PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Differences and similarities in the production mechanism of reeds,
brass, and voice: the source-filter viewpoint
Bernd J. KRÖGER
Department of Phoniatrics, Pedaudiology and Communication Disorders, RWTH Aachen University, Germany

ABSTRACTThe acoustic sound production mechanisms of reed instruments, brass instruments as well as of the human voice(singing and speech) are already well investigated. In this paper these mechanisms will be compared from three
viewpoints: (i) sound source (reeds, lips, vocal folds), (ii) filter, i.e., sound transmission and sound radiation via
tube or pipe and (iii) interaction mechanisms between source and filter. Interaction can be divided in aerodynamic-acoustical interaction and aerodynamic-mechanical interaction. It is known that the aerodynamicmechanical interaction decreases from reeds via brass to voice. In this study the influence of this interaction on
pitch is investigated for reeds, brass and voice by using a computer model for sound production. Simulations using
this model underline the influence of the filter on pitch in reeds and brass while pitch in speech and singing is
mainly controlled by source parameters like vocal fold tension.
Keywords: Sound production, voice, music instruments, reeds, brass

1. INTRODUCTION
While source models for reed and brass instruments are limited, a well-known source model exists for speechand singing. This model is a self-oscillating two-mass model of the vocal folds introduced by Ishizaka &Flanagan (1) and refined by Pelorson et al. (2) and others later. This simulation model constitutes a goodcompromise between computational efficiency and approximation of the mechanical and dynamical properties ofthe vocal folds. The mechanic-dynamical part includes two coupled damped spring-mass pairs simulating thelower part (also: inner part: vocalis muscle) and the upper part (also: outer part: mucosa) of the vocal folds. The
aerodynamic effects taking place within the region of the glottal narrowing are (i) the Bernoulli pressure drop,(ii) viscous losses due to air flow and wall interactions, (iii) the inertia of the mass of the trachealglottal-pharyngeal air column and (iv) turbulent dissipation of kinetic energy occurring in the jet flow at glottal
outlet (2). The detailed modeling of these aerodynamic effects is important in order to get the correct external
driving forces acting on the surface of the masses of the two-mass model and in order to calculate a correct
glottal flow.
The excitation source of a reed instrument, here of a clarinet, can be modelled using a distributed
one-dimensional model or a lumped one-mass model approximation of the mechanic-dynamical systemrepresenting the lips-reed system of player and instrument. Pressure difference and the resulting airflow
occurring between the oral cavity of the player and the mouth piece chamber of the instrument are calculated bytaking into account here the Bernoulli pressure and viscous losses (3, 4, 5).
In case of the excitation source of a brass instrument, here of a trumpet, the vibrating lips can be modelledusing a one-mass model with one or two degrees of freedom concerning movement direction (6, 7). Two
dimensions for lip movement are necessary because the lips move up and down in order to regulate lip aperture(closing and opening) but the front part of the lips as well moves in front-back direction, i.e. inside-outside
direction relative to mouthpiece (7).
For the simulation of the aerodynamic and acoustic characteristics of the vocal tract as well as of the bore or
tube of a reed or brass instrument, a reflection type line analog or transmission line model can be used (for a
vocal tract model, see (8); for a clarinet model, see (9)). In the case of the filter, mainly the radiation losses at theend of the bore or tube (i.e., mouth or bell) as well as the loss due to the backward traveling air flow into thesource (glottis or mouthpiece) needs to be calculated. In addition it is useful to include wall vibration losses(shunt losses) in order to allow oral closures in case of speech and singing or in order to allow a correct modelingof losses in case of long and small bores like in the case of brass and reed instruments. An alternative for a pure
simulation of the acoustics of the bore or tube, i.e., of the filter, is the calculation of its input impedance (see e.g.
10).
Source-filter interaction – i.e. interaction between sound source (vibrating system which produces the initial
air pulses) and the tube (vocal tract tube or instrument bore or tube in which the air pulse is propagated) – can beseparated into aerodynamic-mechanical and aerodynamic-acoustical interaction. These interactions areinvestigated already in detail for speech and singing. Aerodynamic-acoustic interaction influences the glottal
flow shape (11, 12). Aerodynamic-mechanical interaction is stronger than aerodynamic- acoustical interaction

