
12:20
5aMUe5. On sinusoidal modeling of nonstationary signals. Axel Roebel 共IRCAM, 1, pl. Igor-Stravinsky, 75004 Paris, France,
roebel@ircam.fr兲
In this presentation we are going to give an overview over a number of techniques that have been developed in our group to improvethe modeling of musical 共nonstationary兲 signals using sinusoidal models. One of the basic problems with sinusoidal models is the factthat the underlying theory is derived assuming stationary sinusoids, while in the real world all sinusoidal components are non stationary.
The two topics that will be covered main are, first a technique that allows to distinguish between nonstationary sinusoidal components,
noise and transients, and second a new technique for parameter estimation of nonstationary sinusoids using frequency domain
demodulation.
12:40-1:40 Lunch BreakInvited Papers
1:40
5aMUe6. Advances in the tracking of partials for the sinusoidal modeling of musical sounds. Sylvain Marchand 共LaBRI CNRS, University of Bordeaux 1, 351 cours de la Liberation, F-33405 Talence, France, sylvain.marchand@labri.fr兲
Whereas sinusoidal modeling is widely used for sounds, polynomial models are still used for the model parameters, which canhardly handle modulations 共vibrato and tremolo兲 present in musical sounds. Moreover, the partial tracking algorithms are often designed
under stationarity assumptions. Advances in partial tracking may come out of the modeling of the partials themselves. We consider theirparameters 共frequencies and amplitudes兲 as predictable and slow time varying: First, the future of any partial can be determined fromits past evolutions; second, no audible frequency should appear in the spectral content of these evolutions, otherwise it would question
the perceptive consistency of the model. We then choose to handle nonstationary sinusoidal modeling by a deterministic approach basedon linear prediction of the partial evolutions and partial discrimination based on the spectral properties of these evolutions. The underlying model for each partial is now a sum of sinusoids, thus leading to a two-level sinusoidal modeling, well suited for musical sounds,
where modulations are important. The enhanced partial tracking algorithm also handles the case of crossing partials, without the needfor any probabilistic approach. Better modeling the deterministic part of polyphonic sounds leads to enhanced source separation andtime scaling algorithms.
2:00
5aMUe7. Adaptive subspace methods for high resolution analysis of music signals. Roland Badeau 共Télécom Paristech 共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, roland.badeau@enst.fr兲, Bertrand David 共Télécom Paristech
共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, bertrand.david@enst.fr兲
In the field of music signals analysis, the tonal part of a broad variety of sounds is often represented as a sum of slowly varying
sinusoids. The Fourier transform remains a prominent tool for estimating the parameters of this model, due to its robustness and to theexistence of fast algorithms. Its main drawback relies in its spectral resolution, bounded by the length of the analysis window. Subspacebased high resolution 共HR兲 methods are conversely not constrained by this limit, since they rely on the particular geometrical structureof the signal model. Nevertheless, they have been seldom used in audio signal processing, mainly due to their high computational cost.
Based on recent advances in the field of subspace tracking, enhanced adaptive algorithms for HR analysis have thus been developed,
leading to a high resolution time-frequency representation of the signal, called HR-ogram. The application of these algorithms to musicsignals, made difficult by the high dynamics and the presence of colored noise, has required the tuning of well-adapted preprocessing
techniques. The whole tool is now mature, and allows a high quality separation of the tonal part of various musical sounds. This researchis supported by the French ANR under contract ANR-06-JCJC-0027-01 共DESAM兲.

5a FRI. AM

2:20
5aMUe8. Towards an adaptive subspace-based representation of musical spectral content. Bertrand David 共Télécom Paristech
共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, bertrand.david@enst.fr兲, Roland Badeau 共Télécom
Paristech 共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, roland.badeau@enst.fr兲
This study presents an algorithm based on an adaptive framework model for musical sound signals assumed to be composed ofslowly varying frequency components surrounded by additive noise. These components appear as contours in a time-frequency representation, as for instance, a spectrogram. To extract these contours, an often used solution is to estimate the parameters 共amplitude,frequency, and phase兲 of each component at each frame and then to link them from one to the next with the help of a distance measureor an HMM. Conversely, our method attempts to update the estimated values from one time instant to the next. It relies on principal
subspace tracking 共with respect to time兲 together with gradient descent to individually update each of the component parameters. Finally, each extracted contour, which represents the frequency and amplitude variation of a single component, is available for subsequent3803

