The effect of fast trombone slide glissandi on the mechanics of artificial lips
D. M. CAMPBELL(1) , A. LOPEZ-CARROMERO(2) , J. A. KEMP (3)(1) University of Edinburgh, United Kingdom, d.m.campbell@ed.ac.uk(2) University of Edinburgh, United Kingdom, alopezc2@ed.ac.uk(3) University of St. Andrews, United Kingdom, jk50@st-andrews.ac.uk

Abstract
The lips of a brass player can be modelled as a mechanical oscillator which couples with the acoustic resonancesof the instrument to generate and sustain a musical note. On instruments like the modern orchestral trumpet,
operation of a valve changes the length of the resonator without significantly altering the mean pressure of
the air column. On a slide trombone, however, a glissando involves a telescopic change in the length of theresonator, resulting in localised changes in the mean pressure in the air column. The consequent low frequency
fluctuations in mouthpiece pressure can disturb the equilibrium position of the lips, affecting their dynamic
behaviour. This paper describes experimental studies in which an artificial mouth is used to investigate theinfrasound mouthpiece pressure gradients generated by fast glissandi on a trombone, and their influence on themechanics of the oscillating lips.
Keywords: Brass wind instruments, playing transients, lip dynamics

1

INTRODUCTION

Previous studies have shown that fast trombone slide movements, such as the ones performed by the player
during glissando, introduce infrasound pressure (ISP) variations inside the instrument which are approximately
proportional to the slide acceleration. The amplitude of the pressure fluctuations can reach 100 Pa inside theslide when the instrument is connected to a loudspeaker cavity [1, 2]. When the instrument is connected to asoft termination, such as the one present in the artificial mouth used in this experiment, infrasound pressures ofaround half this value have been observed [2].
These pressure fluctuations are transmitted through the instrument to the mouthpiece, where they induce very
low frequency modulation of the position of equilibrium around which the lips oscillate when playing. To
investigate whether this modulation exerts a measurable influence on the behaviour of the lips during fast glissandi, an artificial mouth connected to a King tenor trombone has been studied. The pressure across the lips ismeasured using two high pressure microphones, one in the mouth and another in the mouthpiece, and the lip
opening is tracked using a light transmission setup consisting of an optical rail, lenses, a laser and a photodiode.
The position of the slide against time is also tracked using a distance measuring laser.
The physical effects of ISP variations on the artificial lips are evaluated by performing fast inward and outward
glissandi across different slide positions x, so that a comparison can be established with the playing behaviour
measured with stationary slide at the same positions.

2

METHODOLOGY

The experiments were carried out in an acoustics laboratory in the James Clerk Maxwell building at the University of Edinburgh. The space has low reverberation but is not anechoic, since this characteristic was not neededin the present experiment. Figure 1 shows a general schematic including all the apparatus used in the setup.

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Figure 1. Schematic showing the light transmission setup, allowing the lip opening to be tracked when the slide
undergoes a fast gesture. The blue section of the instrument indicates the slide, which moves in a direction
perpendicular to the plane of the diagram [2],2.1 Technical setup
The artificial mouth was mounted on an optical rail, together with a IIB COHERENT 638DG laser (with its
beam parallel to the rail) a photodiode, two G.R.A.S. 1/4” high pressure microphones and a loudspeaker. The
optical rail allowed an optimum alignment between all the devices. The laser beam was first filtered with apolariser to control the intensity of the light and prevent the saturation of the photodiode located behind theartificial mouth. The beam was then expanded via a divergent lens with a focal length of -8 mm and a diameterof 30 mm, until an area wide enough to illuminate the internal diameter of the mouthpiece was achieved. At
this stage, the beam was made parallel using a convergent lens with its focus located at the position of thedivergent lens, and limited using a circular shutter to ensure that the vertical dimension (parallel to the lips)
remained constant during the oscillation. After reaching the artificial mouth, and crossing the oscillating lips,
the beam was converged at the other side by another lens, of both focal distance and diameter 50 mm, on to
the photometer’s sensor. A photograph of this set up can be seen in Figure 2. The trombone was connected tothe artificial mouth via a transparent mouthpiece, and clamped perpendicularly to the optical rail to minimise
structural vibrations during the manipulation of the slide as shown on the left side of Figure 3. The artificial
lips are water filled balloons, as shown on the right side of Figure 3, which can have their pressure modified
by varying the difference in height between the water bottle to which they are connected and the mouthpieceagainst which they are compressed. Their correct handling requires a degree of expertise and familiarisation
with the system, and there is variation in their behaviour depending on the water pressure. After thoroughadjustment, an embouchure able to play a note close to the third resonance between the first and third positionsof the trombone was achieved.
The position of the slide x was measured using a Baumer OADM 20I4471 laser sensor, powered via a custom

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Figure 2. Optical setup used for the measurements.