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and leads to changes in vocal fold vibration (13). This can be an alteration of fundamental frequency or astrengthening or weakening of glottal vibration. A strengthening occurs in cases where F0 remains below thefrequency of the first (or a higher) resonance of the filter. A weakening occurs if pitch of the source and thefrequency of a resonance of the filter are at about the same value (i.e., in the case of a strong resonance couplingof source and filter) or if the vocal tract is closed in case of speech and singing and thus airflow is massively
obstructed.
In this paper simulations are executed which support the idea that the aerodynamic-acoustical source-filter
interaction is much stronger in case of reeds than in case of singing, while brass instruments are in anintermediate position. In the case of reed instruments the acoustical length of the bore or tube mainly controls
pitch. In the case of speech or singing vocal folds parameters like vocal fold tension and pulmonary or subglottalpressure mainly control pitch while the vocal tract here is of nearly no influence. Thus in the case of singing the
vocal tube is allowed to be modified in shape and length while pitch is not influenced. This allows the
production of different vowel qualities and different sounds with constant glottal excitation. In case of music
instruments the situation is different. Here the sound or timbre of a music instrument is mainly fixed by theshape of the instrument itself. The timbre or sound quality (independent of pitch) of the music instrument is oneof the main perceptual factors for the identification of the instrument.
In and further experiment of this study it will be shown that brass instruments take an intermediate position
concerning pitch control. While F0 is controlled here by lip tension in combination with length of tube or bore, it
is known that in specific cases pitch can be controlled by lips alone. A trained trombone player is able to produce
a glissando of more than one octave without changing the position of the slide, i.e. an experienced player can
produce a glissando covering more than one octave without changing the length of the tube or bore of the
instrument. For reed instruments this is not possible. Here pitch is governed mainly by the acoustic length of thebore and lip as well as jaw articulation lead only to small changes in pitch (cf. the complex production
mechanism for the clarinet glissando in Gershwin’s “Rapsody In Blue”, see (14)).

2. METHOD: THE SIMULATION MODEL
A reflection-type line analog (8) is used here for time domain simulation of the tube aerodynamics andacoustics, i.e. for simulating the aerodynamics and acoustics within trachea, glottis, pharynx and oral cavity incase of voice, for simulating the aerodynamics and acoustics within oral cavity, tip of mouth piece, mouth piecechamber, bore and bell in case of reeds (here: clarinet) and for simulating the aerodynamics and acoustics within
oral cavity, lips, mouthpiece chamber, bore and bell in case of brass (here: trumpet). In case of simulating 20000
time steps per second 22 tube sections (singing) via 68 tube sections (clarinet) up to 162 tube sections (trumpet)with constant length (l = 0.875 cm) and constant cross section area are needed in order to model a tube of 17.5
cm length for vocal tube (voice) via 59.5 cm length for clarinet (reeds) including bell to 140 cm length fortrumpet (brass; Fig. 1) including flare and bell. In each case the first three sections represent the end of trachea,
laryngeal constriction beginning of pharynx in case of voice, represent the end of oral cavity, tip of reed
constriction and begin of mouthpiece chamber in case of reed instruments or represent the end of oral cavity,
labial constriction and mouthpiece chamber in case of brass instruments (see light blue sections in Fig. 2). The
further sections represent the vocal tract tube or the bore and bell of the reed or brass instrument (Fig. 1).
In case of the vocal tract the cross sectional area was set to a constant value from larynx to mouth (A = 4.9
cm2; diameter d = 2.5 cm) representing vowel, i.e., a schwa sound. In case of the clarinet the bore has a diameterof approximately 2.8 cm, leading to a cross sectional area of A = 6.16 cm 2. The bell was modelled by increasing
the cross sectional area in a nearly exponential way for the last 13 tube sections (last 11.5 cm of clarinet length)
up to a maximum area of A = 38.5 cm2 (d = 7.0 cm). The first cross sections representing the upper part of themouthpiece chamber of the clarinet were set to A = 1 cm2 (see Fig. 2). In the case of the vocal tract the firstformant (first vocal tract tube resonance) appears at F1 = 500 Hz while the first resonance for the clarinet bore
appears at about 147 Hz and that of a trumpet at about 63 Hz. While the clarinet is modeled geometrically by acylindrical bore plus a short and small bell, the bore, flare and bell of a trumpet is more complex. Detailed datafor cross sectional diameter values for a trumpet are given by Kipp (15). The diameter of the trumpet bore is verysmall (of about 1.2 cm) while the diameter increases up to 14 cm at the end of the bell.
Losses are modelled (i) at the first tube section as free radiation of the backward traveling partial flow wave
in the trachea (for voice, see (16)) or in the mouth cavity (for reed and brass instruments), (ii) at the second tube
section in order to simulate the Bernoulli pressure drop at the strongest constriction within the whole line (2) and(iii) at the last tube section in form of radiation losses due to radiation at the mouth (for voice, see (16)) or at thebell (for reed and brass instruments). Spatially distributed losses are implemented as shunt losses for simulatingwall vibrations over the whole length of the bore or vocal tract (ibid.).
Concerning the vocal folds which are simulated by the two-mass model mass 1 (m1) represents the lower
muscular part of the vocal folds (main mass) while the smaller and lightweight mass m 2 represents the vocal foldtissue (mucosa) occurring at the outlet region (upper region) of the glottal narrowing. The complete dynamicallycoupled spring mass system is displayed as red structure in Fig. 2. Two masses are needed to model theoscillatory behavior of the vocal folds correctly, because it is an important characteristic of glottal vibration thatthe upper part of the vocal folds (m2) opens and closes later than the lower main part of the vocal folds (m1). This6460

