Figure 4.7 Models of the configurations 1A/1B/1C and logaritim trend of the ST early,d for the configurations 1A/1B/1C depending on the distance...

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1 Contents 1. Chapter Introduction Chapter Background of the study... 8 Introduction... 8 Subjective impression and acoustic problems denounced by musicians... 9 Stage acoustics Summary of design goals Chapter Investigations of the stages of existing concert halls Introduction Stage characteristics of eight concert halls Comparison Architectural guidelines Chapter First stage design Introduction Method Stage design Design steps and results Conclusions and further research Chapter Second stage design Introduction Method First part: omnidirectional sources Second part: sources with directivity Chapter Conclusions and discussion

2 6.1 Conclusions and discussion References Appendix A Orchestra arrangements Appendix B Terminology Appendix C Tables Appendix D Graphs Figures Figure 2.1 Wall reflections from trumpet at 1.5 khz with perpendicular walls and side splayed walls. Trumpet directivity from [4]. Images from [9] Figure 2.2 Reflectogram Figure 3.1 Concertgebouw stage, Amsterdam Figure 3.2 Muziekgebouw stage, Eindhoven Figure 3.3 Bridgewater Hall stage, Manchester Figure 3.4 Großer Musikvereinsaal stage, Vienna Figure 3.5 Berlin Philharmonie stage, Berlin Figure 3.6 Walt Disney Concert Hall stage, Los Angeles Figure 3.7 Symphony Philharmonie stage, Paris Figure 3.8 Casa da Musica stage, Oporto Figure 3.9 Different shape of several concert halls: Muziekgebouw of Eindhoven, Manchester BridgeWater, Concertgebouw of Amsterdam, Vienna Großer Musikvereinsaal, Berlin Philharmonie, Walt Disney concert hall, Paris Symphony Philharmonie and Casa da Musica of Oporto Figure 3.10 Common stage risers types. Image from [9] Figure 4.1. Source and receiver positions and height of sources and receivers Figure 4.2 Concept first stage design Figure 4.3 Height and depth of risers for the visibility of the conductor Figure 4.4 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration from 2B to 0-rectangular shape Figure 4.5 Models of configurations 2A/2B/2C/2D and logaritim trend of the ST early,d for the configuration 2A/2B/2C/2D depending on the distance Figure 4.6 Model of configuration 1B

3 Figure 4.7 Models of the configurations 1A/1B/1C and logaritim trend of the ST early,d for the configurations 1A/1B/1C depending on the distance Figure 4.8 Model of the configuration Figure 4.9 Models of the configurations 0 and 0-fan shape and logaritim trend of the ST early,d for the configurations 0 and 0-fan shape depending on the distance Figure 4.10 Model of configuration 0-empty stage Figure 4.11 ST early,d depending on the distance for every source position for the configuration 0 and 0-empty stage and the source-receiver positions for the first stage design Figure 4.12 Models of configuration 0-rectangular shape Figure 4.13 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 2B, 3 and Figure 4.14 Model of configuration Figure 4.15 Model of configuration Figure Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 2B improvement 1, 2B improvement 2, 2B improvement 3 and 2B improvement Figure 4.17 Model of configuration 2B improvement Figure 4.18 Model of configuration 2B improvement Figure 4.19 Models of configuration 2B improvement Figure 4.20 Average results on the distance of the ST early,d for each source (S1- S5) and for the configuration 2B and 2B with scattering coefficient Figure 5.1 Source-receiver positions and the distances between each other Figure 5.2 Premilinary configuration theoretical study with violin and viola positions Figure 5.3 Different positions of reflective surface for the couple violin- viola: 19 m behind the source, 0.34 m behind the source, 3 m behind the source and 11 m distance from the line source-receiver Figure 5.4 Number of surfaces and elipses used to find the correct position of the reflective surfaces. In order the couples are Violin-Cello, Violin-Woodwind, Violin-Brass and Violin- Percussion and vice versa Figure 5.5 Configuration 0: union of all the surfaces from the study of every instruments couple Figure 5.6 Average results on the distance of the ST early,d for each source (S1- S5) and for the separated configurations and the configuration 1, 2, 3, 4 and Figure 5.7 Model configuration Figure 5.8 Model of configuration Figure 5.9 Model of the configuration Figure 5.10 Model of the configuration Figure 5.11 Directivity in plan at 1000 Hz of the violin, the cello, the oboe, the trombone and the timpani, and direction of the sources in plan Figure 5.12 Reflections intensity from violin to trombone and viceversa considering the directivity Figure 5.13 Ellipses for each couple of instruments Figure 5.14 Model of configuration

4 Figure 5.15 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 1 and Figure 5.16 Model of configuration Figure 5.17 Model of configuration Figure 11.1 Model of the configuration 2A and ST early,d depending on the distance for every source position for the same configuration Figure 11.2 Model of the configuration 2B and ST early,d depending on the distance for every source position for the same configuration Figure 11.3 Model of the configuration 2C and ST early,d depending on the distance for every source position for the same configuration Figure 11.4 Model of the configuration 2D and ST early,d depending on the distance for every source position for the same configuration Figure 11.5 Model of the configuration 1A and ST early,d depending on the distance for every source position for the same configuration Figure 11.6 Model of the configuration 1B and ST early,d depending on the distance for every source position for the same configuration Figure 11.7 Model of the configuration 1C and ST early,d depending on the distance for every source position for the same configuration Figure 11.8 Model of the configuration 0 and ST early,d depending on the distance for every source position for the same configuration Figure 11.9 Model of the configuration 0- fan shape and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 0- empty stage and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 0- rectangular stage and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 3 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 4 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 2B improvement 1 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 2B improvement 2 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 2B improvement 3 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 2B improvement 4 and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 1 (first adjustment) and ST early,d depending on the distance for every source position for the same configuration Figure Model of the configuration 2 (second adjustment) and ST early,d depending on the distance for every source position for the same configuration

