Stringed instruments and technology of their making in Italian acoustics

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2 Stringed instruments and tehnology of their making in Italian aoustis S. Cingolani Dipartimento di Ingegneria Meania, Università degli Studi di Bresia Via Branze 38, I Bresia, Italy The topis of the present artile onerns the studies in the field of musial aoustis applied to stringed instruments. Italy represents no doubt one of the most important ultural referene point in suh a field. In fat, during the enturies, Italy has registered an enormous inrease in the raftmaking of these instruments with respet to all other ountries. The fame that has marked the art of the Italian lutemakers in the past is still very evident, espeially in Cremona, to the extent that it has dimmed the study of the Italian tradition and ulture of stringed-instrument making that support the professional pratial ativity. In this kind of ulture, the study of stringed instruments tehnology, as a part of the vast field of systemati musiology, is inluded. This is a referene point for musial aoustis, that in Italy has represented a portion of a sientifi legay dating from the end of the Nineteenth entury. In fat, the approah to aoustis an be desribed as the slow flowing of a romanti formulation towards the aquisition of new tehniques of researh, above all as regards to the proeedings of non-destrutive methods of restoration. Nowadays, the stringed instruments tehnology, whih is atually onneted with organology, has beome a promoter for a more orret evaluation of the aousti harateristis of stringed instruments, that is to say, of high quality sound soures. As for the study of musial instruments in their old forms, we fortunately have both ionographi and bibliographi soures. As a matter of fat, the sientifi methods onerning any hand-made artile are always to be taken into aount in order to seriously study the aousti harateristis of every musial instrument. The rapporteurs an, therefore, take sides about funtions and aims of aoustis, and also about the usage of musial instruments and their reonstrutions aording to new sound harateristis. This tradition must be speifially deep-rooted in ulture, in the knowledge of produtive progress, and in the possible historial relationships that are emphasized in a partiular musial event. It an be said that studying the aoustis of a musial instrument means to play upon the events that preeeds its ion by transmuting its sensory results thanks to the demythisation of mehanial ation. Thus, the aousti engineer s job turns out to the a simple ring of a hain of interpretations that are meant to be objetive but that are, nevertheless, always partially subjetive. This analysis, moreover, has to be ontextually integrated with an investigation of the interations between musi and ulture: in fat, important infromation about the way in whih a ertain instrument plays or is played helps to better define the taxonomi riteria that the analysis itself must bring on. Finally, researh an be enrihed by speifi empirial studies about what is atually to be regarded as a musial instrument Guizzi [1], When we define an objet as musial instrument, we atually elevate it, and we do that after identifying it and testing its possible phoni powers, as well as by expeting it to possess them. This is what musial aoustis does with a sound objet before it is given its symboli value. What aoustis atually does is to break that mehanism: it turns out to be what quantum mehanis would all an observer of an event that possibly implies the distortion of pre-existing properties. The same thing an be said about aoustis delays in our ountry, though it must be pointed out that Italian aoustis has anyway made good ontributions, at least in the first Romanti Age, when stringed instruments were lassified as rubbing instruments in the Hornbostel-Sahs system. In Italy musial aoustis represents the paradigm of a subjet whih is slow to make a name for itself, but that anyway shows all the harateristis of an anient traditional disipline. In partiular, stringed instr u- ments aoustis learly shares the methodologial and teahing laks of our ountry s musial bakground: it is in fat, an old disipline based upon a pure nineteenth-entury ulture, as in it there is no development of new ideas and of the same interdisiplinary sientifi knowledge that we an find in organology. The history of stringed instruments aoustis begins with the lutemakers tradition: in short, it begins in one of the greatest and liveliest period of our history. The slow aquisition of sientifis methods lead to a lear-ut separation between traditional raftsmanship and aousti analysis of vibratory systems. Anyway,

3 inside Italian ulture this parting between raftsman and sientist kept on diminishing as time passed by: in fat, it maintained a lose relationship with the stringed-instrument making high tradition as opposed to sientifi researh, by giving rise to figures like musi lovers, harlatans, sientists-lutemakers, and aoustis amateurs. In the Nineteenth entury, Italy was in line with German ulture or with Frenh physiist Savart s studies.. Among these onnoisseurs, mention must be made of physiist Pietro Blaserna [2], who in 1875, following German sientist Hermann von Helmholtz, gave urreny to aoustis with speial regards for the auditory physiologial theory. A differene in quality, still based on lassi lute-making ideas, ould be pereived from 1930 to 1950, when aoustis seemed to arve out a plae for itself inside our researh institutes. In the years preeeding Seond World War, several personalities worked in Rome at the National Institute of Aoustis O. M. Corbino, where they were given good tehnologial means. The sientists at the Institute of Aoustis in Rome analysed stringed