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Session 05 - Woodwinds

From sound synthesis to instrument making: an overview of recent researches on woodwinds and organs
B Fabre¹, A Hirschberg²
¹Paris 6 University, Laboratoire d'Acoustique Musicale, Paris, France; ²Eindhoven University, Dept. of Applied Physics, Fluid Dynamics Laboratory, Eindhoven, The Netherlands

Trying to understand the physics of woodwind instruments has been a challenge for many generations of researchers. Although huge progresses have been achieved, it appears today that the physics of woodwind instruments still keeps an exciting part of mystery. Since the years 1980s and 1990s, sound synthesis based on simplified descriptions of the time-domain equations allows to produce interesting sounds, even though many aspects are not well understood, especially the effect of geometrical "details" emphasized by instrument makers. Concerning reed instruments, the details of the fluid mechanics in single reed instruments are not well understood, but simplified models of reed mechanics and flow behaviour in the clarinet mouthpiece yielded interesting results on the dynamics of the clarinet. More recently, part of the research turned towards free reed instruments like the harmonica or the mouth organ. Concerning flute-like instruments, some researchers focused on the analysis of specific oscillating regimes, while others focused on the influences on the sound production of the mouth geometry in the flute or of the nicks at the flue exit of flue organ pipes.
A deeper understanding of the effects of the resonator's geometry (cross fingerings, side holes geometry) is also a goal for present researchers and may keep the most useful aspect for instrument makers.

Experimental research on double reed physical properties and its application to sound synthesis
A Almeida¹, C Vergez², R Causse³, X Rodetº
¹IRCAM - Centre Georges Pompidou, Acoustique Instrumentale / Analyse Synthèse, Paris, France; ²CNRS, Laboratoire Mecanique et d'Acoustique, Marseille, France; ³IRCAM - Centre Georges Pompidou, Acoustique Instrumentale, Paris, France; ºIRCAM - Centre Georges Pompidou, Analyse Synthèse, Paris, France

Physical modeling of musical instruments is usually based on simplified assumptions about the behavior of the instrument, so that only the essential information necessary to reasonably describe the sound production mechanisms by the instrument is kept. Such models are for example able to explain much of the physics of single-reed instruments, and provide convincing synthesized sounds.
A simplified reed model is in fact quite generic and could appear applicable to double-reed instruments. Such a simple model, however, was proven not to be satisfying, and a double-reed model must include a more complete description of the physics of the reed. We have carried out experimental measurements on a real instrument to find the important factors that need to be taken into account in a physical model of the double reed.
The current experimental setup on real double-reed instruments will be presented, as well as some of the results achieved. Among these, there are reed opening area measurements, performed by image processing of stroboscope films, and static pressure vs. flow characteristic determination.
We will show how the analysis of this data allows us to derive a preliminary double-reed model from a single-reed one, which , once coupled to a model of a conical resonator could be used in a synthesis framework.

Investigation of vortex formation in flutes with particle image velocimetry
A Bamberger
Physical Institute of the University Freiburg, Freiburg, Germany

The sound production in flutelike instruments is subject of investigations since some time. This investigation concentrates on the acoustical vortices produced near the labium. For an estimation of the acoustical power of a moving vortex derived from the work of the coriolis force in a potential provided by the acoustical field involves the vorticity (size and direction) as well as the acoustical field. The particle image velocimetry (PIV) provides these quantities and allows a quantitative determination of the power of due to vortex shedding. At moderate blowing pressures it may amount to the order of a percent of the total power. In this paper the systematic investigation of the power as a function of blowing pressure and frequency is presented. The validity of the power estimation is discussed.

The 'Virtual Flute': acoustic modelling at the service of players and composers
A Botros, J Smith, J Wolfe
University of New South Wales, Physics, Sydney, Australia

Among the difficulties facing woodwind players are (i) awkward fingerings for rapid passages, (ii) intonation defects in instruments, and (iii) exotic effects such as microtones and multiphonics. In many cases these may be ameliorated by alternative fingerings.
We report the construction and use of a web service for the flute. An expert system was trained by an experienced flutist to determine playability from features of 957 minima in measured acoustic impedance spectra Z(f) for 76 selected fingerings. Measurements on successively more complicated acoustic systems yielded an accurate waveguide model of Z(f) of the flute, which generated the minima of the 39,744 different acoustic configurations of the flute. The expert system, coupled with the waveguide model, produces a large database of alternative fingerings, microtone and multiphonic fingerings. The database is accessible to flutists and composers via a user-friendly interface that includes user determined constraints on key combinations and ranks fingerings by playability or pitch. This service at is used hundreds of times per day. We report some of the service's uses and discoveries.

