This section briefly discusses the results and open questions of organ research up to now. First, a general modeling approach of wind instruments and its applications are introduced. Then, the results of the research on the sound generation of labial and lingual pipes are summarized.
2.3.1 A general approach for modeling wind instruments
All wind instruments produce sound by means of pressure oscillations of an air column inside the pipe body, also called as the acoustic resonator. In order to achieve steady state sound gen-eration (self-sustained oscillations), the pressure oscillations must be maintained by means of an excitation mechanism. The excitation mechanism is realized in various manners in different families of wind instruments as summarized by Adachi [6]. The excitation and the vibrating air column can also interact in different manners, as it was seen in case of labial and lingual organ pipes. Hence, a complete model of the sound production of wind instruments requires the in-corporation of the excitation mechanism, the acoustic resonator, their interaction, and finally the sound radiation to the listener.
A general approach basics of
the general approach
for modeling wind instruments is the separation of the model into two parts. The excitation is usually treated as a nonlinear system, incorporating the underlying physi-cal model of the aeroacoustiphysi-cal, mechaniphysi-cal, or coupled excitation system. The acoustic resonator is most often treated as a linear, often one-dimensional system. This simplification is justified by the fact that the resonator usually operates at moderate amplitudes, that are in the linear acoustic regime. The feedback from the acoustic system on the excitation must inherently be incorporated into the differential equations describing the physics of the excitation. A brief summary of the papers published about the application of this simple model is given in the sequel.
The McIntyre – Schumacher – Woodhouse model is one of the first applications of this simpli-fied structure [99]. For the nonlinear modeling of the excitation time domain simulation of the sound generation is preferred in this model. The model is very general, it was applied for mod-eling bowed strings, woodwind reeds, and flute-like instruments. The authors have performed simulations on the simplified model of a flue organ pipe and found good agreement with the waveforms of Coltman’s experiments [42].
Fletcher & Douglas [66] presented a simplified model of harmonic generation in flute-like instruments. By means of expressing the harmonic components of the flow entering the pipe, the strength of the harmonics in the steady state sound were predicted for different positions of the upper lip. Measurements performed by the same authors on an experimental organ pipe with adjustable upper lip matched the expectations from the model.
Verge et al. [141] have introduced nondimensional quantities for the analysis of the sound production in recorder-like instruments. It was shown that the amplitude of the fundamental is limited by a nonlinear interaction of the jet and the acoustic resonator. Furthermore, the effect of the size of the mouth opening and the mouth width to height ratio was also examined and found to affect the produced tone to a great extent. Vergeet al.[143] presented a one-dimensional simulation model of the same system. This simple model enabled the correct prediction of the amplitude of the fundamental in the steady state. The authors concluded that even such a simple model can reproduce a large number of observations on the functioning of flue instruments.
2.3. STATE OF THE ART IN PIPE ORGAN RESEARCH 15 Dequandet al.[49] have examined the role of the mouth geometry and the sharpness of the upper lip on the harmonic content of the sound. Two different models of the sound generation mechanism were presented for different mouth width to height ratios. The two models explain the variations of the amplitudes experienced with changing the mouth geometry; however, the two models were not combined in a global model that would allow sound synthesis.
A similar model was also applied for the time domain simulation of the trumpet by Adachi
& Sato [7, 8]. The latter authors introduced one- and two-dimensional lip models for the repre-sentation of the excitation mechanism. By adjusting the lip resonance frequency, trumpet sounds were reproduced operating different acoustic modes of the resonator.
A detailed review of this general modeling approach for wind instruments is found in the paper by Fabre & Hirschberg [60].
2.3.2 Research on labial pipes
Labial organ pipes and the physics of their sound generation have already been studied for long.
The first scientific papers on the topic known to the author were published in the 1930s [32, 90].
These papers do not focus on a particular phenomenon or quality of the sound, but summarize some observations regarding different pipe types.
Later on, specific aspects of the sound generation were investigated in more detail. Nolle &
Boner [112] investigated the steady state sound generation in organ pipes and a vibrating string.
They found that the partials in organ pipe sound are always exactly harmonic, while a string exhibits inharmonic behavior. The same authors examined the transient phenomena of flue and reed organ pipes [113]. They found that the time to reach the steady state sound requires the same number of cycles of the fundamental (i.e. normalized time, see p. 12) for pipes of the same stop. The presence of non-harmonic components at the transient state of the sound was also documented.
Cremer & Ising [43] sound
generation mechanism gave a description of the sound generation in a labial organ pipe. It was
supposed that the jet and the resonator form a coupled system, whose combined transfer func-tion must give unity, due to the balance of energy. In their model, the driving pressure of the pipe is directly proportional to the jet velocity, which contradicts the observations that suggest a square dependence. Coltman [41] expressed the acoustic driving force of the pipe by the momen-tum of the jet, which explained the square dependence of the driving pressure on the jet velocity.