allows the correct modeling of aerodynamic to mechanic energy transfer: During the closure period of the upper
part of the glottis the subglottal pressure acts on the main mass and causes glottal abduction in this lower regionof the vocal folds. Later, the upper part of vocal folds opens, and Bernoulli under-pressure occurs as a result of
the now occurring upstreaming strong air flow. This under-pressure – beside the restoring forces resulting fromthe mechanical part of the two mass oscillators – helps to re-adduct the vocal folds and leads to glottal closure aspart of each glottal vibration cycle. Thus the two mass model is needed in order to generate a stable two phaseenergy transfer (positive pressure on the lower part of the vocal folds for vocal fold abduction in the opening
phase of glottal cycle and later negative pressure on upper and lower part of the vocal folds for vocal foldadduction during closing phase of the glottal cycle) for stabilizing glottal vibration independent fromacoustically generated over- or under-pressure occurring in pharynx right above the glottis which results fromthe occurring standing waves in the vocal tube.

Figure 1 – Geometrical models used for our
numerical simulations for vocal tract (a “technical”
schwa-vowel is articulated, dashed line), for a
Bb-clarinet (all tone and register holes are closed,
solid line) and for a Bb-trumpet (no valve is pressed,
dash-dotted line); x-axis: length x of instrument in
cm; y-axis: diameter d of bore or tube in cm.

Figure 2 – Two mass approximation of the mechanical part of thesound source (red and light red structures: springs and masses) andtube section model of the filter (light blue boxes represent sections ofcavities) for clarinet (a), trumpet (b) and voice (c). The smallest tube
section represents the reed tip narrowing for clarinet, the lip
narrowing for trumpet and the glottis narrowing for voice.