instruments following eletroaousti methods ( , 1940, 1941), so that they ould estimate the sound exellene by objetive methods that they had got out of previous well-known international works. In partiular, Pasqualini [3] exemplified this eletrostati exitement method as follows: first he laid a thin-foil on the wooden surfae of the instrument, and then he made it vibrate by a short-distane positioned eletrode generating an eletrostati field. He also used other mixed methods so that he ould better put them in evidene with the mirophoni systems whih were adopted at that time. Violin is no doubt the instrument that, during the enturies, has mostly fasinated lutemakers as well as ative and passive users, whih has also given rise to embellishments of no tehnial interest and to faniful, sometimes even aberrant, onlusions Tiella [4]. These onlusions, that an still be found in our ontemporary essays, supported a feverish searh for the serets of lutemakers of genius like Stradivari, and above all for the geometrial marking proess of instruments shapes and for the presumed hemial methods that old lutemakers would use. He unwillingly reated this historial referene following a preise aesthethi-aousti point of view, while not reognizing the same phoni importane to violins that are still being made by modern lutemakers even if they are modelled upon original arhetypes. Essentially, in those years Italian researhers did not modifiy their ways of working. On the one hand, in fat, some of them evaluated the aousti phenomena by following their strong ideals of patrioti lutemakers, as we an see in Cremona Shool; on the other hand, an attempt was made to disset the sound objet far beyond its own musial and material harateristis. As for aousti researh in Italy during the post-war period, an intermediate position is oupied by the almost harismati figure of Pietro Righini. At the same time organology researhers felt the need of better heking the variability of musial phenomena. So, apart from hemial methods, metallurgy, and dendrohronology, they appealed to musial aoustis. In 1985, during the international Meeting on Preservation, Restoration, and Re-Utilization of Old Musial Instruments, in Venie preise suggestions were made about the studies on stringed instruments (Pietro Righini, Giuseppe Righini, Sergio Cingolani). Viniio Gai and Maro Tiella, two well-known organology sientists, were the atual promoters of this New Renaissane of a systemati view about musial i n- struments. Certainly, these sholars onveyed their professional knowledge of international museologi requirements to the study and the preservation of musial instruments, being Viniio Gai the diretor of the Musial Instruments Museum in Florene and Tiella the hairman of the Stringed Instruments Triennial Board in Cremona. At present, many efforts have been done (and many will be done in future) as well as many years have passed from the beginning of so-alled sientifi researh on the subjet Cingolani [5]. Coneptualization is atually onfronted with the most advaned tehnologial ontributions ever possible about sientifi researh on stringed instruments; and all this leaves the question open with regards to the fat that a musial instrument is neessary in produing musi but not in determining its harateristis. REFERENCES 1. F.Guizzi, La lassifiazione degli strumenti musiali popolari: appunti per una riflessione ritia, in Per una arta Europea del restauro, Venezia Olshki, Firenze, P. Blaserna., La teoria del suono nei suoi rapporti olla musia, Fratelli Dumolard, Milano, G. Pasqualini, L elettroaustia appliata alla liuteria in Annuario della Reale Aademia di S. Ceilia, Istituto Nazionale di Elettroaustia, Roma, M. Tiella, L offiina di Orfeo. Tenologia e pratia degli strumenti musiali. Il Cardo, Venezia, S. Cingolani, Aoustis of the Musial Instruments, Bibliography , edited by Turris, Cremona, 1992.

4 Aspets of Bowed-String Dynamis J. Antunes a, L. Henrique b, and O. Ináio b, a Applied Dynamis Laboratory, Instituto Tenológio e Nulear ITN/ADL, 2686 Saavém odex, Portugal b Esola Superior de Músia e Artes do Espetáulo, Instituto Politénio do Porto ESMAE/IPP, R. da Alegria, 503, Porto, Portugal Visiting researher at Applied Dynamis Laboratory, Instituto Tenológio e Nulear Many relevant aspets of the bowed-string dynamis an be readily implemented using a modal method for numerial simulations. Some of these aspets are the subjet of the present ommuniation, namely: (1) the string inharmoni behaviour; (2) the finite width of the bow; (3) the string torsion modes. We start by reviewing our omputational method, whih onsists in projeting the fritional fores on the transverse and torsion modes of the unonstrained string. The frition model developed is able to ope with both sliding and adherene states, using an expliit time-step integration method. We then disuss the above-mentioned dynamial aspets and present a few illustrative omputations. INTRODUCTION We reently developed a modal-based method for the numerial simulation of bowed systems [1-4]. Although still unable to ahieve real-time performane, our approah enables very detailed modelling of the non-linear frition interation fores, as well as an aurate representation of the string dynamis, in both time and spae. Furthermore, many relevant aspets of the bowedstring an be readily implemented when numerial simulations are based on a modal approah. We have reently explored several suh aspets, whih are the subjet of the present ommuniation, namely: (1) the string inharmoni behaviour; (2) the finite width of the bow; (3) the string torsion modes. We feel that some of these aspets have not been fully exposed in the literature see, for instane, referenes [5-8]. We start by quikly reviewing our omputational method, whih is based on a modal