Figure 3. Left: artificial mouth clamped on the optical rail, on which the laser used to measure the slide
displacement x is also visible. Right: deflated rubber tubes used as artificial lips before being connected to theelevated water bottle which ensures equal static pressures on both lips.
made supply box. The laser sensor was attached firmly to the mouthpiece end of the instrument and remained
static during the whole process. The laser beam was intercepted by a small reflector attached to the mobile partof the slide, as can be seen in the left side of Figure 3
An air blower was used to create an excess pressure inside the artificial mouth. When the lips were correctly
adjusted this overpressure in the mouth set the lips into motion, coupling with the instrument and playing anote.
All signals were acquired via code written in MATLAB using National Instruments C-Series digital modules
mounted on a CompactDAQ Chassis connected to the desktop computer. The sampling frequency used was
51200 Hz. The transducers were calibrated during the post processing, using information from their technicalspecifications documentation. All signal processing was also coded using MATLAB.

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2.2 Experimental protocol
2.2.1 Lip characterisation
In order to determine the physical characteristics of the lips, the mechanical response of an embouchure able tocouple to the instrument and play it for slide extensions x varying between 0 and 0.45 m was measured.
]The mechanical response is defined as the relationship between the opening height H(f ) of the lips and the^pressure ∆P(f ) acting across them, both given as a function of frequency f .
^
]
^
MR(
f ) = H(f )/∆P(
f)(1)

This was achieved experimentally by driving the whole system acoustically (the mounted lips connected to the
instrument) via the loudspeaker connected to the artificial mouth. The signal played by the loudspeaker in thiscase was a sine sweeping exponentially in time over a frequency range that varied from 2 Hz to 1 kHz in atime interval of 10 s. This measurement was repeated ten times and averaged using the median value of all
the repetitions. The pressure acting upon the lips ∆P(t), was obtained as the difference between the pressure
measured in the mouth pm (t) and in the mouthpiece pmp (t) in Pascals. The lip opening height was taken to be
proportional to the voltage signal collected by the photodiode H(t), and was not calibrated as only magnitude
ratios are of interest here. These experimental magnitudes were transformed into the frequency domain via the
Fourier transform:]^
H(f ) = F (H(t)), and ∆P(f ) = F (pm (t) − pmp (t))(2)

Phase MR [rad]Amplitude MR [ ]The artificial lips are a non-linear system whose behaviour depends on the equilibrium position imposed by thestatic overpressure in the mouth. This has been previously reported and studied in [6], and can be observed in
the particular case under study in this article. A static overpressure in the mouth, just below the playing threshold, modifies the dynamic characteristics of the lips, which are pushed slightly outwards into the mouthpiece.
Figure 4 shows the mechanical response of the artificial lips both for a static overpressure in the mouth (blueline) and no static overpressure (black dashed line).
Static overpressure
No static overpressure
Playing range

60

80

100

120

140
160
Frequency [Hz]

180

200

220

240

60

80

100

120

140
160
Frequency [Hz]

180

200

220

240

2
0
−2

Figure 4. Mechanical response of the lips in a configuration able to play between first and third position of theslide in dimensionless magnitude (upper subplot) and phase (lower subplot).