Relationship between blowing pressure, pitch, and timbre of a Scottish bellows blown bagpipe
S Carral, D M Campbell
University of Edinburgh, School of Physics, Edinburgh, United Kingdom

Bellows blown bagpipes have a long tradition in many European countries, and interest in these instruments has grown in recent years. However, little has been studied about how small changes in the playing parameters affect the way this instrument sounds. It is generally considered that there is a feedback loop in the way wind instruments are played, in which parameters such as blowing pressure and embouchure are changed to adjust the pitch and timbre dynamically. In the case of the bellows blown bagpipes, the only parameter that appears to be controlled by the player is the pressure exerted on the bag of the instrument. This paper describes studies carried out on a small Scottish bellows blown bagpipe. Analysis of a recording of a performance by an expert player reveals significant fluctuations in pitch during the sounding of a given note, which in turn are related to modulation of the timbre of the sound. The relationship between blowing pressure, pitch, and timbre has been investigated using an artificial blowing machine.

The free reed coupled to a pipe resonator
J P Cottingham
Coe College, Physics, Cedar Rapids, United States

The free reed coupled to a pipe resonator occurs in various forms of the mouth organs of Asia as well as in some organ pipes. A number of acoustical measurements have made on this reed-pipe combination, including studies of reed vibration and impedance measurements of the pipes. Particular attention has been paid to the coupling of the reed vibration with the pipe resonator. Although most examples of the free reed pipe employ the reed at the end of a closed tube, as expected in reed wind instruments, the khaen and related instruments employ an open tube of effective length L, with the reed located at approximately L/4. Most examples of Asian mouth organs are constructed with one note per pipe, as in the pipe organ, but the free-reed pipe with finger holes, exemplified by the bawu, is a closed cylindrical pipe with the free reed at one end, in which the effective acoustical length is varied by the use of tone holes. This configuration demonstrates the degree to which the reed frequency can be altered by the pipe resonance frequency.

Waveguide modelling of the Panpipes
A Czyzewski, B Kostek
Gdansk University of Technology, Sound & Vision Engineering, Gdansk, Poland

Waveguide modelling is nowadays a common technique used in the musical instrument sound synthesis domain. Still, not all instruments can be precisely modelled using this technique. Some simplifications are often required in order to fulfil computational needs. On the other hand, the only way to assess the quality of the synthetic sound resulting from the waveguide model is by means of subjective tests. This paper presents a digital waveguide model of the Panpipes. For the efficient modelling of the Panpipes instrument its structure and its physics were studied and discussed. Principles of the digital waveguide modelling of woodwind instruments were also briefly reviewed. In the paper two digital waveguide models of Panpipes instruments differing from each other in their complexity were presented. Consequently it enabled studying the influence of the decreasing complexity of the model on the resulting synthetic sound quality. The subjective tests performed showed that the simplifications in digital waveguide models introduced reveal no noticeable influence on the sound quality. Comparison of synthetic and real Panpipes sounds was also made and conclusions reached.

Playing frequency shift due to the interaction between the vocal tract of the musician and the clarinet
C Fritz¹, J Kergomard², J Wolfe¹, R Causse³
¹UNSW, School of Physics, Sydney, Australia; ²CNRS, LMA, Marseille, France; ³IRCAM, Acoustique Instrumentale, Paris, France

Previous qualitative studies (Mooney, Benade, Hoekje) confirm many musicians' opinions that the vocal tract (VT) affects both timbre and pitch. Johnston, Troup and Clinch analytically modelled the VT as a one peak resonator, which, if tuned to the fundamental f0 of a clarinet, gives a playing frequency of f0. But this result depends upon their particular tract impedance Z, which is small and real at harmonics of f0. In general, the playing frequency is shifted.
We relate the flow u and the pressure difference at the reed Δp=pclar-pmouth by the usual non linear time domain equation, simplified as a third order polynomial. In the frequency domain we set ΔP=(Zclar+ZVT)U. To obtain an analytical result for the frequency shift, we expand about the threshold oscillation. We compare this result with numerical results from the harmonic balance method. Finally impedance spectra measured on the VT of a musician miming different configurations and an artificial VT with a discrete but variable area function are used in this theoretical study. The result is then tested using sound spectra obtained with playing the clarinet with this artificial VT, which avoids the variability of real musicians.
This shift in playing frequency suggests that, while the VT may control pitch, its resonance frequency is probably not tuned to the fundamental of the clarinet.

