Acoustical evaluation of historic wind instruments

D. M. Campbell School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, U.K, e-mail: [email protected]

The later decades of the twentieth century saw a remarkable revival in the use of wind instruments of pre- modern design in historically informed performances of Renaissance, , Classical and Romantic music. In some cases surviving historic instruments have been available, but more frequently museum spec- imens have been carefully measured and reproduced for peformance. This process raises many questions; for example, original reeds and mouthpieces are often missing, and curators are increasingly unwilling to permit playing tests and invasive mechanical measurements of rare and fragile instruments. This paper sur- veys the use of acoustical techniques to study original instruments, to model their playing behaviour, and to guide manufacturers in the creation of musically excellent reproductions.

1 Introduction the assumption that a carefully made replica should re- produce not only the physical shape but also the acousti- The acoustical study of a of any genre cal behaviour of the original. Further questions are raised or period can yield valuable information about its phys- by study of these replicas. Are the originals typical of ical and musical properties. In recent years, signal pro- their period? Should perceived acoustical faults be cor- cessing techniques of increasing sophistication have been rected in reproductions designed for performance, or are applied to analyse the sound output of the played instru- they part of the historic character of the instrument con- ment, while mechanical and acoustical excitation meth- cerned? ods have been used to determine the linear response of This paper reviews some of the ways in which the meth- the resonators in the instrument. The non-linear sound ods of musical acoustics have been adapted to meet the generation systems which are at the heart of bowed and specific challenges of working on historic wind instru- blown instruments have been investigated using a variety ments. Rather than attempting a comprehensive cover- of experimental and numerical modelling approaches. age of a very extensive field, the review focuses on a The study of historic instruments using acoustical tech- number of specific examples. Section 2 outlines various niques raises a number of specific issues. In this con- approaches to the problems of understanding the acous- text, the term “historic” is used to describe a musical in- tics of prehistoric flutes and horns, Section 3 surveys a strument which is either no longer manufactured in the number of pioneering studies of Renaissance wind in- form considered, or is made as a conscious replica of struments, and Section 4 offers a brief summary of some an instrument of a previous time (“period reproduction”). acoustical studies of the rapid evolution of wind instru- This description thus covers a very wide range of differ- ments through the Baroque, Classical and Romantic pe- ent types of instrument. Some instruments, such as the riods. sixteenth century Phagotum, survive only through illus- trations and/or written descriptions, while many prehis- toric instruments exist only in broken and fragmentary 2 Prehistoric Wind Instruments forms. Musical instrument museums contain numerous examples of instruments from the Renaissance onwards 2.1 Reindeer phalanx whistles which are more or less complete structurally, but which often lack crucial adjuncts such as woodwind reeds or Among the earliest wind instruments to have been studied mouthpieces. In addition, the conserva- acoustically are the whistles made from reindeer phalanx tion policy of most museums now prohibits the playing of bones by the people of the Palaeolithic era. These have fragile wind instruments because of the danger of crack- been discussed in detail by Michel Dauvois and Benoit ing or other physical damage. Fabre [1]. One of the principal predators of the reindeer In the last few decades of the twentieth century, many in this era was the wolf, and many reindeer phalanx bones museum specimens of historic wind instruments were have been found with indentations and irregular holes physically measured, and reproductions were made to be probably caused by the teeth of wolves. In a number of played in “historically informed” performances of music surviving bones, a hole near the upper end of the phalanx ranging from the Middle Ages to the nineteenth century. has been carefully extended and made more regular, ap- These reproductions have provided one approach to the parently by human hands (Figure 1, right). When a jet of acoustical investigation of the original instruments, on air is blown across the hole by a player, resting the lower

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Figure 1: Reindeer phalanx whistle. Left: reproduction; right: original. Photograph: Michel Dauvois [1] Figure 3: Spectrogram of a note played on the Reindeer phalanx whistle [1] lip in the indented end of the phalanx as though it were the plate on a modern flute, a piercing whis- The first admittance maximum, at around 2 kHz, is the tle is produced. Dauvois and Fabre have suggested that frequency at which the self-sustained oscillation excited this is the earliest evidence of a human sound production by an air jet would be expected. Sounding the instrument device. does indeed yield a frequency in the vicinity of 2 kHz, to- gether with some relatively feeble upper harmonics aris- ing from the non-linear nature of the jet excitation mech- anism, as can be seen in the spectrogram in Figure 3. In addition, the turbulent nature of the jet generates a broad- band noise, which appears in the spectrogram filtered by the (inharmonic) resonances of the cavity. One further aspect of the spectrogram should be re- marked upon. When a historic instrument can be played, either in its original form or as a replica, it is possible for the player to determine by experiment whether specific musical effects can be produced. Figure 3 shows that a wide vibrato can be readily generated on the reindeer phalanx whistle. Whether such a technique was used by Palaeolithic players is of course a matter for conjecture.

