Improvement of the Acoustic Quality of Brass Wind Instruments. ... Summary: This paper describes evaluation methods for brass wind instrument quality where ...
Diagnosis and Therapy for Brasses. Measurement, Evaluation and Improvement of the Acoustic Quality of Brass Wind Instruments. Gregor Widholm University of Music and Performing Arts Vienna, Institut für Wiener Klangstil, Singerstrasse 26, A-1010 Wien, Austria Summary: This paper describes evaluation methods for brass wind instrument quality where the results of measurement and subsequent data processing predominantly match the individual judgments of the player. The problem of correspondence between physical measurements and quality parameters defined by musicians is discussed and solutions presented. In the second part of the paper a method for improvement of intonation and response quality is introduced. A particularity of the presented method is that it completely comes up to the expectations of instrument makers and musicians. The optimization algorithmus used takes target specifications even expressed in the terminology of musicians.
INTRODUCTION For the audience the definition of brass wind instrument quality is reduced to the quality of radiated sound in the far-field. The listener evaluates the sound produced by the player with his instrument, modified by the acoustic properties of the room. Quite different is the situation for the player. The quality of the instrument is mainly defined by three parameters: the intonation (correspondence of the instruments resonance frequencies with the equal tempered scale), the response (ease of tone production) and the sound color in the near-field. The problem is that with exception of the sound quality (whose evaluation is a business of the psychoacoustics), one has to deal with criteria of quality defined by musicians which unfortunately do not match to the results of simple physical measurements. This is because brass player often tend to evaluate the quality of the interaction between their lips and the instrument (control loop) instead of the quality of the pure instrument and integrate a lot of different acoustical properties of the instrument into one single parameter (for instance “response”). An additional problem may occur if the results of measurement get correlated with the judgements of more than one player. It is well known by instrument makers because of their highly dependence on the evaluation of their instruments by professional players: whilst player one is impressed of the quality of the instrument, player two locates the same instrument only in the mid or lower range of the quality scale. Needless to say, that nearly all professional players are convinced that their expert opinion has to be taken as an objective “factual statement”. If one takes this phenomenon seriously –and it has to be taken seriously because of a lot of proofs- it means, that a brass wind instrument has a definitely objective quality and can have two or more different subjective qualities because the player and the instrument form a control loop. Such phenomena have to be taken into account by developing a diagnosis system which is capable to produce results matching the (different) playing experience of (different) professional players with one and the same instrument (1). Based on these results strategies for instrument quality improvement can be successfully established.
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INTONATION To get the basic data a simple input impedance measurement is sufficient if the effect of the reduction of the mouthpiece cup volume by the players lips is taken into account. The relationship between impedance peaks / phase and the resonances of the air column inside the instrument respectively its natural tones is well known (2). For diagnosis several steps of processing are necessary: at first the pitch corresponding to a1 has to be determinated. As reference we use the equally tempered scale. Although brass player insist that they play just intonation a recently finished study with 37 professionals by M. Bertsch showed that the played intonation primary follows the intonation offered by the instrument and secondly is closer to the equally tempered scale than to any other musical scale (3). 30 Cent
20 Cent
10 Cent
0 Cent
-10 Cent
offered intonation -20 Cent
played intonation
-30 Cent g0
a0
h0
c1
d1
e1
fis1
g1
g1
a1
h1
c2
d2
e2
fis2
g2
Fig.1: Mean values of intonation offered by 37 instruments and played intonation by 35 players in relationship to the equally tempered scale (0 cent). g0 and d1 are usually played with and measured without the use of a trigger.
Commonly not used resonances like the 7st, 11st, 13st are not included into the pitch determination process. Having found the reference pitch, the deviation of each tone can be calculated. Practical experience shows that such results can correspond with players judgments (particular for piano notes), but mostly do not. The player excites the instrument with a more or less broad spectrum containing a lot of harmonics with different amplitudes. This has to be taken into account by convoluting the impedance curve. At each frequency point the value of the fundamental and weighted values of its harmonics are superimposed. An example shows Fig.4. The weights for this operation can be obtained by statistic estimation of a sufficient quantity of measurements and judgments. The standarized weightings of Fig. correspond fairly well to playing reality. If weighting for an individual player and dynamic range with a given instrument is of interest, then its excitation spectrum has to be determinated. 1
1
0.8
5 0.6
x
1 4
x
3
1
1
x
x
1 x
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0.2
without weights
Fig.2: various weighting factors 2
4
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A comparison between the unweighted impedance plot (corresponds to piano) and “fortissimo” weighting (factor 5) makes the effect clear: the shift of most resonance frequencies agree with the well known phenomenon by brass players that particular notes get 2
sharp or flat if one changes from piano to fortissimo or vice versa. In most cases standard weighting produces results which match the judgments of the players.