5 Tables Table 3.1 Objective data different concert halls Table 5.1 ST early,d of different configurations of the couple violin- viola Table 5.2 ST early,d reached, number of surfaces used and number of ellipses used for every case studied Table 10.1 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design Table 10.2 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design (configuration 2B improvement 2)

6 Chapter 1 Introduction Concerns about acoustics have become a central issue in the design of concert halls, opera houses, theatres and other venues for performing arts. The audience should be allowed to appreciate the concert and be surrounded by the sound. Musicians in a symphony orchestra rely on the direct and reflected sound in a concert hall stage to be able to hear their own instrument, others instruments and the acoustic response of the hall. Studies undertaken by many researchers have investigated the aspects of improving acoustic conditions for audiences as well as for musicians. Gade (1989) proposed the first dedicated stage acoustic measures, the ST support (ST early and ST late), to understand the acoustic conditions for the performers [1,2]. A few years later, Beranek (1992) interviewed 23 musicians about their evaluation of existing concert halls around the world and found positive results both for performers and audience when reflectors were applied above the orchestra within certain limits of dimensions [3]. In addition, Meyer (2004) found other conditions that could be favorable for the conductor (of a symphonic orchestra); examples are walls at the side of the stage and large volume in front of the conductor [4]. More recently, Dammerud has contested the results of Beranek and Meyer by finding that reflectors above the orchestra should be avoided; however, reflectors could be arranged in lateral positions towards musicians [5]. Moreover, from a design point of view, Barron has found some practical requirements for the stage design, such as dimensions and shapes of stages and audience, positions of reflectors and materials of walls and risers, to improve the acoustics for both the performers and the audience [6]. However, research on stage acoustics has shown that one problem remains: architectural choices for the design of stages may not always be in agreement with acoustics requirements. These two aspects are straightly correlated to each other, and the research is still in process. ST early is an acoustics parameter, formulated by Gade and included into the ISO standard, that describes subjective impressions of stage acoustics by performers [7]. More recent studies, conducted by Wenmaekers, Hak and van Luxemburg, show that this parameter is affected by the delay of direct sound by increased distance; as a result, it depends on the source-receiver distance on the stage and it is called ST early,d [1,8]. This parameter defines the assistance of early reflections for the ensemble playing of the orchestra and depends on the 6

7 geometric characteristics of the stage; therefore, it could provide informations on how the stage design influences the acoustic quality of the room for the performers. The goal of this master s thesis is to find possible solutions for design of concert hall stages with different dimensions, materials and designs by optimizing their physical descriptor ST early,d and to attempt to understand how to connect uncommon designs for a stage, even when they are architecturally troublesome for the audience, with the acoustic quality best suited for musicians. 7

8 Chapter 2 Background of the study Introduction The review of the literature on stage acoustics for symphony orchestras in concert halls can be splitted in two sections. The first section discusses the objective parameters of the stage compared to the subjective impression and request of the orchestra members. The second section describes the geometrical and architectural stage characteristics of different existing concert halls useful to the design of one of them. 8

9 Subjective impression and acoustic problems denounced by musicians The most important acoustical aspects for performers are the hearing of their own instrument, the hearing of others instruments and the hearing of the acoustic response of the hall. To successfully accomplish this goal, musicians rely on the direct and reflected sound. The reflected sound considers the early reflections as well as the late reflections. The early reflections are associated with the musicians and the stage. The late reflections are related to the audience and to the overall concert hall. The orchestra needs the early reflections because they contribute to raise the usefull sound pressure level for players on stage. The sound pressure level, in fact, is attenuated by the orchestra itself, masked by the sound power level of other instruments and influenced by the different positions of the instrument sections on the stage [9]. Musicians create attenuation of sound when they are on stage. This attenuation is more evident at higher frequencies and in particular above 500 Hz, and it might reduce the ensemble condition for the musicians and the acoustic quality of the concert hall. Meyer, focusing his studies in the directivity and the sound pressure level of every instuments, has found that the brass instruments are 10 db louder than the string instruments and 5 db louder than the woodwinds. [4]. This confirms what Gade has observed in his research: the strings struggle to hear the other strings players at the opposite side of the stage and their own instrument and they complain about the loudness of the percussion and brass [10]. The separated positions of the different instruments on stage also generate some problems. Usually, there are three different layouts determing the position of the players: the European way, the American way and the Fürtwangler way (see Appendix A for more details). By choosing one of these configurations any stereophonic effect can be avoided and high and low frequencies can be balanced. In addition, the issue of raising the sound level is related to the size of the stage and, in particular, to the width and the depth. If the width is larger compared to the depth, the string section on the flat floor can have difficulty in hearing each other on the two side of the stage and this can raise the audibility of the percussion and brass (which is not always beneficial) [9]. Consequently, compensating reflections are needed to improve the acoustic condition for musicians. The compensating reflections are reflections that can compensate for low withinorchestra level. Usually, they are created by adding reflective surfaces in/above/around the stage and, in particular, by adding stage enclosure for musicians. However, these stage enclosures are not always beneficial for string sections because they can also raise the level of percussion and brass, and, as a result, mask the string sound. In such cases, the reflections are 9