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2.2.2 Experimental protocol
The embouchure achieved in this experimental work was able to play a musical note close to the third resonanceof the instrument for slide extensions between 0 m and 0.45 m. These lengths ensured that the Baumer OADM
20I4471 laser sensor remained inside its range for a reflector attached to the slide at 5 cm distance. It also
ensured that the artificial lips would not stop buzzing at any time, playing fundamental frequencies that spanned
between 143 Hz (for the longest slide extension) and 163 Hz (for the shortest one).
In a realistic musical context with a human player sounding the third regime of the instrument, this slide
movement would correspond to a pitch interval of 4 semitones, from F3 (173 Hz) in first position (slide fully
contracted) to C]3 (131 Hz) in fifth position (slide extended by around 0.4 m). The difference between thenormally played pitch interval and the experimentally observed one is explained by the fact that a humanplayer modifies the embouchure when operating the slide in order to match the resonances of the instrumentwith those of the lips. The adjustment of the artificial lips before playing sets a fixed embouchure, which is notdeliberately changed during the glissando.
The position of equilibrium of the lips does however have an effect on the mechanical resonances, as shownby the comparison in Figure 4 between the lip response curves with and without the sub-threshold overpressurein the mouth. It is therefore a plausible hypothesis that a negative infrasound pressure in front of the lips,
sucking them out from their normal equilibrium position, could create a transient modification of the mechanicalresonance curve in similar in character to that caused by a static mouth overpressure, as represented by theblue line in Figure 4. In the absence of slide movement the curve would be expected to resemble more themechanical response measured with no mouth overpressure (dashed black line in Figure 4).
The amplitude of the infrasound pressure generated during the playing experiments was estimated by low passfiltering ∆P(t) using a Hanning filter with a cutoff frequency of 10 Hz. The microphones used to determine∆P(t) have been shown to operate consistently at infrasound frequencies, although their calibration is not specified by the manufacturer below 3.15 Hz [7].
The experimental protocol was designed to look for differences in the playing amplitude, pressure across thelips and lip opening height which can be correlated with changes in the slide velocity and therefore the ISP.
Results were obtained from two different playing situations:• a quasi-static slide position x which was either constant or varying very slowly;• a rapidly changing slide position x during the playing of a fast glissando, either outward or inward.
This dataset was sorted as independent data points according to increasing slide position x. Three different datasubsets were selected, based on the values of the slide velocity ẋ:
1. −0.01 m/s < ẋ < +0.01 m/s (quasi-static);
2. ẋ < −0.5 m/s (inward glissando);
3. ẋ > +0.5 m/s (outward glissando).

3

RESULTS AND DISCUSSION

Figure 5 plots the variation of ∆P(t), lowpass filtered with a cutoff frequency of 10 Hz, as a function of theslide velocity ẋ for several inward and outward glissando gestures. As expected, the ISP is predominantly
positive for inward glissandi and negative for outward glissandi, athough there is a wide variation in the curves
for different gestures. In interpreting this graph it should be borne in mind that the stationary endpoint of aglissando corresponds to ẋ = 0. The ISP values continue to fluctuate for a significant fraction of a second after
the gesture has finished; the initial pressure swing generated by a glissando will be followed by a series of
decaying swings of alternating polarity, all of which are superimposed at ẋ = 0.

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ISP [Pa]

50

0

−50

−100
−4

−3

−2

−1

0

1

2

3

4

ẋ [m/s]
Figure 5. Infrasound pressure (ISP) as a function of slide velocity ẋ.
Figure 6 shows the recorded data, processed to allow comparison between the cases with static slide (leftcolumn), negative slide velocity (middle column) and positive slide velocity (right column). The first row of thisFigure shows the RMS value of the acoustic pressure variation across the lips ∆P(t). This value was obtainedusing a time window of 1000 samples which included over three cycles of the signal for frequencies in theplaying range, and a 50 % window overlap. The middle row displays the RMS value of the dimensionless lip
opening H, responding to the acoustic pressure. The RMS was calculated in the same way as described above.
The bottom row displays the infrasound pressure ∆P(t) low pass filtered by a Hanning filter at 10 Hz.
The results shown in the first column, for the stationary slide case, are in line with what is expected fromthe mechanical response characterisation presented in Figure 4. The resonance located around 140 Hz has agreater amplitude than the one just above 160 Hz, therefore the extended slide, which facilitates lower resonant
frequencies, displays larger amplitudes in both the RMS values of ∆P and H. In the absence of slide motion
there is no significant ISP.
It appears from the results presented in the middle and right column that fast slide gestures in either direction
reduce the amplitudes of both the acoustic pressure and the lip opening at a given value of slide displacement
x. In both negative and positive velocity cases, there are appreciable trends, albeit with different degrees ofdispersion, suggesting that the artificial lips may be susceptible to infrasound pressures capable of altering theposition of equilibrium around which they oscillate. However the interpretation of the results is complicated by
the fact that the decay time of the infrasound pressure fluctuations is typically longer than the duration of afast glissando gesture. The ISP force exerted on the lips for a given slide position x therefore depends on thepast history of the gesture as well as the current value of ẋ. This hysteresis could help to explain the different
shapes of the curves in Figure 6.