Fig.3: trumpet Bb (pure impedance, without convolution)
Fig.4: trumpet Bb, fortissimo weighted
The consequences for intonation are shown in table 1 on the left side: playing fortissimo mostly lowers the notes of the high register and makes the low notes sharp. Instruments with a poor intonation quality (unweighted) tend to increase this effect. Another aspect of using a weighted convolution is that a player can bee seen as represented by his input spectrum. In this case the evaluation process
TABLE 1: Comparison of deviations due to the equally tempered scale in cent (data from Fig. 3,4) note unweighted weighted difference c1 -28 0 +28 g1 -17 -5 +12 c2 +8 +4 -4 e2 +18 0 -18 g2 +25 +17 -8 c3 +9 +6 -3 e3 -19 -22 -3
can be adapted according to the characteristic of the excitation spectrum (bright sound with many partials, or dull with less partials). Experience shows that players which differ extremely in tone color usually produce a different intonation with one and the same instrument. RESPONSE This term is created by musicians, means how easy it is to produce correct notes with the instrument and consists of two main components: the energy input needed during the initial settling time and during the stationary part of the played note. If the settling time is short players tend to take this as an advantage. But it means that the vibrating system is fairly damped – either of losses because of a thin wall or incorrect located resonance frequencies, both of them need an increased energy input during the steady state part of the played note which is on the other hand rated as a disadvantage. Response therefore consists of two contradictory components and it depends on the individual player which of the two components are more important to him. In addition to this two meanings are existent: on the one hand the player means the instrument generally, this would require an „over all value“ for the entire instrument; on the other hand the term response is related to a particular single note. In this case the response of the note is compared with other notes of the instrument. The „over all value“ is easy to calculate from the basic impedance data. Inverse FFT and Hilpert Transform allow to calculate the pulse response. Setting the amplitude of the reflection at the end of the bell in relation to the amplitude at the mouthpiece, one gets a response factor which represents the behaviour of the entire instrument. This value matches very well the judgments of players. The response of a particular note in relation to the others unfortunately turned out as a matter of individual feeling: whilst the response of a note is inacceptable for one player, another does not even take notice of it. Whereas the „over all value“ corresponds very well 3
with players judgment, the frequency depending response of a particular note seems to depend highly on the individual setup of the players lips (mass, stiffness, etc). A way out of this problem is to give only hints with an objective background. A measure for the easyness of tone production in dependence of the instruments acustical properties is the group delay time for each frequency which can be quite different for certain notes. According to our experience it is the best approximation for the time.
IMPROVEMENT Intonation depends to a great extend on the geometry i.e. the shape of the tube. The fact that a reduction of diameter at the location of a pressure antinode of the standing wave inside the tube for a given note increases its frequency and vice versa is well known, but requires the knowledge of the allocation of nodes and antinodes. As the geometry of the instrument is known its input impedance can be calculated using the transmission line model (4). From there the relationship between pressure and velocity at any point can be calculated and allows the determination of pressure nodes and antinodes for given frequencies inside the instrument. The problem is that an alteration of the shape at any place which improves the intonation of a note influences several other notes because of the harmonic structure of the system. To obtain a practicable compromise the use of an optimization target specifications bore list algorithm is indicated. We use an algorithm published by Rosenbrock in the seventies and adapted by W. Kausel tra nsm issio n Rosenbrock (5). The input information can be a line m od e l Algorithm measured impedance or a bore list. m ea sure d im p ed an ce
calcu la te d im p ed an ce
As target specifications the algorithm accepts measured impedance data, frequency alterations of the natural notes in cent or Hz and relative or absolute values for amplitudes. Areas where no alterations are allowed (for example the valve section) can be specified and the importance of particular modifications can be assessed by assignment of weights. The result is an optimized bore list which indicates the instrument maker the location and dimensions of alteration to do. This allows to optimize either the intonation or the response or both. Successful examples are given in (6), more detailed information on the adapted optimaziation algorithm can be found in (5).
REFERENCES
Widholm, G., Proc. Stockholm Music Acoustics Conference, pp. 560-565, (1993) Benade, A. H., Fundamentals of Musical Acoustics, New York, pp. 391-429 (1976) Bertsch, M., Studien zur Tonerzeugung auf d. Trompete, Diss. Univ. Vienna (1998) Mapes-Riordan, D., J. Audio Eng. Soc. 41(6), pp. 471-482, (1993) Kausel, W. et al., A Computer Program for Brass Instrument Optimization. Part I. Concept and Implementation, Proc. Forum Acusticum, Berlin (1999) (6) Anglmayer, P. et al., A Computer Program for Brass Instrument Optimization Part II. Applications, Practical Examples. Proc. Forum Acusticum, Berlin (1999)
(1) (2) (3) (4) (5)
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