Influence of losses on the saturation mechanism of single reed instruments
J Gilbert, J Dalmont, M Atig
Universite du Maine, Laboratoire d'acoustique UMR CNRS 6613, Le Mans, France

When blowing a reed instrument using an artificial mouth, the sound level is limited by the fact that when the blowing mouth overpressure increases the level also increases until a maximum Psmax (saturation mouth pressure) beyond which the reed closes suddenly. Then if the mouth overpressure is decreased, the reed oscillates again from a value of the mouth pressure Psmin (mouth pressure lower than Psmax). These two pressure are different from the minimum pressure Pm for which the reed is closed in static regimes. If Pm is difficult to estimate from the experimental point of view, it is easy to measure Psmax and Psmin using a given clarinet-like instrument adapted on an artificial mouth. These values were compared to theoretical ones coming from time domain simulations based on an elementary model with two kinds of losses taken into account (visco-thermal losses inside the tube, non-linear losses localised on the open end of the tube). Results were obtained by varying the non-linear losses using different end geometries. The influence of the losses on the values of Psmax and Psmin is discussed.

Vibrato of single reed instruments
J Gilbert, L Simon
Universite du Maine, Laboratoire d'Acoustique UMR CNRS 6613, Le Mans, France

Vibrato is one of the common ornaments in occidental classical music, particularly in singing and in wind instruments music. When the instruments are played using vibrato ornaments, deliberate fluctuations in the period and the amplitude of the acoustic pressure signals are applied. Several alto saxophone players' vibratos have been recorded. The signals are analysed using time-frequency methods (Short-Time Fourier transform, Wigner distributions) in order to estimate the frequency modulation (vibrato rate) and the amplitude modulation (vibrato extent) of each vibrato sample. The nature of the sound production of single reed instruments is now well understood. Using an elementary model for the reed and the mouthpiece, coupled with an idealised clarinet (cylindrical tube) or with an idealised saxophone (conical tube), a large range of the musical behaviour of the single reed instruments is described. For a given instrument, the model is controlled by two parameters : the mouth overpressure and a parameter characterising the reed mouthpiece. By controlling the two parameters independently or together, time domain simulations of vibratos are created. These are discussed in comparison with the recorded vibratos and with the musician's experiences.

Acoustical and psychoacoustical investigations of the effect of crook bore profile on the playability of bassoons
T J W Hill, D B Sharp
Open University, Department of Environmental & Mechanical Engineering, Milton Keynes, United Kingdom

Bore profile measurements from a selection of different bassoon crooks (bocals), taken using acoustic pulse reflectometry, are presented and the key differences highlighted. Input impedance measurements of a standard bassoon using various fingerings and the same set of crooks are also presented. Between-crook comparisons are made using modal parameters to characterise the impedance curves. Key features in the input impedance curve thought to influence players' performance on the bassoon are discussed and psychoacoustical investigations of players' appraisals of the effect of different crooks are proposed.

RIAM (Reed Instrument Artificial Mouth): A computer controlled excitation device for reed instruments
A Mayer
University for Music, IWK, Vienna, Austria

This paper describes the development and function of a computer-controlled device to excite reed instruments for music acustic studies. On the one hand the aim of this artificial "woodwind player" is a reproducible sound generation as close as possible to the real playing situation, but without the influence of a human player. On the other hand it provides the opportunity for a comparison of different reeds or different embouchure positions, both in conjunction with quantifying their contribution to the timbre. Due to the transparent assembly, recording of motion pictures of the reed oscillation is possible. Using the computer as a cloosed loop control ensures the reproducible excitation.