approah, using an expliit time-step integration algorithm. The frition model developed adequately simulates the slip-stik bow/string interation fores, while inorporating a veloity-dependent frition oeffiient. We then briefly disuss the above-mentioned aspets and onlude with some relevant illustrative omputations. The main purpose of this paper is to highlight the apabilities of the omputational method. Thorough disussions of the dynamial results will be presented elsewhere. COMPUTATIONAL METHOD Any solution of the string PDE an be formulated in terms of the modal parameters m n, ω n, ζ n and modeshapes ϕ (x), n = 1, 2,, N : n [ ]{ } M Q( t) + [ C]{ Q( t) } + [ K]{ Q( t) } = { Ξ( t) } (1) The modal fores I n (t ) are obtained by projeting the external fore field on the modal basis: L In ( t) = F( x, t) ϕ n ( x) dx (2) 0 The physial motions are omputed from the modal amplitudes q n (t ) by superposition: y( x, t) ϕ ( x) q ( t) (3) = N n= 1 and similarly for the veloities and aelerations. The previous system of equations an be integrated using an expliit time-step integration algorithm. In our implementation, we used a simple Verlet sheme. To solve equations (1-3), we inlude in I n (t) all nonlinear (fritional) effets. The modes of the linear system are then oupled by the nonlinear terms. Consider the frition fore arising when the bow is applied at loation x of the string: Fs ( x, t) = µ d ( y ) FN sgn( y ) ; if y > 0 (4,5) Fa ( x, t) < µ S FN ; if y = 0 where y is the relative transverse veloity between the bow and the string, F N (t) is the normal bow/string fore, µ is a stati frition oeffiient (during S adherene) and µ d ( y ) is a dynami frition oeffiient (during sliding). We use the following exponential model: C y µ y d ( ) = µ D + ( µ S µ D ) e (6) where, 0 µ D µ and C ontrols the deay rate of S the frition oeffiient with the sliding veloity. When a near-zero veloity is deteted at the ontat point(s), the sliding fore (4) is replaed by the following expliit model for adherene: n n

5 Fa ( x, ti ) = K a y ( ti ) Ca y ( ti ) (7) The idea in (7) is to attah the string to the bow at point x using a suitable adherene stiffness and to damp-out any loal residual motion with an adherene damping term see [1] for details. The adherene fore (7) is ompared with the maximum allowable value (5). If this ondition is not fulfilled, the system is sliding and formulation (4) is used. STRING INHARMONIC BEHAVIOUR Wave propagation in non-ideal (rigid) strings is dispersive. This effet is most easily simulated using a modal model, as the bending stiffness effet is automatially inorporated in the string modes, with modified frequenies 2 ω = n ( 1 + Bn ) 1/ 2 n ω, where B is an 1 inharmoniity oeffiient [6]. Computations show that an inrease in the string bending stiffness leads to a progressive rounding of the Helmholtz orner and, in general, to a deterioration of the response spetrum, as illustrated in Figure 1. Our results are ompatible with previous investigations [6,8]. P.S.D. Displaement [m 2 /Hz] P.S.D. Displaement [m 2 /Hz] Frequeny [Hz] Frequeny [Hz] FIGURE 1. Response spetrum of Helmholtz motion of a violin G string ( x = 30 mm, F N ( t) = 1 N, y bow = 0.1 m/s ): 4 (a) Ideal string ( B = 0 ); (b) Inharmoni string ( B = 2 10 ). FINITE WIDTH OF THE BOW Our omputational model an be applied to finitewidth bowing, simply by onsidering multiple adjaent ontat points subjeted to the frition interation model. In general terms, our omputations onfirm the differential slipping mehanism, proposed by MIntyre et al. [5]. Small-sale slips during adherene are more frequent and pronouned for bow-hairs loated near the bridge, a result that an be understood on simple geometrial terms. Simulations performed with many bow-hairs displayed omplex spatial patterns of differential slipping, however without disrupting the mainly periodi string motions. Figure 2 shows a typial result from a 10 mm width bow, simulated by 10 equidistant bow-hairs. Two string veloity-plots are shown at the loations of the extreme bow-hairs. Veloity [m/s] Veloity [m/s] Time [s] Time [s] FIGURE 2. Veloity-plots of Helmholtz motion of a violin G string ( x = 25 ~ 35 mm, F N ( t) = 1 N, y = 0.1 m/s ): bow (a) At bow-air Nr.1 ( 25 mm );(b) At bow-air Nr.10 ( 35 mm ). STRING TORSION MODES Inlusion of torsion and/or axial dynami effets in our simulation method also presents no oneptual diffiulties. One only has to inlude the new relevant modes in the omputational sheme. Transverse and torsion modes are heavily oupled by the frition fores. Beyond the additional damping, inlusion of the string torsion modes an affet both the transient durations and the steady state regimes, depending on the ratio of propagation wave-speeds α = Tor. Tra Indeed, opposing a onlusion from the restrited analysis [8], our systemati simulations suggest that torsion should not be negleted if α < 4. Gut strings should then be partiularly prone to torsion effets. ACKNOWLEGEMENTS This projet has been endorsed by the Portuguese FCT and POCTI, with funding partiipation through the EC programme FEDER. REFERENCES 1. J. Antunes, M. Tafasa and L. Borsoi, Revue Française de Méanique 3, (2000). 2. J. Antunes, M. Tafasa and L. Henrique, 5e Congrès Français d Aoustique, Lausanne, 3-6 Septembre M. Tafasa, J. Antunes and L. Henrique, 5e Congrès Français d Aoustique, Lausanne, 3-6 Septembre O. Ináio, L. Henrique, J. Antunes, 8th Int. Congress on Aoustis and Vibration, Hong Kong, 2-6 July M. MIntyre, R. Shumaher, J. Woodhouse, Aoustia 49, (1981). 6. L. Cremer, The Physis of the Violin, MIT Press, Cambridge (1984). 7. R. Pitteroff, J. Woodhouse, Austia-Ata austia 84, , and (1998). 8. S. Serafin, J. Smith III, J. Woodhouse, IEEE Workshop on Appliations of Signal Proessing to Audio and Aoustis, New York, Otober 1999.