For reeds as well as for brass, a one mass model would be sufficient as sound source (see Introduction). We
approximate that one mass approach by increasing the coupling stiffness k c between m1 and m2 in our two massmodel by a factor 1000, which leads to a relatively tight mechanic coupling between both masses. In case ofclarinet m2 represents the upper part of the reed (tip of the reed) in the region of the buffle and tip of themouthpiece while the main mass m1 represents the main vibrating part of the reed in the region of the mouth
piece window (upper thin part of the reed; upper half length of the reed). This mass m1 is mainly driven by thepressure occurring in the chamber region of the mouthpiece below the buffle (roof region) while the small mass
m2 is driven by the pressure occurring in the buffle and tip region of the mouthpiece.
In case of the lips as sound source of a brass instrument the main mass m 1 represents the main part of the lips
and the small mass m2 represents the front part of the lips within the mouthpiece. But because of the stiff
coupling between both mass pairs the oscillation of both mass pairs is nearly identical. The driving force for thespring mass system is the oral pressure for lip opening and thus the situation for energy transfer from theaerodynamic to the mechanical system is comparable to the situation already described above for the vocal folds.
But it should kept in mind that the acoustically generated over- or under-pressure occurring in the mouthpiecetube right in front of the lips which results from the occurring standing waves in the bore or tube now is higher
compared with that occurring in the pharynx during phonation and thus may influence lip vibration (see below,
experiment 6).
The spring mass parameters of the two mass model representing the vocal folds in case of singing,
representing the lips in case of brass instruments (here: trumpet) and representing the reed plus lips in case of thereed instruments (here: clarinet) are listed in Table 1. The masses of both mass pairs are set a factor 10 lower forthe reeds and set a factor 2 lower for the lips in brass mouthpieces in comparison to vocal folds. The stiffness
value of the springs of both oscillators is set a factor 10 higher in case of the reed and a factor 2 in case of thelips in the brass mouthpiece in comparison to the vocal folds. This leads to a resonance frequency of 109 Hz incase of vocal folds to 218 Hz in case of the lips in the brass mouthpiece and to 1092 Hz in case of the reed if
only the resonance of the main mass m1 is taken in consideration, i.e., using the formula for an undamped single
spring mass system:f = 1/(2*pi) * sqrt(k/m)(1)
In case of reeds and brass the damping parameters of both oscillators are reduced by a factor 100 incomparison to vocal folds. For the reeds the stiffness parameters are increased by a factor 100 for the impact
case, i.e. for the case of a correct modelling of the hard collision of reed with the mouthpiece table in comparison
to the soft collision of the left with the right side of the vocal folds in case of the voice source or the soft
collision of the upper with the lower lips in case of the brass source.

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Table 1 – Parameters of the spring mass system for all three cases (voice, reed instrument, brass instrument).
mass [g]stiffness
resonance
oscillation[N/m] frequency [Hz]frequency [Hz](note)
voice
oscillator 1
0.170
80
109
109
(vocal folds)(A2)
oscillator 2
0.030
8register: bass
coupling
55
trumpetoscillator 1
0.085
160
218
(lips)
oscillator 2
0.015
16
coupling
55000
clarinet
oscillator 1
0.017
800
1092
127
(reed+lips)(B2)
oscillator 2
0.003
80
coupling
55000-

In the case of the vocal folds for singing as well as in the case of the lips for brass instruments a q-factor
called vocal fold or lip tension is introduced in order to allow the parameters of the coupled spring mass system(increasing stiffness and decreasing mass, see equation 2 and 3; the index tab represents the values, listed in table1) to change. This is needed in order to tune the vocal folds or lips with respect to a specific pitch. The
introduction of the q-parameter in case of the vocal folds is described in detail in Ishizaka & Flanagan (1972) for
vocal folds.
(2)m = mtab * (1/q)(3)
k = ktab * q
In this study the q-parameter is adapted for lips as well as a first approximation in order to be able to control
pitch in case of brass instruments. The q-parameter was set to q = 1 for the reeds without any variation.
Simulations are carried out for different pulmonary pressure values (see below), different mass and stiffness
values for vocal folds, lips or reed as well as for different bore or tube length in case of vocal tract, reed andbrass instruments as introduced here. Six simulation experiments are executed using the parameter settings
introduced above.