Figure 2: Calculated input admittance curve for the re- production reindeer phalanx whistle [1] 2.2 The Isturitz flute A Palaeolithic bone flute discovered at Isturitz, in the The study of these earliest instruments illustrates a tech- Pyrenees, has also been studied acoustically [2]. The nique which has been widely applied to the detailed in- original instrument, which has four finger holes, was vestigation of historic instruments: the fabrication of an judged to be too fragile for playing tests, so the inves- accurate copy (Figure 1, left). The hypothesis that the tigation used replicas and numerical modelling of the cavity of the instrument could be treated as a Helmholtz resonance properties of the instrument. Input admit- resonator was considered and discounted, since the calcu- tance curves were calculated for different fingerings cor- lated Helmholtz resonance frequency of the reproduction responding to the successive opening of the side holes. was 3.4 kHz, and the half wavelength at this frequency From these, the probable playing frequencies of the flute (around 5 cm) is comparable to the long dimension of the could be deduced. elongated cavity. Instead the instrument was modelled as a tube closed at the lower end, and the input admittance The flute, in its present form, is considerably shorter than at the open hole was calculated. The resulting input ad- the bone from which it appears to have been constructed. mittance curve is shown in Figure 2. Is it possible that it was originally longer, and part of it

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has been lost? The acoustical study, while not capable of giving a definitive answer to this question, certainly pro- vided some important guidance. It is possible on this type of flute to overblow from a first register (using the first air column modes) to a second register (using the sec- ond air column modes). For a model flute with the exist- ing dimensions, it was shown that the highest obtainable first register note (with all holes open) had practically the same frequency as the note obtained in the second reg- ister with all holes closed. This continuity of registers, which is also found on modern flutes, has obvious mu- sical advantages. Similar admittance calculations for a model instrument with additional length showed that this advantage was lost, suggesting that the existing length may well have been a deliberate choice.

2.3 Neolithic Chinese flutes

Another important collection of early bone flutes, dat- ing from around 7000 BC, was found in 1999 at Jiahu in Henan Province, China. The collection included instru- ments with 5, 6, 7 and 8 holes. Playing tests were carried Figure 4: A reproduction sounded by an artificial out on the best preserved instrument, with seven holes, mouth and playing frequencies were recorded [3]. Attempts to extend the tests to other seven hole specimens were dis- Museum of Scotland, which in 1994 commissioned the continued when cracking sounds were heard. reconstruction of a complete carnyx. Since then a fur- This discovery stimulated a team including Patricio de la ther reconstruction has been made for the musician John Cuadra and Chris Chafe at CCRMA, Standford Univer- Kenny, who has played it extensively in concerts and on sity, to develop a digital waveguide model which would recordings [9]. be capable of replicating the sound of the flutes now A number of acoustical studies were carried out on the judged to be too fragile to play, using as input data the replicas in the Musical Acoustics Laboratory of the Uni- measured physical dimensions of the instruments. This versity of Edinburgh [10, 11]. In an attempt to clarify the is a step further than the calculation of the passive linear acoustical behaviour of the complicated boar’s head bell, frequency response of the instruments, since it is also at- a reconstruction was performed using the acoustic tempting to model the non-linear air jet sound generator pulse reflectometry technique [12]. This derived the bore and its coupling to the resonator. The ultimate goal is a profile of an equivalent tube with cylindrical symmetry, time domain model which can generate a sound output shown in Figure 5; it can be seen that the head is equiva- equivalent to a playing test of the real instrument. lent to an approximately conical final bell section. Development of the model is still in progress; a report of Since no complete instruments were known to have sur- its use in a different context will appear shortly [4]. vived at the time of the reconstruction of the Deskford carnyx, the gently conical bore, made up of a number 2.4 Bronze horns of separate sections, was based on pictorial evidence. These images give very little guidance as to the type of Various types of bronze age horns have been discovered (if any) employed. A number of conjec- in Celtic and Scandinavian countries, and a number of re- tural mouthpieces were constructed, ranging from one construction and acoustical evaluation projects have been with a narrow throat similar to that on a modern trom- undertaken [5, 6, 7, 8]. bone mouthpiece to one with effectively no bore constric- tion. Input impedance curves were measured for the re- Horns with bells in the form of animal heads appear in constructed carnyx with different mouthpieces, and com- numerous illustrations during the period of the Roman parisons were made between the playing frequencies pre- Empire. One such instrument was the carnyx, in which dicted from the impedance curves and the frequencies of the bell took the form of a boar’s head complete with the notes actually played by John Kenny. Some tests were tongue (Figure 4). In the early nineteenth century the up- also carried out in which notes in the upper part of the in- per section of a carnyx was discovered in a bog at Desk- strument’s compass were played by an artificial mouth ford in Scotland. This fragment is now in the National

