# Aided Design of Brass Musical Instruments

Jean-François Petiot, Joël Gilbert

► To cite this version:

Jean-François Petiot, Joël Gilbert. Aided Design of Brass Musical Instruments. Integrated Design and Manufacturing in Mechanical Engineering '98, May 1998, Compiègne, France. pp.497-504, 10.1007/978-94-015-9198-0_61. hal-05389714

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# AIDED DESIGN OF BRASS MUSICAL INSTRUMENTS

## Jean-François PETIOT

Equipe CMAO et Productique. IRCyN. UMR C.N.R.S. 6597
Ecole Centrale de Nantes. 1, rue de la Noë
BP 92101, 44321 Nantes Cedex 3, France.

## Joël GILBERT

Institut d'Acoustique et de Mécanique de l'Université du Maine
Laboratoire d'Acoustique UMR CNRS 6613
Avenue Olivier Messiaen
72085 Le Mans Cedex 9, France

## 1. Abstract

The manufacture of musical instruments is a domain where the know-how is primordial and rules of the profession are hard to explain and to formalise. In this article we present a new experimental approach with the aim of assisting the manufacture of musical instruments. In this perspective, we have developed an "artificial mouth" that permits to make objective tests on instruments (trumpet or trombone), overlooking the natural adaptation faculty of the musician.

Moreover, the artificial mouth is a useful set-up to understand the basic behaviour of brass instruments, and to improve physical modelling.

## 2. Introduction

The manufacture of musical instruments is a multi-disciplinary activity. Indeed, to conceive and to manufacture a musical instrument, it is necessary to take into account several requirements [1] [2] :

- ergonomic requirements. The instrument must be adapted to the musician on the physical level and on the perceptive level (domain of psychoacoustics),

- economic and manufacturing requirements,

- musical requirements. It is the most important criteria. Musicians assign to sounds three main qualities : the intensity, the pitch and the timbre. A good instrument must allow the musician to control easily, separately or simultaneously these four parameters.
In centuries, to take these constraints into account, instrument builders have accumulated know-how and experience, constituting the memory of the past. In the past, industry was a craft, but nowadays instrument manufacturing requires modern production devices, adapted to small and average quantities and to the control of product quality. The design and adjustment phases of an instrument are made by the realisation of prototypes, with a test-mistake reasoning.

Recently, a better understanding of the physical phenomenon used in the sound emission has offered an assistance to the design. Furthermore, progress in numerical simulations allows the instrument maker to control the quality of an instrument and to predict some of its performances before the manufacturing. The work presented in this article stands in this context.

This paper is limited to brass instruments (trumpet, trombone, frenchhorn...). Their behaviour is described in section 3. In order to study this type of instruments, we have developed an artificial mouth, presented in section 4. In this section, we expose its contribution to the aided design of musical instruments and their objective characterisation. In the perspectives, we explain how the use of the artificial mouth for the validation of physical model can for the future lead to a Computer Aided Design.

# 3. Brass Musical Instruments

## 3.1 FUNCTIONING

Wind instruments (with the exception of those with a flute-like embouchure) are acoustic sources using a valve effect : the acoustic oscillation is a result of the destabilisation of a mechanical element whose movement changes the entrance cross-section of the instrument. This destabilisation is the result of a complex aeroelastic coupling between the mechanical element (the reed of a clarinet or the lips of a trombonist), the air flow entering the instrument as a result of the static overpressure in the mouth of the musician, and the instrument itself (the acoustic resonator) [3] [4].

The vibrations of the lips of the trombonist are controlled both by the musician and the instrument itself [5]. Several parameters condition the natural frequency of lips (tension, geometry, visco-elastic properties, ...). The control and the management in "real time" of these parameters allow to obtain a great variety of musical sounds, this after several years of daily practice for the musician [6].

The resonator is described by its input impedance, giving the amplitude of its acoustic response to an excitation (response in forced oscillations). This characterisation of the instrument alone is not sufficient to define the quality of an instrument. For example, this approach does not enable us to take into account the possibilities for the musician to change the pitch of the playing note, and to play notes of various sounds colours and intensities.