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processing. Applications are demonstrated in the fields of harmonic plus noise decomposition and analysis”transformation”synthesis.
This research is supported by the french Institut Telecom, TAMTAM project.
2:40
5aMUe9. Damped sinusoids and subspace based approach for lossy audio coding. Olivier Derrien 共Université de Toulon, Av
Georges Pompidou, BP 56, 83162 La Valette du Var, France, olivier.derrien@univ-tln.fr兲, Gaël Richard 共Télécom Paristech 共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, gael.richard@enst.fr兲, Roland Badeau 共Télécom Paristech
共ENST兲”TSI - CNRS LTCI, 46, rue Barrault, 75634 Paris Cedex 13, France, roland.badeau@enst.fr兲
The new subspace-based techniques recently introduced appear to be well adapted for the parameters estimation of a damped sinusoids ⫹ noise signal model. These high-resolution 共HR兲 methods have a better frequency resolution than the Fourier analysis, butthey are rarely used in audio coding. Although HR methods would be suitable for parametric coding at low bitrates, we show that they
are also efficient for high-bitrate coding where state-of the art codecs are usually transform-based. Our coding scheme first includes a
8-band PQMF filter-bank decomposition. Then, each subband signal is segmented in onsets and a maximum-order HR analysis is performed on each segment with the ESPRIT algorithm. For each component of the model, frequency, damping, amplitude and phase arequantized. The residual signal is not coded. This codec is compared to a MDCT framework, where transform and quantization are thesame as in a MPEG-AAC but without inclusion of perceptual modelling and entropy coding. Preliminary objective and subjective tests
show the potential of this approach which requires, on mostly tonal signals, significantly less bits than the traditionnal MDCT method
for a given quality.
3:00
5aMUe10. Auditory model based analysis of polyphonic music. Anssi Klapuri 共Tampere University of Technology, Korkeakoulunkatu 1, 33720 Tampere, Finland, anssi.klapuri@tut.fi兲
This study is about the use of an auditory model to extract multiple pitches from polyphonic music signals. One goal was to identify
the conditions where pitch analysis using an auditory model is advantageous over more conventional time or frequency domain
approaches. It is shown that these conditions include especially the processing of band-limited signals or signals where important partsof the audible spectrum are corrupted by band-limited interference. An efficient implementation strategy is described which reduces thecomputational complexity of the auditory model roughly by factor 10. Further prospects of bandwise processing and redundant signal
representations in general are discussed.
3:20
5aMUe11. On perceptual distortion measures and parametric modeling. Mads G. Christensen 共Aalborg University, Niels Jernes
Vej 12 A, DK-9220 Aalborg, Denmark, mgc@es.aau.dk兲
Over the past two decades, there has been much interest in incorporating human sound perception in signal processing algorithms,
often in the form of perceptual distortion measure or an approximation thereof. An example of this is MDCT-based audio coding wherea good quality can be achieved at very low bit-rates by taking masking effects into account. More recently, the same principles havebeen applied to parametric modeling and coding of audio signals. We discuss the inherent tradeoffs in choosing a perceptual distortion
measure and a parametric model and the pros and cons of various ways of implementing such perceptual distortion measures isdiscussed. An important question that we seek to answer is whether perception should be taken into account in the estimation of model
parameters or this should be done in a separate step.

Contributed Paper
3:40
5aMUe12. Efficient coding of a xylophone sound using spikogram
nonredundent coding. Rolf Bader 共University of Hamburg, Institute ofMusicology, Neue Rabenstr. 13, 20354 Hamburg, Germany, R_Bader@tonline.de兲
Sensory systems try to use the incoming data most efficiently. Studies of
Lewicki et al. lately showed, that a representation of a spike train just representing the sound and not having any redundancy is how the auditory system of the cat represents incoming sounds. To compare this theory with musical instruments, a xylophone sound was analyzed in terms of a spikogram.