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using a material (polymethyl methacrylate enriched with aluminium hydroxide) whose density is similar to that of ivory. The aim of this “research facsimile” was to make an instrument as close as possible to the present state of the original instrument in all acoustically significant as- pects. It could then be reasonably expected that playing tests on the facsimile would mirror the current behaviour of the original instrument if it were possible to play it.

Figure 5: The internal equivalent cylindrical bore of the carnyx, measured by acoustic pulse reflectometry [11]

(Figure 4). Figure 6: Variation of pitch with blowing pressure for For the higher notes, the playing frequencies could be re- a Renaissance , original (solid line) and liably predicted from the frequencies of the impedance replica (broken line) [14] peaks. However, the player found a strong and well- [ centred low note (E2) which bore no obvious relationship To verify that the playing behaviours of the two instru- to the impedance curve. This reinforces the desirability of ments were indeed comparable, a number of tests were attempting to find a method of modelling the instrument carried out in which each instrument was blown artifi- which takes account of the non-linear coupling between cially using air with ambient temperature and humidity; the resonator and the lip valve. it was considered that this posed a negligible risk to the In September 2004 an excavation at Tintignac in the Cor- ivory. The result of a test on the variation of playing pitch rèze district of France revealed a buried horde of bronze with blowing pressure is shown in Figure 6. It can be seen instruments, including parts of five [13], al- that there is a small difference between the two instru- most certainly dating from the first or second century BC. ments, but the overall level of pitch control with pressure The acoustical study of replicas and numerical models is similar, and also closely similar to the behaviour of a of these instruments will surely enrich greatly our unde- high quality modern tenor Renaissance recorder. standing of these fascinating and mysterious instruments of Celtic civilisation. 3.2 and crumhorns

In 1981 an exciting discovery was made in Salamanca 3 Renaissance Wind Instruments Cathedral in Spain [15]. A chest underneath one of the benches in the archive room was found to contain an 3.1 The recorder extensive collection of Renaissance double reed instru- ments: five crumhorns, two shawms, five bombards and In 2000 the Edinburgh University Collection of Historical a fragment of a sixth bombard. The instruments had lain Musical Instruments acquired a rare ivory tenor recorder forgotten and ignored for several centuries. dating from the sixteenth or early seventeenth century. The collection was catalogued in 1995 by Romà Escales Since ivory is a more stable material than wood, it was and John Hanchet. The crumhorns are all by the same considered that this instrument provided a particularly maker, Jörg Wier of Memmingen in , who was valuable record of the constructional practice and musical active in the first few decades of the sixteenth century; expectations of recorder makers of the late Renaissance. most of the other instruments are by well known makers Because of the high danger of cracking the ivory by blow- from the same period. ing warm moist air through the instrument, the decision This was an important discovery because of the light was taken that it should not be blown at all by a human it shed on religious music practice in sixteenth century player. An accurate reproduction was reconstructed [14] Spain. The circumstances of the discovery made it very