6 Psyhoaousti Aspets of Violin Sound Quality and its Spetral Relations -âw SiQHN=2WþHQiãHN Sound Studio of the Faulty of Musi, Aademy of Performing Arts Prague, Malostranské nám. 13, Praha 1, Czeh Republi, The term 'sound quality' expresses timbre, enumeration of sound properties, or sound evaluation. Sound quality assessment depends on the evaluator and evaluation purpose. Psyhoaoustis studies seleted aspets of sound quality in a hosen sound and listener ontext. An experiment establishing sound quality preferene and its spontaneous word desription on five violin tones H3, F#4, C5, G5 a D6 is desribed. Connetions of sound quality preferenes to sound ontext, frequenies of ourrene of desriptive words, and spetral features of the sound are disussed. Common properties of stationary spetra of a high quality violin tone are formulated: a suffiient level of the fundamental; deep and narrow nothes and well pronouned and filled elevations in speified frequeny regions; and a balaned onseutive derease of levels of harmonis aross elevation bands. SOUND QUALITY AND PSYCHOACOUSTICS The term 'sound quality' an represent a ommon property of sound (timbre), enumeration of sound properties (distintive features) or aestheti evaluation of sound (preferene). The listener, musiian, and instrument maker pereive quality of the sound of a musial instrument differently. The omplete set of features of musial instrument sound quality onsist of: dynami properties; players instrument ontrol; timbre aspets of individual tones and their balane in the whole dynami range and diapason; possibilities to modifying the sound and ahieving the required sound impression. The goal of psyhoaoustis is to asertain the properties of the interation of sound and human onsiousness and express its ausal relations. Psyhoaousti researh may fous on defined sound quality aspets and a speifi sound ontext. The goal of one experiment arried out in our laboratory was to study sound quality as a set of timbral properties in words and quality evaluation. EXPERIMENT The violin sound quality was studied on reordings of tones H3, F#4, C5, G5, and D6 of eleven instruments of various qualities reorded in an anehoi room and played détahé, naturale, non-vibrato, and mezzoforte. The duration of all tones and their transients and transient shapes were unified [1]. A pair test with headphones was administrated with ten listeners. Pereived sound quality preferenes and spontaneous word desriptions of timbre differenes for eah pair of sounds were registered. Using this data, individual and group preferenes and later individual and group ranks in pereived sound quality were alulated. Internal onsisteny of individual preferene judgements and onordane of individual ranks in the group of judges were established in all five studied tones. Correlations between sound quality ranks and frequenies of ourrene of individual words were also alulated. Amplitude spetrum, SPL in individual harmonis, and spetral enter of gravity were alulated from quasistationary part of signals [1]. These spetral properties together with word desriptions and determined quality preferenes were used to interpret the results. RESULTS AND DISCUSSION Only words with an overall frequeny of ourrene of at least ten were evaluated. This represents 65 words for the H3 tone, 64 for F#4, 58 for C5, 64 for G5 and 65 for D6 tone. Correlations of ourrene of seleted words with sound quality evaluation rank are found in Table 1. These twenty words belong to the thirty most frequently used in all five tones. The words lear, voied, damped, unvoied have highly signifiant orrelation only in the G5 tone; this implies that this tone sound quality preferene was based on different sound properties than other tones. It is possible to observe a division of tested tones in two groups H3, F#4, C5 and G5, D6 based on the frequeny of ourene of the words dark and lear (Table 2). The words voied, dumped

7 Table 1. Correlations between sound quality ranks and frequeny ourrene of words used for timbre desription. Signifiane: bold α 0.01, normal α 0.05, italis α 0.1. H3 F#4 C5 G5 D6 balaned (vyrovnaný) lear (jasný).82 dark (tmavý) deliate (jemný) full (plný) pure þlvwê round (kulatý) smooth (hladký) soft P NN ê voied ] Q O ê.80 wide (široký) bleaty P H þly ê damped S LGX ã H Q ê -.76 metalli (kovový) narrow (úzký) penetrating (pronikavý) rustle (šustivý) sharp (ostrý) tinny (plehový) unvoied Q H] Q O ê -.78 Interesting orrelations between sound quality ranks and some spetral harateristis are found in Table 3, where the G5 note is again exlusive. Comparing spetral envelopes of different quality sounds with the envelope of the highest quality sound, and omparing the envelope of the best tone in all five tested pithes enabled formulation of a hypothesis on the spetral shape of a high-quality violin tone [1]: The harmoni spetrum of a high-quality violin tone has a suffiient level of the fundamental; its envelope is haraterized with deep and narrow nothes N0-N4 and wide, wellpronouned and filled elevation bands E1-E4 in frequeny regions given in Figure 1; and it has balaned onseutive derease of levels of harmonis aross elevation bands. A steeper derease of the spetral envelope in the H3, F#4, and C5 tones versus G5 and D6 (Figure 1) agrees with frequenies of use of the words dark and lear in the desription of sound properties (Table 2). With inreasing pith it beomes more frequent that no harmoni falls into the noth, and the spetrum envelope of a high-quality tone fills and smoothes out. This may be the probable reason for the onnetion of quality evaluation in the G5 note with different words whih desribe other perepts indued through other spetral envelope properties. Subjetive evaluation of the quality of violin sounds depends on the number of spetral properties, whih listeners desribe in appropriate and different words. Spetral properties and their desriptive words an feature in various ombinations and to different degrees onsistently with listened sound ontext. Table 2. Contrasts in ranks of overall frequeny ourrene of seleted words in individual tones, high ranks are bold. H3 F#4 C5 G5 D6 sharp (ostrý) dark (tmavý) lear (jasný) narrow (úzký) voied ] Q O ê damped S LGX ã H Q ê rustle (šustivý) Table 3. Correlations between sound quality ranks and spetral harateristis. Signifiane see Table 1. H3 F#4 C5 G5 D6 Level of the 1 st harmoni Spetral enter of gravity FIGURE 1. Harmoni spetra of the highest sound quality violin tones and positions of nothes (Ni) and elevations (Ei). ACKNOWLEDGMENT The investigation was supported partly by the Grant Ageny of the Czeh Republi (Grant No. 202/93/2522) and partly by the Ministry of Eduation and Youth (Projet No ). REFERENCES âw SiQHN - 2WþHQiãHN = 0HOND $ 6\URYê 9 Violin Tones Spetra and their Relationship to Pereived Sound Quality, In Proeedings of ISMA 97, 19 (5), Edinburgh, ( 1 ( 1 ( (1997). âw SiQHN-2WþHQiãHN=., CASJ Journal of the CATGUT Aoustial Soiety, Vol. 3, No. 8 (Series II), (1999).

