Romain Cousseau
email: romain.cousseau@univ-artois.fr

Raphaël Romary

Miftah IRHOUMAH François Balavoine

Miftah Irhoumah

Remus Pusca

Comparative study of permanent magnet synchronous machine vs salient pole synchronous machine in high temperature application

Keywords: Motor sizing, high temperature, permanent magnet, anodized aluminum tape, thermal study

teaching and research institutions in France or abroad, or from public or private research centers.

Comparative study of permanent magnet synchronous machine vs salient pole synchronous machine in high temperature application

INTRODUCTION

In a large variety of fields, electrical machines are more and more preferred to traditional actuators (pneumatics or hydraulics) [1]. Indeed, thanks to their compactness and efficiency, machines like PMSM (Permanent Magnet Synchronous Machine) are very attractive [START_REF] Zhu | Electrical machines and drives for electric, hybrid, and fuel cell vehicles[END_REF] [START_REF] Uddin | Performance of interior permanent magnet motor drive over wide speed range[END_REF]. However, because of the use of permanent magnets, this kind of machine is not very suitable in high temperature operating conditions [START_REF] Huber | Monitoring critical temperatures in permanent magnet synchronous motors using low-order thermal models[END_REF].

The field of high temperature machine design has been specially investigated during the last decade [START_REF] Marcin | Comparison of the reluctance laminated and solid rotor synchronous machine operating at high temperatures[END_REF]. Two different applications of high temperature winding are identified, the first one is related to operation in a harsh environment where the external temperature can be very high, like aircraft application with the concept of More Electric Aircraft (MEA) [START_REF] Vannini | Materials for Electric Machines Suited for High-Temperature Applications: a Survey[END_REF] where electrical machines operated in an environment with high ambient temperature (more than 200°C [1]). The second one concerns machine designed with high power density where line current and surface current density are very high [START_REF] Laidoudi | High-power density induction machines with increased windings temperature[END_REF]. In addition to the issue of magnet demagnetization, the other weak point of high temperature machines is related to wire insulation. Organic insulation using Polyamide Imide (PAI) and Polyester Imide (PEI) material does not allow to exceed 200°C at the hottest point of the machine (the conducting copper). To go beyond this limit, inorganic insulation can be an alternative solution [START_REF] Iosif | Assessment and improvements of inorganic insulation for high temperature low voltage motors[END_REF][9] [START_REF] Roger | Design of inorganic coils for high temperature electrical machines[END_REF], like ceramic copper wire, nickel-plated copper wire, or anodized aluminum tape. However, the mechanical characteristic of inorganic insulation is different than this of PEI-PAI; what requires specific know-how in winding and machine building, which can bring real manufacturing difficulties. Anodized aluminum tape has a real advantage in high temperature machine design [START_REF] Babicz | Behavior of anodized aluminum strip under sine and square wave voltage[END_REF]. Firstly, the aluminum is flexible and enables a low bending radius which make it easier to wind the coil. Therefore, an Anodized aluminum coil fits well with a concentrated winding machine. The inter-turn voltage is well controlled, and the anodized layer insure a good inter turn insulation to more than 350°C. The anodized aluminum strip has also the advantage to be available in the marketplace at different wanted dimensions (width, thickness).

The aim of this paper is to present the sizing of two machine topologies of 40 kW for 4500 rpm with similar sizes and performances. The purpose is to lead to the design of a laboratory prototype that could fit with aircraft or car industries requirements. The first machine is made with a permanent magnet rotor whereas the other one is made with a salient pole wound rotor to operate at high temperature. The second machine uses anodized aluminum tape [START_REF] Babicz | Preliminary study of using anodized aluminum strip for electrical motor windings[END_REF] [START_REF] Babicz | Dielectric characteristics of an anodized aluminum strip[END_REF] as windings. The stator windings use the same conductor to hold the high temperature.

The paper is organized as follows: Section 2 presents the sizing of a three-phase 12/10 (12 slots, 10 poles) synchronous machine with a concentrated winding. Section 3 gives comparisons between the two machines through finite element simulations. Section 4 presents a complete thermal study for both machines. Section 5 brings an explanation of the wound rotor construction. Section 6 gives conclusions and highlights works that will be made for the future machine that is currently being built.

SIZING AND DESIGN OF THE MACHINES

2.1

Main dimensions First, it is necessary to find the main dimensions of the machine as a preliminary sizing process. The purpose is not to optimize the compacity of the machine but to get an easily achievable electrical motor. To achieve that, the sizing formula in (1) is used. This is a simplified version of the sizing equation given in [START_REF] Cassoret | Influence of the Pole Number on the Magnetic Noise of Electrical AC Machines[END_REF].

  

With Da: the inner diameter of the stator, La: the active length, C: the rated torque, A: the current linear density, B: the peak airgap flux density and K1 s : the winding factor.

The winding factor depends on the chosen topology such as the number of phases, slots and poles as explained in [START_REF] Libert | Investigation on pole-slot combinations for permanent-magnet machines with concentrated windings[END_REF]. Considering (1), parameters are chosen as well as the active length to obtain a coherent stator diameter. The purpose is to obtain a mean torque of 100 Nm in a 0-4500 rpm speed range for two machines: the first one is a reference machine with a permanent magnet rotor that will be considered in the design process. The second machine has the same dimension as the reference one but with a wound rotor designed to provide the same magnetic effect than the permanent magnet rotor. In order to reach the same magnetic performance as the initial machine, the wound rotor machine uses anodized aluminum tape able to operate at high temperature (more than 350°C). To simplify, both machines have the same stator with concentrated winding, also made with anodized aluminum tape. Parameters are summed up in Table I, where the Torque C comes from desired specifications described before, the line current density A is a usual design value of permanent magnet machine to achieve acceptable heating [START_REF] Cassoret | Influence of the Pole Number on the Magnetic Noise of Electrical AC Machines[END_REF] because the reference permanent magnet machine is a low temperature one. The peak airgap flux density B has been chosen as the more probably attained regarding magnet characteristic associated with the flux concentrated effect of the rotor magnet configuration. This value will be checked with a finite element simulation. The airgap width has been set to 1 mm which is a reasonable value for manufacturers. In previous studies about other types of machines, an active length La of 150 mm was defined. To keep approximatively the same volume regarding the existing testbench, the choice has been made to keep this characteristic value. This leads to an inner stator diameter of 126 mm.

Magnets have been taken the thickest of possible to be less sensitive to the temperature and to bring the highest flux density in the airgap, considering an interior magnet structure with flux concentration effect. The permanent magnet machine is not supposed to heat over some range; however, it is safer to use SmCo magnets that can handle higher temperature than NeFB magnets. Teeth wide has been determined to be minimum without being saturated.

To determine the external diameter, it is considered that half of the magnetic flux of a rotor pole flows through this part of the machine. Considering the principle of flux conservation, the iron thickness can be calculated. Finally, the external diameter is 206 mm.

2.2

Winding determination The method presented in [START_REF] Libert | Investigation on pole-slot combinations for permanent-magnet machines with concentrated windings[END_REF] is used to determine the optimum winding sequence of the concentrated winding machine. The chosen structure of the machine is three-phase 12/10 (12 stator slots, 10 poles) with double layer concentrated winding. At first, the SPP (number of slots per poles and per phase) needs to be determined [START_REF] Zhu | Electrical machines and drives for electric, hybrid, and fuel cell vehicles[END_REF].

 SPP = 

The purpose is to compare a sequence of "zeros" and "ones" to a reference sequence. According to the method, our comparative sequence will have 2 "ones" and 3 (5-2) "zeros" and will be "01010". The sequence is shown in Fig. 1 and the corresponding winding factor is 0.933.

2.3

Results of the sizing Once sizing and winding have been determined, it is possible to draw both machines. Fig. 2 and3 show the two machine configurations having similar dimensions. For the wound rotor machine, saliencies have been designed to let enough space to place rotor windings. Based on these geometries, finite element simulations with Altair Flux 2D software will be performed in the next section. Fig. 5 presents the spectrum of the normal flux density in the airgap. As expected, the 5 th harmonic is the principal because of the 5 pairs of poles. It is slightly higher for the permanent magnet machine but not significatively. However, some other harmonics like the 15 th are higher. Fig. 6 gives the torque of both machines at rated stator and rotor currents. It can be observed that the target torque was 100 Nm but, in both cases, simulated torques are weaker. This can be accounted for by assumptions used in the sizing formula. For example, the airgap flux density taken at 1.5 T in (1) has roughly this value in the simulation for the peak value in Fig. 4, but the fifth harmonic in Fig. 5 falls to 0.85 T.