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plausible that the instruments had been the working tools of the band of instrumentalists known to have been em- ployed in the Cathedral in the sixteenth century. In prin- ciple, therefore, many questions could be answered about the relative pitches of the members of a double reed en- semble, and the absolute pitch standard employed by a Spanish wind band at the time. Unfortunately several crucial elements were missing from the instruments: the double reeds, and the bocals (short metal tubes which connect the reeds to the wooden main bores of the instruments). Smaller shawms nor- mally had an additional wooden flange known as the pirouette between the reed and the bocal, against which the player could press the lips; if these had existed on the Salamanca shawms they had also been lost. Figure 8: Input impedance curves for different fingerings of a Salamanca crumhorn [16]

Figure 7: Measuring the input impedance of a in Salamanca Cathedral [16]

In the course of restoration, some playing tests were done by a musician using modern reproductions of reeds and bocals, but for a combination of practical and conserva- tion reasons the scope of such tests was severely lim- ited. Instead, an acoustical investigation was carried out Figure 9: Input impedance curves for different fingerings by Ana Barjau and Vincent Gibiat [16], using the TMTC of a Salamanca shawm [16] input impedance measurement technique [17]. It was im- possible to move the instruments to an acoustics labora- tory, so a portable version of the apparatus was used in notes. This is related to the very low cutoff frequency the archive room of the Cathedral (Figure 7). A practical of the lattice of very small diameter toneholes on the advantage of this technique is that an impedance curve crumhorn; the musical consequence is that the crumhorn for a given fingering of the instrument can be obtained in will not overblow to a second register. A similar be- under 30 seconds. There is also no risk of cracking due to haviour is found with modern reproduction crumhorns. the influx of warm moist air from the breath of a player, The shawms display a much more irregular pattern of res- or of damage due to wall vibrations induced by the very onance peaks. For the lowest fingerings, the second peak high internal pressure amplitudes when the instrument is dominates over the first, which would allow the shawm to sounded. overblow easily to the second register; indeed, it could be Figure 8 shows a set of input impedance curves obtained difficult to avoid overblowing on the lowest fingering. On by successively fingering one of the crumhorns to obtain the other hand, only the first six fingerings show well de- a diatonic scale as described in playing instructions of veloped second mode peaks, so the second register would the period. Figure 9 shows a corresponding set of input not extend over much more than a musical fifth. Again, impedance curves for one of the shawms. Several inter- these musical properties are typical of modern reproduc- esting conclusions about the likely playing behaviour of tion shawms. the instruments can immediately be drawn from the in- In attempting to deduce the relative and absolute playing formation supplied in these figures. For example, the first pitches of the shawms and crumhorns, numerical mod- mode impedance peak is dominant for all the crumhorn elling of the bore was used to add virtual bocals of various fingerings, and is almost the only resonance for the higher

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lengths. The goal was to predict the probable dimensions of the best bocal for each instrument, using the criterion 9 seventeenth century that the resulting fundamental mode resonance frequen- 8 Monk reproduction cies should give a well tuned scale using conventional 7 fingered D fingerings. In addition, for the shawms it was desired that 4 the second mode frequency should be close to twice the 6 first, to permit accurate overblowing to the second regis- 5 ter. 4 mode number It was found possible to meet these criteria with reason- 3 able success, and playing tests on one instrument con- firmed the musical validity of the approach. The study 2 of the absolute frequencies of the resonances of the vir- 1 tual instruments also yielded a prediction of the absolute 0 pitch standard to which the instruments were tuned: the -200 -100 0 100 200 300 equivalent fundamental pitch /cents above C relatively high (but not unknown) value of A = 520 Hz. 4

3.3 The cornett Figure 11: Comparison of the equivalent fundamental pitches of a seventeenth century cornett and a modern re- production scaled to play at A = 440 Hz [19]

judgment it is important to take the overall pattern of the impedance peaks into account, rather than relying on the frequency of one (possibly anomalous) peak.