Experimental investigation of clarinet reed operation and its consequence on the non-linear characteristics of the mouthpiece
S Ollivier, J P Dalmont
Université du Maine, Laboratoire d'Acoustique (UMR CNRS 6613), Le Mans, France

When the clarinet reed is submitted to a mouth overpressure, reed bends and closes progressively the reed slit. A common and intuitive idea is that the reed rolls up on the lay which would lead to a progressive reed stiffness increase. However, some recent works suggest that the rolling up of the reed on the lay is limited, with the top of the reed touching the lay before the lower part. To investigate this, an experimental device was build in order to detect the contact area between the reed and the lay while being blown by an artificial mouth. Results show that the rolling up of the reed on the lay is not systematic. Measurements of the non-linear characteristics in quasi-static conditions show that when the reed does not roll up on the lay the reed stiffness is constant and increases suddenly when the top of the reed almost closes the reed channel. On the other hand, when the reed rolls up on the lay the reed stiffness increases more progressively.

Resonance curves and frequencies in multi-holed ocarinas
D Peterson
University of Central Arkansas, Mathematics, Conway, United States

The traditional American Indian ocarina, dating back perhaps 5,000 years, consists of a clay vessel with 4 to 10 sound holes and a fiple for splitting the air jet created by the player. Musical pitches, though not necessarily diatonic scales, are created by covering the holes in various fingering patterns. As in the Helmholtz resonator it is the vessel volume V and the geometry of the holes and fiple that determine the resonant frequencies f. In particular,
f²= K(Sf/Lf + sum(Sj/Lj)),
where Sj and Lj are the surface area and the depth, with end correction, of the open holes. Sf/Lf respresents the experimentally derived equivalent quantities for the fiple and K = (c/2π)²/V, c = speed of sound.
In the case that all holes have the same geometry, the linear formula for f² allows an accurate measurement for Lj and therefore, the end correction.
Verification of this model requires the analysis of resonance curves (the response in db plotted with respect to blowing pressure or frequency). An unexpected result is that there can be more than one maximum for the fundamental frequency, depending on hole configuration.
The most common modern ocarina has 4 holes of different sizes and plays one ocatave. With cross fingering, 16 distinct frequencies are possible, but it can be shown that an accurate 8 note diatonic scale is impossible without using partial holes or overblowing.

Modeling vocal-tract influence in reed wind instruments
G P Scavone
CCRMA, Stanford University, Dept. of Music, Stanford, United States

This paper explores the influence of upstream vocal tract resonances in reed wind instrument performance and modeling. Vocal tract manipulations are now a common, though sometimes subtle, performance practice exploited by experienced musicians to produce a variety of important acoustic affects, including contemporary performance techniques such as multiphonics and extended range playing. Several previous acoustic studies have been conducted and most agree that the upstream system can have significant influence under certain circumstances. There is less agreement regarding the importance of this mechanism in "traditional" playing ranges and conditions. Several models are developed using digital waveguide techniques to investigate this element of the performer-instrument system. The simplest such system involves modeling the oral cavity as a Helmholtz resonator with a single resonance peak which can be easily controlled to test coupling and reed entrainment, as well as upstream-downstream interactions. The model verifies upstream influence and demonstrates real-time behavior very similar to that experienced in reed wind instrument playing. Multi-resonance vocal tract models are presented as well and issues of real-time control are discussed. The presentation will include a live demonstration by the author of vocal tract influences in saxophone performance.

Head joint, embouchure hole and filtering effects on the input impedance of flutes
J Smith, J Wolfe
University of NSW, Physics, Sydney, Australia

A study of Z(f), the input impedance of the Boehm flute, measured from 200 Hz to 12.5 kHz shows the expected set of strong resonances in the frequency range that corresponds to fundamental frequencies of the playing regime. These frequencies are below the expected cut-off frequency (due to an array of open tone holes) for propagation along the bore of the flute. Above this frequency, in a range that affects the harmonics rather than the fundamental of played notes, the inertive reactance of the tone holes increases with frequency until the standing wave propagates along the tone hole lattice with little attenuation. Harmonic resonances are again evident, but now correspond to resonances of the whole length of the instrument. However the resonances associated with the bore are strongly attenuated over an intermediate frequency range. This appears to be a consequence of a Helmholtz resonator formed by the air in the embouchure hole and the sealed end of the head joint. Experiments with different head joints confirm this mechanism. The envelope of Z(f) shows a broad maximum near 10 kHz that we attribute to the resonance of the embouchure riser tube.