Here, gammatones of a 64 channel filterbank with different attack and decay
values are superposed in a way to reconstruct the original sound. Only thosegammatones were used which are needed to result in the sound used as input
and so no redundancy is present in the analysis of the sound. It was found,that the most reasonable fit of the gammatone shape with the empirical data
indeed made the representation most efficient and so the xylophone sound ismost easily represented by the auditory system. Although more analysis areneeded here, musical instruments could show up to be built in a way to fit amost efficient coding by listeners and so fulfill a middle-of-the-road rule of
not too much and not too few information so that listeners are interested in
but not overtaxed by the sounds.

4:00-4:20 Break

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Invited Papers

4:20
5aMUe13. A frequency shifting model of pitch. Paris Smaragdis 共Adobe Systems Inc., 275 Grove St., Newton, MA 02466, USA,
paris@media.mit.edu兲
We present a model useful for tracking of melodies of sounds that can have arbitrary harmonic structure 共including inharmonic
instruments and noise sources兲. This model is based on a spectral shift assumption which is capable of tracking melodic movements ofan instrument regardless of the irregularity of its spectrum. This technique can be used to simultaneously estimate the spectral characterof the instrument to be analyzed in addition to its melody. It is capable of dealing with multiple instances of the same instrument,
thereby recognizing chords as well as notes, and can also extract multiple melodies in audio signals composed out of many instruments.

4:40
5aMUe14. Modeling vocal sounds in polyphonic musical audio signals. Masataka Goto 共National Institute of Advanced Industrial
Science and Technology 共AIST兲, IT, 1-1-1 Umezono, Tsukuba, 305-8568 Ibaraki, Japan, m.goto@aist.go.jp兲, Hiromasa Fujihara
共National Institute of Advanced Industrial Science and Technology 共AIST兲, IT, 1-1-1 Umezono, Tsukuba, 305-8568 Ibaraki, Japan,
h.fujihara@aist.go.jp兲
This paper describes our research aimed at modeling vocal sounds 共singing voices兲 in available music recordings and its applications
to singer identification, singer similarity, and lyrics synchronization. Our predominant-F0 estimation method, PreFEst, can obtain the
melody line by modeling the input sound mixture as a weighted mixture of harmonic-structure tone models 共probability density
functions兲 of all possible F0s and estimating their weights and the tone models by MAP estimation. Since the PreFEst was designed forgeneral melodies, we extended it to specialize in vocal melodies by using vocal timbre models --- vocal and nonvocal GMMs. Those
GMMs are trained beforehand and used to evaluate the vocal probability. The GMMs are also used to identify vocal regions, but its
strategy should depend on applications. For singer identification and singer-similarity calculation, since the purpose is to model singer’s
identity by training each singer’s vocal GMM, certainly reliable vocal regions should be identified even if most true regions were
missed. On the other hand, for lyrics synchronization, since the purpose is to align each phoneme to the estimated vocal melody, vocal
regions should be identified without missing any true regions. We achieved this by biasing log likelihoods provided by vocal and nonvocal GMMs.

5:00
5aMUe15. Music and speech signal processing using harmonic-temporal clustering. Jonathan Le Roux 共University of Tokyo,
Sagayama”Ono Laboratory, 7-3-1 Hongo, Bunkyo-ku, 113-8656 Tokyo, Japan, leroux@hil.t.u-tokyo.ac.jp兲, Hirokazu Kameoka 共NTT
Communication Science Laboratories, NTT Corporation, 3-1 Morinosato wakamiya, 243-0198 Atsugi, Kanagawa, Japan,
kameoka@eye.brl.ntt.co.jp兲, Nobutaka Ono 共University of Tokyo, Sagayama”Ono Laboratory, 7-3-1 Hongo, Bunkyo-ku, 113-8656
Tokyo, Japan, onono@hil.t.u-tokyo.ac.jp兲, Alain De Cheveigne 共CNRS, Universite Paris 5, Ecole Normale Superieure, 29 rue d’Ulm,
75230 Paris, France, alain.de.cheveigne@ens.fr兲, Shigeki Sagayama 共University of Tokyo, Sagayama”Ono Laboratory, 7-3-1 Hongo,
Bunkyo-ku, 113-8656 Tokyo, Japan, sagayama@hil.t.u-tokyo.ac.jp兲
We present here the principle of the recently introduced harmonic-temporal clustering 共HTC兲 framework and its applications in bothmusic and speech signal processing. HTC relies on a precise parametric description of the harmonic parts of the power spectrum throughconstrained Gaussian mixture models. The model parameters of all the elements of the acoustical scene are estimated jointly by an
unsupervised 2D time-frequency clustering of the observed power density. HTC is effective for multi-pitch analysis of music signals andF0 estimation of single and multiple speaker speech signals in various noisy environments. It also enables to perform extra processingof monaural music and speech signals, such as isolation or cancellation of a particular part, noise reduction and source separation.