Because of the magnet configuration, the PMSM is a flux concentrated machine, that leads to a slightly higher induction in stator teeth (around 1.3 T vs 1.2 T for the wound rotor machine). This can justify that the mean torques are not the same for both machines. Additionally, an interesting point is that the 12 th harmonic (which corresponds to the number of slots) is the main one for the PMSM torque ripple whereas it is the 6 th for the other rotor.

3.2

Flux lines comparison Fig. 7 and8 present the mapping of flux lines for both machines. As it can be seen, the direction of the lines differs for the two rotors. They follow the pole in the radial way for the salient wound rotor whereas in the permanent magnet rotor they are oriented in an orthoradial way. This is due to the magnetization direction that enables to have a flux concentration machine. Therefore, only a part of the magnet flux crosses the airgap. The other part flows towards the shaft, and this part can be reduced using a special shape at the level of the magnet inner part as shown in Fig. 7. II. These values correspond to the rated point (4500 rpm and rated current as described in section 3). Rotor Joule losses for the wound rotor seem to be quite important. This is due to the rotor direct current of 30 A which is injected in a thin aluminum tape. Thus, the rotor electric resistance is relatively high (around 2 Ω) which leads to high Joule losses. Comparatively, the stator current is higher (around 56 A RMS), but the tape is wider and shorter so with a small electric resistance.

4.2

Geometry for the thermal study using Motor-Cad software The machines that have been designed using Flux2D software for the finite element study, have been rebuilt in the Motor-Cad software. Dimensions have been respected but some differences can be observed between Fig. 8 and 11 considering the head of rotor poles. The design has been adapted in Motor-Cad software to achieve the same performances (same torque) even if drawings are not identical. Indeed, Motor-Cad software can be used as a fast analytical electromagnetic predesign tool to get some data as the torque. However, because results are not obtained in the same way as with Flux2D, it doesn't lead exactly to the same values. Choice has been made to adapt the design to get the same torque because it is the main comparison indicator of the study. Furthermore, it has been verified that the impact of the slightly different design is not significant at all on thermal behaviour.

The other principal difference is the addition of a cooling part around the stator. This is a water jacket housing in a spiral. The characteristics of this cooling part are set to default in the software. An improvement of the cooling system could be made in further works.

4.3

Thermal results From the losses in the different parts of the machines, a thermal study has been performed using Motor-Cad software. The ambient temperature is set to 20°C. The purpose is to evaluate the temperature range that could be attained at the most severe operating point. In a harsh environment with higher ambient temperature, machines would operate at reduced performances. In addition to losses repartition, the different materials are filled out (aluminum, steel and magnet) to get suitable thermal coefficients that are included in the software. Moreover, other characteristics, like interfaces behavior, are set to idle.

Table III presents thermal conductivity of the different materials used in both machines. These values are quite arbitrary because the exact composition of the machines that are being built is not known. However, because values from one steel alloy or aluminum alloy to another are very close, as a preliminary study, it has been considered that these coefficients are accurate enough to obtain representative results. Different values come from Motor-Cad database. Presented results are given for steady state. This explains that temperatures can be rather high at specific critical points.

First, temperatures reached in the permanent magnet machine are quite usual (165.5°C) as it can be found in other studies [START_REF] Guedia Guemo | Application of Classic and T Lumped Parameter Thermal Models for Permanent Magnet Synchronous Machines[END_REF]. This leads to be optimistic about the quality of the simulations, both for losses determination and the thermal study. Moreover, the maximal temperature in magnets is less than 170°C. This is clearly in the range of the selected magnets which are Samarium Cobalt-based. This kind of magnet can usually withstand up to 300°C [START_REF] Liu | Thermal stability and performance data for SmCo 2:17 high-temperature magnets on PPM focusing structures[END_REF].

Considering pure aluminum, the welding temperature is around 660°C. In the worst case, which is the wound rotor machine, the highest temperature reached is less than 520°C thanks to the cooling. It should be noticed that to simplify the simulation, the evolution of the electric resistivity of the aluminum with temperature has not been considered. It means that at 400 or 500°C the electric resistance of the tape would be higher, leading to even more losses, and higher temperatures. However, this machine has been designed to obtain the same performances with a wound rotor as with a permanent magnet rotor at least for short time.

Another point to be considered is the bearings temperature. Classical bearings are not suitable to withstand such temperatures (almost 300°C) [START_REF] Henao-Sepulveda | Contactless Monitoring of Ball Bearing Temperature[END_REF]. So, in further works, a full study should be made to design bearings with innovative materials that could hold these temperatures. A specific rotor cooling system could also be implemented.

4.4

Study in transient Steady state has been studied and it can be interesting to observe the evolution of some temperatures for a short period. This time the ambient temperature starts from 40°C. Fig. 13 and 14 present transient evolution of the temperature at different points on both machines for ten minutes.

First, concerning the permanent magnet rotor machine, only the stator winding is heating the most alongside the stator surface but in a reasonable range (≈ +40°C). This can be accounted for by stator Joule losses that are quite low thanks to a small electric resistance and because the cooling device is close to these windings. Also, the magnet and bearings stay at very low temperature which is a good result for the future testbench.

Concerning the wound rotor machine, the temperature rise of the stator winding is quicker and goes up to +70°C. Indeed, the losses of the rotor are higher and are the principal heating source of the machine. Moreover, the temperature in rotor windings rises also quickly. It reaches more than 300°C (starting at 40°C) after ten minutes. The interesting point is that even if the shaft heats up also significantly, bearings stay under 80°C until 5 minutes have passed, without considering the thermal inertia. This is reassuring concerning the experimental machine that is being built and it can be considered that tests could be executed for several minutes at rated operating conditions. Fig. 15 presents a comparison of transient temperature evolution for some characteristic points between both machines. Temperatures in wound rotor machine rise quicker than for the permanent magnet one. Stator rising temperature is almost linear while it starts to inflect on the rotor side. Even if results are not shown here, transient study showed that the steady state occurs after one hour and a half at rated operating conditions.

4.5

Thermal improvement in steady state It has been shown previously that steady state temperatures for the wound rotor machine are quite high and would be even higher by considering the electric resistance increase. This could cause insulation deterioration or even critical failure in rotor windings.

To prevent any risk, a simple way to limit the heating is to decrease rotor direct current. In this case, airgap flux density will be lower than in the permanent magnet rotor machine. So, the stator current needs to be increased to compensate and to obtain the same torque. By coupling losses and thermal analysis with simple mathematical considerations, new configurations are obtained. Table IV sums up the results and compares values for the critical points which are stator and rotor windings. There is a quite noticeable impact on stator iron losses, but not on rotor iron losses.

As it can be observed, decreasing the rotor direct current by only 5 A leads to more than a 100°C reduction in windings rotor. An interesting fact is that even if stator current has been increased to get the same torque, stator temperatures are also lower. This means that for the wound rotor machine, heating is largely due to rotor losses. Moreover, the cooling water jacket is close to the stator so, it is easier to evacuate the heat in this area.

A very important result can be observed for the configuration 3, it is the optimum. Indeed, configuration 3 can be considered as the best because this is where stator temperature starts to inflect while rotor temperature is still decreasing. Moreover, configuration 4 demands a really high stator current. Configuration 3 presents the most balanced losses distribution and temperatures are much more convenient.

4.6

Thermal results considering a harsh environment As mentioned earlier, the purpose is to design a synchronous machine without magnet that could operate at high temperature. Studies have been made at classical ambient temperature (20°C) in order to see the attained temperature range. With the improvement presented in the last subsection, it is interesting to evaluate what could happen in a harsh environment like in car or aircraft applications where ambient temperature is higher. As indicated in [START_REF] Falahi | High temperature, Smart Power Module for aircraft actuators[END_REF], the temperature range for the aircraft industry is very wide (from -55°C to 200°C). To stay relatively representative, the following study has been made with an ambient temperature of 150°C.

A simple way to extrapolate precedent results with a new ambient temperature is to reevaluate losses at 150°C. Concerning Joule losses, aluminum electrical resistivity is the only parameter to increase. In [START_REF] Giancoli | Physics principles with applications[END_REF], the aluminum temperature coefficient is around 0.004 1/°C, this means that from 20°C to 150°C, resistivity increases by approximatively 50% and so do the Joule losses.

On the other way, [START_REF] Xue | A New Iron Loss Model for Temperature Dependencies of Hysteresis and Eddy Current Losses in Electrical Machines[END_REF] shows that iron losses decrease with temperature because both hysteresis and Eddy current loss coefficients are decreasing. This is also dependent to flux density, but the choice has been made to consider a 20% decrease for iron losses from 20°C to 150°C. Table V compares results obtained for the configuration 3 presented before for both ambient temperatures (20°C and 150°C).

As could be expected, the hotspots for both rotor and stator raise a higher temperature because global losses and ambient temperature are higher. It should be noted that when stator and rotor windings are at 300°C or more, the aluminum electrical resistivity is even higher and the same applies to the Joule losses. As explained before, a steady state operating condition at high temperature could lead to reducing the machine performances, but a transient operation (several minutes) could be achieved without any problem as shown in the transient study.