10 competing reflections and they affect negatively on the audibility of musicians that are distant from each other, on stage [5]. Installing risers is likely to raise the orchestra levels. Therefore, the need of compensating reflections depends on the presence or the absence of risers. Although the presence of the risers decrease the string-brass/percussion comunication, it can improve the visibility of the conductor for the brass/percussion players and can decrease the probability of masking the sound by the brasses/percussions particularly at higher frequency, when the brasses and percussions are more omnidirectional sources. The most effective surface for providing early reflection is the ceiling. According to Barron, the optimum height of the ceiling to reach this goal should be 6-8 m from the stage floor, considering it as reflector [6]. Moreover, to avoid the problem of loudness produced by percussion and brass sections, the ceiling should be designed in a proper way. Meyer has found an equation aiming to understand the minimum height of the ceiling in order to not create excessive levels at the front of the stage. h mmmmmm = 0.5 (dd tan αα + h rr + h tt + h ee ) Where d = floor distance between the trumpet and the string player; α = angle between the horizontal direction and -6 db direction upwards that defines the main radiation sector of the trumpet directivity at 1.5 khz (according to Meyer, α= 55 ); hr = height above the stage floor of the trumpet riser; ht = height of the trumpet above the riser; he = height of the string ear above stage floor [4]. Another issue that can be analysed on a stage is the parallel effect. This effect occurs in rectangular-shaped stage, where there is an angle of 90 between the back wall and the side walls of the stage. Figure 2.1 illustrates the problem generated in such occasions and provides a solution. Figure 2.1 Wall reflections from trumpet at 1.5 khz with perpendicular walls and side splayed walls. Trumpet directivity from [4]. Images from [9]. 10

11 As can be seen, if the sound comes from the percussion or brass section, the wall creates a reflection that returns to the same place from where it comes from and a reflection to the front of the stage. This means that the percussions or brasses level increases and the competing reflections rises. A possible solution consists of using splayed side walls or absorbing walls that can direct the reflection away from the percussion and can reduce the competing reflections. Musicians, in particular the strings, struggle to hear double basses during the ensemble playing. This occurs because the mid-frequency of the double basses are masked by other instruments. Considering the fact that double basses are extremely important instruments in the orchestra for the rhythim and the temporal cues, a solution to the problem should be provided: a hard reflecting surface close to the double basses will generate a reflection in phase with the direct sound at low frequencies that will theoretically raise the level of 6 db [9]. Stage acoustics The general subjective impressions and problems denounced by musicians can be examined using different objective stage parameters theoretically described in this section. Impulse response The acoustic behaviour in a hall can be investigated by the measurements that produce a room impulse response (RIR). The RIR is the response of the room to an impulse source, such as a gun-shot, an explosion of a balloon and, most frequently, a known special signal (MLS, Linsweep and E-sweep), that provide the amount of sound reflections arriving to a certain receiver position. In fact, the RIR changes depending on the source-receiver positions, since the distances from the surfaces of the hall varies between different positions in the space. A RIR can be presented in different ways (function of time and pressure, squared pressure, 10log (p^2(t)) and backwards integrated), and, hence, it is possible to obtain the so-called reflectogram, shown in Figure 2.2. Figure 2.2 Reflectogram 11

12 Figure 2.2 shows the three main parts of the reflectogram: the direct sound, the early reflections and the late reflections (reverberant sound). As can be observed, the direct sound is the first sound that arrives at the receiver travelling via the shortest path between source and receiver. After the direct sound, the early reflected sound arrives within 100 ms (value limited for stage acoustics) after the production of the sound from the source, bouncing into the closest reflected surfaces. It has a lower intensity than the direct sound as a consequence of the absorptive capabilities of the surfaces and of the sound travels via longer paths. When the sound wave is reflected by numerous surfaces before arriving at the receiver position and it is blended with other reflections, it forms the reverberant sound of the hall. The late reflections arrive later than 100 ms after the production of the sound from the source. Different parameters can be derived from RIRs, such as reverberation time (RT), early decay time (EDT), sound strenght (G) and clarity (C80), but the most important parameters for this study are the Stage Parameters (ST early and ST late) and the Early Ensemble Level (EEL). Support parameters and Early Ensemble Level (EEL) The first dedicated stage acoustic measures are used to describe acoustic conditions on stage. These parameters are proposed by Gade and they are based on field and laboratory experiments and are typically derived from impulse responses; in total they are: Early Support (ST early), which assesses the ensemble conditions, Late Support (ST late), which assesses the impression of reverberation, ST 2 or ST total, which assesses support from the room and from the musician s own instrument, Clarity Stage (CS) and Early Ensemble Level (EEL) [11,12]. ST early and ST late are the two most important and valid parameters used to discuss particular acoustic characteristics of stages and they are included in the ISO standard [7]. The ST early measures the amount of early reflections that assist musicians in hearing their own instrument objectively. It measures the difference between the reflected sound level within the ms time interval after the arrival of the direct sound and the sound level of the direct sound and floor reflection, measured in the time interval 0 10 ms of the RIR. This ratio is measured with a microphone placed only 1 m from the source at 1 m height. This parameter depends on the geometrical and material properties of the stage. It is defined as: SSSS eeeeeeeeee = 100mmmm pp2 (tt) dddd pp 2 (tt) dddd 0 [dddd] The ST late describes the perception of reverberance. It measures the difference between the reflected sound level in the time interval ms after the arrival of direct sound and the sound level of the direct sound plus floor reflection, measured in the time interval 0 10 ms of the RIR. This ratio is measured with a microphone placed at only one meter from the source. It is defined as: 12