5:20

5a FRI. AM

5aMUe16. Timbre transposition based on time-varying spectral analysis of continuous monophonic audio and precomputed
spectral libraries.
James W. Beauchamp
共University of Illinois, 1002 Eliot Drive, Urbana, IL 61801, USA,jwbeauch@uiuc.edu兲, Mert Bay 共University of Illinois, 212 W. Healey, Apt. 303, Champaign, IL 61820, USA, mertbay@uiuc.com兲
A sinusoidal model for solo musical sounds consisting of time-varying harmonic amplitudes and frequencies allows for convenient
temporal and spectral modifications. With a harmonic model, analysis frames can be grouped by fundamental frequency 共F0兲 and thenclustered in terms of their harmonic spectra. The resulting cluster centroid spectra are used as spectral libraries. When continuous audio
monophonic passages are analyzed in the form of harmonic components, F0 vs. time data are used to guide the extraction of parametersfrom the sound in order to find appropriate library spectra for resynthesis. Two methods for finding appropriate spectra are: 共1兲 best rms
match with the incoming spectra and 共2兲 best spectral centroid match. These give similar results, but centroid matching yields smootherspectra over time. Timbre transposition is performed by using a library that belongs to another instrument. We have found that when thetarget instrument has a unique timbral quality based on its spectrum, the synthesis sounds mostly like that instrument. However, if thetarget instrument’s spectral characteristic is not sufficiently differentiated from the source, the source timbral quality may dominate,probably due to its temporal behavior being transmitted. Results will be demonstrated by audio examples.
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Contributed Papers
5:40
5aMUe17. Comparison of the sound of a grand and an upright pianousing wavelets. Grigorios Plitsis 共Greece, grigoriosplitsis@merseymail.com兲
Wavelet analysis is useful for extracting patterns and thus analyzing
signals. Although the Fourier analysis can reveal different features of a signal, it is less appropriate for describing transient phenomena and suddensound changes. As a result, Fourier-based music reconstruction cannot exactly imitate the physical sound, as it is not possible to know at the sametime a specific frequency as well as the time of occurrence of this frequency.
Wavelet analysis is capable of highlighting different attributes of a signal.
Different types of wavelets are thus used in the present study in order tocompare the sound produced by a grand piano with that produced by an upright piano.
6:00
5aMUe18. Modeling of piano sounds using FEM simulation ofsoundboard vibration. Luis I. Ortiz-Berenguer 共Universidad Politecnica
de Madrid, Ctra.Valencia km7, 28031 Madrid, Spain, lortiz@diac.upm.es兲, Francisco J. Casajus-Quiros 共Universidad Politecnica de Madrid,