8 On the Preision of the Pith Sensation in Sound of Bowed Instruments A. Rakowski and A. Miśkiewiz Musi Aoustis Laboratory, Department of Sound Engineering, Chopin Aademy of Musi, Okólnik 2, Warszawa, Poland Frequeny disrimination thresholds, DLs, were measured with the use of an adaptive, two-interval, fored-hoie proedure, for tones played on bowed instruments and for pure tones. Results show that DLs obtained for musial tones are relatively small, and range from 4 to 6 ents in most pith registers. Frequeny DLs determined for pure tones are in lose agreement with those obtained for musial tones in all but the low pith register. In the lowest pith register, the DLs of pure tones are by about ten times higher than DLs determined for musial tones. The DL values obtained in the present study are taken as a diret reiproal measure of the pith strength (the preision of pith sensation) of tones under investigation. INTRODUCTION Among the bowed stringed instruments, violin is known for its high preision of pith ontrol. In ontrast, the double bass, whih produes sounds of the lowest pith register used in musi, is often onsidered an instrument with a hard-to-define pith. The preision of pith sensation is alled pith strength. Pith strength may be derived from the measurement of frequeny disrimination. The purpose of the present study was to assess the pith strength of bowed instrument tones and of pure tones with the use of an adaptive, two-interval, two-alternative, fored hoie proedure (2I, 2AFC). PITCH STRENGTH OF BOWED INSTRUMENT TONES Frequeny disrimination of bowed instrument tones was measured with the use of an adaptive, twointerval, two-alternative fored hoie adaptive proedure with feedbak [1]. The stimuli were two tones (D1 and B1) played on a double bass, two tones (E2 and A2) played on a ello, and three violin tones (G#5, G6, and F#7). All tones were presented diotially at a loudness level of 75 phons. Tone duration was 2 s. The tones were reorded digitally at a sampling rate of 44.1 khz and stored on a omputer hard dis. A PCompatible omputer with a TDT AP2 signal proessor ontrolled stimulus presentation and the adaptive proedure. The sound file was played bak by a DD1 D/A onverter, led through an FT5 antialiasing filter, two PA4 attenuators, and an HB6 amplifier to a Beyerdynami DT 911 headphone set. On eah trial, the subjet heard two tones presented in random order: a tone at its original frequeny f, and a tone at a frequeny of f+ f, and was requested to indiate whih of the tones had a higher pith. The subjet reeived visual feedbak on the response box. The tone frequeny was varied by hanging the sampling rate during playbak, aording to a twodown/one-up deision rule that estimated the 70.7% orret point on the psyhometri funtion. Eah run started 10 Hz above the original tone frequeny and terminated after 50 trials. The size of f was hanged by a fator of r. The value of r, initially set at 1.58 (log(1.58) = 0.2), was redued to 1.26 (log(1.26) = 0.1) after two reversals of signal frequeny. The threshold was estimated as the geometri mean of f at the reversals, following the fourth reversal. Four students with normal hearing served as subjets. Eah subjet ompleted six series of runs. Figure 1 shows the group means and standard deviation of DLs, alulated in ents. Results indiate that the DL is almost invariant in a pith range from B1 to G6, and ranges from 4 to 6 t. The DLs obtained for the lowest double-bass tone, D1, orresponding to a fundamental frequeny of 36.7 Hz, and the highest violin tone (F#7, 2794 Hz) are appreiably larger, and so is the standard deviation of data. DL (t) Hz 82 Hz 831 Hz 2960 Hz 62 Hz 124 Hz 1567 Hz J J J J J J b-d1 v-e2 vn-g#5 vn-f#7 b-b1 v-a2 vn-g6 FIGURE 1. Frequeny DLs for bowed instrument tones. Group means and standard deviation aross four listeners. J

9 Frequeny Disrimination thresholds for pure Tones In order to ompare the frequeny DLs determined for musial tones with data obtained for pure tones, frequeny disrimination in pure tones was measured using the same adaptive 2I, 2AFC proedure, at 14 frequenies spanning a range from 25 to 8000 Hz. Three students who also partiipated in the previous experiment served as subjets. Eah subjet ompleted five series of adaptive runs. The set-up was same as in the previous experiment exept that the tones were not stored on hard disk, but generated by a DD1 D/A onverter, and presented monaurally. The tone sensation level was 20 db at 25 and 31.5 Hz, 30 db at 40, 50, and 63 Hz, and 40 db at 80 Hz and higher frequenies. Sensation levels were set for eah listener individually. Individual detetion thresholds, orresponding to a 70.7% orret point on the psyhometri funtion were measured in a preliminary experiment, with the use of an adaptive, 2I, 2AFC proedure. Figure 2 presents the group means and standard deviation of DLs obtained for pure tones. The data are shown in ents. DL (t) 150 O O 100 O 50 O O O O O O O OOO O Tone Frequeny (Hz) FIGURE 2. Frequeny DLs for pure tones. Group means and standard deviation aross three listeners. To enable a omparison of DLs obtained for musial tones and pure tones, the data plotted in Figs. 1 and 2 have been ombined in Fig. 3. Figure 3 also shows the values of frequeny DL for pure tones, obtained by Wier et al. [2] with the use of a 2I, 2AFC proedure. Disussion and onlusions The measurements of frequeny DLs of bowed instrument tones have shown that the pith strength of bowed instruments is uniform in the greater part of the musial sale. Only the lowest tone of the double bass and the highest tone of the violin show an about twofold inrease of their frequeny disrimination threshold measured in ents. In light of the above finding, an opinion shared by many musiians, that the pith of double bass tones DL (t) O OO J musial tones 100 O pure tones O O C pure tones, Wier et al. [2] O J OC 10 OC O J J J O O O J C C OO C J J CC C Tone Frequeny (Hz) FIGURE 3. A omparison of frequeny DLs obtained for bowed instrument tones and for pure tones. is less learly defined than that of the other bowed instruments, requires some orretion. In the lowest musial pith register, frequeny DLs of double-bass and ello tones, measured in ents, are about 10 times smaller than DLs for pure tones (Fig. 3). The frequeny DL of a pure tone is on the order of a semitone at frequenies below 50 Hz. The high sensitivity to hanges of low musial tones in frequeny is an effet of the presene of overtones in the sound spetrum, as reported in other studies, e.g. [3]. The physiologial mehanism of pith disrimination is related with various phenomena desribed by the plae theory and the temporal or time theory (see [4] for a disussion of experimental data). Due to the mehanial properties of the basilar membrane, the mehanism of pith disrimination, based on the plae theory, beomes ineffetive at very low frequenies. At very low frequenies, pith is identified and differentiated on the basis of the time pattern of neural impulses evoked by the sound, and the presene of overtones failitates pith disrimination. ACKNOWLEDGMENTS This work was supported by the Polish Committee of Sientifi Researh, Grant H01F The authors wish to thank Patryk Rogoziński for his help in data olletion. RERERENCES 1. H. Levitt, J. Aoust. So. Am. 49, (1971). 2. Wier, C.C., Jesteadt, W. and Green, D,M., J. Aoust. So. Am. 61, (1977). 3. G. B. Henning and S. L. Grosberg, J. Aoust. So. Am. 44, (1968). 4. B. C. J. Moore, An Introdution to the Psyhology of Hearing, 4th Edition, Aademi Press, London (1997).