13 SSSS llllllll = 1000mmmm pp2 (tt) dddd pp 2 (tt) dddd 0 [dddd] Recently, Wenmaekers et al. proposed to modify and extend the commonly used ST parameters considering the dependence of the parameter from the source-receiver (S-R) distance [8]. This modification is determinated by the growing interest in measuring stage acoustic parameters at various source-receiver distances, by the ease to understand the influence of architectural, geometrical aspects in the overall acoustics of the stage and by the possibility to understand the contribution of early reflection to the ensemble playing. Moreover, the delay, which is the S-R distance divided by the speed of sound, is indicated in the time interval. These parameters are denoted as ST early,d and ST late,d and are defined as: SSSS eeeeeeeeee,dd = 103 dddddddddd pp dd 2 (tt) dddd pp 1mm2 (tt) dddd 0 [dddd] SSSS llllllll,dd = 103 dddddddddd 10 0 pp dd 2 (tt) dddd pp 1mm2 (tt) dddd [dddd] Where pd is the sound pressure measured at distance d; p1m is the sound pressure measured at 1 m distance in free field (derived from lab measurements); and delay is the S-R distance divided by the speed of sound. The Early Ensemble Level (EEL) parameters describe the ease to hear the other members of the orchestra. It consists of a measurement of the difference between the early energy within the time interval 0-80 ms after the arrival of the direct sound and the sound level of the direct sound and floor reflection, measured in the time interval 0 10 ms of the RIR. EEEEEE = 80mmmm pp dd 2 (tt) dddd 0 10mmmm pp 1mm2 (tt) dddd [dddd] 0 However, the objective parameters that characterize a stage are only the STsupports and the EEL. According to Gade, comparison between the parameters and subjective parameters obtained thorugh listening tests showed that ST early seems to explain better the easy of ensemble or the hearing of others than the EEL, which was initially supposed to be used for this purpose [11]. Consequently, the EEL was no longer used to describe a stage and was not added to the ISO standard [7]. 13

14 Summary of design goals Examinating this first section of the background, some guidelines/goals, such as shape, size, layout and ST early,d values, can be summarized. Considering the shape of the stage, a trapezium shape, oriented toward audience, is preferred to the rectangular one; it provides an improved reflecting environment for the sound (avoiding the parallel effect), a more confortable space for the musicians and a better view fom the conductor and the audience. The width of the stage should be equal to the depth for a maximum of 15 m in order to integrate the sound from the different orchestra sections, mostly the string section, and create good ensemble conditions. Narrow and high stages are preferred to wide and low ones. To improve the visibility for the conductor and increase the sound pressure level generated by the orchestra, the stage should be designed installing risers. The stage should be surrounded by enclosures in the string section only, because strings need support from reflecting surfaces, and not in the percussion and brass sections. In particular, to improve the low frequency enhancement of double basses, they should be positioned close to a hard reflective surface. The position of the different sections of the instruments should be considered in the design of the stage because it defines the enclosures and reflectors positions in the stage and the size of the stage. Based on the directivity and on the sound pressure level of the different instruments, the optimal values for ST early,d parameter are -11/-14 db for string section, since it is composed by the lowest instruments in the overall orchestra that need more support, -14/-16 db for the woodwind section, since it is, in terms of SPL, 5 db louder than violins and 5 db lower than percussion/brass sections, and -15/-18 db for brass and percussion sections, since they are the loudest sections in the orchestra (with an SPL 10 db higher than string one). 14

15 Chapter 3 Investigations of the stages of existing concert halls 3.1 Introduction The acoustic design of a stage is a complex aspect of the holistic design of a concert hall that requires high precision, since the musicians have the need to play in the best acoustic conditions. It requires the cooperation between architects, engineers and acousticiants, who might suggest always different and efficient ideas to reach the goal. Designing a stage requires to know, recognise and distinguish every single characteristic of the existing concert hall stages and understand them from an acoustical point of view. This Chapter analyses eight different concert hall stages for symphonic orchestras in order to comprehend the general characteristics, the common properties and the differences between all of them. The goal is to find features, guidelines for the design of concert hall stages. 15

16 3.2 Stage characteristics of eight concert halls Concertgebouw, Amsterdam (AMC) Figure 3.1 Concertgebouw stage, Amsterdam Hall configuration: Shoebox with curved corners Stage configuration: Curved shape Architects: Adolf L. van Gendt Acoustics design: Dolf van Gendt Stage area Wrs 1 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m T 30,unocc. = 2.6 s (500 Hz) [13,14] T 30occ. = 2.0 s (500 Hz) [13,14] ST early = db [13,14] Designed by Adolf L. van Gendt, the Grote Zaal of the Concertgebouw is rectangular and it has a shoebox configuration like the Grosser Musikvereinssaal in Vienna. The inner surfaces of the hall are in thick plaster and heavy wood with a deeply coffered ceiling about 15.8 m high above 1 Measures suggested by Dammerud and explained in Appendix B [9]. 16

17 the stage. The stage is wide and high and it presents a high (2.00 m), raked, wooden platform; the enormous width of the stage is not best suited for musicians because they might not hear the other musicians optimally. There are no walls closing the stage, but behind it there are seats that can be used by audience or choir. Reflectors above the stage are not needed, since the highly ornaments of the hall walls with deep fissures, statuary, organs, recessed windows, balconies help to create a diffuse sound. The risers are fixed and they create a curved shape where musicians can be positioned [13,14]. 17

18 3.2.2 Muziekgebouw, Eindhoven (EMG) Figure 3.2 Muziekgebouw stage, Eindhoven Hall configuration: Stretched octagon Stage configuration: Pentagon fan-shape Architects: R.J. van Aken, L.L.J de Bever, C. van der Ven Acoustics design: TU/e, TNO Stage area Wrs 2 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m T 30,unocc.= 2.0 s (500 Hz) [17] T 30occ.= unknown ST early = db [17] The stage of the Muziekgebouw Eindhoven presents a pentagon fan-shape with an area of 225 m2; this configuration allows an optimal disposition of the musicians (around 80) and creates a better scattering of the sound because of the walls angled differently. The back and side walls around the stage follow this shape; they are covered in wood with a percentage of QRD diffusers that should create a scattered sound. The white part above the wood walls around 2 Measures suggested by Dammerud and explained in Appendix B [9]. 18

19 the stage is a reflector made of painted gypsum board that produce early reflections through the stage, beneficial for the musicians. Moreover, reflector panels are also positioned at 9.2 m above the stage to reach this goal. The wood-covered stage floor is 1.20 m high and is flat with a riser for the percussion, brass and woodwind musicians [17]. 19