ROTOR WINDING REALIZATION

As previously explained, the winding is quite unusual because it is made of anodized aluminum tape. So, it is interesting to present technical solutions that have been chosen to make the windings, especially concerning the rotor.

First, rotor windings are coiled up around a plot corresponding to a rotor pole. Then, each plot will be screwed to the main piece of the rotor. Fig. 15 shows one plot with the anodized aluminum tape around. In the final version, each winding will be protected with fiberglass paper and filled up with a high temperature resin to ensure good rigidity and isolation. Because this kind of tape is relatively brittle and the rotor will turn up to 4500 rpm, a solution has been developed to ensure good stability and to connect the ten poles together. This is achieved with a connection disk attached to the rotor. One part of the tape goes through the disk and is screwed to the part of the tape from the direct next pole. Concerning the two parts of tape in contact on the disk, the anodized isolated surface has been removed. The disk is made in PEEK which is a polymer with good structural characteristics and a high welding point (343°C) [START_REF] Xiaoyong | Experimental Analysis of High Temperature PEEK Materials on 3D Printing Test[END_REF]. Fig. 16 presents the connectivity principle on the disk. The same idea has been developed for stator connectivity. First, a sizing method has been presented and main dimensions have been given. Also, the way to find the ideal winding sequence has been presented. Then, finite element simulations have been carried out with Flux2D software to compare the performances of the two machines with the same stator configuration. It appears that the obtained torque is quite similar with a small advantage for the permanent magnet rotor machine. This has been explained previously.

Thanks to these simulations, Joule losses and iron losses have been determined and used in the Motor-Cad software to evaluate temperatures in steady state for an ambient temperature of 20°C. A transient study has also been proposed. It appears that the permanent magnet rotor machine ends with totally acceptable temperatures especially concerning magnets. However, temperatures reached in the wound rotor machine are relatively high and could deteriorate the machine especially the insulation in rotor windings. So, other configurations have been presented by decreasing rotor direct current and increasing stator current. Results show a better heat repartition and an optimum configuration while performances are not altered. A study has also been carried out for a higher ambient temperature with relevant results. Problems concerning some exterior parts such as classical bearings that cannot handle such temperature have been evocated. Moreover, the transient study has shown that machines could operate at rated conditions for several minutes without any risks.

From a technical point of view, the way to create winding with anodized aluminum tape has been shown.

Finally, design and simulated results have been conducted successfully with promising results to get a high temperature machine with great performances while avoiding magnets and classical winding that are not suitable with such temperatures.

Future works will consist of testing these machines which are currently being built in real conditions. Moreover, a study about the efficiency of both machines needs to be carried out and the environmental impact of these two technologies needs to be evaluated.

Fig. 1 .

 1 Fig. 1. Determination of the optimal winding sequence

Fig. 2 .

 2 Fig. 2. Permanent magnet configuration

Fig. 4 .

 4 Fig. 4. Normal flux density comparison along an airgap lap

Fig. 7 .

 7 Fig. 7. Flux lines for the permanent magnet rotor machine

Fig. 9 .

 9 Fig. 9. Temperatures of the permanent magnet machine in radial view

Fig. 13 .

 13 Fig. 13. Transient temperatures of characteristic points for the permanent magnet rotor machine

Fig. 16 .

 16 Fig. 16. Example of winding around a pole rotor

TABLE I

 I

	.	DESIGN PARAMETERS
	Torque C	100 Nm
	Line current density A	27000 A/m
	Peak airgap flux density B	1.5 T
	Winding factor K1 s	0.933
	Active length La	150 mm

TABLE II

 II

		.	LOSSES REPARTITION FOR BOTH MACHINES
	Losses (W)	Permanent magnet machine	Wound rotor machine
	Stator Joule		356	356
	Rotor Joule		None	1827
	Magnet		91	None
	Stator iron		465	420
	Rotor iron		76	48

TABLE III

 III

	.	THERMAL COEFFICIENTS OF THE DIFFERENT MATERIALS
			Thermal conductivity (W/m/°C)
	Aluminum winding	170
	Stator lamination (M250-35A steel)	30
	Rotor (stainless steel)	15
		Magnet	8
	Wire insulation (default)	0.2

Fig. 9, 10, 11 and 12 present temperatures at different critical points for both machines in axial and radial view.

TABLE IV

 IV

	.	COMPARISON OF DIFFERENT CONFIGURATIONS FOR THE
		WOUND ROTOR MACHINE
	Configuration	1	2	3	4
	Current rotor Ir	30 A	25 A	20 A	15 A
	Current stator (peak) Is	80 A	92 A	112 A	157 A
	Rotor Joule losses	1800 W	1264 W	812 W	458 W
	Stator Joule losses	356 W	471 W	700 W	1372 W
	Stator iron losses	420 W	420 W	425 W	538 W
	Rotor iron losses	48 W	48 W	48 W	48 W
	Torque (average)	76 Nm	77 Nm	77 Nm	76 Nm
	Rotor highest temperature (winding)	517°C	406°C	329°C	309°C
	Stator highest temperature (winding)	269°C	237°C	223°C	263°C

TABLE V .

 V IMPACT OF AMBIENT TEMPERATURE FOR THE CONFIGURATION 3

	Ambient temperature	20°C	150°C
	Rotor Joule losses	700 W	1050 W
	Stator Joule losses	812 W	1218 W
	Stator iron losses	425 W	340 W
	Rotor iron losses	48 W	38 W
	Rotor highest temperature (winding)	329°C	539°C
	Stator highest temperature (winding)	223°C	387°C

ACKNOWLEDGMENTS

This work has been achieved within the framework of CE2I project (Convertisseur d'Energie Intégré Intelligent). CE2I is co-financed by European Union with the financial support of European Regional Development Fund (ERDF), French State and the French Region of Hauts-de-France.

AUTHOR CONTRIBUTION STATEMENT R. Cousseau and R. Romary conceptualized the study and developed the methodology. R. Cousseau performed design, simulations, analyses and wrote the manuscript. F. Balavoine helped for the thermal study analysis. R. Pusca and M. Irhoumah validated results and worked on the winding manufacture. All authors brang feedback and advises on the manuscript.


Claudia Fritz

Romain Viala

Victor Salvador-Castrillo

Violinist, violin, bow: What can we hear and recognize?

Keywords: Violin, Bow, Perception

The Science and violin making workshop organized every year by researcher Claudia Fritz and violin maker Paul Noulet in France gathers researchers, instrument makers and musicians to make progress in our understanding of the bowed string instruments. One of the daily sessions consists in critical listening, to train our ears, learn how to express and share what we hear, and search for correlations with construction parameters or study various modifications on the instrument, the bow or the playing technique.

It is generally accepted that the sound of a bowed string instrument depends on three parameters: the player, the instrument and the bow. During the 2021 workshop, formal listening tests were conducted to explore what a group of trained listeners is able to hear and recognize when one of these three parameters varies. Results challenge common ideas among violinists about the sound quality associated to the bow. A large difficulty of comparing instruments when listening was observed, as the musician keeps adapting to the instrument and only few cues are available to the listeners to decouple the player's actions and the instrument behavior with respect to their influence on the resulting sound.

INTRODUCTION

Many listening tests have been recently designed in violin acoustics to better understand how listeners evaluate violins as well as explore the influence of various parameters (the age (1), the model (2), the soundpost (3), the thickness of the plate (4), the effect of playing [START_REF] Inta | Measurement of the effect on violins of ageing and playing[END_REF], etc.) on the perceived sound. While being live or via recordings, they all involved at least one player, playing many times the same short musical excerpt on various instruments. These studies involved a lot of discussions and pilot tests to design experimental conditions and protocols which could counterbalance the influence, on the quality evaluations of the instruments by the listeners, of the player, the reproducibility of the player, the bow that was used, the chosen excerpt, the order of the violins, the types of comparisons, … But to which extent? This study aims at investigating to which extent an instrument has a sound quality per se, independently of the player and the bow, by exploring what can be heard and discriminated within these experimental conditions (beyond the qualitative evaluations for which a large disagreement between listeners has been shown by these studies).

We took advantage of the gathering of violin and bow makers and scientis ts during a European workshop 'Science and lutherie' organized yearly by the first author and violin maker Paul Noulet. Critical listening sessions are part of the workshop daily routine, which thus make this group of people a relatively well trained audience. These sessions have many goals: ear training, negotiating some common vocabulary, comparing instruments and testing the influence of various modifications which are done during the workshop in order to correlate them with measured acoustical differen ces. We used these sessions during the 2021 workshop to design a series of listening tests to investigate what, among the three factors that are the player, the bow and the violin, can be recognized and discriminate d.

