Tamara Smyth

Toward an estimation of the clarinet reed pulse from instrument performance.

In this work, a technique is presented for estimating the reed pulse from the pressure signal recorded at the bell of a clarinet during performance. The reed pulse is a term given to the typically periodic sequence of bore input pressure pulses, a signal related to the volume flow through a vibrating reed by the characteristic impedance of the aperture to the bore. The problem is similar to extracting glottal pulse sequence from recorded speech; however, because the glottis and instrument reeds have very different masses and opening areas, the source-filter model used in speech processing is not applicable. Here, the reed instrument is modeled as a pressure-controlled valve coupled to a bi-directional waveguide, with the output pressure approximated as a linear time invariant transformation of the product of reed volume flow and the characteristic impedance of the bore. By noting that pressure waves will make two round trips from the mouthpiece to the bell and back for each reed pulse, yielding a distinct positive and negative lobe in the running autocorrelation period of the recorded signal, the round-trip attenuation experienced by pressure waves in the instrument is estimated and used to invert the implied waveguide, producing reed pulse estimates.

The syrinx: Nature’s hybrid wind instrument

Birdsong is commonly associated with the sound of a flute. Although the pure, often high pitched, tone of a bird is undeniably flutelike, its sound production mechanism more closely resembles that of the human voice, with the syringeal membrane (the bird’s primary vocal organ) acting like vocal folds and a beak acting as a conical bore. Airflow in the song bird’s vocal tract begins from the lungs and passes through two bronchi, two nonlinear vibrating membranes (one in each bronchial tube), the trachea, the mouth, and finally propagates to the surrounding air by way of the beak. Classic waveguide synthesis is used for modeling the bronchi and trachea tubes, based on the model of Fletcher [J. Acoust. Soc. Am. (1988, 1999)]. The nonlinearity of the vibrating syringeal membrane is simulated by finite‐difference methods. This nonlinear valve, driven by a steady pressure from the bronchi, generates an oscillatory pressure entering the trachea.

Trombone Synthesis by Model and Measurement

A physics-based synthesis model of a trombone is developed using filter elements that are both theoretically-based and estimated from measurement. The model consists of two trombone instrument transfer functions: one at the position of the mouthpiece enabling coupling to a lip-valve model and one at the outside of the bell for sound production. The focus of this work is on extending a previously presented measurement technique used to obtain acoustic characterizations of waveguide elements for cylindrical and conical elements, with further development allowing for the estimation of the flared trombone bell reflection and transmission functions for which no one-parameter traveling wave solution exists. A one-dimensional bell model is developed providing an approximate theoretical expectation to which estimation results may be compared. Dynamic trombone model elements, such as those dependent on the bore length, are theoretically and parametrically modeled. As a result, the trombone model focuses on accuracy, interactivity, and efficiency, making it suitable for a number of real-time computer music applications.

Estimating Waveguide Model Elements from Acoustic Tube Measurements

One-dimensional digital waveguides are widely used to model traveling pressure waves along wind instrument bores comprised of concatenated cylindrical or conical sections. Waveguide filter elements model frequency-dependent losses and delay (dispersion) occurring during propagation and at any boundary or discontinuity producing reflected and transmitted waves. In this work, a technique is described for estimating wind instrument waveguide elements from several measurements of the systems impulse response, each measurement taken with the system having incrementally varying termination/boundary conditions. The measured impulse responses yield sequences of multiple arrivals from which estimates of waveguide element transfer functions may be formed. The measurement and post signal processing technique is explored using simple structures consisting of cylindrical and conical tubes, as these are well described theoretically and provide a basis for validating measured data. All waveguide elements necessary for modeling typical wind instrument bores are collected here, each presented with a theoretical description and accompanying measurement. The measurement and processing system is then shown to yield data closely matching the theory, thus providing confidence that the technique may be extended to accurately measure structures which are more difficult to describe theoretically, such as an instruments flaring bell.