20 3.2.3 Bridgewater Hall, Manchester (MAB) Figure 3.3 Bridgewater Hall stage, Manchester Hall configuration: Parallel side Stage configuration: Elongated hexagon shape Architects: Renton Howard Wood Levin (RHWL) architects Acoustics design: Arup Acoustics Stage area Wrs 3 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m ?? various T 30,unocc. = 2.4 s (500 Hz) [15] T 30occ. = 2 s (500 Hz) [15] ST early = unknown Renton Howard Wood Levin (RHWL) architects designed the BridgeWater Hall in 1993 after a competition organized for Manchester architects. Many aspects in the design of the stage are in common with the Muziekgebouw of Eindhoven. The structure consists of solid, reinforced concrete, moulded and cast like a huge sculpture that compose also the back and side stage walls covered internally in Jura Limestone wood. These walls follow the elongated hexagon 3 Measures suggested by Dammerud and explained in Appendix B [9]. 20

21 shape of the stage and are covered by an upper band of wood as a not tilted reflector. The stage floor is 0.9 m high from the audience floor and it is covered in wood. The ceiling is 22.9 m high from the audience area and it is a double-skinned roof with a stainless steel outer shell where glass panels (convex down ward) are hung as reflectors [16]. 21

22 3.2.4 Großer Musikvereinsaal, Vienna (VIM) Figure 3.4 Großer Musikvereinsaal stage, Vienna Hall configuration: Shoebox Stage configuration: Rectangular shape Architects: Theophil Hansen Acoustics design: Theophil Hansen Stage area Wrs 4 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m T 30,unocc. = 3.3 s (500 Hz) [13] T 30occ. = 2 s (500 Hz) [13] ST early = db [13] The Grosse Saal der Gesellschaft der Musikfreunde in Vienna is the musicians most preferred concert hall. Its small shoebox configuration creates good acoustics conditions best suited for both musicians and the audience, according to Beranek [13]. The stage is a simple rectangular wooden platform, 1 m high from the audience floor. It is not surrounded by wooden walls, but just by some small wooden panel and by seats used by the listeners. The diffuse and scattered field is created thanks to the numerous irregular statues and surfaces, offset and indented 4 Measures suggested by Dammerud and explained in Appendix B [9]. 22

23 doors and windows, irregular balcony fronts, and chandeliers close to the stage; as a result, the stage does not need reflectors above and around the stage. The percentage of wood used is less than 15% and it is used mostly for doors [13]. 23

24 3.2.5 Berlin Philharmonie, Berlin (BEP) Figure 3.5 Berlin Philharmonie stage, Berlin Hall configuration: Vineyard terraced Stage configuration: Complex shape Architects: Hans Scharoun Acoustics design: Hans Scharoun Stage area Wrs 5 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m T 30,unocc.= 2.2 s (500 Hz) [1,10] T 30occ.= 1.9 s (500 Hz) [15] ST early = db The innovative configuration of the Philharmonie concert hall in Berlin is called vineyard terraced because the seating that surround the stage are risen up in serried rows as the sloping terraces of a vineyard. The stage, which is located at the centre of the hall, presents a complex shape formed by protruding terraces. It is possible to divide the stage into two parts: the front part resembles a simple fan-shape with back walls and front of the terraced blocks as tilted reflectors; the back part is connected to the first one in the centre and hosts the choir. 5 Measures suggested by Dammerud and explained in Appendix B [9]. 24

25 Additional early reflections are provided to the orchestra by ten large trapezoidal suspended panels in polyester, spaced the 50% of their surface apart from each other. Combination of sound diffusing and reflecting is provided by 136 pyramidal-shaped, low frequency Helmholtz resonator type absorbing units, positioned in a convex and tented shape ceiling in order to provide early reflections. Both the stage floor, on planks over airspace as common in concert hall stages, and risers are made of wood. The organ was designed along with the concert hall by the architect Hans Scharoun and it is not centred behind the stage, but it stays on his right side [8,10]. 25

26 3.2.6 Walt Disney Concert Hall, Los Angeles (LWD) Figure 3.6 Walt Disney Concert Hall stage, Los Angeles Hall configuration: Vineyard layout Stage configuration: Vineyard style; convex back and lateral surfaces Architects: Frank Gehry Acoustics design: Yasuhisa Toyota and Nagata Acoustics, Inc., Charles M. Salter Associates, Inc. Stage area Wrs 6 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m unknown unknown 2325 T 30,unocc.= 2.2 s (500 Hz) [18] T 30occ.= 2.0 s (500 Hz) [18] ST early = db [18] The Walt Disney Concert Hall was designed principally from an acoustic point of view. The acoustics of the hall needs surfaces that can provide early reflections to the orchestra and the audience. These surfaces are created according to the vineyard layout and to the layout of the stage. The stage, in fact, is surrounded by concave surfaces on the back and convex surfaces on 6 Measures suggested by Dammerud and explained in Appendix B [9]. 26

27 both sides. In addition, the height of the ceiling was determined by the need for extended reverberation, therefore it becomes a reflector itself. The interior material consists principally of wood used for walls and floor covering the concrete. The stage floor is in Alaskan yellow cedar wood but, under it, there is airspace that allows the floor to vibrate and resonate in conjunction with the cavity underneath. It has a 50-foot-high organ weighing more than 40 metric tons with 6,134 pipes, only two percent of which are visible. The stage has 13 elevators [18]. 27

28 3.2.7 Symphony Philharmonie, Paris (PSP) Figure 3.7 Symphony Philharmonie stage, Paris Hall configuration: Union of vinejard style and shoebox style Stage configuration: Trapezium fan shape Architects: Jean Nouvel Acoustics design: Harold Marshall Stage area Wrs 7 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m 3 19 unknown unknown unknown 14 unknown 283 unknown T 30,unocc.= 3.1 s (500Hz) T 30occ.= 2.6 s (500Hz) ST early = unknown The Symphony Philharmonie in Paris was designed by Jean Nouvel according to a new typology of hall. This typology consists of a combination of the vinegard style that can be observes in the Berlin Philarmonie and the shoebox of the Vienna Musikvereinsaal. The shape given to the stage is a simple trapezium surrounded by tilted wooden walls. The stage is 1 m higher than the audience floor and is a flat wooden platform. Risers go up from the floor creating an 7 Measures suggested by Dammerud and explained in Appendix B [9]. 28