LISTENING TESTS 2.1 General design

All the listening tests were designed as N successive trials, during which one or two violins were played by one or two musicians, behind an acoustically transparent screen, on stage of a 340-seat auditorium. For each test, the participants (between 11 and 12 violin/bow makers and violin acousticians) had to answer the same yes-no question. The probability of a correct answer being 50% for each trial, the distribution of answers for a given participant follows a binomial law with p=1/2. Based on how this law varies with N, we considered that N=8 was an interesting number as the probability of making one or no mistake is below the usual 5% chance threshold. Therefore, we can rule out that a participant did the test by chance if they made no more than one mistake.

The downside of such design is the repetition. Both the audience and the players can get tired over the length of the test. This tiredness can lead the players to be less reproducible. But at the same time, the repetition can make them adapt more and more to obtain the sound that they want, thus smoothing the differences. This will be discussed more later.

Violin recognition

A first series of tests was conducted to investigate whether a trained audience could reliably distinguish between two violins and could recognize specific characteristics of an instrument across players and trials.

Tests 1a et 1b

For each trial, two violins were played successively. They were chosen randomly among a group of 8 violins. The participants had to tell whether they were two different violins or the same one played twice. In test 1.a, the two violins were played by two professional orchestra players, using their own bow. In test 1.b, they were played by only one of these two players, the same one for all trials. After a few pre-tests, the chosen musical excerpt consisted in only 9 notes, a G Major diatonic scale on the G string with 5 notes up and 4 notes down, to keep the length of the test reasonable and, so we thought, to reduce the difficulty with a short excerpt, which is not too mus ical.

Test 2a and 2b

Here, only one violin is played per trial, which shortens the test by more than half and thus reduce s the tiredness and the problems of reproducibility. The violin played was selected randomly among two violins, labelled A and B, which were chosen collectively before the test as being the most different among the 8 that were available. So for each trial, participants had to tell whether it was violin A or not (i.e. violin B). The violins were played by a semi-professional violinist, who played an ascending and descending A Major scale (covering the register of the violin) followed by the opening of the Tchaikovsky concerto. We thought that the test being reduced, we could afford hearing a bit more and thus have more cues to make our judgment on. In test 2a, the player played with a different bow (selected randomly among a pool of 10 bows) for each trial to limit the adaptation of the player while in test 2b, the player always used his own bow, to reduce the source of variation.

Bow recognition

Talking about the famous recording by Janine Jansen of 12 Stradivari for which she chose carefully which bow to use among her two bows for each violin, Pauline Harding wrote: "Her two bows had a dramatic effect. It was interesting how everything changed." [START_REF] Harding | A spiritual connection[END_REF] This resonates with beliefs in the community of violinists and bow / violin makers who claim that changing bow can completely change the sound of an instrument, and even that a bow has a sound per se. We thus designed two tests to study whether an audience could reliably recognise a bow. As pre-tests made us realise that it may be much harder than expected based on the beliefs, we decided to use two extreme bows: a violin bow made by a renown bow maker and and a middle-range viola bow (about 10g heavier).

Tests 3a and 3b:

For each trial, a violin was played with either the violin or the viola bow, by the same semiprofessional violinist as in test 2. The musical material included a Ab Major scale covering the register to the violin, with one bow stroke per note on the way up and with an alternating of six rapid and staccato up and down bows (to illustrate the attacks allowed by the bow) on the way down followed by a very short excerpt from a Bach sonata. Similarly to what was done in test 2, test 3a was done with a different violin for each trial (chosen randomly among the pool of available violins) while test 3b was done on the player's own violin.

RESULTS AND DISCUSSION

The number of participants among the total number of participants who did each test at better than chance level is reported in table 1. 1 shows that for each test, only a very limited number of participants were able to succeed at better than chance level. The results of test 1.a seem to indicate that the same violin played by different players can have very different sound qualities which makes it difficult to tell whether it is the same violin or two different ones. Test 1.b's results show that it is not easier when it is the same player. This seems to indicate that the way a violinist play can have as much influence on the timbre than playing different violins. It is difficult for a violinist to play in a strictly reproducible way along the course of the test because of tiredness but more importantly because of adaptation. A good player is always trying to achieve "his/her" sound and so will modify his/her technique to get the sound he/she wants. Therefore, the differences decrease along the test and so it becomes harder for the audience to tell apart the violins. We thought that this adaptation could be limited by playing less the violins, as in test 2 (only one violin per trial instead of 2) and by playing them with different bows (2a) rather than one bow (2b). This seems to be the case, though not to a large extent, with still fewer than half of the participants being able to succeed. The protocol with only one violin in each trial allows a shorter test, but at the same time, may be more difficult because participants need to remember which violin is violin A. If a participant loses track at some point during the experiment, he may well be wrong for the rest of the test. This could be possibly solved in future tests by providing participants with the correct answer after each trial.

The last two tests, about bow recognition, have not been able to show any "bow sound" with only very few people having been able to distinguish two very different bows at better than chance level. Though players claim that the bow can have a large influence on the sound, one can expect, from a mechanical point of view, that this influence will be rather on temporal aspects (like the precision of the attacks or the articulation between notes for instance) rather than on the timbre of the instrument [START_REF] Ablitzer | Influence des paramètres mécaniques et géométriques sur le comportement statique de l'archet de violon en situation de jeu[END_REF]. Therefore, one may expect a smaller influence on the resulting sound from the bow than from the violin, and it is thus not surprising that participants could not recognize bows if they were not able to recognize violins.

CONCLUSION

These series of listening tests are a first attempt at exploring, beyond any qualitative judgement, what can possibly be recognized in a reliable way by a trained audience when violins are played in similar experimental conditions as previous published studies on violins sound quality, involving the repetition of rather short excerpts on various violins. The results raise interesting questions about the timbre of an instrument: can a violin have some intrinsic sound qualities that can be recognized across players and bows and if yes, how can we access/perceive them in a reliable way? Further work and more listening tests are definitely needed. They could be of significant importance in the current context about the shortage of the Pernambuco wood (traditionally used for bows), which is still used, despite more and more CITES regulations attempts [START_REF]Consideration of Proposals for Amendment of Appendices I and II[END_REF], since makers and musicians claim it gives a "better sound".

Table 1 :

 1 Proportion of participants who succeeded better than 5% chance level, i.e. who made no more than one mistake for each test.

	Test	1a	1b	2a	2b	3a	3b
	Number of participants who	1/11	1/11	5/11	5/12	3/12	2/12
	succeeded better than chance level
	Table

claudia.fritz@sorbonne-universite.fr

ACKNOWLEDGEMENTS

We would like to thank the "Villefavard team", the dedicated group of violin makers who took part in all the discussions and pre-tests to design the protocols and then participated in the tests.


Víctor Salvador-Castrillo
email: victor.salvadorcastrillo@sorbonne-universite.fr.

Amélie Picard

Duilio Spalletta

Frédéric Ablitzer

Claudia Fritz

Towards understanding the influence of mass distribution on the

Keywords: violin bow, perception, mechanics, bow making, human-instrument interaction

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Bows mainly consist of two parts (Fig. 1): the hair that is in contact with the strings, traditionally made of horsehair to which rosin is applied to increase its adherence; and a wooden stick whose main function is to maintain the tension of the hair, traditionally made of pernambuco wood. In this study, we focus on the latter. When playing, violinists hold the bow with their right hand and control the main bowing parameters: speed, position and vertical force on the string. Different parameters trigger different vibratory regimes of the string, which are transmitted through the bridge to the sound box and finally to the air, resulting in different sounds (see [START_REF] Schoonderwaldt | The violinist's sound palette: spectral centroid, pitch flattening and anomalous low frequencies[END_REF]). Fiddlers learn to control bowing parameters to produce the sound they want following their interpretative will. Despite being an essential element for the musician, the bow has not been studied as thoroughly as the violin until the end of the twentieth century. Concerning the musicians' perception of bows, only a few studies have been conducted. One of the first attempts to unveil how bow mechanical properties are linked with its perceived qualities was conducted by Bissinger in 1995 [START_REF] Bissinger | Bounce tests, modal analysis, and the playing qualities of the violin bow[END_REF]. He did modal analysis and bounce tests of eight violin bows and had them tested by an expert violinist. The bow with highest modal damping was perceived as "squishy, soft," whereas the least damped were perceived as with "out-ofcontrol feeling to spiccato and ricochet." 1 Those classed as being "excellent spiccato bows" had damping values in between. A few years later, Caussé et al. [START_REF] Caussé | Study of violin bow quality[END_REF] conducted a dissimilarity test on twelve expert violinists with a set of seven carbon fiber composite bows and a pernambuco bow. They could not correlate quality criteria with physical properties like mass, center of gravity, stiffness or hair tension. However, they identified three important bow playing properties among all violinists: balance, flexibility and responsiveness. Ablitzer [START_REF] Ablitzer | Influence des paramètres mécaniques et géométriques sur le comportement statique de l'archet de violon en situation de jeu[END_REF] explored the influence of camber (i.e. the curve of the stick) on the playing qualities of the bow during his PhD. He used three bows with different camber, which he characterized and were tested by two expert violinists. He remarked that violinists tend to adjust hair tension based on the hair-stick distance, and make finer adjustments after playing with this initial tension. The variations on hair tension -determined by camber for a given hair-stick distance -influenced the perceived attack transients (consonant sounds) and reactivity of the bow, as well as the timbre of the sound. Bow maker Joseph Regh published recently the result of a lifetime's study of the bow [START_REF] Regh | Violin Bow Playability -A Players View[END_REF]. For years, he asked professional violinists to play and rate a set of 75 bows of varying quality with measured physical properties. Three properties stood out as determining the perceived bow quality: moment of inertia, total mass and stick stiffness. For all three, the higher they were, the better the bow was rated.