Modern brass instruments have reached a high level of acoustic quality, and it is now very difficult for the manufacturer to improve them. How can one be sure that a slight difference of tone or pitch of note is the consequence of a modification of the bore and not the consequence of an unconscious modification of the "embouchure" (the
way the mouthpiece and lips interact) of the musician? Is the instrument wrong or does the musician play it incorrectly?

This sentence sums up the difficulty of objectively characterising the quality of an instrument.

## 3.2 PERFORMANCE EVALUATION OF AN INSTRUMENT

It is difficult to define the quality of an instrument. Many factors come into play, for example the history of the instrument, its appearance or its price [7].

From an acoustical and musical point of view (for example, aesthetic considerations are not taken into account), one can quote criteria of evaluation of wind instruments in a non-exhaustive way:

- accuracy, and freedom field of pitch,

- ease of playing,

- quality of timbre,

- freedom field of timbre,

- homogeneity of the timbre over the complete range<fnref n="1" />,

- freedom field of intensity.

To evaluate an instrument, a musician tester must give an account of the performances of the instrument, according to previous criteria. Essential for the manufacturer, the opinion of the tester is global and can be inaccurate for several reasons:

- a lot of coupled parameters must be evaluated,

- the tester adapts to the instrument, and corrects more or less unconsciously for any possible drawbacks,

- the opinion is subjective,

- comparisons between several instruments are difficult to do,

- it is difficult to do acoustical measurements under playing conditions and it is difficult for the tester to guarantee reproducible playing conditions during such measurements.

In order to complement the opinion of the tester, we have developed an experimental device, the artificial mouth [8]. With this experimental system, it is possible to generate steady and reproducible playing parameters. Previous systems for reed instruments (clarinet, saxophone) have already been used [9]. The main objective is to allow the characterisation of an instrument by objective measurements, in order to answer (at least partially) whether the instrument or the musician plays incorrectly.

# 4. The Artificial Mouth

## 4.1 PERFORMANCE SPECIFICATION

The device must satisfy the following functions:

- to guarantee emission of sound in steady conditions (permanent regime),

<footnote n="1">¹ scale of sounds of an instrument, from lower to higher notes</footnote>
- to generate several notes over the range of the instrument, by adjusting playing parameters,

- to guarantee a very good reproducibility of adjustments, so that several instruments may be compared with the same embouchure,

- to recreate for each note freedom fields of timbre and intensity characteristic of the musical instrument,

- to fit to several instruments (trumpet, trombone),

- to allow the measurement of pressure and velocity inside the mouth cavity, as well as the visualisation of the lip motion.

After a physiological analysis of a musician playing a brass instrument [10], three control parameters have been kept to change the timbre and the pitch of notes:

- air supply pressure,

- mechanical tension of lips,

- support force of the mouth on lips.

## 4.2 DESCRIPTION

The artificial mouth (Fig.1) is a hermetically sealed box fed by a high pressure (5 bar maximum) air supply, in which the artificial lips are fixed. The mouth pressure in the box is controlled with a pressure regulator. In order to approach the visco-elastic properties of real lips, the artificial lips are latex tubes filled with water. A jaw presses the lips against the mouth with an adjustable support force.

<figure><img src="image_2.png" /><figcaption>Figure 1. The artificial mouth</figcaption></figure>

The adjustment of the support force and the lip tension allows the stiffness of lips, and therefore their natural frequency to be altered. The mouthpiece is clamped and remains fixed with the artificial mouth. Therefore, it is possible to replace one brass
instrument with another without perturbation of the "embouchure" adjustment (the instrument is clamped on the mouthpiece using an adaptation cone). It guarantees a perfect stability of the embouchure when the instrument is replaced by another one.

The timbre obtained with the artificial mouth is quite realistic, the sound can be compared to those obtained with a musician (an opinion confirmed by several professional musicians).

## 4.3 UTILISATION

The artificial mouth eliminates the musician's natural faculty of adaptation, as the artificial mouth does not adapt its playing parameters according to the produced sound. It is then possible to compare two instruments, being sure that the differences that we observe are not the consequences of a modification of the "embouchure" of the musician. The artificial mouth is integrated into a functional chain, the structure of which is given Fig.2. This SADT representation encapsulates the parameters and data when relevant to our problem.