10 THE BH-PEAK OF THE VIOLIN AND ITS RELATION TO CONSTRUCTION AND FUNCTION Erik V Jansson a, Benedykt Niewzyk b, and Lars Frydén a, a Dept of Speeh, Musi and Hearing, KTH, SE Stokholm Sweden b Violin Workshop, POZNAN, ul. Wozna 6, Poland The violin bridge has its first in-plane resonane at approximately 3 khz. Experiments, measuring bridge mobility, prove that the BH-peak between 2 and 3 khz of an assembled violin is not onfined to this resonane only. By exhanging a normal bridge to a bridge blank with its first in-plane resonane at approx. 8 khz the BH-peak remains mainly unhanged. Also, the main properties of the BH-peak of a Stradivarius violin and a newly assembled violin are different, but independent of bridges. Comparisons between bridge mobility and radiated sound display similarities but the similarities are not easily reprodued. Analysis of played sales proved that the tonal spetra are limited up to somewhat above the BH-peak frequeny. Played tonal spetra are limited to approx. 4 khz although the radiation of a violin generally extends to muh higher frequenies. However, this frequeny limitation is at least partly aused by string inharmoniity, whih inreases onsiderably above the BH-peak frequeny INTRODUCTION Previously a new professionally made violin (S Niewzyk) of good quality was measured with its original bridge and an espeially made bridge blank [1]. The bridge blank was made of bridge maple and shaped as a violin bridge but without the traditional ut-outs as heart, ear, nose et. Measured properties as bridge mobility of the new Niewzyk violin were found to be losely the same in spite of 3.0 khz resonant frequeny of the bridge and 7.6 khz of the blank. The Sound radiation of 11 Italian Master Violins measured by Dünnwald and the Bridge mobility measured by Jansson show rather similar frequeny responses in the 1.5 to 3.5 khz range [2,3]. Thus it may be onluded that the 2.3 khz BH-peak is not onfined to the first in-plane resonane alone and that the BH-peak shows up both in bridge mobility and sound radiation. But what is its relation to the onstrution and to the funtion of a violin? NEW AND OLD VIOLIN The properties, measured as bridge mobility, of a Stradivarius violin typially show a broad rounded BH-peak in the 2-3 khz range, see Fig. 1. The same bridge on the newly made Niewzyk violin shows a prominent, rather marked peak in the same frequeny range. Thus experiments indiate again that the BHpeak again is mainly set by the violin and not by the bridge. Furthermore laboratory experiments with experimental violins indiates that the violin top plate is a onstrution parameter determining the main properties of the BH-peak rather than the violin bridge. FIGURE 1. Bridge mobility a) of a Stradivarius violin (upper frame) and b) of the S Niewzyk violin with the same bridge as the Stradivarius (lower frame). TWO VIOLINS WITH DIFFERENT BH- PEAKS The bridge mobility was measured of two good referene violins, one with a more brilliant tone (LB) than the other (GL), see Fig. 2. The LB-violin has a more lear BH-peak maximum just below 2 khz. The GL violin has no lear suh peak maximum, but rather a smooth peak maximum. The level of the mobility response around 2 khz is also somewhat higher for the LB violin. The sound radiation of the two violins was measured in different diretions in the anehoi hamber of the Norwegian Tehnial University, NTNU, using a newly developed tehnique, see fig 3 [4]. The level of radiated sound varied greatly with diretion but the averages as shown in fig 3 beomes rather stable with an average over a moderate number of diretions. Again it an be seen that the LB violin has a more

11 prominent BH-peak at 2 khz than the GL violin. The frequeny region marked with horizontal lines at the same level shows the more olleted and higher level response for the BL violin. BH-PEAK AND PLAYED TONES Long-time-average spetra of full-tone sales played on the four strings of a violin indiate a maximum at approx. 3 khz followed by steep slope utting off higher frequeny omponents (the LTAS-diagrams are plotted with properties of the hearing inluded), see Fig. 4 [5]. The spetra indiate that the ut-off is a general and a wanted property. Reent experiments indiate that string inharmoniity may be the dominant fator here rather than boundary onditions set by the non-rigid end support, the violin bridge. Thus our study indiates that the bridge mobility predits the BH-peak in the radiated sound signal, but averaging over many diretions is needed to remove diretional masking, and that string properties in playing also an enhane the BH-peak. FIGURE 2. Bridge mobility of the LB and GL violins ACKNOWLEDGEMENTS The sound radiation measurements were made by LH Morset at NTNU, Trondheim in ooperation with the first author. REFERENCES 1. E. V. Jansson and B. Niewzyk, CASJ 3. No 7 (Series II) (May 1999) 2. H. Dünnwald, Austia 51, (1982) 3. E. V. Jansson Austia ata austia 83, (1997) 4. L. H. Morset, 137thASA paper 3AMU-12 (Berlin, 1999) 5. A Gabrielsson and E. V. Jansson, Austia 42, (1979) FIGURE 3. Sound radiation of the LB and GLviolins. Markings: horizontal sale at 2 and 3 khz, vertial sale at 10 db level steps, and a thik horizontal line BH-peak range. FIGURE 4. Long-time-average-spetra of a played soloist violin (F Ruggeri homogenous line) and, average of 22 violins (dotted line).