4

CONCLUSIONS AND FURTHER WORKThe acoustic behaviour of a trombone sounded by artificial lips, as measured by the RMS values of the pressure difference ∆P across the lips and the lip opening H, was found to depend on the direction of slide movement during fast glissandos. Infrasound fluctuations in ∆P with amplitudes ranging from +60 Pa to -90 Pa were
measured during these gestures. Further experiments and physical modelling simulations will be necessary toestablish whether there is a correlation between the infrasound pressure fluctuations and the changes observedin lip behaviour. It is expected that any effect of infrasound will be greatest for quiet playing, as the infrasoundpressure amplitudes will then be a more significant fraction of the static excess mouth pressure.

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negative slide velocity ẋ
1,600

1,400

1,400

1,400

1,200
1,000

1,200
1,000
800

0

0.2

600

0.4

0

0.2

0.8

0.6
0.2

0.8

0.4

0

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0

0.2

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0

0.2
x [m]

0.4

1

0.6
0

1,000

600

0.4

1

rms H [ ]

1

1,200

800

rms H [ ]600rms ∆ P [Pa]

1,600

800

rms H [ ]positive slide velocity ẋ

1,600
rms ∆ P [Pa]rms ∆ P [Pa]zero slide velocity ẋ

0.8

0.6
0

0.2

0.4

100

0

80

−20

0
−20

ISP [Pa]20

ISP [Pa]ISP [Pa]

40
60
40

−40
−60
−80

20
−40
0

0.2
x [m]

0.4

0

0

0.2
x [m]

0.4

−100

Figure 6. Analysis of three different stages of the mouth and trombone system, processed from data collectedfrom numerous slide gestures during playing. Left column: slide velocity smaller than 0.01 m/s (quasi-static).
Middle column: slide velocity less than than -0.5 m/s (inward glissando). Right column: slide velocity greaterthan +0.5 m/s (outward glissando). Top row: RMS acoustic pressure in Pa, measured across the lips. Middle
row: adimensional RMS lip opening height. Bottom row: infrasound pressure (ISP).

ACKNOWLEDGEMENTS
The authors of this paper are thankful to Dr. Alan Woolley for assisting with instrumentation.

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REFERENCES[1] Kemp, J. A., López-Carromero, A., Woolley, A. and Campbell, D. M., Experimental investigation of
Doppler shift and infrasound generation during wave propagation within the bore of the trombone during
slide movement. Proceedings of the Third Vienna Talk on Music Acoustics, 9-14, 2015..
[2] López-Carromero, A., Kemp, J. A. and Campbell, D. M., Experimental investigations of the effects offast slide movements in the trombone on the behaviour of an artificial mouth. Proceedings of the 24th
International Symposium on Musical Acoustics, Montreal, CA, 2017.
[3] Richards, O. F., Investigation of the lip reed using computational modelling and experimental studies withan artificial mouth. PhD thesis, University of Edinburgh, 2003.
[4] Bromage, S., Visualisation of the lip motion of brass instrument players, and investigations of an artificial
mouth as a tool for comparative studies of instruments. PhD thesis, University of Edinburgh, 2007.
[5] Newton, M. J, Campbell, M. and Gilbert, J., Mechanical response measurements of real and artificial brass
players lips. J. Acoust. Soc. Am. 123: EL14-20, 2008.
[6] Neal, M. Study of the brass instrument lip reed mechanism using artificial lips and Lattice Boltzmann flow
simulations. PhD thesis, University of Edinburgh, 2003.
[7] López-Carromero, A. Experimental investigation of acoustic characteristics of radiation and playing gestures
for lip-excited musical instruments. PhD thesis, University of Edinburgh, 2018.

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