Flute Performology;
Statistical Analyses and Numerical Simulation of Flute Tone Excitation.

Jan Tro, Ulf Kristiansen & Aslak Bjerkvik.
Norwegian University of Science and Technology (NTNU) ,NO-7491 Trondheim, Norway.

The present analyses are based on a large number of anechoic solo flute recordings. Using a near field microphone recording technique it is possible to distinguish between the sound of the shutting key and the following tone transient. For a rapid tone sequence in a professional musical context the precision of the key shutting action is of utmost importance. Furthermore it is assumed to exist a minimum (optimum) time delay between the action of closing a hole and the possible start of the correct tone transient based on the behaviour of the standing wave build up in the flute tube. Variation of average time delays and deviations is calculated.
In a two-dimensional numerical model of the flute sound field build up we demonstrate tone transient variations as a function of the hole size (from totally open to totally shut). Simulation parameters are compared with the measured values.
The present study which is part of the ongoing performology projects at the NTNU-Acoustics Lab., emphasizes the advantage of analysing instrument tones in a musical context

Relating the harmonic-rich sound of the Chinese flute (dizi) to the cubic non-linearity of its membrane
C G Tsai¹, J Wolfe², J Smith²
¹Humboldt-University, Musicology, Berlin, Germany; ²University of New South Wales, Physics, Sydney, Australia

The dizi, a Chinese membrane flute, has a thin membrane covering a hole in the wall of the instrument about halfway between the embouchure hole and the first finger hole. The non-linear membrane produces the rich spectral content that is associated with the characteristic bright, buzzing timbre of the dizi. In the second register, where the membrane is located near a pressure node of the second harmonics and the driving force is quasi-sinusoidal, dizi tones are always dominated by odd-numbered harmonics. We therefore model the membrane as a Duffing oscillator with a hardening spring. This model is tested by two kinds of tones driving the membrane: tones generated by blowing the instrument or by external excitation. We measure the acoustic pressure in the pipe under the membrane, and the sound radiated by the membrane. The phase plots of the membrane show interlocking spirals, which are predicted by a quasi-sinusoidally driven Duffing oscillator model. We estimate the membrane's resonant frequency, damping coefficient, effective mass, and cubic non-linearity by fitting the experimental results. Waveforms and spectra of tones generated by external excitation are successfully simulated. For normal dizi tones the agreement is restricted to frequencies < 10 kHz. Rich harmonics above 10 kHz in loud dizi tones, not predicted by the quasi-sinusoidally driven Duffing oscillator model, may be associated with the jet's sensitivity to high harmonics generated by the membrane.

Some effects of the player's vocal tract and tongue on wind instrument sound
J Wolfe¹, A Z Tarnopolsky¹, N H Fletcher², L C L Hollenberg³, J Smith¹
¹University of New South Wales, Physics, Sydney, Australia; ²Australian National University, Physical Sciences and Engineering, Canberra, Australia; ³Melbourne University, Physics, Melbourne, Australia

The reeds in wind instruments (including lips in lip-reeds) interact with the acoustic impedances of the instrument's bore, Zb and the player's vocal tract, Zt. The bore has high Q resonances, the maxima in Zb are large and determine the playing regime to first order. The tract has resonances with lower Q which act on a small area of the reed. So how do the weak maxima in Zt affect the timbre (eg didjeridu) and pitch?
We use a mechanical reed with geometrically simple resonators both up- and downstream to model wind instruments. We compare impedance spectra and sound spectra with those from real instruments and players.
Among other effects, we report the importance of the anterior tongue. The small area of the reed (or lips) that vibrates in the player's mouth means that the fundamental resonance of the tract it 'sees' is weak, with Zt << Zb. The tongue, when raised at the tip, acts as an impedance matching transformer by approximating a horn linking the small area of the reed (or lips) that vibrates in the player's mouth and the larger cross sectional area of the lower tract. With the tongue lowered, the peaks in the impedance of the tract and its low frequency value are low compared to those of the instrument and have little effect. With the tongue raised, the magnitude of the peaks and low frequency values of Zt are closer to those of the Zb, so the tract configuration can affect the timbre and intonation.

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