Ctra.Valencia km7, 28031 Madrid, Spain, javier@gaps.ssr.upm.es兲,David
Ibanez-Cuenca 共Universidad Politecnica de Madrid, Ctra.Valencia km7,28031 Madrid, Spain, dibanez@alumnos.euitt.upm.es兲
Pattern-matching methods for polyphonic transcription of piano sounds
require a set of patterns that can be obtained by modeling the piano-soundspectra. The modeling should take into account not only the string stiffness
but also the effect of the soundboard impedance on the string vibration.
Studies on that effect corresponding to a wide range of impedance values
have previously been carried out by the authors. However, actual impedancevalues for real pianos must be used in the model. Although the impedancevalue of a few grand-pianos have been measured by the authors, these results are not significative enough to create a model. Thus, a FEM simulationof soundboard vibration is proposed to obtain nearly-actual impedancevalues. The simulation considers several cases of vibrating plates from thesimplest rectangular one and increasing the similarity to real pianosoundboards. The quality of the simulation is verified comparing the obtained results with either recognized theoretical results for the simplest cases
or measured values for the more complex ones. The complexity of the simulated soundboard is limited to the case that produces only slight variations in
the modeled spectrum. 关This work has been supported by Spanish National
Project TEC2006-13067-C03-01”TCM.兴

FRIDAY MORNING, 4 JULY 2008

ROOM 202”203, 11:00 A.M. TO 12:00 NOON
Session 5aMUf

Musical Acoustics: Plucked and Struck Idiophones II
Thomas D. Rossing, Cochair
Stanford University, CCRMA, Department of Music, Stanford, CA 94305, 26464 Taaffe Rd, Los Altos Hills, CA 94022, USA
Charles Besnainou, Cochair
Institut Jean le Rond d’Alembert, Laboratoire d’Acoustique Musicale, 11, rue de Lourmel, Paris, 75015, France
Contributed Papers
11:00
5aMUf1. Characterizing the sound of an African thumb piano(kalimba). David M.f. Chapman 共Scientific Consultant, 8 Lakeview Avenue, Dartmouth, NS B3A 3S7, Canada, dave.chapman@ns.sympatico.ca兲
The kalimba is an African percussion instrument whose notes are generated by vibrating metal tines of various lengths attached to sound board orsound box. Unlike a vibrating string or organ pipe, the overtone structure isanharmonic, that is, the overtone frequencies 共which determine soundquality兲 are not simple integer multiples of the fundamental frequency
共which determines pitch兲. The ratio of the first overtone to the fundamental
is in the range 5.3-5.9, depending on the tine geometry. The vibrating tines
are modeled as a clamped-supported-free beam and the observed overtone
structure is shown to be in accordance with this model. Audio examples will
be provided.

11:20
5aMUf2. The jew’s harp, experimental study and modeling. Charles
Besnainou 共Institut Jean le Rond d’Alembert, Laboratoire d’AcoustiqueMusicale, 11, rue de Lourmel, 75015 Paris, France, chbesnai@ccr.jussieu.fr兲, Joel Frelat 共Institut Jean le Rond d’Alembert, Lab.
d’Acoustique Musicale, 11, rue de Lourmel, 75015 Paris, France,
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frelat@lmm.jussieu.fr兲,Adrien Mamou-Mani共Institut Jean le Rondd’Alembert, Lab. d’Acoustique Musicale, 11, rue de Lourmel, 75015 Paris,
France, mamou-mani@lmm.jussieu.fr兲
Under its archaic aspects jew’s harp is a musical instrument highly
subtle. Indeed, a metal blade 共or wooden兲 attached to a rigid frame put into
vibration by the musician, and coupled to the buccal resonator allow nicetune. The skilt of the jew’s harp focuses on the conformations of this cavity
whose function is to select the right components of the vibration to be
amplify. In our study, we have modelled a playing technique which involves
blowing during the blade vibrates. In the lake of breath, the spectre of soundproduced by the blade is odd, i.e., it includes at first approximation odd
components 共n⫹1兲 multiple the fundamental. Whereas when the musician
adds breath the spectrum turns into a spectrum containing all components ofbasic integer multiples 共n兲. This work takes place in the context of studies ofvibrating systems under prestress and loaded. In that case the load, and theprestress are generated by the musician breath by bending the blade On theother hand, experimental studies are compare with the model results.

11:40
5aMUf3. Sound of the HANG. Thomas D. Rossing 共Stanford University, CCRMA, Department of Music, Stanford, CA 94305, 26464 Taaffe Rd,
Los Altos Hills, CA 94022, USA, rossing@ccrma.stanford.edu兲, David
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