EXTENDING THE GENERALIZED REED MODEL WITH MEASURED
REFLECTION FUNCTIONS
Tamara Smyth
School of Computing Science
Simon Fraser University
[email protected]
ABSTRACT
In previous work, the authors presented a generalized parametric model of a pressure controlled valve, allowing the
user to design a continuum of reed configurations, including "blown open", "blown closed" and the "swinging door".
Though the generalized reed model behaved as expected,
the quality of the produced sound was somewhat limited,
likely due to the dependence of reed oscillation on the
connected instrument bore and bell.
In this work we further explore the sound production
of the generalized reed by incorporating reflection filters
measured from actual musical instruments. The measurement technique is shown to produce results closely matching theoretical expectation for cylindrical and conical tubes,
and is applied to the clarinet and trumpet. Measurements
are incorporated into a waveguide model using the generalized reed.
1. INTRODUCTION
Jonathan Abel
CCRMA, Dept. of Music
Stanford University
[email protected]
strongly coupled to the bore, making playability highly
dependent on the bore resonances. Any trumpet player
will agree that initiating, and sustaining, oscillations of the
lips when blowing into a cylindrical tube is considerably
different than when blowing into the bore of a trumpet,
with its flared opening serving to "shift" resonant peaks.
Coupling a simulation of a "blown open" reed to a model
of a cylindrical bore would present similar difficulties,
and in particular, would not yield the quality of sound
one might expect from a trumpet, even if oscillation were
achieved. A parametric change in the configuration of the
generalized reed model would, therefore, also likely require a change in the model of the bore.
In an approach similar to that described in [2], in this
work we further explore the sound production of the generalized reed by incorporating measured reflection filters
corresponding to different musical instrument bores. The
measurement technique was originally demonstrated by
the authors using simple cylindrical and conical tubes (and
their combination), and and produced results closely matching theory [3].
A physics-based synthesis of a reed instrument typically
involves simulating the dynamics of a pressure-controlled
valve, and coupling the result to a model of the propagat- 2. THE GENERALIZED REED MODEL
ing pressure waves travelling along the instrument bore.
In many cases the bore is modelled using digital waveg- In reed instruments, as well as many vocal systems, air
uide synthesis [1], that is, the right and left travelling pres- pressure from a source such as the lungs controls the ossure waves are modelled using a bi-directional delay line cillation of a valve by creating a difference between its upand filter elements accounting for losses occurring during stream (incoming) and downstream (outgoing) pressure.
propagation and at boundaries. This primary resonator, known as a pressure-controlled
In previous work, the authors presented a model for valve, is classified according to its behaviour in the presthe reed element, and in particular a generalized paramet- ence of additional upstream or downstream pressure [4].
ric model of a pressure controlled valve, allowing the user If an increase in blowing pressure causes the valve to close
to design a continuum of reed configurations, including further, and a bore pressure increase causes the valve to
"blown open", "blown closed" and the "swinging door" open further, the reed is said to be blown closed, the clas(reviewed in Section 2). Though the generalized reed model sification of most woodwind instruments. If a blowing
behaved as expected, the quality of the produced sound pressure increase causes the valve to open further, and an
was somewhat limited, likely due to the simplicity of the increase in bore pressure causes the valve to close, the
connecting tube employed. Since the nature of the tube reed is blown open, the typical configuration of brass (lip
and bell, and the resulting pressure fluctuations at the mouthieceleed) instruments, and the human voice. A swinging door
influence the opening and closing of the reed, an improved or "transverse" reed, typically found in the avian syrinx,
synthesis is expected by using more accurate bore and bell is one where a pressure increase from either side of the
models. valve will cause it to open further.
The oscillation of a "blown open" reed, such as one The generalized reed model was first introduced in [5],
might find in a trumpet or other lip-reed instrument, is providing a configurable model of a pressure controlled
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