Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
The exciter mechanism of double-reed
instruments
A. Almeida
C.Vergez, R.Caussé
IRCAM – Centre Georges Pompidou
Instrument Acoustics and Analysis / Synthesis Teams
Sep 20, 2006 – Musical Acoustics Network Conference,
London
Motivations of my PhD work
Double-reed
physics
Almeida
Motivations
Models
Resonator
General objective
understand the behavior of double-reed instruments
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
compare to other reed instruments
Applications
sound synthesis
validate generic models of reed
physical interpretation for methods of fabrication of
double reeds
From reed to sound
Double-reed
physics
Almeida
Motivations
Fabrication
procedures
Models
Resonator
Exciter
Tools for reed
characterisation
Instrument
behavior
Embouchure
Material
properties
Reed characteristics
Vibrational analysis
Sound
Conclusion
Reed
configuration
From reed to sound
Double-reed
physics
Almeida
Motivations
Empirical knowledge
(musician, reed maker)
Models
Resonator
Fabrication
procedures
Exciter
Tools for reed
characterisation
Instrument
behavior
Embouchure
Material
properties
Reed characteristics
Vibrational analysis
Sound
Conclusion
Reed
configuration
From reed to sound
Double-reed
physics
Almeida
Motivations
Models
Empirical knowledge
(musician, reed maker)
Resonator
Exciter
Tools for reed
characterisation
Reed
configuration
Instrument
behavior
Embouchure
Material
properties
Reed characteristics
Vibrational analysis
Conclusion
Fabrication
procedures
Sound
Measurements
Physical
parameters
Outline
Double-reed
physics
Almeida
Motivations
1
Reed instrument models
Resonator
Exciter
2
Tools for reed characterisation
Reed characteristics
Vibrational analysis
3
Conclusion
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Instrument models
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Pressure varies periodically inside the bore (resonator):
Conclusion
Period of oscillations determined by the bore geometry
Pressure variations cause the reed to open and close
Flow and pressure are modulated by the reed opening,
feeding the oscillation in the bore
Instrument models
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Pressure varies periodically inside the bore (resonator):
Conclusion
Period of oscillations determined by the bore geometry
Pressure variations cause the reed to open and close
Flow and pressure are modulated by the reed opening,
feeding the oscillation in the bore
Instrument models
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Pressure varies periodically inside the bore (resonator):
Conclusion
Period of oscillations determined by the bore geometry
Pressure variations cause the reed to open and close
Flow and pressure are modulated by the reed opening,
feeding the oscillation in the bore
Instrument models
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Pressure varies periodically inside the bore (resonator):
Conclusion
Period of oscillations determined by the bore geometry
Pressure variations cause the reed to open and close
Flow and pressure are modulated by the reed opening,
feeding the oscillation in the bore
Instrument models
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Pressure varies periodically inside the bore (resonator):
Conclusion
Period of oscillations determined by the bore geometry
Pressure variations cause the reed to open and close
Flow and pressure are modulated by the reed opening,
feeding the oscillation in the bore
Outline
Double-reed
physics
Almeida
Motivations
1
Reed instrument models
Resonator
Exciter
2
Tools for reed characterisation
Reed characteristics
Vibrational analysis
3
Conclusion
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Resonator
Double-reed
physics
Almeida
Motivations
Models
Resonator
Measured oboe impedance
for note B3
[Plitnik and Strong, 1979]
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Linear system
Pressure/flow independent of intensity
Depends strongly on frequency
Reeds work on maxima of pressure/flow
Outline
Double-reed
physics
Almeida
Motivations
1
Reed instrument models
Resonator
Exciter
2
Tools for reed characterisation
Reed characteristics
Vibrational analysis
3
Conclusion
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Exciter model
Mechanics
Double-reed
physics
Almeida
Linear spring model for the reed opening
Motivations
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
1111
0000
0000
1111
0000
1111
pr
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
0000
pm 1111
0000
1111
Models
S
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
Vibrational analysis
Conclusion
Displacement of the reed blades proportional to applied
force [Almeida et al., 2006]
Force caused by:
lips
pressure difference pm − pr
S0 − S proportional to pm − pr
Flow
Double-reed
physics
Almeida
Bernoulli model at the reed entrance
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
pm
1111
0000
0000
1111
0000
1111
0000
1111
0000
1111
pr
0000
1111
0000
1111
0000
1111
0000
1111
0000
1111
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
0000000000000000000000000000000000000000000000
1111111111111111111111111111111111111111111111
(∆p)r
Flow induced by the pressure difference between
mouth (pm ) and reed (pr )
√
Flow velocity (v ) proportional to ( pm − pr )
Non-linear characteristics
Double-reed
physics
PT
PM
Almeida
Motivations
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
(l/s)
Resonator
Exciter
0.25
Flow
Models
0.2
0.15
0.1
0.05
0
Conclusion
0
5
10
Pressure
Remarks
Dynamic effects neglected
PT = PM /3
15
(kPa)
20
Comparison between instruments
Pressure flow characteristic
Double-reed
physics
0.5
Clarinet
Oboe
Bassoon
Almeida
0.4
Motivations
