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Session 04 - Brasses

Brass instruments as we know them today
D M Campbell
School of Physics, University of Edinburgh, Edinburgh, United Kingdom

Since the time of Helmholtz, models of brass instruments have been developed in which the lips of the player are treated as a pressure-controlled flow valve coupled to the resonating air column inside the tube of the instrument. In more recent years it has been recognised that the coupled system of lip valve and acoustic resonator is a classic problem in non-linear dynamics. A simple one degree of freedom model of the lip valve coupled to an air column treated as a passive linear resonator has been shown to yield surprisingly realistic trumpet sounds, but many more subtle features of brass playing are not captured. Attention is currently focused on developing more sophisticated lip models, guided by experiments using artificial lip excitation systems and visualisations of human lip motion during playing. It is also now clear that modelling of the air column must take account of non-planar modes in rapidly flaring tubes, and non-linear propagation in longer instruments. Experiments are in progress to investigate the nature of resonances in the player's mouth and windway, and the extent to which these resonances influence the behaviour of various categories of lip-reed instrument.

Harmonics: what do they do in the didjeridu?
N Amir
Tel Aviv University, Dept. of Communication Disorders, Tel Aviv, Israel

The characteristic timbre of the australian didjeridu varies over a much wider range than that of most wind instruments, due to two factors: 1) the large variability in bore shape between instruments, 2) the great extent to which the player can control the timbre of the instrument. In this study we wish to examine several aspects of this timbre. Analyzing recordings of several instruments, each played over a range of possible timbres, we track the amplitudes of a large number of harmonics. Using this data we attempt to define the components of the timbre that are governed mainly by the instrument, which give the didjeridu its recognizable color, as opposed to those that are more easily controlled by the player. This is carried out both by visual examination of the harmonic tracks, and also through selective resynthesis. The same analysis is performed over instruments judged by a professional player to be of inferior quality, and used to give at least a partial explanation of the shortcomings found in these instruments.

Bridging instrument control aspects of brass instruments with physics-based parameters
M Bertsch
University for Music, IWK - musical acoustics, Vienna, Austria

Is there a connection between what we feel when playing an instrument and what we can measure? Physical models and measuring tools have been developed for a better understanding of brass instruments and to provide objective physical documentation of their acoustics.
Musicians and instrument makers still criticize the enormous gaps between the physics-based parameters and the empirically reported feelings of brass players on quality aspects of their instruments. Deviations between played and measured parameters like intonation and their variability have already been focused on in earlier studies. Attempts for a theoretical explanation of these deviations using physical modeling continues.
For musicians, one of the most important quality factors of a brass instrument is its response. A new series of playing tests has been designed to correlate empirical data with objective physical parameters (impedance measurements). International Instrument makers provided special test instruments (modular trumpets).
This paper will show the difficulties in defining response and setting up suitable playing tests. Preliminary results and correlations of the data will be presented.

Reproducibility and control of the embouchure of an artificial mouth for playing brass instruments
S R Bromage, O F Richards, D M Campbell
University of Edinburgh, School of Physics, Edinburgh, United Kingdom

Artificial mouths, based on the modelling of lips with latex tubes, have been extensively used in studies of brass instruments. The ability to make accurate comparisons between instruments, for example in spectral or listening studies, relies on the reproducibility and control of the embouchure (the static configuration of the lips). The mechanical resonance behaviour of the lips of an artificial mouth is related to characteristic parameters of the embouchure. These parameters include the rest position and internal pressure of the lips, and the extent to which the lips are squeezed by the pressure of the mouthpiece. Measurements of the mechanical response of the lips and the spectrum of the radiated sound were studied for a range of different embouchure settings. These indicate that the frequencies of the resonance peaks are well reproduced for repeated resetting of the embouchure parameters. However, the magnitudes of the peaks are less well reproduced. Reasons for this variability, and possible improvements aimed at its reduction, are discussed.