4 Baroque, Classical and Romantic

Figure 10: Cornett (Italian 17th century, Edinburgh Uni- Instruments versity Collection of Historic Musical Instruments) 4.1 Woodwind instruments A number of studies have been carried out on the acous- tical properties of the cornett, a Renaissance lip reed in- In the eighteenth and nineteenth centuries the design of strument with finger holes [18, 19, 20, 21, 22, 23]. An ex- woodwind instruments evolved rapidly, partly because of ample of a seventeenth century cornett is shown in Figure advances in the understanding of the acoustics of the in- 10. struments and partly because of the pressure of changing musical requirements. This process has been reviewed Figure 11 illustrates the use of data derived from input by Benade [25]. The transformation of the flute has been impedance measurements to determine the absolute play- discussed by Castellengo [26] and by Wolfe et al [27]. ing pitch of the seventeenth century instrument without Acoustical studies of historic clarinets have been pub- the intervention of a human player. The equivalent fun- lished by Jeltsch and collaborators [28, 29]. The acousti- damental pitches [19] for the first 8 modes of the early cal development of the saxophone has been reviewed by instrument are compared with similar data for a modern Kergomard [30]. Measurements on the tonehole lattice reproduction instrument, scaled to play at A = 440 Hz and cutoff frequencies of historic oboes have been reported used regularly by a professional performer. Tests were by Benade [31]. carried out for a number of conventional fingerings; the illustration shows the results for the note D4. Although the first mode of the early instrument is only 4.2 Lip reed instruments around 30 cents higher than that of the modern instru- ment, the overall form of the curves clearly suggests that Numerous studies of the historical development of brass the early instrument was built to play at a pitch about 100 instruments have been undertaken, using many of the cents higher than modern concert pitch. Similar mea- acoustical techniques previously described [32, 33, 34, surements with other fingerings confirmed this conclu- 35, 36, 37, 38]. The interesting topic of the evolution of sion. In fact, the majority of instruments surviving from brass instruments in Vienna, with their own distinctive the seventeenth century are at this high pitch, correspond- acoustical and musical characteristics, has been studied ing roughly to A = 465 Hz [24]. In making this type of for some years by the Musical Acoustics Group at the

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Institut für [39]. Baudouin , first three holes open 8 10

7 10 input impedance / ohms

6 10 0 500 1000 1500 frequency / hertz

Figure 14: Input impedance curve for serpent by Bau- douin, Paris, c.1820, lowest three holes open [20]

the small diameter of the finger holes in comparison with the bore diameter gives a very low cutoff frequency. Al- though the mode frequencies with all holes closed form a reasonably harmonic sequence (Figure 13), the open- ing of several finger holes results in a highly irregular in- put impedance curve (Figure 14), and a correspondingly complicated fingering scheme in the higher registers.

Figure 12: Serpent (Edinburgh University Collection of Historic Musical Instruments)

The serpent is a lip reed instrument with a conical bore. It was invented in the late sixteenth century, and con- tinued in use until the middle of the nineteenth century. Figure 12 shows a typical eighteenth century French ser- pent. The original serpents had six finger holes irregu- larly spaced along the sinuous tube; later versions had a number of additional holes closed by pads and keys. The acoustical features of the serpent have been documented in a number of studies [40, 20, 41].

Baudouin serpent, all holes closed

8 10

7 10 input impedance / ohms

6 10 0 500 1000 1500 frequency / hertz Figure 15: (Edinburgh University Collection of Historic Musical Instruments) Figure 13: Input impedance curve for serpent by Bau- douin, Paris c.1820, all holes closed [20] This problem was addressed in the ophicleide (Figure 15, which supplanted the serpent for orchestral use in the A striking feature of the acoustics of the serpent is that early decades of the nineteenth century. Much larger

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Bb ophicleide, fingered C2

7 10 input impedance / ohms 6 10

0 500 1000 frequency / hertz

Figure 16: Input impedance curve for B[ ophicleide (EU- CHMI No.2157), fingered C2

Bb ophicleide, fingered D2

7 10 Figure 18: (Edinburgh University Collection of Historic Musical Instruments)