3. SIMULATION RESULTS
3.1

Experiment 1: basic settings of model parameters for singing (low male voice: bass
register), brass (trumpet) and reeds (clarinet)

In this first experiment a preliminary adjustment of the parameters of the self-oscillating source model and of
the reflection type line analog for the singing voice, for a Bb-trumpet (brass) and for a Bb-clarinet (reeds) is
realized. The parameter settings for the self-oscillating source model, i.e. of the two-mass model, as well as forthe filter, i.e. for the tube section model or reflection type line analog, are already discussed in the Method
section of this paper.
In addition, the pulmonary pressure (PP) which is inserted in the trachea for singing or in the oral cavity ofthe player for reeds and brass, i.e. in the first tube section of the model, is set to PP = 1000 Pa for singing, to PP= 1500 Pa for brass and to PP = 2500 Pa for reeds. In case of voice and brass the q-parameter is set to q = 0.75
(low pitch). The q-parameter is always set to q = 1 for the reed.
Typical oscillation patterns of both mass pairs, of the time course of the forces acting on each mass as well asof the time course of the aerodynamic parameters glottal flow and sub- and supraglottal pressure are displayed in
Figure 3. From these patterns typical differences in in aerodynamic-mechanical interaction can be unfoldedwhich lead to the resulting differences in vocal fold oscillations. These differences are discussed in the results
section.

3.2

Experiment 2: constant pitch in singing despite varying tube length (low male voice)In this experiment the tube length is varied from 14 cm (like it occurs during production of vowel /i/ or /a/) to24.5 cm (like it may occur in vowel /u/ for some speakers) in steps of 2*0.875 cm. The vocal folds were adjusted
as defined in experiment 1 (male singer with PP = 1000 Pa and q = 0.75). It can be seen from Fig. 4 that thefundamental frequency F0, i.e., the pitch of the singing voice remains stable (F0 = 120 Hz), while the frequency
F1, i.e., the frequency of the first resonance or first formant of the vocal tract tube decreases with increasing tube
length. The interpretation is given in the discussion section.

3.3

Experiment 3: variation of pitch in singing (low male voice: bass register) due to varying
vocal fold tension and varying pulmonary pressure

In this experiment vocal fold tension q is modified in combination with pulmonary pressure PP in order todemonstrate the range of pitch variation for a low male voice (bass register). In the first part of the experiment
the phonation threshold pressure PPthreshold is estimated for a wide range of vocal fold tension (q = 0.5 to q = 2.5).
PP is decreased continuously until vocal fold vibration ends. The pressure at that end point is labeled as PP (seeblue dotted line in Fig. 5).
In the second part of the experiment, pitch (fundamental frequency F0) as generated by the self-oscillating6462

glottis model is measured for each q value (vocal fold tension) in combination with a co-varying pulmonarypressure PP which is set 300 Pa above the phonation threshold value (see blue dashed line in Fig. 5) in order toguarantee a stable vocal fold oscillation, i.e., a stable phonation even if vocal fold tension changes. Our model iscapable to produce a pitch range of about two octaves (F0 = 80 Hz [Eb2] to F0 = 320 Hz [Eb4] (normal bass
register is from F2 (87 Hz) to D4 (293 Hz); normal tenor register is from C3 (131 Hz) to G4 (392 Hz)).

Figure 3 – Oscillation patterns of self-oscillating source model ag (solid line, blue), ag1 (dash-dotted line, green) and ag2(dotted line, green), subglottal pressure psub (solid line, blue), pressure pg acting on the inner sides of both mass pairs pg1(dash-dotted line, green) and pg2 (dotted line, green), glottal flow ug (solid line, blue) and pressure at glottal outlet psupra (solidline, blue) for singing voice (a), for trumpet (b) and for clarinet (c).

Figure 4 – Variation of pitch (fundamental frequency F0,
solid line, blue) as function of vocal tube length L for a malesinger. Beside pitch the frequency F1, i.e., the frequency of
the first resonance of the vocal tube is displayed as well(dashed line, blue).

3.4

Figure 5 – Variation of pitch F0 as function of vocal foldtension q and pulmonary pressure PP for a low male singer(bass register). The co-varying pulmonary pressure PP isbased on phonation threshold pressure PPthreshold.