29 optimal disposition for musicians. The acoustic is enhanced by floating clouds, wooden acoustic reflectors that control the sound in the space. The ingenious solution allows the creation of a large volume of space for the sound to resonate [19,20]. 29

30 3.2.8 Casa da Musica, Oporto (OCM) Figure 3.8 Casa da Musica stage, Oporto Hall configuration: Shoebox with transparent rear and back wall Stage configuration: Rectangular shape Architects: OMA-Rem Koolhaas Acoustics design: TNO Eindhoven and Dorsser Blesgraaf, Renz van Luxemburg, Theo Raijmakers Stage area Wrs 8 Hrb Prefl,area Ph,ceil Pdepth = D Pelev Parea Pvolume m m m 2 m m m m 2 m unknown unknown T 20,unocc.= 2.3 s (500Hz) T 30occ.= 1.7 s (500Hz) ST early = db The Sala Suggia of the Casa da Musica de Oporto has a suitable acoustics thanks to its innovative acoustic design. The stage is a simple rectangular shape surrounded by walls on its right and left side and by the choir balcony located at the back. The wooden platform is 1 m high from the audience floor. The side walls of the stage are made of wood and include the QRdiffuser that create a diffuse sound for musicians. There are no risers. Moreover, it is 8 Measures suggested by Dammerud and explained in Appendix B [9]. 30

31 important to mention the presence of an enormous reflector positioned at 9m above the stage floor and made of plastic cashion; it contributes to create early reflections which are beneficial to the orchestra having, consequently, a higher ST early compared to the other concert hall [21]. 31

32 3.3 Comparison According to Dammerud, the acoustics of stages can be described through some objective measures that characterize its geometry, such as W rs, H rb, and D (see Appendix B for more details), and through some other elements such as shape, side and back walls, presence of reflectors, risers and materials [9]. Within the concert halls previously investigated, it is possible to observe some common aspects and some differences. The first feature in common is the fan-shape layout of the stage; it is always opened to the audience to allow the visibility of the scene and it is surrounded by walls on both sides. Pentagon fan-shape Elongated hexagon shape Complex shape Rectangular shape 32

33 Complex shape Concave back and convex lateral surfaces Trapezium fan shape Rectangular shape Figure 3.9 Different shape of several concert halls: Muziekgebouw of Eindhoven, Manchester BridgeWater, Concertgebouw of Amsterdam, Vienna Großer Musikvereinsaal, Berlin Philharmonie, Walt Disney concert hall, Paris Symphony Philharmonie and Casa da Musica of Oporto. Figure 3.9 shows the multiple shapes of stages investigated. As can be seen, just the Vienna Großer Musikvereinsaal, the Concertgebouw of Amsterdam and the Casa da Musica of Oporto have a clear rectangular shape, given by the position of the stage in one side of the shoe-box hall. Manchester BridgeWater Hall, Berlin Philharmonie, the Muziekgebouw in Eindhoven and the Symphony Philharmonie in Paris stages have complex shapes due to the position of the stage at the centre of the concert hall and due to the position of the walls surrounding them. In fact, walls are commonly split into multiple parts in order to generate extra reflections of the sound, to avoid the parallel effect explained in Chapter 1 (Section 1.3) and contribute to improve the acoustics for musicians. A special case is the Walt Disney concert hall in Los Angeles in which walls surrounding the stage are concave and convex surfaces that contribute, in addition, to increase the number of early reflections reaching the audience. Table 3.1 Objective data different concert halls W rs H rb P refl,area P h,ceil P depth=d P elev P area P volume 33

34 m m m 2 m m m m 2 m 3 EMG MAB unknown various AMC VIM BEP LWD unknown unknown 2325 PSP 19 unknown unknown unknown 14 unknown 283 unknown OCM 22 9 unknown unknown In addition, Table 3.1 shows the dimensions in terms of width and depth of the stages. Most of them have a width around m, even though Barron advises that the average width should not exceed 17 m to allow the audibility of the two sides of the string section [6]. The width of the Concertgebouw in Amsterdam is larger than the others (29 m) and that could create difficulties in the hearing of the sound by the musicians. The depth is nearly the same for every concert hall (9-10 m) except for the Symphony Philharmonie in Paris and the Manchester BridgeWater concert hall. In fact, in Manchester the depth is 14.5 m, and, as a result, with a width of 23.0 m, it has a stage area of 276 m2. Compared to the other concert halls, which have an area of about m2 (appropriate for 100-piece orchestra), the value of 276 m2 is considerably high and it can constitute a problem for those instruments that are at a large distance from each other and it can affect the effectiveness of reflections. The volumes of these stages are dissimilar as a consequence of the influence of the position of the reflectors (or the ceiling if there are not reflectors) above the platform. According to Barron, reflectors should be placed at 6-8 m, in order to create more early reflections which are beneficial for the orchestra [6]. Generally, the investigated concert halls do not follow this recommendation, adding 5-6 m to the height of the reflectors. Reflectors are not always placed in the concert hall, and sometimes irregularities of the ceiling surfaces, or the presence of balconies can replace them creating a reflecting field and, consequently, a respectable acoustics best suited by musicians; good examples are the Vienna Großer Musikvereinsaal, the Concertgebouw of Amsterdam and the newest Walt Disney concert hall in Los Angeles, where reflectors are not placed because of the low height of the ceiling that it could be considered as an ineffective reflector it-self, since is too high from the stage platform. Reflectors differ in shapes, in numbers, in areas and in materials depending on the concert hall. In the Muziegebouw in Eindhoven, there are only two rectangular reflectors placed above the two sides of the string sections with an area of 13 m 2 each. They contribute to increase the reflections from one side to the other of the string section thanks also to the material they are made of: painted gypsum. In the Manchester BridgeWater Hall, there are ten reflectors which consists of glass panels with a convex down-ward shape, placed in the centre and in the side above the string section to compensate to the lack of reflections caused by the relatively large stage area. In the Berlin Philharmonie, the positions of the reflectors resembles those of the BridgeWater Hall in Manchester, however the shape and the material are 34