None of the works cited above focused on how mass distribution influences bow quality. In addition, most of them used different bows with their own characteristics (wood, hair, mass distribution or total weight). Their respective influences on the perceived qualities are hard to uncouple. In 2017, an experiment was conducted at the University of Montreal under the direction of Aurélie Tomezzoli [START_REF] Tomezzoli | Effect of bow camber and mass distribution on violinists' preferences and performance[END_REF] on the influence of bow camber but also its mass distribution on violinists' preferences. In this experiment, a single 62 g bow was used, and different masses were added at different locations (tip and frog, +1 and/or +2 g). In general, the masses added at the tip and/or frog had a negative impact on musicians' ratings, which could be caused by big changes in bow mechanical properties as the center of mass and the moment of inertia. Furthermore, in the case of adding +2 g to the tip and frog, the total weight would be closer to the standard weight of a viola bow (70 g) than that of a violin bow (60 g) [START_REF] Stagg | Bow Making and Repair[END_REF], quite far from what violinists are used to play with.

The present study adopts a similar approach as that of [START_REF] Tomezzoli | Effect of bow camber and mass distribution on violinists' preferences and performance[END_REF]. Using one single bow that has been built as light as possible, we try to find how different mass distributions are perceived by musicians by adding masses along the stick. The tested bow weighs around 60 g -the standard for violin bows [START_REF] Stagg | Bow Making and Repair[END_REF] -for any configuration of the added masses. This allows for test conditions closer to those a violinist would encounter when trying out different bows.

STATIC FORCE CONTROLLABILITY

This section was inspired by the work of Askenfelt on finger touch sensation in stringed instrument playing [START_REF] Askenfelt | On vibration sensation and finger touch in stringed instrument playing[END_REF]. When playing the violin's low-pitched strings (G and D) the bow is drawn horizontally. Its weight has to be compensated by the musician in order to press the string with the desired force, mainly with both index and little fingers depending on the bow-string contact point. As will be shown, the position of the center of gravity -given by mass distribution -influences the necessary finger forces that control the vertical pressure on the string.

The bow can be modeled as if moving along an axis perpendicular to the string. In a playing situation bow kinematics are way more complex and rich (see [START_REF] Schoonderwaldt | Mechanics and acoustics of violin bowing[END_REF]), but it is a good first approximation to picture how violinists control vertical force on the string. Let us also consider that its movement is restricted to a plane perpendicular to the direction of gravity, like when playing on the G string, and that it does not rotate around any axis. Hence, the only forces acting on the bow are its weight, the restoring force of the string and the musician's control forces, applied by thumb, index and little fingers (Fig. 2).

Axis of rotation

Center of Mass Index F I and little F L finger forces are defined positive and parallel to the direction of gravity, which is also positive. From rotational equilibrium on a pivot placed at the thumb position, it is then possible to infer the formula of F I and F L as an expression of its total weight W bow , the restoring force of the string on the hair F S -which is negative -and the distances between the pivot and the center of mass x CM , little x L and index x I fingers:

   F I = F S x I x S -W bow x CM x I x eq ≤ x S < L F L = -F S x L x S + W bow x CM x L 0 < x S ≤ x eq (1)
Where x eq = x CM W bow /F S represents the position of the bow on the string where violinists should stop pressing with the little finger and start pushing with the index on a down-bow stroke (vice versa for an up-bow stroke) in order to obtain an homogeneous force on the string. At this point x eq , no finger force is required to have a force equal to F S on the string, and it depends on the position of the center of mass of the bow and thus on its mass distribution. In the case of higher pitched strings (A and E), bow motion happens in a direction very close to the direction of gravity. When playing on these, the contribution of bow's weight to string force is insignificant, and thus bow mass distribution would not have an impact on the required finger forces to press the string.

In Fig. 3 an example of this forces for a given bow is shown. Experimental validation was made with a setup consisting on a force sensor placed on the little or index finger positions respectively (Fig. 4). A mass of 101 g was attached to one end of a light wire hanging from a pulley, while the other was tied to the bow at different x S positions, giving a constant vertical force of about 1 N. The pivot position was fixed with a metallic hook.

The moment of weight, i.e. the product of the bow's weight W bow times the distance from the pivot axis to its center of gravity x CM , determines the range of finger forces. For the same weight, a bow with the center of gravity closer to the tip would reduce the index finger force necessary to trigger a vibratory regime. On the other side, playing at the frog would require greater little finger force to compensate bow's weight than in the case of a center of gravity closer to the frog. The perfect bow should have the center of gravity placed in such a position that the violinist feels comfortable playing anywhere from the frog to the tip.

x S )URJ 7LSFP Top: index finger (Fig. 3, squares). Bottom: little finger (id., circles).

)RUFH1 7KHRUHWLFDOF I 7KHRUHWLFDOF L 0HDVXUHGF I 0HDVXUHGF L

BOUNCING BOW

Some classical bow strokes like spiccato or ricochet involve a bouncing motion of the bow on the string. This behavior has been described thoroughly by Askenfelt and Guettler [START_REF] Askenfelt | Observations on the dynamic properties of violin bows[END_REF][START_REF] Askenfelt | On the kinematics of spiccato and ricochet bowing[END_REF][START_REF] Askenfelt | The bouncing bowsome important parameters[END_REF]. The first mode of vibration of the bow on the string is known as the bouncing mode. Askenfelt [START_REF] Askenfelt | Observations on the dynamic properties of violin bows[END_REF] proposed a rigid stick, quasi-static bow model to obtain the bouncing frequency, which is replicated hereinafter.

When the hair of the bow is in contact with the string, it bends approximately in a shape similar to a triangle. In Fig. 5 this shape of the loaded hair is represented with the main forces that take part in this deformation (scale of yaxis is much smaller than scale of x-axis). Through some simplifications, it is possible to obtain an expression of the restoring force that acts to bring the hair to its equilibrium position (dashed line in Fig. 5). First, let us apply Newton's second law to the loading point of the hair, which is in translational equilibrium:

-→ F S + -→ T α + -→ T β = 0 (2)
For this particular problem, let us assume that the point of contact between the hair and the string is frictionless. In that case, tension is constant along hair length and we have | -→

T α | = | -→ T β | = T
. Projecting Newton's second law onto the y-axis gives then:

F S -T (sin α + sin β) = 0 (3)
From Fig. 5 can obtain both tangents of α and β angles. Small-angle approximation (sin x ≈ tan x) simplifies the restoring force F S formula:

F S ≈ T (1 -γ) γL y (4)
where

T [(1 -γ) γL] -1
is the equivalent stiffness of the hair for an in-plane vertical displacement y. Let us suppose that the bow can rotate around an axis at γ = 0, perpendicular to the x-y plane. Let us assume that the only force that acts on the system is the restoring force -→ F S . The application of the rotational analog to Newton's second law using small-angle approximations leads us to the following equation of motion:

ÿ + T γL (1 -γ)I y = 0 (5)
This equation describes the motion of a simple harmonic rotating oscillator, characterized by its natural angular frequency ω BN C = 2πf BN C . This bouncing (BNC) frequency depends on the tension of the hair T , the position of the loading point along the x-axis γ and the rotational inertia of the bow I:

f BN C = 1 2π T γL (1 -γ)I (6)
First described and measured by Askenfelt in 1992 [START_REF] Askenfelt | Observations on the dynamic properties of violin bows[END_REF], this frequency is valid for on-string motion, i.e. when the bow stays in contact with the string. It takes values between 7 and 30 Hz along the stick, and it depends on the moment of inertia of the bow and thus on its mass distribution. Colin Gough refined this model [START_REF] Gough | Violin bow vibrations[END_REF] through modal analysis, showing that Askenfelt model describes the bouncing mode well for positions between the frog and the middle of the bow. For the upper part of the bow, he demonstrated that the bouncing rate is influenced by the lowest frequency vibrational modes of the bow stick.