Experiment 4: pitch variation in reeds resulting from varying bore length (clarinet)

In this experiment the bore or tube length L of the clarinet is modified (shortened) in order to mimic theopening of tone holes in order to play different tones. It can be seen that the pitch is changing together with thefrequency of the first resonance of the bore and thus is changing with bore length L. The frequency F1 of thefirst resonance is simply calculated for quarter-length standing waves in a tube. csound is propagation velocity ofsound waves (about 350 m/sec):(4)
F = csound / (4*L)
This calculated resonance frequency (dashed line in Fig. 6) is higher than that of the pitch F0 resulting fromthe self-oscillating source model (frequency of source oscillator, solid line in Fig. 6) if tube length becomes short.
That results from the fact that the influence of the bell becomes more prominent for shorter tubes. This effect is
not included in equation 4 but occurs in our simulation model of the clarinet.

3.5

Experiment 5: constant pitch for a reed resulting from constant bore length despitechanging mass or stiffness of the reed

In the first part of this experiment (experiment 5a) the bore or tube length is held constant (L = 59.5 cm)
representing the condition that all tone and register holes are closed. But one main parameter of the source
oscillator, i.e., the stiffness of the reed (stiffness of both oscillators) is varied. The stiffness of spring-mass pair 1
is changing from k1 = 400 N/m to k1 = 800 N/m in steps of 50 N/m and in parallel the stiffness of the second
spring mass pair is changed from k2 = 40 N/m to k2 = 80 N/m in steps pf 5 N/m. The masses of both oscillators
are held constant (m1 = 0.017g, m2 = 0.003 g). Results of the simulation are displayed in Fig. 7. No change ofpitch F0 occurs (frequency of the source oscillator, i.e., of the two-mass model) despite a change in the oscillator
dynamics reflected by the frequency of the reed resonance F reed which varies from 750 Hz up to 1100 Hz (Freed is
calculated using eq. 1).

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In the second part of this experiment (experiment 5b) the bore or tube length is held constant (L = 59.5 cm)
as well but now the other main parameter of the source oscillator, i.e., the mass of the reed, i.e., the masses ofboth oscillators are varied (m1 = 0.0085g in 3 steps to m1 = 0.017g and in further 4 steps to m1 = 0.034g; m2 isvaried with same amount of steps from m2 = 0.0015g via m2 = 0.003 to m2 = 0.006g ). Results are displayed inFig. 8. Like in the first part of the experiment, no change of pitch F 0 occurs (frequency of the source oscillator,i.e., of the two-mass model) despite a strong variation of oscillator masses reflected by the frequency of the reed
resonance Freed which now varies from 1550 Hz down to 700 Hz.

3.6

Experiment 6: glissando experiment for trumpet: varying pitch in brass resulting fromvarying lip tension in case of constant bore length

While the lip parameters are already adjusted for normal vibration of lips in case of the lowest note of a
Bb-trumpet (table 1, fig. 3b) in this experiment a glissando is simulated by increasing the lip stiffness (q = 0.5 toq = 3.5) and at the same time increasing pulmonary pressure and thus oral pressure from PP = 1000 Pa to PP =3500 Pa). The length of the bore is not changed in order to mimic a trumpet glissando without pressing any valve.
Fig. 9 illustrates that our virtual trumpet player can perform this glissando by covering a pitch interval from F0 =120 Hz to F0 = 470 Hz. But the increase in frequency is not as linear as is in case of the singing (see forexample Fig.5). It can be speculated that the occurring irregularities result from an interaction of higher
resonances of the bore of the trumpet (res2, res3, res4) with the source oscillator, i.e., with the lips of the trumpet
player. It can be assumed that the resonances of the bore try to “catch” and “hold” a tone. Thus the fundamental
frequency is no longer controlled by the lips alone, i.e., by varying lip tension (changing mass and stiffness of
the lip mechanical resonator), but in addition the resonances of the bore become important and try to “catch” and“hold” the fundamental frequency F0 generated by the source oscillator (self-oscillating two-mass model). That
seems to be comparable to the mechanism how beginners search for their first notes on the trumpet, i.e., how
they try to adjust lip tension in the right way for producing a note referring to the bore length and thus to thefingering of the player.