35 different. They are ten large trapezoidal suspended panels in polyester (7.5 m 2 each), spaced the 50% of their surface apart from each other. In the Symphony Philharmonie in Paris there are three reflectors, that are placed at the centre of the stage and that have a particular curved shape in order to create all together a circle shape in the ceiling. Instead, in the Casa da Musica of Oporto the reflector is only one, it is positioned at 9m high from the stage floor and it consists of a rectangular shape made of plastic cashion recapturing the rectangular shape of the stage. Frequently, reflectors are also arranged above the walls around the stage and tilted of nearly 10 as it can be observed in the Manchester BridgeWater Hall, Berlin Philharmonie and the Muziegebouw in Eindhoven, and they are made of concrete, wood or gypsum. In order to contribute to the visibility of the orchestra, the stage should be higher towards the audience floor. According to Barron, the minimum value of the stage height is 0.5 m, however these values usually vary from a minimum of 1 m to a maximum of 2 m, as in the Concertgebouw of Amsterdam in which this value was imposed by architectural structural choices [5,10]. On the stage, risers are elements used to raise the direct sound level and to improve the sightlines for the performers as well as for the audience. Usually, risers only cover the rear part of the stage only (for the woodwind, brass and percussion sections) as it happens in the Muziegebouw in Eindhoven, or they have a semi-circular pattern, where woodwind, brass and percussion as well as the upper string are located, as it can be noticed in the Berlin Philharmonie and the Symphony Philharmonie in Paris. Figure 3.10 shows the layout for these two types of risers systems. Risers at the back of the stage Semi-circular riser system Figure 3.10 Common stage risers types. Image from [9]. The acoustics of a stage is also determined by the materials of every object in the stage and, consequently, by their amount of absorption of them. Musicians preferred material is wood, firstly because it is associated with warmth and resonance that make the stage more comfortable, secondly because of its acoustics properties. In fact, wood is a reflecting material and produces early reflected sound helpful for the orchestra. For this reason, walls around the orchestra are usually made of wood. Even though wood is desirable for the musicians, other materials can be used to achieve this purpose. The Vienna Großer Musikvereinsaal, the Concertgebouw of Amsterdam reach the goal using other materials such as gold and marble 35

36 present in numerous irregular statues, surfaces, windows and balcony fronts. In fact, the percentage of wood used is less than 15% and it is used mostly for doors. The T 30 for most of the concert hall is 2 s with the overall concert hall occupied. The ST early varies depending on the size of the stage area and volume. Even though the recommended value by Gade is -14, most of them have a ST early value equal to -17 generally because the stage area is vast [22]. However, in the Vienna Großer Musikvereinsaal and in the Casa da Musica of Oporto the ST early is higher (-14 and -11 db) and this can be explained by the presence of the low ceiling in Vienna Großer Musikvereinsaal and the low reflector in the Casa da Musica of Oporto. This description illustrates the architectural common characteristics of these stages and shows objective data. However, to judge the effective acoustics properties of a stage, this description is not sufficient because subjective data of the overall concert halls are needed. 3.4 Architectural guidelines Based on this concert hall stages description, some architectural guidelines can be summarized: The shape of the stage is usually a fan shape opened to the audience and surrounded by stage enclosures differently for each concert hall stage. Usually, the width of the stage varies between 19 and 23 m, even though it is advised 17 m by Barron [6]; The depth of the stage varies between 9 and 12 m; The height of the ceiling varies, mostly, between 15 and 18 m, and occasionally it is used as reflectors itself, even though it seems to be extremely high, according to the literature; When the reflectors are places, their height vary between 9 and 10 m from the stage floor with some exceptions. Mostly, the reflectors are placed above the stage, since they help considerably musicians and in particular strings; The installation of the risers is common in every concert hall stages: at least one riser at the back of the stage; Stage enclosures and panels on the stage are usually made of wood. The stage area varies between 160 and 280 m 2, even though the advised for a full-100 piece orchestra is 200 m 2 ; The height of the stage platform is mostly 1 m. Commonly, the material stage platform is on planks over airspace; The T 30 for most of the concert hall is 2 s with the overall concert hall occupied The ST early varies between -16 db and -18 db, lower compared to the value advised by the literature. 36

37 Chapter 4 First stage design 4.1 Introduction Based on the design goals defined in Chapter 1 and based on the architectural guidelines defined in Chapter 2, a first idea of stage design is proposed in this Chapter. This Chapter analyses the changes in terms of ST early,d when the stage varies its geometry, its materials and its elements. The goal is to optimize the ST early,d parameter values in order to avoid the main problem denounced by the musicians: the loudness of the percussion/brass section for the string section. 37

38 4.2 Method The approach used in this study consists of three steps: designing the stage, modelling the stage and simulating the stage. The design of the stage is based on the literature studies, on musicians requests, on musicians communication problems and on the stage design of existing concert halls. It is designed from a musicians point of view without taking into account the audience. The design includes the definition of a plan and sections using the software Autodesk AutoCAD 2016 and the description of architectural and acoustics details. Considering just the inner surfaces of the stage only, it is modeled using the software SketchUp 2016 in order to create a 3D model. The stage is delimited by surfaces that make sure that, in the simulating fase, no rays are lost. The simulation of the stage is studied using the software ODEON Combined in which it is necessary to set source-receiver positions, materials, room properties and parameters definitions and to perform a Job to obtain the RIR and parameter results. Positions The source-receiver positions are set as in Figure 4.1. Figure 4.1. Source and receiver positions and height of sources and receivers 38