12 Measurements of radiation effiieny and internal mehanial loss applied to violins Lars H. Morset Group of Tehnial Optis, Institute of Physis, Norwegian University of Siene and Tehnology (NTNU), NO Trondheim, Norway. lars.morset@phys.ntnu.no Internal mehanial losses were determined by measuring the normalized radiated power and the real part of the mobility at the bridge. Radiated power was determined by measuring the far-field sound pressure in an anehoi room at a spherial surfae with a radius of 1.05 m and an angular resolution of 22.5 degrees. The total power transferred to the violin at the bridge is determined as the real part of the input mobility, Re[Y]. The two violins tested had radiation effiienies that varied with frequeny and had an average of 1.54 % and 1.24 % in the frequeny range Hz. INTRODUCTION The main goal of this study was to test a method for aurate measurement of internal mehanial loss and radiation effiieny of violins. The method desribed an be applied to different types of aoustial soures and e.g. plates as well. In order to obtain the mehanial loss, two types of measurements were performed: 1) Measurement of the radiated power normalized with respet to the fore, Power_rad, norm 2) Measurement of the input mobility. The real part of the input mobility, Re[Y], gives the total normalized power transferred to the violin, whih is the sum of the radiated power and the mehanial loss. This gives the radiation effiieny, η: η = Power_rad,norm / Re[Y] In this study, two violins were measured, a new unonventional model built by Hagetrø Fioliner and an old top-quality Stradivari opy built by J. P. Thibout in Paris parallel to the top-plate. The fore transduer was alibrated and an be used up to 8 khz. Alternative methods of exitation would be using a hammer, but that would give a dereased signal-to-noise ratio for the aousti measurements, and an eletrodynami shaker would add more weight to the violin bridge than the small magnet that was used. To make the onditions equal, the violins were mounted and exited exatly the same way in the measurements desribed in the two hapters below. RADIATED POWER MEASUREMENT The normalized radiated power was found measuring the far-field sound pressure in an anehoi room using two mirophones to san a sphere with a radius of 1.05 m and an angular resolution of 22.5 degrees. The relatively small radius may introdue an error in the far field approximation (at low frequenies). However, previous measurements indiate that the radius and the angular resolution are suffiient in the frequeny range 200 Hz to 10 khz [1]. EXCITATION AND MOUNTING The mounting method will affet the aousti properties of the violin. Here, the violin was held with piees of rubber at the bottom part of the body and the upper part at the nek. A ustom-made fore transduer used a 60 mg magnet, attahed with wax at the G-string side of the bridge, and a small oil positioned near the magnet. Pseudo-random noise (MLS) was used as exitation signal, using the software WinMLS and the fore was direted INPUT POWER MEASUREMENT The power transferred to the violin at the bridge was found as the real part of the input mobility, Re[Y], by measuring the veloity in the same plane as the exitation at the bridge using a laser vibrometer. The laser beam an be pointed through the oil at the magnet and thus the fore and the veloity an be measured in exatly the same point, whih in priniple

13 should be the optimum measurement point. Here, however the veloity was measured at the opposite side of the bridge sine measuring through the oil gave less stable results (this will be investigated further). Measuring the mobility of the violin bridge this way is ommon [2]. This method does not depend on an anehoi room, and it an be fast, simple and inexpensive. A laser vibrometer is preferred to an aelerometer for measuring the veloity beause it adds no weight to the bridge. [db] RESULTS Fig. 1 shows the results for the Thibout violin. It has a wolf tone at C (525.6 Hz). The peak of Re[Y] was found exatly at this frequeny, whih shows that it is possible to aurately measure wolf tones using this setup. At this frequeny, the mobility of the bridge is large, the bridge simply moves so muh that it is impossible for the string to maintain a standing wave. [db] Log Frequeny [Hz] FIGURE 1. The urves show, from the top, the total normalized power (Re[Y]), the normalized radiated power, and the radiation effiieny (dotted line) for the Thibout violin. Fig. 2 shows the results for the Hagetrø violin. The average radiation effiieny in the frequeny range Hz was omputed to 1.24 % for the Thibout violin and 1.54 % for the Hagetrø violin. The maximum value was ~5 % (-26 db) and was found in the frequeny range Hz for both violins. From the figures we see that the radiation effiieny depends largely on frequeny, but does not show an inreasing or dereasing trend. The repeatability of the measurements was good Log Frequeny [Hz] FIGURE 2. The urves show, from the top, the total normalized power (Re[Y]), the normalized radiated power, and the radiation effiieny (dotted line) for the Hagetrø violin. CONCLUSION A method for the aurate measurement of the radiation and the losses in a violin has been presented. The method an be fast (~15 minutes per violin if a 8- hannel system is used). The results will tell whih modes are effiient radiators. Further work will inlude a study of the relationship with the modal shape and the radiation effiieny. For the two violins measured the radiation effiieny in the frequeny range Hz was measured to be 1.54 and 1.24 %, having peak values at ~5 %. Sine the radiation effiieny is small and depends largely on frequeny, measurement of the mobility at the bridge will not indiate all fators affeting the quality of a violin. ACKNOWLEDGMENTS The author wishes to thank the professors A. Krokstad, U. P. Svensson and E. V. Jansson for their suggestions, violinist A. Larsen and Hagetrø Fioliner for supplying violins and engineer Ø. Lervik for help with the measurement setup. REFERENCES 1. Morset, L. H., 137th ASA paper 3AMU-12, Berlin, Jansson, E. V., Aoustia-ata aoustia, 83, pp (1997).