<figure><img src="image_3.png" /><figcaption>Figure 2. SADT model of the functional chain</figcaption></figure>

The objective is to evaluate the performances of an instrument (according to the previous criteria) by physical measurements.

In fact, to establish such a correspondence is quite ambitious because it involves comparing two quantities of different kinds, i.e. physical quantities (objective) and perceptive quantities. Studies in psychoacoustics show that things are obvious, and that mechanisms of perception are subtle<fnref n="2" />. The major difficulty is in finding sensible physical parameters and the experimental conditions leading to pertinent measurements of the studied criteria. For that, we have chosen :

<footnote n="2">² For example, the sensation of pitch, relating to the accuracy, is not always dependent only on the playing frequency. It depends in particular on the intensity, the length and the timbre.</footnote>
- to separate the variables. We take an interest in only one criteria at a time, all others being constant,

- to work by comparison between instruments,

- to have reproducible experimental conditions, for the playing parameters of the artificial mouth, but also for parameters conditioning the measurements (temperature, acoustics of the room,...)

## 4.4 MEASUREMENTS

We do not claim to define complex criteria, which give an exact account of notions as subtle as "accuracy" or "ease of playing". But we propose to analyse physical quantities, taken directly from measurements which are easily made on our experimental device (static pressure in the mouth, acoustic pressure in the mouth and radiated acoustic pressure). These physics quantities are linked to the criteria of evaluation:

1) the study of the accuracy is brought back to the study of the fundamental frequency (also called playing frequency). This frequency is compared to the frequency of the even tempered scale, having for reference the A4 = 440Hz.

2) the study of the timbre, the freedom field of timbre, the homogeneity of the timbre over the entire range amounts to an analysis of the spectrum radiated by the instrument for signals in permanent regime. The control parameters are : the air supply pressure, mechanical tension of the lips and the support force of the mouth on the lips.

3) we propose to characterise the ease of playing by the measurement of the minimum static pressure necessary to generate a sound. The lower the value of static pressure is, the easier the note production on the instrument is.

4) the freedom field of intensity is evaluated by a measurement of the radiated acoustic pressure, according to the supply pressure in the mouth.

Criteria of evaluation and associated measurements are summed up in table 1.

<table><caption>TABLE 1. Criteria of evaluation and associated measurements</caption><thead><tr><td>Evaluated criteria</td><td>Measures</td></tr></thead><tbody><tr><td>accuracy</td><td>fundamental frequency</td></tr><tr><td>ease of playing</td><td>static pressure supply</td></tr><tr><td>timbre</td><td>internal and radiated</td></tr><tr><td>freedom field of timbre</td><td>spectrum in</td></tr><tr><td>homogeneity of timbre</td><td>permanent regime</td></tr><tr><td>freedom field of intensity</td><td>acoustic pressure/ static pressure</td></tr></tbody></table>

Today, the artificial mouth is not suited to the study of the behaviour of brass instruments in transient regime. The response of the instrument in transient regime is nevertheless essential for the musician. The study of these regimes remains the domain of the tester. The artificial mouth provides a complementary opinion on an instrument, but can never replace the musician. He will always remain the only one who can judge.
## 4.5 APPLICATIONS

According to the different tests that we have completed, artificial mouth playing tests on instruments can cover two aspects: aided design of instrument or control of production.

### 4.5.1. Aided design of instrument

In case of a new design of an instrument, the major interest is to be able to evaluate the influence of a modification of the instrument (geometry, materials, assembly...) on the criteria of performance, this one without any a priori on the result (the musician is sometimes subject to a "placebo" effect, his opinion changing whereas the instrument is identical). By performing artificial mouth tests, it is possible to quantify the influence of design parameters on the criteria of performance.

These measurements allow the designer to control with accuracy the expected performance of the new instrument.

### 4.5.2 Control of Production

The manufacture of instruments for the general public is of order of small to average quantities. The concern of manufacturers is to control the quality of products, in order to have an homogeneous production. For that, it is necessary to bring under control the variance of the manufacturing processes (assembling, forming, milling, welding,...), because the acoustic result is very sensitive to slight variations of the design parameters (dimensions, surface quality, state of stresses of the material,...).