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Flow (l/s)
Models
0.3
Clarinet measurement
at LAUM
[Dalmont et al., 2003]
0.2
0.1
Conclusion
0
−5
0
5
10
15
20
25
30
Pressure difference (kPa)
Remark
Bassoon reed is wider than oboe
Clarinet opening still wider
Comparison between instruments
Normalized pressure flow characteristic
Double-reed
physics
1.2
Almeida
Clarinet
Oboe
Basoon
1
Motivations
0.8
Models
Exciter
Tools for reed
characterisation
Flow
Resonator
Clarinet measurement
at LAUM
[Dalmont et al., 2003]
0.6
0.4
Reed characteristics
Vibrational analysis
0.2
Conclusion
0
0
1
2
3
4
5
6
Pressure difference
Observation
Double-reeds curve has longer tail beyond curve top
(PT ∼ PM /5)
Clarinet closer to theoretical model (PT ∼ PM /3)
Outline
Double-reed
physics
Almeida
Motivations
1
Reed instrument models
Resonator
Exciter
2
Tools for reed characterisation
Reed characteristics
Vibrational analysis
3
Conclusion
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Static characterisation
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Observations
Non-linear characteristic maintains shape
Scale is determined by:
Vibrational analysis
Conclusion
Reed elasticity
Reed opening at equilibrium
Variability within a same reed
natural cane reed no. 4 (humidified)
Double-reed
physics
0.35
Almeida
0.3
0.25
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
flow (l/s)
Motivations
Models
run 13
run 14
run 17
0.2
0.15
0.1
0.05
Vibrational analysis
Conclusion
0
0
10
20
30
40
50
pressure (kPa)
Reasons
Reed damping changes along one experiment
Viscoelasticity (memory effects):
reed does not re-open instantly to the same position
measurements correspond to different reed openings at
equilibrium
Outline
Double-reed
physics
Almeida
Motivations
1
Reed instrument models
Resonator
Exciter
2
Tools for reed characterisation
Reed characteristics
Vibrational analysis
3
Conclusion
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Dynamic properties of the reed
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Reed does not behave equally when subject to a static
force or to an oscillating one
Previous static characterisation needs to be completed
with an exploration of the dynamic properties of the
reed
Dynamic effects are due to:
Inertia of the reed (cannot move between two states
instantaneously)
Inertia of the air
Viscosity and damping
In practice, the curve measured for static regimes is
changed when the frequency of oscillation changes
Patterns of vibration in the reed
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Remarks
Different modes of vibration of the structure respond to
different frequencies of the diving force
Both the shape and frequency of these modes change
with the shape of the structure
Patterns of vibration in the reed
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Remarks
Different modes of vibration of the structure respond to
different frequencies of the diving force
Both the shape and frequency of these modes change
with the shape of the structure
Patterns of vibration in the reed
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Remarks
Different modes of vibration of the structure respond to
different frequencies of the diving force
Both the shape and frequency of these modes change
with the shape of the structure
Patterns of vibration in the reed
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Remarks
Different modes of vibration of the structure respond to
different frequencies of the diving force
Both the shape and frequency of these modes change
with the shape of the structure
Mechanical admittance of the reed
Double-reed
physics
100
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Amplitude (dB)
Almeida
Dry
5 min soaking
30 min soaking
50
0
−50
0
500
1000
1500
2000
2500
3000
Frequency (Hz)
3500
4000
4500
5000
Remarks
Different modes of vibration of the structure
Respond to different frequencies of the diving force
Both the shape and frequency of these modes change
with the shape of the structure
Observations
Double-reed
physics
Almeida
Sound
Influences:
←
Meas.
←
Geometry
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
sound amplitude
beating regime
Char.
changing S0 scales p,q
changing k scales p,q
closed/open time ratio
admittance peaks ⇒
harmonic enhancement
in final sound
induced flow depends
on mode pattern
clarinet
[Pinard et al., 2003]:
important torsional
mode
Can be easily
simulated with FEM
algorithms
Dyn.
Simple models:
clamped beam
Ex: increase tip mass
⇒ increase 1st mode
frequency
Conclusion
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Vibrational analysis
Conclusion
Remarks
Both measurements shown are incomplete and
complement each other
Vibration modes and elastic properties are related to
changes in timbre
Complex relation of measurements to final sound. . .
. . . but a step towards understanding the role of the
reed details
Bibliography
Double-reed
physics
Almeida
Motivations
Models
Resonator
Exciter
Tools for reed
characterisation
Reed characteristics
Almeida, A., Vergez, C., and Caussé, R. (2006).
Experimental investigation of reed instrument functionning through image analysis of reed opening.
Submitted to Acustica.
Dalmont, J. P., Gilbert, J., and Ollivier, S. (2003).
Nonlinear characteristics of single-reed instruments: quasi-static volume flow and reed opening
measurements.
J. Acoust. Soc. Am., 114(4):2253–2262.
Vibrational analysis
Conclusion
Pinard, F., Laine, B., and Vach, H. (2003).
Musical quality assessment of clarinet reeds using optical holography.
J. Acoust. Soc. Am., 113(3):1736–1742.
Plitnik, G. and Strong, W. (1979).
Numerical method for calculating input impedances of the oboe.
J. Acoust. Soc. Am., 65(3):816–825.