Australian Aboriginal musical instruments -- the gum-leaf
N H Fletcher
Australian National University, R.S.Phys.S.E., Canberra, Australia

The Australian Aboriginal people have lived in this country for more than 40,000 years with almost no contact with the outside world. During that time they developed sophisticated tools such as the woomera spear-thrower and the returning boomerang. They also developed three musical isntruments -- the didjeridu, the bullroarer, and the gum-leaf. Most well known is the didjeridu, a simple wooden tube blown with the lips like a trumpet, which gains its sonic flexibility from controllable resonances of the player's vocal tract. The bull-roarer, called by other names in Aboriginal languages, is a simple wooden slat whirled in a circle on the end of a cord so that it rotates about its axis and produces a pulsating low-pitched roar. This talk, while mentioning these two instruments, will concentrate on the gum-leaf lip instrument. This was originally developed to imitate bird-calls, but these days can also be used to play tunes at a pitch about an octave above that of the human voice. Analysis shows that the leaf acts as a valve with configuration(+,-) and that the sounding pitch is determined by the frequency of an upper vocal tract resonance.

Studying lip oscillators of brass instruments: A distributed two dimensional lip model and its electrical equivalent circuit
W Kausel
Univ. of Music, Inst. f. Musical Acoustics, Vienna, Austria

In order to understand the mechanism of sound production in brass wind instruments, valuable theoretical and experimental work has been published by several authors. They proposed to model lips as outward or inward striking doors, opened by positive or negative pressure differences between mouth and mouthpiece, or as sliding doors, driven by the Bernoulli pressure between the lips. All three simple models exhibit self sustained oscillations when combined with a pressure source (lung) and an input impedance (instrument). Anyhow, the fact that a human player can easily play above as well as below the air resonances of an instrument cannot be reproduced by any of the simple models. Therefore a combination of two simple models (stretchable outward striking door) has been proposed by Adachi. This combined model exhibits the observed bi-directional pitch controllability at least for the two lowest played notes. In order to enable application of more realistic complex models, a simulation environment based on electrical equivalent circuits has been proposed by the author and a one dimensional distributed wave guide model of the lip has been presented. In this paper a two dimensional distributed lip model is proposed which is able to exhibit surface waves travelling between the teeth and the mouth piece rim. Surface waves are interacting with forces originating from the pressures in the mouth, the mouthpiece and the lip orifice. Phase speed is controlled by the tension of the lip.

Physical modeling of the trombone player's lips
D O Ludwigsen
Kettering University, Science & Mathematics, Flint, MI, United States

Physical modeling techniques are employed in this effort to better understand the behavior of the the lips in a trombone/player system. The lip model incorporates the geometry and physical properties of the tissue in a solid model subject to finite element analysis. To drive the model dynamically, a simplified aerodynamic model applies pressure from the mouth, the mouthpiece, and the aperture between the lips. Feedback from the instrument informs the mouthpiece pressure. The resulting oscillation of the lip structure may be compared with that of previous models and experimental studies, and is seen to depend on both the instrument feedback and player control, as modeled by material properties of the lip tissue.

Trumpet bell vibrations and their effect on the sound of the instrument
T R Moore, E T Shirley, A E Daniels
Rollins College, Departement of Physics, Winter Park, FL, United States

The acoustic spectrum of a modern trumpet with the bell section heavily damped has been compared to the spectrum of the same instrument with the bell section left free to vibrate. Measurements of the amplitude of vibration indicate that the damping significantly reduces the movement of the metal, and a corresponding change in the acoustic spectrum between the two cases is found. It is shown that the relative power may change by as much as a factor of two in some of the harmonics. The experimental results can be explained by assuming that the vibration of the bell causes a change in the viscous boundary layer within the bell.

Corrections to the plane-wave approximation for acoustic waves in rapidly flaring horns
C J N Nederveen
AC Pijnacker, The Netherlands

Horns on wind instruments complicate calculating the input impedance of the air column. For a low flare, solving the wave equation assuming plane waves is sufficiently accurate. In some cases analytical solutions are possible. Otherwise a one-dimensional transmission-line (TL) method, in which the horn is described as a succession of cones, is adequate. This fails for a large flare. Cross flow then demands energy, effectively increasing the inertance. The magnitude of this inertance was numerically determined by a finite difference method, where space was filled with a fine grid. Applying cylindrical symmetry reduced the number of points. Studied were conical, hyperboloid and catenoidal horns. In reality horns are found in many other shapes, which would make general use of this method very cumbersome. However, the additional inertance could be expressed as a simple fit-formula applicable to any shape. It is applied as a correction in the TL method. The formula can also be used for a sudden diameter change and for a flange (which is a horn of zero length). For most geometries found on wind instruments its accuracy is within the 0.2% detection threshold of the ear.