5 Conclusion input impedance / ohms 6 10 In one sense, the process of development and evolution of 0 500 1000 frequency / hertz musical instruments which we have traced over several millennia has been a process of improvement. Yet the Figure 17: Input impedance curve for B[ ophicleide (EU- modification or abandonment of an instrument which has CHMI No.2157), fingered D2 been the voice of great players or composers, or which has been a central part of the musical daily life of a soci- ety, inevitably involves some loss as well as gain. Acous- holes, covered by pads, raised the typical cutoff fre- tical studies can help to bring into focus the precise nature quency from around 100 Hz to around 400 Hz, while the of the differences between historic and modern instru- use of keys and levers allowed regular spacing of the ments, and can provide guidance to makers and players toneholes [42]. Input impedance curves measured on a of historically accurate reproductions. In this way musi- nineteenth century ophicleide show that for most finger- cal acoustics is deepening our understanding of our mu- ings the first three modes have frequency ratios close to sical heritage, and helping to enrich the sound world of harmonic, which simplifies the relationships between the the present with the lost voices of the past. fingerings of different registers and provides a more sta- ble regime of oscillation in first two registers (Figure 16). Certain notes require venting by much smaller holes, and 6 Acknowledgements the corresponding input impedance curves are more ir- regular (Figure 17). The author would like to pay tribute to the many col- By the latter part of the nineteenth century the ophicleide leagues in musical acoustics whose work is described in was in turn replaced for orchestral use by members of this review, and to express particular gratitude to Ana the saxhorn family (Figure 18). The acoustical and mu- Barjau, Chris Chafe, Benoit Fabre, Vincent Gibiat and sical reasons for the eventual triumph of the valved brass Arnold Myers for help in its preparation. basses over the lip reed instruments with toneholes were reviewed by Myers et al [43].

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[28] J. Jeltsch, V. Gibiat, L. Forest, ‘Acoustical study of [42] D. M. Campbell, ‘An acoustical comparison of the a set of six key Baumann’s clarinets, Proc. Interna- serpent and the ophicleide’, J.Acoust.Soc.Amer. 108, tional Symposium on Musical Instruments, Dourdan, 2617 (2000) 134-140 (1995) [43] A. Myers, S. Bromage and M. Campbell, ‘Acousti- [29] J. Jeltsch, N. Shackleton, ‘Caractéristation acous- cal factors in the demise of the ophicleide’, Proc. In- tique de trois clarinettes de facteurs lyonnais: ternational Symposium on Musical Acoustics, Nara, Alexis Bernard et Jacques Francois Simiot’, Col- Japan, CDROM (2004) loque Acoustique et Instruments Anciens: Factures, Musiques et Science, Cité de la Musique, Paris, 103- 124 (1999) [30] J. Kergomard, ‘Une révolution acoustique: le saxo- phone’, Colloque Acoustique et Instruments Anciens: Factures, Musiques et Science, Cité de la Musique, Paris, 237-254 (1999) [31] A. H. Benade, ‘Fundamentals of Musical Acous- tics’, Oxford University Press, New York (1976) [32] D. Smithers, K. Wogram, J. Bowsher, ‘Playing the Baroque ’, Scientific American 254, 108- 115 (April 1986) [33] D. M. Campbell, ‘The , the cornett and the serpent’, Acoustics Bulletin 19(3), 10-14 (1994) [34] R. W. Pyle, R. Pyle, ‘The modern ’, J. Acoust. Soc. Amer. 95, 2912-2913 (1994) [35] D. B. Sharp, D. M. Campbell, A. Myers, ‘Pulse re- flectometry as a method of leak detection in histori- cal brass instruments’, Proc. Forum Acusticum 1996, Acustica/Acta Acustica 82, S189 (1996) [36] A. Myers, ‘Characterization and Taxonomy of His- toric Brass Musical Instruments from an Acousti- cal Standpoint’, PhD thesis, University of Edinburgh (1998) [37] R. W. Pyle, ‘The evolution of lip-reed instruments and their manufacture’, J. Acoust. Soc. Amer. 108, 2617 (2000) [38] A. Myers and D. M. Campbell, ‘Trumpet Design and Acoustical Characteristics’ in Proceedings of Cuivres Anciens: Symposium of the Historic Brass Society, Paris, March 1999. Historic Brass Society, New York [in press]. [39] G. Widholm, ‘The Vienna – a historic relict successfully used by top of the 21st cen- tury’, Proc. Forum Acusticum 2005, Budapest (2005) [40] E. Leipp, ‘Le serpent: un monstre acoustique’, Bul- letin du Groupe d’Acoustique Musicale, Université de Paris 6 63(a), 1-12 (October 1972) [41] V. Hostiou, ‘Contribution of acoustic in playing early instruments in agreement with historical us- age: the serpent as example’, Proc. Forum Acusticum 2005, Budapest (2005)

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