For off-the-string bowing techniques, the total bouncing period corresponds to the half-period of the on-thestring cycle -Eq. ( 6) -plus the time it takes the bow to return to the string [START_REF] Gough | Violin bow vibrations[END_REF]. This second off-the-string halfperiod may be controlled by the violinist by exerting a couple on the bow with his or her index and little fingers (see Fig. 2), modifying the net bouncing rate. Moreover, the deflection of the string under the influence of the bow force would also modify the bouncing frequency. Askenfelt [START_REF] Askenfelt | Observations on the dynamic properties of violin bows[END_REF] estimated a reduction of the bouncing frequency for the violin G string of about 15%.

MATERIALS & METHODS

Previous studies [START_REF] Fritz | Violinist, violin, bow: What can we hear and recognize?[END_REF] have shown that even for a well trained audience, it is almost impossible to differentiate between a violin and a viola bow only from the perceived sound. On the other side, musicians are able to feel the difference between those bows, notably from haptic perception and from playing qualities. Professional violinists seem to not only distinguish a viola bow from a violin bow, but also between two violin bows. With the aim of understanding how musicians perceive changes in the mass distribution of the bow, a series of perceptual tests have been planned with professional violinists using an experimental bow whose mass distribution can be easily modified.

Table 1. Set of bow mass configurations tested by musicians and measured bow mechanical properties. {∆m tip , ∆m clamp , ∆m f rog }: added masses at the {tip, clamp, frog}. The masses of the clamp, foam and paper hiding the magnets (Fig. 6, bottom) are considered. m bow : bow total mass; x CM : distance from the center of mass to the pivot point (beginning of the hair at the frog); I: moment of inertia with respect to the pivot point; {∆x CM , ∆I}: variation of mechanical properties with respect to the reference bow A in percentages.

Bow

∆m tip

[g] ∆m clamp [g] ∆m f rog [g] m bow [g] x CM [cm] ∆x CM [%] I [g m 2 ] ∆I [%] A 0.

The experimental bow

In April 2023, bow maker Duilio Spalletta 2 made a violin bow specifically for this project. The total mass of the bow, equal to 52.6 g, is significantly lower than the standard (about 60 g). Lightening was possible thanks to the use of low density pernambuco wood for the stick (0.850 g cm -3 ). Also, the tip plate was removed and the head was carved following a thin model. At the frog, several elements were lightened as well using different materials: titanium screw, round-shaped ebony frog without eye, silver-wound silk winding, kangaroo leather and nickel ferrule and adjuster (see [START_REF] Stagg | Bow Making and Repair[END_REF] for detailed information on bow making). The lightness of this bow allows to modify its mass distribution by adding masses along the stick until reaching the standard weight, which gives a margin of about 7 to 8 g. In order to facilitate the task and easily switch from one mass configuration to another, we added small neodymium magnets (0.07 , 0.35 , 0.56 and 1.98 g) on a magnetized nickel clamp (1.67 g). In addition, the nickel screw adjuster at the frog was magnetized to hold the magnets, as well as a thin nickel plate glued at the tip.

Mass distributions to be tested

Because of their influence on different aspects of controllability (see sections 2 and 3), the two physical properties on which we focus here are the moment of bow's weight and the moment of inertia. In order to explore the influ-2 contact@duiliospalletta.com 6 shows the detail of the added magnets along the stick. For all configurations, the metallic clamp at the middle of the bow was at the same position (15 cm from the pivot position) to avoid any difference between bows that could be perceived visually. All distributions give values that are into the typical limits of modern violin bows [START_REF] Regh | Violin Bow Playability -A Players View[END_REF].

Measurement of bow mechanical properties

Bow mass was measured with a precision balance. The centers of mass were determined through empirical estimation using a narrow square piece measuring 2 mm in width: the stick was carefully positioned on this piece until the point of balance was achieved. The moment of inertia was determined by suspending the bow from the pivot point (the axis of rotation shown in Fig. 2) and allowing it to oscillate freely. The motion of this physical pendulum can be described using Newton's second law for rotation, which results in a period equal to:

T = 2π I m bow gx CM (7)
The moment of inertia about the bow's point of suspension is subsequently calculated from the oscillating period and the measured values of the bow's mass and center of mass position. Hair tension was determined by measuring its deflection after applying a mass of 50 g at the midpoint of its total length, following the methodology described by Regh [START_REF] Regh | Violin Bow Playability -A Players View[END_REF].

Protocol of the perceptual tests

The different mass distributions described in Tab. 1 are tested by musicians in two different tasks: discrimination and constrained playing tests. Six professional violinists (42.2 ± 9.9 years of experience) and two students (13.0 ± 1.0 years of experience) participated in the test. All of them were trained in the Franco-Belgian violin school, or had it as an important influence. The study was reviewed and approved by the Ethics Committee of Sorbonne University (CER-2023_SALVADOR_CASTRILLO_ARCHET).

One participant did not complete the last test due to lack of time. At the beginning of the session, players were asked to adjust the hair tension of bow A according to their personal preference while their own bow properties were being measured. Subsequently, the hair tension of bow A was recorded prior to the test, and participants were instructed not to make any further adjustments to it during the session. Visual cognitive biases were avoided by hiding magnets with light pieces of paper and foam (Fig. 6, bottom).

Discrimination test

To explore to what extent musicians are able to perceive little (bows A-B, A-D) or big (bows A-C, A-E) changes on both center of mass position and moment of inertia, a same-different test is performed. For each trial, the violinist was asked to play with two presented bows and to indicate if they were different or not. They were also encouraged to verbalize comments on what they perceive as soon as they pick up the bow. First was always bow A, presented as the reference bow, while the second was any of the bows of the set presented in Tab. 1 (A-X, where X ∈ {A, B, C, D, E}).

Each participant performed six trials. All five bows from A to E were tested by each judge, and one of them was repeated randomly. The order of presentation of the bows was also random.

Constrained playing test

A semantic classification of the verbalized comments given by participants could allow to perceptually characterize each mass distribution, as has also been done before for the acoustic qualities of different violins (Bilbao Project [START_REF] Fritz | The Bilbao project: searching for relationships between sound and playing properties of violins with their construction parameters[END_REF][START_REF] Salvador-Castrillo | Liens entre paramètres de facture, propriétés acoustiques et qualités perceptives sur un lot de 13 violons[END_REF]). To analyze how musicians describe big changes in bow properties when playing, we asked them to evaluate the pairs A-C (big change in moment of inertia) and A-E (big change in center of mass position):

• Bows A-C: all-string scale in spiccato (2 octave G major, first position), ricochet (note A on G string and on E string, first position), 4-string ricochet (G major chord, first position). For spiccato and ricochet, they were asked to play in tempo with a metronome that was set to the same rhythm for both bows.

• Bows A-E: on the G string, one-string détaché scale (A major) played at the frog and at the tip in forte. Here the metronome was also used.

After each constrained test, they were allowed to play freely in spiccato (A-C) and legato on the G string (A-E) in order to give a complete evaluation.

RESULTS AND DISCUSSION

The average values for the measured properties of the bows from the eight participants in the test are as follows: bow mass m bow = (61.21 ± 2.00) g, center of mass position x CM = (18.6 ± 0.9) cm, and moment of inertia I = (5.12±0.37) g m 2 . The average bow mass is 1.21 g higher than the standard value of 60 g, which represents a variation of only 2%. The average center of mass position and moment of inertia values validate the choices made during the design of this experiment, as shown in Table 1, as they fall within the typical ranges for the participants' bows.

Bow B had the closest moment of inertia to the average of those owned by the participants. On the other hand, when considering the bow moment of weight (bow mass multiplied by the center of mass position), bow D was the closest to the average. Regarding hair tension, the average tension for bow A was (46.4 ± 1.8) N, whereas with their own bows, the average tension was (41.2 ± 5.1) N. Participants showed greater consistency in hair tension when using bow A compared to the tension chosen for their own bows. This observation is in line with Ablitzer's findings [START_REF] Ablitzer | Influence des paramètres mécaniques et géométriques sur le comportement statique de l'archet de violon en situation de jeu[END_REF], which suggest that musicians typically select hair tension based on the hair-stick distance initially and then make minor adjustments.