Figure 6 – Variation of pitch (F0) as
function of bore or tube length L for aclarinet. Beside pitch F0, resulting
from the self-oscillating source model(solid blue line), the calculated lowest
resonance frequency of the bore F1 isdisplayed (dashed blue line).

Figure 7 – Variation of pitch (F0) for
clarinet as function reed stiffness if ofbore or tube length is constant. Besidepitch the eigenfrequency of the source
system Freed is displayed as well(dashed line).

Figure 8 – Variation of pitch (F0) for
clarinet as function reed mass if of boreor tube length is constant. Beside pitch
the eigenfrequency of the source
oscillator Freed is displayed as well(dashed line).

Figure 9 – Display of simulation parameters for a trumpet glissando

4. DISCUSSION
The basic differences and similarities of the acoustics and aerodynamics of a clarinet as example for a reed
instrument of a trumpet as example for a brass instrument and of a low male singing voice were illustrated in thispaper by using a computer simulation model. A reflection type line analog representing the filter coupled with aself-oscillating damped spring-mass model representing the sound source is used for modelling all three cases(voice, reeds, brass).

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Experiment 1 clearly indicates aerodynamic-acoustical interactions like the ripple within air flow of thesource ug in case of the clarinet (see (12) for voice). Strong aerodynamic-mechanical interaction is found forclarinet as well as for trumpet. While in case of voice the pitch is mainly controlled by the vocal folds itself (i.e.,
by vocal fold tension, see experiment 3) and while here vocal tract shape and vocal tract length has nearly no
influence on pitch (see experiment 2) the situation is different for reeds and brass. Our simulations indicate thatthe pitch of the clarinet is mainly determined by the first resonance of the bore or tube and thus strongly
depending on bore length (experiment 4) while the dynamic parameters mass or stiffness of the oscillating
source can be varied in a relatively wide range without influencing the pitch (experiment 5).
The brass instruments are in an intermediate position between voice and reeds. Simulating a trumpet
glissando by increasing lip tension and oral pressure indicates an increase in pitch comparable to increasing
vocal fold tension and pulmonary pressure for a low male voice (experiment 2). But in the case of the trumpet
this increase in pitch is not as linear as it occurs for the voice. In case of the trumpet the increase in pitch iscomparable to a step function despite the fact that the lip tension and oral pressure increase continuously(experiment 6). A possible explanation is that pitch seems to “being hold” in frequency regions representing the
2nd and higher resonances of the bore. This aerodynamic-mechanical interaction seems to be lower for brass incomparison to reeds – where pitch always is in line with the first resonance of the bore – but higher than
aerodynamic-mechanical interaction for voice if the pitch of voice is below the first tube resonances, i.e. below
the frequency of the first formant.
These differences in degree of aerodynamic-mechanical interaction can be understood if we compare thetransfer of energy from the aerodynamic system to the mechanic source system. The occurring forces on bothmasses of the coupled spring-mass pairs in the oscillator system representing the source are displayed in Fig. 3(experiment 1). It can be seen that the pressure-induced forces acting on the reed is different from those acting
on the vocal folds in case of singing or on the players lips in case of brass instruments. In the case of the vocal
folds subglottal pressure is acting on both masses during the closed phase which forces the vocal folds to open.
Within the open phase of the glottis – beside the (not shown) restoring forces of the spring-mass system – anunder-pressure acts on the masses within the closing phase of the vocal folds. Thus a phase-correct transfer ofenergy occurs during the closed and open phase of the glottis and the same holds for the closed and open phaseof the lips in case of the brass instrument. The only difference is that in case of brass no phase lag occurs
between both mass pairs which leads to a shorter closed phase and the occurring forces on the open phase arestrongly related to the pressure in the mouthpiece resulting from the standing waves established in the bore. Thispressure right above the oscillator – i.e., pressure in the pharyngeal cavity in case of singing, pressure in themouthpiece in case of brass instruments – is much lower in the case of singing. During singing, the main effect isthe small negative pressure occurring within the closing phase of the glottal open phase which results from
Bernoulli under-pressure, while the stronger negative lip closing pressure in the case of the brass instrument
stems from a phase-correct occurring standing wave established in the instrument bore. During the closed phasethe subglottal pressure for singing as well as the oral pressure for the lips-mouthpiece system of the bass
instrument is positive in order to allow the vocal folds (respectively the lips) to open again.
In the case of the reed the force acting on the tip of the reed during closure of the reed-mouthpiece system isthe oral cavity pressure which acts on the outer side of the reed in order to hold the closure. This pressure – incontrast to the subglottal pressure in case of singing which acts on the inner side of the vocal folds and incontrast to the oral pressure in case of the brass player’s lips which act on the inner side of the lips – is negative.
Thus the related resulting force tries to hold the closure of the reed-mouthpiece system. Consequently in case ofreeds the opening and closing mainly results from the pressure acting on the inner side of the reed and thispressure as function of time results from the standing waves occurring in the bore. Thus these standing waves
within the bore dominate the changes of pressure within the chamber of the mouthpiece and let the reed moveoutside in the case of positive pressure or sucks in the reed in the case of negative pressure. Thus thefundamental frequency of reed oscillation is driven by the frequency of the standing wave (first resonancefrequency of the bore or tube) and not by the dynamical parameters of the two-mass oscillator itself as it is thecase for singing. The resonance frequency of the damped mass-spring oscillator representing the reeds alone ismuch higher (about 1000 Hz, see table1; 1400 Hz to 3000 Hz following (17, 4)).
It should be kept in mind that in the case of singing specific vocal tract shapes lead to a better sustain andthus professional singers change vocal tract shape with pitch even for producing the same vowel quality. This is
an indicator that aerodynamic-mechanical interaction is important for singing as well, but only, if pitch is nearand possibly higher than the first vocal tract resonance frequency (which is tried to be avoided, see (18)).
One more important difference between reeds and brass is that the bore or tube of reeds (here clarinet with
about 60 cm) is short in comparison to brass instruments (here trumpet with about 140 cm). But because of theflare and huge bell of brass instruments the resonances of brass instruments do not form a strict harmonic row
and the first resonance frequency F1 is far below pitch F0. Thus brass players adjust pitch with respect to thesecond and the higher resonance frequencies (F2, F3, …) while the pattern of resonance frequencies due to the
instrument bore is much more regular in case of reeds and here the pitch is strictly oriented with respect to thefirst resonance frequency F0 as well as to higher resonance frequencies of the bore in case of playing higher
registers. Thus pitch for brass is above first resonance or bore, pitch of reeds in its lowest register exactly equals
that of the first resonance of the bore and pitch of voice preferably is below the first resonance of vocal tract.