Observing the effects of waveguide model elements in acoustic tube measurements

The theory of digital waveguide synthesis and its use in modeling virtual musical instruments, and in particular for cylindrical and conical bores, is well documented. Current models rely on certain approximations, however, particularly in cases where the theory provides no exact closed form solution, such as the reflection and transmission occurring at the bore’s open end. In this research, we observe, from a time domain, waveguide model perspective, how the theory corresponds to actual acoustic measurements. We consider four simple acoustic tube structures, incorporating both open and closed boundary conditions for both a simple cylinder and a cylinder with a conical flare, allowing us to isolate, and observe, the filtering effects of each model component.

Discrete-time simulation of air-flow cut-off in pressure-controlled valves

Pressure controlled valves exist in musical instruments such as brasses and woodwinds and are also found in many biological sound producing mechanisms such as the human larynx and the avian syrinx. The behaviour of the differential equation governing volume flow through a pressure-controlled valve is examined with particular attention given to the rather troublesome transition between an open and closed valve. A closed-form solution for the time evolution of volume flow is given and used to derive an update for the volume flow. The result is a smooth, nearly alias free transition between the two states. The form of the update is similar to that of a leaky valve where the leakage decreases as the volume flow decreases. This research was developed while modeling the avian syrinx.

Convolutional Synthesis of Wind Instruments

In this work we propose a new physical modeling technique whereby a waveguide structure is replaced by a low latency convolution operation with an impulse response that is either measured, modified, and/or constructed, optionally parametrically. By doing so, there is not longer the constraint that successive arrivals be uniformly spaced, nor need they decay exponentially as they must in a waveguide structure. Measured impulse responses allow for the estimation of filter transfer functions normally seen in a waveguide model of an acoustic tube, some of which are difficult to obtain theoretically, which may then be used to synthesize new impulse responses corresponding to wind instrument bores both existing and imagined. The technique is presented in the context of reed-based wind instruments, but may be extended to other musical instruments.

Exploring the Virtual Reed Parameter Space Using Haptic Feedback

A high quality computer synthesis of an acoustic sound source does not necessarily yield a playable virtual musical instrument. A computer simulation of an acoustic musical instrument creates a disconnect between sound production and user input, and correspondingly, between hearing and feeling, in contrast to their interconnection in an acoustic instrument. This disconnect denies the user important haptic clues well known to help instrument control, impeding the users ability to find, and remain inside, regions of playability. This research explores the addition of haptic feedback to a virtual reed model. In particular, we render the instruments parameter space as a dynamic force field in order to support fine motor movements and, in turn, provide the user with cues regarding the instruments oscillatory state and possible regions of playability. We then observe the effects that this additional feedback has on the users ability to play the virtual instrument

A Musical Controller Inspired by the Cicada’s Efficient Buckling Mechanism

The cicada uses a rapid sequence of buckling ribs to initiate and sustain vibrations in the tymbal plate – the primary mechanical resonator in its sound production system. “ The Tymbalimba,” a music controller inspired by this mechanism, has a row of four convex aluminum ribs arranged much like the keys on a kalimba. Each rib is spring loaded and capable of snapping down into a V-shape (a motion referred to as buckling) under the downward force of the user’s finger. The displacement of the rib during buckling is measured by a sensor and then passed through a differentiating circuit to obtain velocity. The velocity is then converted to energy and used as the input signal to a computer synthesis model – a physical model which simulates the mechanical and acoustic elements of the cicada’s sound production mechanism.

Saxophone modelling and system identification

In this work, saxophone instrument frequency responses are estimated at both the mouthpiece (corresponding to the input impedance) and outside the bell, using acoustic measurement and post signal processing. The measurement technique is based on one previously developed for measuring the acoustic properties of instrument bells, but is adapted to account for the fact that the saxophone bell does not easily separate from the instrument bore and must be measured as a single unit. Furthermore, measurements are taken of the instrument configured with all possible fingerings covering the playable range of the B-flat tenor saxophone, and instrument reflection and transmission functions are estimated for, and applied to a waveguide model of, each tone-hole configuration. Having the instrument frequency responses at both the mouthpiece and the bell for every possible fingering allows for an improved parametric synthesis, but also allows for saxophone system identification, inverse modelling and estimation of playe...