Discrimination test

The percentage of responses "different" to the samedifferent test are given in Tab. 2. These results indicate that, based on the protocol described in Section 4.4.1, participants were unable to discriminate when the second bow was identical to the first more of half of the time. In the test of the bows with contrasting moment of inertia, two violinists clearly expressed a preference for bow C over bow A when playing spiccato or ricochet. They described it as "vigorous (nerveux)", "reactive (réactif )" or "precise (précis)". On the other hand, five violinists did not like bow C, with four of them stating that it produces excessive bouncing and is challenging to control compared to bow A. One violinist was unsure about their preferred bow. Interestingly, the moments of inertia of the bows owned by the two violinists who favored bow C over bow A were not particularly close to the moment of inertia of bow C (5.05 and 5.14 g m 2 ). Overall, all participants noticed a significant change when the moment of inertia was dramatically altered. The majority of them encountered difficulties in controlling the bow, although they exhibited less consistency in describing this modification.

Regarding the test of different center of mass positions, one of the participants was unable to participate due to time constraints. Out of the remaining seven participants, six of them perceived bow E as lighter than bow A. Lightness was the most prominent quality verbalized by the participants in relation to both bows; however, their preferences varied. Two participants preferred bow A when playing at the tip, while the other five preferred bow E. At the frog, four participants favored bow A over bow E, two of them were uncertain about their preference, and only one clearly preferred bow E. Notably, this last violinist consistently preferred bow E in both tests and possessed a bow with a center of mass closest to the frog among all participants (x CM = 16.65 cm).

Across all evaluations, the vocabulary employed to articulate playability factors encompassed the quality of attacks, stability throughout the stroke, awareness of different bow parts (notably the tip) and controllability. However, in both tests, participants also evoked various sound qualities such as roundness or clarity.

CONCLUSION AND PERSPECTIVES

In this paper, we presented a preliminary study aimed at investigating how violinists perceive different bow mass distributions. By utilizing a lightweight bow, we were able to create five distinct mass distributions by adding small masses while maintaining a consistent total mass across all cases. The resulting mechanical properties of the bows, specifically the moment of inertia and center of mass position, were observed to fall within the typical ranges found in the bows owned by the participating violinists.

A same-different discrimination test was conducted to assess the extent to which violinists perceive changes in moment of inertia and center of mass position. No measure of confidence was recorded regarding their responses. Regrettably, the results of this test were not satisfactory: most participants were unable to detect when the second bow was identical to the first one.

In addition, a constrained playing test was conducted, in which participants were aware that the first and second bows presented to them were different. The task consisted in describing the changes that they perceive, if any. Participants showed little consistency among them when evaluating big changes in moment of inertia. On the other side, the consistency of participants on the perceived change of lightness suggest potential correlations between this quality and the position of the center of mass. This relationship is linked to the range of finger forces required by the right hand to control the bow stick effectively. This raises questions about the results of the discrimination test: when violinists were aware of a change, they expressed very similar descriptions of that change.

Based on this circumstance, several attempts have been made to choose a more effective protocol for the discrimination test. The decision strategy for the samedifferent test turned out to be psychologically intricate: musicians often detect even the slightest difference between bows and tend to conclude that the bows are different. This phenomenon can be attributed to the complexity of bow quality evaluation, which involves considering multiple sensory aspects including auditory and kinesthetic perception. We finally chose to perform a dualreference Duo-Trio test, with the reference at First and Middle positions (DTFM): A-X-A-Y where X or Y are equal to A and X is different from Y. The cognitive strategy for this discrimination test is less demanding since the reference bow is presented twice, and the participant has to choose which of the bows X or Y is the reference. This has already been confirmed by three musicians who performed both type of tests. Additionally, a level of confidence in their answers, ranging from 1 (not sure at all) to 5 (very sure), will be collected.

Figure 1 .

 1 Figure 1. Overview of the violin bow main parts.

Figure 2 .

 2 Figure 2. Forces on the bow and distances to the pivot point.

Figure 3 .

 3 Figure 3. Theoretical -Eq. (1) -and measured righthand finger forces against bow-string contact position, for a constant vertical string force F S of about 1 N. Error bars are smaller than symbol size. Bow properties: x CM = 29.6 cm, W bow = 66 g. Finger distances to pivot: x I = 6.3 cm, x L = 5.6 cm.

Figure 4 .

 4 Figure 4. Setup for measuring static finger forces. Top: index finger (Fig. 3, squares). Bottom: little finger (id., circles).

Figure 5 .

 5 Figure 5. Shape and forces on the loaded bow hair.

Figure 6 .

 6 Figure 6. Test bow with added masses. Top: detail of the magnets (bow B of Tab. 1). Bottom: bow as seen by participants, with paper covering tip and frog magnets, and a light piece of foam covering the magnetic clamp.

Table 2 .

 2 Proportion of responses "different" to the same-different test. First bow was always bow A.

			Second bow
	A	B	C	D	E
	70% 90% 70% 56% 89%
	5.2 Constrained playing test

Spiccato and ricochet are bow strokes (bowing techniques) involving notes played with a bouncing bow.

Turin, Italy • 11 th -15 th September 2023 • Politecnico di Torino


Claudia Fritz
email: claudia.fritz@sorbonne-universite.fr

George Stoppani

Developping methodologies to

published or not. The documents may come

DEVELOPING METHODOLGIES TO CORRELATE PERCEIVED SOUND QUALITIES OF VIOLINS WITH CONTROLLED CONSTRUCTION PARAMETERS

Claudia Fritz 1* George Stoppani 2 1 Institut Jean Le Rond D'Alembert, UMR 7190, CNRS/Sorbonne Université, France 2 Violin maker, 31A Derbyshire Road, Manchester M40 1QN, UK

ABSTRACT *

The holy grail for violin makers is to find correlations between construction parameters and sound qualities. This is challenging for two main reasons: it is difficult to build violins reliably enough to ensure that the change in the sound is indeed a result of the change of construction parameters; when listening to the violins being played, differences are smoothed out by the players who adapt very quickly. Therefore, while players had so far been preferred in our experiments to maximise the ecological validity and take into account the complexity of the interaction between the player and the instrument, we have decided to test whether other methods, that reduce the influence of the player but are quite artificial, may be useful to explore the influence of some construction parameters on the tone. In the context of two sets of violins built with controlled thickness variations of their plates, we will compare the results of listening tests based on real recordings with a player and with a bowing machine as well as synthesised recordings (from the convolution of an excerpt recorded with piezo sensors and radiation measurements in an anechoic chamber) and discuss them in the light of vibroacoustical measurements.

Keywords: violin, perception, construction parameters, sound quality.

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INTRODUCTION

Since the pioneering work by Carleen Hutchins and Frederik Saunders in the 1950s, a lot of studies by researchers and violin makers have been dedicated to the finding of relationships between construction parameters and sound qualities of violins [START_REF] Hutchins | A history of violin research[END_REF]. However, there were two main limitations. First, the control of the construction parameters was difficult because the violins were made by hand. Second, the sound qualities were almost taken for granted and not really studied as perceived by players and listeners.

Recent projects [START_REF] Fritz | The Bilbao project: How violin makers match backs and tops to produce particular sorts of violins[END_REF][START_REF] Jost | Work in progress for a PhD[END_REF] have used modern technology, in particular CNC routing, to control with high accuracy the constructions parameters. The resulting violins have been used in playing and listening tests but results were less clear than expected. Three main aspects are of relevance to players: the playability (response, comfort), the sound intensity and the timbre/tone quality [START_REF] Saitis | Perceptual evaluation of violins: A psycholinguistic analysis of preference verbal descriptions by experienced musicians[END_REF]. These three aspects seem to interact and players may find it difficult to judge them separately. Moreover, they may be largely influenced by what instrument they usually play.

In addition, violin makers would like to find correlations with vibro-acoustical measurements as well, and the ones that are commonly conducted rely on removing the player and replacing them by a controlled excitation via an impact hammer, and looking at frequency responses (measured with a microphone or an accelerometer). Such measurements for sound radiation will certainly be difficult to relate to playability but may be informative about tone quality and sound intensity which are the two quantities we would like to focus on for now. In the very particular case of the wolf note a bridge admittance (processed to estimate minimum bow force) is a better predictor.

Due to the difficulty for players to decouple the various qualities, we believe that listeners may have more robust judgements, which could be more easily correlated with acoustical measurements. Of course, we do not advocate total disregard of the player's responses but recognize that they have a different relationship with the instrument. Many questions follow. How to listen to the violins? Played by whom? What excerpt? In which venue? Live or via recordings? So far, the authors have tried to favor ecological validity [START_REF] Gibson | The ecological approach to visual perception[END_REF] though there is a fundamental conflict of requirements. On the one hand we would like the listening judgements to be made in the most natural conditions while collecting data that is free of bias and can be meaningfully processed statistically. Our natural listening involves combining all our senses plus all kinds of prior knowledge about what we are observing. When we know the "answer" we can usually hear it, which does not constitute a valid psychoacoustic experiment. compromise, so far, has been to allow the player to perform the selected material as they wish, but to deprive the audience of knowing which instrument they are playing by interposing an acoustically transparent screen. This is usually short musical phrases from famous violin concertos, covering the full range of the instrument [e.g. 6] Also the player may be asked to were dark goggles so that they cannot see which instrument is in their hands. Others like Nastac et al. [START_REF] Nastac | Correlation between Acoustic Analysis and Psycho-Acoustic Evaluation of Violins[END_REF] preferred to record one violinist in a concert hall and use the recordings in a listening test. In both cases, the listening test relies on the reproducibility of the player, which appears to be lower than expected due to a strong (presumably unconscious?) will to make their "own sound". Their goal is to deliver a "musical" performance. Thus, differences between instruments seem to be smoothed out, to the extent that listeners are not even able to tell whether a player plays twice on the same violin or two different violins in a row [START_REF] Fritz | bow: what can we hear and recognize?[END_REF]. In addition, if the player plays slightly differently, only very experienced listeners may be able to tell whether the differences heard are due to differences in playing or differences between instruments.