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5. CONCLUSIONS
A first main result of this study is that different control mechanisms of pitch in source-filter systems likevoice, brass or reeds can be modelled by a time domain simulation of tube acoustics coupled with a two-mass
damped mass-spring oscillator as source model. The interaction between the tube system and the source
oscillator is simulated by calculating the time varying pressure inside the tube sections acting on the mass pairsof the source oscillator. Using this simulation system, different degrees of source-filter interaction can be
simulated as they occur for the speaking and singing voice, for brass instruments and for reed instruments. Voice
pitch is mainly determined by vocal fold tension. On the other hand we were able to demonstrate that pitch for areed instrument (here for a clarinet) is mainly controlled by the length of the bore, i.e., by the fingering of theplayer. Brass instruments take and immediate position. Here the lip tension of the player always needs to be
adjusted correctly with respect to bore length in order to produce clear sounds.
Some of these results are already known and published but this study clearly indicates how these basic
findings can be easily simulated in a simple geometrical and time domain simulation system representing voice
as well as music instruments like reeds and brass. Thus the software used here and the parameter optimizations
discussed in this study can be taken as a basis for developing a valuable demonstration tool in music acoustics.

ACKNOWLEDGEMENTS
This paper is dedicated to Josef Wilhelm (called: Joe), Marcus and Michael Buschmann (Cologne, Germany)for developing an artificial tuba and sousaphone player as part of their “Pneuphoniker Tünnes un Schäl”
orchestra.

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