Elder [56] proposed a model of the sound generation based on the conservation of linear momen-tum that comprehends the models of Cremer & Ising and Coltman. Coltman further examined the jet drive mechanism in edge tones and organ pipes [42]. He found that the presence of the resonator introduces an additional phase shift between the volume displacement of the jet and the sound pressure compared to the edge tone case.
Based on the idea of Coltman [41] jet–
resonator interaction , a nonlinear model of jet and resonator interaction was
developed by Fletcher [63]. This model was limited to a pipe with a few natural resonances, but the model gave results quantitatively comparable to experimental data. Fletcher [64] extended his model to incorporate the theory of Elder [56]. He concluded that although the model gives good agreement with experiments in certain regimes of the blowing pressure, it fails to predict the effects for low blowing pressures. Thwaites & Fletcher [137] further investigated the interaction of the jet and the acoustic resonator by determining the admittance of the jet in an experimental manner. They concluded that the current theory of jet–resonator interaction is still not capable of comprehending all effects occuring in measurements. Later, Vergeet al.[142] examined the interaction of the jet and the resonator in the onset of the pipe sound. It was found that the steepness of the pressure rise in the pipe foot has a great effect on the transient behavior of the jet.
Voicingsteps affecting the air jet generation have also been studied in a number of papers. The voicing first review known to the author that summarizes different voicing techniques is by Mercer [100].
Since voicing is a delicate procedure that requires expertise, it was already found that the inter-operation of researchers and organ builders is essential for examining the effect of voicing steps.
Nolle [110] examined voicing steps using an organ pipe constructed with certain parameters of its geometry adjustable. It was found that the pipe can only function properly in a very lim-ited range of geometrical parameters. Angsteret al.[12] performed measurements on adiapason (Prinzipal) pipe carrying out subsequent voicing steps, starting from the “raw” (unvoiced) pipe.
The expected effects of voicing steps were in good qualitative agreement with the measurement results.
Paál et al.[119, 120]
flow visualization
utilized thelaser doppler anemometry(LDA) andSchlierenimaging tech-niques for the visualization of the air jet of open and stopped labial pipes. They observed that the measurements show large differences of real instruments and simplified models. By means of flow visualization techniques and high speed camera recordings the jet-wave amplification and the vortex formation in the transients of flue organ pipes was studied by Yoshikawa [147, 148]. He found that an envelope-based estimation method for the jet-wave amplification and the mouth field strength provides good agreement with measurements. Later, Yoshikawaet al.[149]
proposed a jet–vortex-layer formation model for the vortex-sound generation in an organ pipe.
This model provided more information on the generation of acoustic velocity at the pipe mouth than previous models.
The effects of wall vibrations wall
vibrations
in the sound generation of labial pipes was also a subject of numerous publications. Backus & Hundley [20] performed experiments to find that the magni-tude of wall vibrations is negligibly small in most organ pipes, so as their effect on the sound character of the pipe. They concluded that stronger vibration of the walls is undesired. Kob [85]
analyzed the effect of wall vibrations on the attack of organ pipes. It was observed that the thin walls of a baroque flue pipe are likely to exhibit strong vibrations. These vibrations were found to have remarkable effect on the transient spectrum of the pipe; however, the influence on the steady state spectrum was found negligible. Nederveen & Dalmont [107] showed that the wall vibrations of a thin-walled, slightly elliptical pipe can have a significant effect on the pitch and the level of the produced sound. They found instabilities similar to wolf tones of bowed string instruments, which were explained by a proposed phenomenological model.
A high precision model pipe foot
model
of the foot of a labial organ pipe was assembled by Außerlechneret al.[19]. In this model various parameters of the geometry were adjustable by means of micro-meter screws. In reproducible measurements using a hot wire anemomicro-meter and a microphone, velocity profiles of the free air jet and the frequencies of the tonal components of the edge tone were determined in various configurations. The evaluation of the measurements have revealed that different hydrodynamical modes of the air jet coexist in a realistic edge tone configuration.
Außerlechner [18] also presented visualizations of the transient and steady state movement of the air jet by means ofparticle image velocimetry(PIV) measurements.
With the increased computational capacity at hand numerical
simulation
, computer simulation of the edge tone by means of numerically solving the Navier – Stokes differential equations has become feasible in the last decade. Adachi [5] performed thecomputational fluid dynamics (CFD) analysis of an air jet deflected by acoustic waves and found good agreement with Nolle’s measurements [111].
Kühnelt [87] performed simulation of the sound generation mechanism of a stopped rectangular labial pipe by means of thelattice Boltzmann method(LBM). Nevertheless, due to limitations of computational capacity, the viscosity had to be increased in the simulations which rendered the results incomparable to measurements.