Gradient based optimisation of brass instruments
J O D Noreland
Uppsala universitet, Information technology, Uppsala, Sweden

This paper presents how the shape of a brass instrument can be optimised with respect to its intonation and response properties. The instrument is modelled employing a one-dimensional transmission line analogy with segments shaped as truncated cones. Using the end diameters of the segments as design variables, the task to find a design with desired input impedance peak frequencies and magnitudes is formulated as a non-linear least squares problem. This problem is solved using a gradient based minimisation algorithm. The necessary gradient of the objective function is found by analytic manipulation of the transmission line model. Through the use of an appropriate design variable transformation, it is possible to quickly find smooth horn profiles, and to prevent the minimiser from getting stuck in local minima corresponding to irregular or jagged designs.

Differentiation of trumpets' sound: experimental study with an adaptable depth mouthpiece
J F Petiot¹, E Poirson¹, J Gilbert²
¹ECN , IRCCyN, Nantes, France; ²Université du Maine, LAUM, Le Mans, France

In order to isolate and finely control the influencing variables of the quality of brass instruments, a trumpet mouthpiece with a depth that can be easily and continuously adjusted from "deep" to "shallow" has been developed. Using this device and the same trumpet, we have generated a set of instruments with notably different acoustical behaviour, varying only the internal geometry of the mouthpiece. In parallel, in the context of virtual acoustics, time domain simulations seem to be promising tools for predicting the acoustical behaviour of instruments.
In this paper, time domain simulations were used as predictive tools for pitch and tone colour differentiation. First, the following objective measurements were performed on the set of trumpets: 1) measurement of the input impedance 2) measurement of the radiated sound with an artificial mouth. Secondly, hearing tests with a set of subjects and sounds generated by three different methods were performed: 1) with the artificial mouth 2) with synthesis of sound by physical modelling, using the measured impedance as input data 3) with a real player. As a result, an analysis of the sensitivity of each sound generation procedure for sound differentiation is presented

Measurement of the force applied to the mouthpiece during brass instrument playing
J F Petiot
Ecole Centrale Nantes, IRCCyN, NANTES, France

In order to assess the load produced on the lips of the musician during brass instrument playing, a measuring system was developed. It permits the recording in real time of the axial force created on the mouthpiece, and allows the players to perform on their own instrument and mouthpiece, in their usual manner. Tests involving 3 categories of players (professional - advanced - beginners) were conducted with various musical phrases, articulations and nuances. For all players, the force between the mouthpiece and instrument always increases with increasing loudness and ascending pitch, but in different proportions. After an analysis of the causes of this force, the extent of these variations is described and an interpretation of the results is proposed. These measurements are particularly interesting for musicians and physicist as well, in order to understand what the control parameters of the embouchure are, and how to manage them.

Modelling the lip reed - computational and experimental investigations of two-mode inward/outward striking behaviour
O F Richards¹, D M Campbell¹, J Gilbert²
¹University of Edinburgh, School of Physics, Edinburgh, United Kingdom; ²Universite du Maine, Laboratoire d'Acoustique, Le Mans, France

The physiology of the vocal folds is similar to that of the lips of a brass player. This paper adapts a two-mass vocal fold model to represent the behaviour of the lips and compares results obtained from modelling with results obtained from experimental studies of both human and artificial brass players' lips. Of particular interest is the mechanical response of the opening area between the modelled lips - which is directly compared to experimental measurements performed on an artificial mouth. Several important characteristics observed experimentally are reproduced in this analysis, including the presence of a pair of inward/outward striking resonances and the waveforms produced during self-sustained oscillation.

An investigation of wall vibrations induced in artificially blown wind instruments of varying wall thickness and constructed from different metals
J W Whitehouse, D B Sharp, T J Hill
The Open University, D.E.M.E., Milton Keynes, United Kingdom

A simple instrument (a trombone mouthpiece coupled to a section of brass pipe) was blown using an artificial mouth and the induced wall vibrations measured using a Laser Doppler Vibrometer. The wall vibrations were shown to be strongest at harmonics of the played note and the variation in velocity amplitude along the pipe to match the bending mode shapes at these frequencies. Results indicate that it is the motion of the lips against the mouthpiece, rather than air pressure changes within the pipe, that is the dominant mechanism in exciting wall resonances. The measurements were repeated and compared for pipes of identical dimensions but manufactured from different metals and for pipes of the same material but differing wall thickness.

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