14 Modal And Aousti Analysis On The Violin Otet George Bissinger Physis Department, East Carolina University, Greenville, NC Modal analysis was performed on a omplete Huthins-Shelleng violin otet, along with A0 and A1 avity mode analysis and room-averaged aousti analysis, to help haraterize the dynami harateristis of the otet. Signature orpus and avity modes were traked aross the otet, along with aousti radiativity harateristis of eah mode. The main air and main wood resonane results are ompared with Shelleng s saling preditions INTRODUCTION John Shelleng, in ollaboration with Carleen Huthins, worked out physial saling equations to sale the violin to other pith ranges [1]. Shelleng made the substantial, limiting assumptions of flat plates and similar shapes for all the instruments, and restrited the saling to the main air (A0) and main wood (B1) resonanes only. A later, ompliating development was the retroative inlusion of the A1 avity mode in the main wood resonane by Huthins [2]. A1 is the lowest avity length mode that sales diretly with instrument length. Shelleng s saling laws all had length dependenes to the 2 nd or 4 th power, however, presenting an inherent onflit with A1 saling. the otet. The A0, A1, A2 and A4 avity modes indued mirror modes in the orpus that allowed ready identifiation (A0 and A1 were also observed in avity aousti spetra). In Figure 1 normalized, room-averaged pressure results were superimposed over normalized summed-over-top-and-bak-plate mobilities for omparison of mehanial vs. aousti strength. EXPERIMENT AND ANALYSIS As part of the VIOCADEAS Projet experimental modal analysis, avity mode analysis, and room-averaged aousti analysis on a omplete violin otet was ombined to judge the overall suess of the saling. The modal analysis of a violin suspended in approximate free-free onditions employed fore hammer impat exitation at the bridge on the bass bar side and a sanning laser vibrometer to measure the veloity response. These were ombined to reate mobilities Y(ω) over the entire violin inluding all major substrutures. Strings were undamped (but unmeasured). Cavity mode analysis employed two interior mirophones plaed in the upper and lower bouts and internal or external aousti exitation. Roomaveraged aousti radiation was reorded for later analysis using hammer impat exitation with a sound quality head onneted to a DAT reorder. Modal analysis measurements were analyzed to extrat mode frequenies, dampings and shapes. Certain signature shapes were lassified and tabulated for eah instrument and orrelated aross Figure 1 Superimposed normalized averaged orpus mobility (thin line, shaded) and room averaged aousti pressure (thik line) for mezzo, tenor and large bass. Desired saling positions for A0 and B1 noted with arrows. Note B1 + doublets for tenor.

15 DISCUSSION The summary mode frequeny results for the entire otet are given in Table 1. These have been normalized to the frequeny of the lowest string and to the desired saling plaement so that the suess of the intended saling an be judged. The original saling attempted to plae the A0 resonane seven semitones, and the B1 resonane 14 semitones above the lowest string. Comparisons with Shelleng s main wood resonane plaement was ompliated by the fat that it now inludes three disparate omponents A1, B1 - and B1 +. A further ompliation arose when the latter two showed signs of oupling to substrutures like the nekfingerboard and the tailpiee. For omparison purposes with the original main wood saling all the B1 orpus mode frequenies have been averaged. Perfet saling would then be denoted by values of 1 in Table 1. Table 1 Ratios of A0 ( main air ) and main wood to intended saling values. "main wood" Instrument A0 A1 B1 - B1 + B1 av treble soprano mezzo alto tenor baritone small bass large bass doublet average value Main Air A0 All the instruments showed A0 falling below the intended plaement. The poorest agreement was for the treble and large bass, the size extremes. Surprisingly the 4 largest instruments had already had their ribs ut bak from the original heights, but still fell short of desired plaement [2]. At least part of this failure was due to Shelleng s (and Huthins ) use of an insuffiient theoretial model for A0, whih negleted oupling with A1 and orpus ompliane. Main Wood B1 (Corpus) The B1 mode frequenies generally braket the desired plaement for the main wood. Sine Shelleng s saling employed flat plate theory, this is a positive result that indiates that flat plate saling provides a reasonable - and analytial -- approximation for the violin otet saling. The baritone was the only instrument that learly failed to have the B1 modes braket the desired plaement (the treble had the B1 + mode oinide with the intended plaement). Overall the main wood resonane plaement was generally suessful. Main Wood A1 For the two smallest instruments A1 fell right on top of the B1 - mode. For all the larger instruments exept the baritone A1 fell between B1 - and B1 +. This result is surprising due to the fat that A1 sales with the length, but all the larger instruments were dropped in size relative to perfet saling [1]. The agreement is onsistent with orpus ompliane effets [4]. SUMMARY The violin otet saling of Shelleng was unsuessful for the main air resonane beause of a faulty theoretial model for A0 that did not inlude oupling to A1 or orpus ompliane. The main wood saling was generally suessful. ACKNOWLEDGEMENTS Researh supported by the National Siene Foundation under grant no. DMR REFERENCES 1. J.C. Shelleng, "The violin as a iruit", J. Aoust. So. Am. 35, (1963); also see erratum, pg C.M. Huthins, "A 30-year experiment in the aoustial and musial development of violin-family instruments", J. Aoust. So. Am. 92, (1992). 3. G. Bissinger, "A0 and A1 oupling, arhing, rib height, and f-hole geometry dependene in the 2-degree-of-freedom network model of violin avity modes", J. Aoust. So. Am.104, (1998). 4. G. Bissinger (submitted for publiation)