Further contributions recent
con-tributions
have appeared recently on the numerical simulation of wind instru-ments. Vaik & Paál [140] published the results of two-dimensional numerical simulations of the edge tone using various turbulence models. Agreement with the measured data of Außerlechner et al.[19] was found regarding the velocity profiles of the free air jet and the mode frequencies of the edge tone. The latter were determined from the spectra of the pressure forces acting in the upper lip. Fischer & Abel [62] have utilized two-dimensional Large Eddy Simulation (LES) of the
2.3. STATE OF THE ART IN PIPE ORGAN RESEARCH 17 compressible Navier – Stokes equations to model the synchronization effect of two organ pipes.
Akamuraet al.[10] proposed a numerical approach for calculatng Howe’s integral formula (see [75]) for the vortex sound sources of a wind instrument. The current challenges of numerical simulation of flue influenced were reviewed recently by Takahashiet al.[136].
As it is seen, a good amount of knowledge is already available on the sound production of flue instruments such as labial organ pipes. Nevertheless, there are phenomena—such as the role of the edge tone after the attack—in the sound generation mechanism that are still not completely understood, neither explained by theoretical models or numerical simulations.
2.3.3 Research on lingual pipes
While the sound generation mechanism of labial organ pipes has already been studied by a great number of researchers, and a remarkable amount of knowledge on the physics of the sound generation process has been obtained, much less is known about the physics of lingual pipes.
The reason for this might be that the process of sound generation is even more complicated than in case of labial pipes: the vibrating tongue is coupled to the acoustical system consisting of the shallot and the resonator, while its motion is driven mostly by flow effects. Therefore, a complete and reliable model of a lingual pipe needs to handle all three subsystems and their interaction.
The preliminary steps towards such a model are summarized in the following.
Fletcher [65]
pressure-controlled valves classified pressure-controlled valves that are responsible of sound generation
in woodwind and brass intruments and the vocalization of a lot of animals. In a model with a single degree of freedom, four configurations are possible, among which lingual organ pipes belong to the group labeled as “striking inwards”. It was shown that depending on the valve configuration, there exist particular ranges of acoustical input impedance where self-sustained valve oscillations are possible.
A simple analytical model of the stationary flow through the mouthpiece of a single reed instrument was developed by van Zonet al.[152].
analytical stationary flow model The flow was determined and measured in the
high and low Reynolds number limit and a good agreement for a clarinet reed has been found.
A similar model for a reed organ pipe was given by Hirschberget al.[72] and a nonlinear relation of the hydrodynamic forces acting on the tongue and the gap size between the tongue and the shallot has been obtained.
plucked and blown reeds Miklóset al.[103] compared the vibration frequency of plucked and blown reeds of lingual
organ pipes without the resonators, which lead to interesting observations. It was found—among other phenomena—that the frequency of the blown reed is significantly greater than that of the plucked reed, which is explained by the shortening of the free length of the tongue due to the blowing pressure in the boot. Later, the same authors have examined the interaction of the reed
with the shallot–resonator system [104]. coupling of
reed and resonator It was observed that when a strong coupling of the two
system occurs—i.e. the vibrating frequency of the reed is close to a natural resonance frequeny of the acoustical system—the fundamental frequency of the pipe jumps abruptly and the pipe can not be tuned to a pitch that is in one of these “forbidden” domains of frequencies. The investigations of the aforementioned papers [103, 104] resulted in a better understanding of the physics of reed pipes; however, the physical model used for the explanation of the observed phenomena was not verified quantitatively due to the large number of parameters involved.
Reed vibration of lingual pipes was also studied by Huber et al. [76]. They developed a methodology by which non-contact modal analysis of the reed can be performed, providing use-ful information on the modal behavior of the tongue. Vibration characteristics of different types
of reed curvatures reed
curvature and their effects on the tone were studied by Plitnik [125] and Plitnik &
Ang-ster [126]. By means of comparing different shallots with different reed curvatures, it was found that both the shallot and the reed curvature have a remarkable effect on the sound quality of the pipe. Nevertheless, a simple relation between reed curvature and the speech and stationary sound characteristics was not found.
The most recent work
recent work in the topic known to the author is by Preukschatet al.[127, 128]. They examined the behavior of lingual pipes by decomposing the complete system and performing measurements on the different parts separately. Preukschat also set up a pressure pulse reflec-tion model of the sound generareflec-tion in lingual pipes, which gave good match with the measured waveforms.
Although the last two decades provided a lot of new information on the physics and sound generation mechanism of lingual organ pipes, all details of the process are still not completely understood. A complete model of a lingual pipe—that can be utilized for sound reproduction, for example—has to able to handle the coupled fluid dynamical–mechanical–acoustical system, which seems to be a very challenging task due to its complexity.