The goal of this study is therefore to explore and compare, within an online listening test, different recording methodologies in order to investigate which one would be best for maximizing i) differences between instruments and ii) likelihood that these differences can be correlated with acoustical properties and construction parameters (and not with playing variations). To this end, two sets of violins (described in Section 2) whose manufacturing was carefully controlled were recorded with three different methodologies (described in Section 3): live recordings, recordings with bowing machine and synthesized recordings. The recordings were then used in an online listening test that is presented in section 4. The results of the listening test will be presented at the conference.

VIOLINS USED IN THE STUDY

The heritage of high quality old instruments has all kinds of graduation schemes for which we lack knowledge of how the playing quality is affected and how the decisions were made. To this end, two series of violins have been made to study different graduation patterns.

The Bilbao set

In the Bilbao project [START_REF] Fritz | The Bilbao project: How violin makers match backs and tops to produce particular sorts of violins[END_REF], six instruments were carefully built to investigate the influence of the plate thickness on the sound qualities: three instruments with normal backs, each paired with a pliant (thin), normal, or resistant (thick) top; similarly, three with normal tops, each paired with a pliant, normal, or resistant back. The two examples of normal top paired with normal back serve as a control. Plate weights and mode frequencies were used to estimate characteristic impedance values. Wherever possible, thicknesses were kept uniform to avoid the effects of localized differences. Wood for tops and backs were closely matched in density and sound speedsall tops and backs from the same trees. Greater control was achieved by having all plates and scrolls cut by CNC routers. The outside surface was not changed during the experiment, as the graduation was performed entirely on the inside surface.

The high control of the construction parameters of these violins provide unprecedented opportunities for exploring correlations with sound qualities.

The ABCD set

This is another set of four violins that was carefully built (though with a bit less control than for the Bilbao set) after a pilot experiment during which we experimented with plates (CNC routed) simply supported around the edges (pinned edges) giving boundary conditions that are very different from the usual free plate measurements but closer to those of the closed corpus and reasonably reproducible. We graduated the plates in three zones, one zone changed at a time: upper bout, lower bout and central area (which was the "island", bounded by the f-holes, and for the back the area between the C bouts. We found that for the top the upper bout had little influence on mode frequencies and amplitude but the island, followed by the lower bout did have a large effect. Conversely, for the back it was only the upper bout that was very sensitive to thickness.

The ABCD set were created from a selection of factory build corpora and necks that were alike in arching shapes and wood characteristics. We wanted to see to what extent the behavior in the "pinned edge" state is carried over to the assembled violin. From the structural measurements perspective this was shown to be the case. We

THREE RECORDING METHODS

Live recordings: a real player and real violins

We recorded a semi-professional violinist in a large seminar room, playing a short excerpt from the Glazunov concerto (Fig. 1) on the ten violins described above. The position of the player was kept constant relative to the microphone (DPA 2006C) throughout the session, at a distance that had been adjusted at the beginning of the session to obtain pleasant recordings.

Figure 1. Excerpt from the Glazunov concerto

Each violin was recorded between two and three times, so we can potentially study reproducibility.

Bowing machine: an artificial player and real violins

The goal of this methodology is to replace a not so reproducible player by a reproducible excitation (though artificial). The bowing machine is shown on Fig. 2. The ten violins were recorded on each of the four open strings with an omnidirectional microphone (DPA 2006C) placed vertically above the bridge at a distance of 185 mm when the violin lays flat. That distance was adjusted to have, qualitatively, a strong direct sound with a bit of reverberation, in the room that was available at the time to make the recordings (different from the seminar room used for the live recordings). The violins were rotated for the different strings in order to keep a bowing direction tangent to the bridge curvature. The hybrid synthesis is based on the convolution of the recording of an input signal (the force applied by the bowed strings on the bridge) during a live performance with the inverse Fourier transform of a frequency response function of the chosen violins [START_REF] Fritz | Perceptual thresholds for detecting modifications applied to the acoustical properties of a violin[END_REF]. For the input signal, we used recordings of the same Glazunov excerpt made on a violin whose bridge was instrumented with a piezoelectric force sensor under the G string. For the frequency response function, we used a complex average of twelve radiation measurements, made in an anechoic chamber, with a hammer excitation, and an omnidirectional microphone (see Fig. 4). The violin could rotate around the vertical axis, and the measurements were taken at six different angles (every 60°) between the violin plane and the microphone for two excitation directions (tangential and perpendicular to the bridge). The distance between the microphone and the bridge was set to 20 cm when the microphone was at the front. This hybrid synthesis allows to drive different virtual violins by the same realistic forcing waveform (measured during real playing) so that sound differences can be compared with no complications arising from variations in playing. We opted for an online test which allows a larger number of participants (in particular the violin makers who took part in both the Bilbao and ABCD projects and who live across Europe), without necessarily compromising the results due to a lesser control [START_REF] Parizet | Sound quality assessment: comparison of in-situ and on-line experiments[END_REF]. As the differences between the instruments can be subtle, the participants are recommended, at the beginning of the test, to use the best audio equipment possible (good quality headset). We used the option Audio Perceptual Evaluation [START_REF] De Man | Audio Perceptual Evaluation toolbox for MATLAB[END_REF] available in the Web Audio Evaluation Tool [START_REF] Jillings | Web Audio Evaluation Tool: A Browser-Based Listening Test Environment[END_REF]. This consists in comparing and ranking stimuli on a criterion, using a 0 to 10 scale. We decided to focus on the two main criteria that are relevant for players (see introduction) and which can also be evaluated by listeners: loudness and timbre quality.

Each test is thus divided in two sub tests, one for each criterion. Each sub test consists of a series of 6 pages (in random order): on each one, recordings made with a given methodology (real player, bowing machine on each of the 4 open strings, hybrid synthesis) for a given violin set are compared. As timbre quality differences are hard to evaluate when there are loudness differences, the stimuli were compensated in loudness for the timbre sub test. Fig. 5 illustrates one page of the timbre quality test on the ABCD violin set and one page of the loudness test for the Bilbao set. The green bars correspond to the stimuli. Listeners first click on them to listen to all stimuli (in any order and as many times as they want) and can then move them freely along the scale to order them according to their judgements). 0 on the left corresponds to the poorest timbre quality / softer stimulus while 10 on the right corresponds to the highest timbre quality / loudest stimulus.

CONCLUSION

Tools that can in some way quantify perception and relate it to construction differences are needed. This study aims, via an online listening test, at exploring the influence of three recording methodologies on perceived differences between violins in order to investigate which methodology leads to the largest and most robust differences, that could then possibly be linked with acoustic properties and construction parameters.

The results of the listening tests will be presented and discussed at the conference.

  reduced the number of zones to two per plate (top: upper bout & lower bout plus island; back: upper bout & lower bout with no change to the C bout region). We started with four very similar factory violins and each instrument was measured and evaluated at three steps: both plates full thickness, one zone in either the top or back reduced and one zone each in top and back. Here we will only consider the fours instruments in their final state (thinner upper (resp. lower) zones for both plates; thinner upper (resp. lower) zone for the top and thinner lower (resp. upper) zone for the back).

Figure 2 .

 2 Figure 2. The two zones (per plate) in which the thickness could be reduced to constitute the ABCD set: for the top plate (red) on the left, for the back plate (grey) on the right.

Figure 3 .machine 3 . 3

 333 Figure 3. Bowing machine

Figure 4 .

 4 Figure 4. Radiation measurement rig

Figure 5 .

 5 Figure 5. Listening test interface: Ranking by timbre for the ABCD set (top) and ranking by loudness for the Bilbao set (bottom).

ACKNOWLEDGMENTS

The authors would like to thank Marion Caumartin and Thibault Ernoult for their help with the live recordings, the design of the listening test interface, and the radiation measurements; Benoît Dupeux, Paul Noulet and Silvian Rusu for their help with the recordings made with the bowing machine; and finally Victor Salvador-Castrillo for playing the 10 violins for the live recordings.