Artificial mouth measurements, compared to those of a reference instrument, judged high-performance by the tester, will enable the following controls to be made :

- end of production line quality control on the finished product, to provide an initial assessment of the product before seeking the definitive opinion of the tester,

- control on different stages of the manufacturing, in order to control the quality of the manufacturing process.

## 5. Conclusions - Perspectives

The objective characterisation of musical instruments is an important contribution for the instrument builder. It allows production instruments to be compared one with the other and with reference instruments selected by the musician. The features of the artificial mouth (stability and reproducibility) permit this characterisation using physical measurements taking perceptive notions into account.

The acoustic criteria used in this article are basic. Further work must be done to refine the definition/relation between the perceptive domain and physical measurements (psychoacoustics) [11][12]. This work will be useful for an optimal use of the artificial mouth, with a view qualifying musical instruments.

Artificial mouth measurements complement the opinion of the tester and the musician. They do not permit complete qualification of the instrument because all
playing modes cannot be taken into account. In particular, the study of the transient regime is not yet possible, measurements being limited to the permanent regime. It is not possible to do without the opinion of the musician.

On the other hand, the artificial mouth is an experimental device which is essential for the development of a global physical model of the "instrument and musician" combination [8][13]. In the context of virtual acoustics, it is now possible to listen to very realistic synthesis of brass instrument sounds [14][15]. But important work has to be carried out in order to adapt these tools to a computer aided design approach in the context of virtual acoustics.

## 6. References

[1] D.M. CAMPBELL. C.GREATED "The musician's guide to acoustics" Oxford University Press, New-York, 1998.

[2] D. KOPPE : "La trompette dans la seconde moitié du XXe siècle : Facture, technique et interprétation". Thèse de doctorat. Université de Paris IV, U.F.R. de Musique et de Musicologie. 1996.

[3] A.HIRSBERG, J.KERGOMARD, G.WEINRACH "Mechanics of musical Instruments" CISM courses and lectures n° 355. Springer Verlag, Wien, New-York, 1995.

[4] N. H.FLETCHER, T. D.ROSSING. "The physics of musical Instruments" Springer Verlag, New-York, 1991.

[5] J.GILBERT, J-F. PETIOT "Brass instruments : some theoretical and experimental results". Proc. Institute of Acoustics, Vol 19 Part 5, 1997, pp 391-400.

[6] J-J.GREFFIN R.PERINNELLI "Méthodologie pour trompette et instruments à embouchure" Editions BIM, Suisse, 1984.

[7] J-P.DALMONT, J.GILBERT, J.KERGOMARD "Des instruments à vent harmoniques" Pour la Science, n°238, Août 1997, pp. 78-85.

[8] J. GILBERT, S. PONTHUS, J.F. PETIOT "Artificial buzzing lips and brass instruments : experimental results". Journal of the Acoustics Society of America,, Vol. 104(3), pp 1627-1632, 1998.

[9] J-P.DALMONT,, B.GAZENGEL, J.GILBERT, J.KERGOMARD "Some aspects of tuning an clean intonation in reed instruments". Applied Acoustics N° 46, 1995, pp.19-60.

[10] L.PIAU "Conception et réalisation d'une bouche artificielle pour instrument à vent de type cuivre". Rapport de recherche de troisième année, Ecole Centrale de Nantes, 1997.

[11] R.CAUSSE, N.MISDARIIS, S.ThORETON "Caractérisation objective de la qualité d'un instrument de musique". Quatrième congrès français d'Acoustique, Marseille, 1997.

[12] J.KRIMPHOFF "Analyse acoustique et perception du timbre". DEA d'Acoustique appliquée de l'Université du Maine, 1993.

[13] J.S.CULLEN, J.GILBERT, D.M CAMPBELL, « Brass instruments : linear stability analysis and experiments with an artificial mouth » submitted to ACUSTICA.

[14] R.MSALLAM, S.DEQUIDT, S.TASSART, R.CAUSSE "Physical model of the trombone including non linear propagation effects" Proc. Institute of Acoustics. Vol 19 Part 5, 1997, pp.419-424.

[15] C.VERGEZ, X.RODET "Model of the trumpet functioning : real time simulation and experiments with an artificial mouth". Proc. Institute of Acoustics. Vol 19 Part 5, 1997, pp.425-432.