39 These source-receiver positions are the same as used by Gade for his studies, however Source 4 (S4), Source 5 (S5) and Receiver 7 (R7) are added as a consequence of the need to understand the acoustic behaviour in the rear part of the stage [23]. The sources are omnidirectional and the receivers are omnidirectional. Certain receivers are positioned 1 m in front of the sources in order to calculate the ST early. The sources and the receivers are located 1 m above the floor where they are positioned (as it can be seen in Figure 4.1). The material selection is based on the material list found in ODEON and on the musicians needs. Parameter calculation ODEON does not have the definition of some parameters as the ST early,d. As explained in Section 2.3, It measures the difference between the reflected sound level within the 10-(103-delay) ms time interval after the arrival of the direct sound and the sound level of the direct sound and floor reflection, measured in the time interval 0 10 ms of the RIR. Therefore, the definition of the parameter ST early,d is added to the list of parameters as described below: SSSS eeeeeeeeee,dd = 10 log(ee OOOOOOOO10103 ) without removing in the time interval the delay and without considering the reference level. ODEON considers the emission of the sound as the starting point for the calculation of the parameters. Instead, the definition of the parameter ST early,d considers as the starting point 10 ms after the arrival of the sound to the receiver. So, if the ST early,d defined in ODEON is referred to the emission of the sound, the time interval becomes (10+delay)-(103+delay). However, the need of the study is to calculate the real ST early,d; consequently, the delay should be removed from the calculation. To accomplish the goal, the impulse response length should be set to 103 ms. In this way, ODEON cuts the impulse response length at 103 ms and removes the delay from the results. Accordingly, all the other parameters, which ODEON provides as results, are not valid because a larger impulse response length and the overall concert hall are needed for them. In order to remove from the formula of the ST early,d the reference level, this pp 1mm (tt)dddd must be 1. To reach a p 1m=1, the Sound Pressure Level (SPL) at 1 m distance must be 0. So, LL pp(dddddd,1mm) = 0, but it is possible also to calculate LL pp(dddddd,1mm) with the following formula: LL pp(dddddd,1mm) = LL ww 11 Since LL pp(dddddd,1mm) must be 0, the LL ww = 11. Consequently, LL ww = 11 = GGGGGGGG. To obtain more accurate results, the number of late rays is set as For the impulse response details, ODEON is set with the following default settings: 39

40 Max. reflection order 2000 (ODEON will stop after 103 ms anyway) Impulse response resolution 3 ms Min. distance to walls 0.1 m For the early reflections, ODEON is set with the following default settings: Transition order 2 Number of early rays 2000 Number of early scatter rays (per image source) 100 In addition, ODEON is set also for the air conditions of the stage: Temperature: 20 C Relative Humidity: 50% Jobs At the end of the preparation of the file, ODEON requires the creation of Jobs. The Jobs allows the calculation of every parameter associated to the model. In one Multiple Job, the parameter are calculated considering just one source (from 1 to 5) and every receiver (from 1 to 7). In addition, ODEON also calculates parameters for Jobs composed just by one source and one receiver, because of the need to look at the reflectogram and, consequently, at the reflections created between the source and receiver considerated. Purpose To judge the acoustics of the stage, only the ST early,d parameter is needed from the extensive list of parameters that ODEON provides. The ST early,d values should vary from -11 to -18 db depending on the instruments to reach a respectable acoustics and many reflections on the stage. In particular, the ST early,d value for the precussion and brass sections should be lower than the ST early,d value for the string section. 4.3 Stage design The concept of the first stage design idea is shown in Figure 4.2, and it is the configuration 2B. The basic feature that characterize this new stage design is to use reflector panels or walls inside the stage. These reflectors are positioned in the middle of the stage, and they are the risers of the woodwind, brass and percussion sections (they are indicated in the picture with a bordeaux color). They could contribute to increase the amount of reflections on the stage, in particular for the string section, which always struggle to hear it-self as explained in Section

41 Figure 4.2 Concept first stage design Even though wide and low stages are common, as enlightened in Section 2.3, with the description of existing concert hall stages, the stage design is narrow and high, as recommendend by Dammerud, and is designed with a average width of around 15.3 m, a depth of 13.8 m and a height of 12 m [9]. The width of 15.3 m, compared with m of existing concert hall stages, is chosen based on the investigation of Dammerud in which musicians, expecially the strings, prefer a narrow and high stage than a wide and low one [9]. This could be explained by the fact that the string musicians are closer to each other and they can hear the strings better on the other side of the stage. To improve this communication between strings at the opposite part of the stage, angled front walls of 100 compared to the back wall are designed. The depth is just 2 m more than normal stage configurations; the purpose is to create more space between percussions/brasses and strings and, consequently, to try to avoid the masking of the string sound by the percussion/brass. Moreover, to avoid the problem of loudness produced by percussion and brass sections, the ceiling should be designed in a proper way. Using the equation of Meyer explained in Section 1.2, it is possible to calculate the minimum height of the ceiling in order to not create excessive levels at the front of the stage [4]. Considering the dimensions of the stage proposed, d = 9/10 m; α= 55 ; h r=1.30 m; h t=1m; h e=1m, the minimum height of the ceiling should be: h mmmmmm = 0.5 (dd tan αα + h rr + h tt + h ee ) = 0.5 (10 mm tan(55 ) mm + 1 mm + 1mm = 8.79 mm 9 mm In the stage design, a flat horizontal ceiling 12 m high is chosen. Even though the ceiling provides some reflections for the musicians, it is not considered as reflectors for the stage. In fact, as explained in Section 1.2, the height of the ceiling should not exceed 6-8 m to be considered as reflector for the stage [6]. The stage area varies from 210 m 2 to 180 m 2 depending on the configuration, appropriate for 100-piece orchestra. The shape of the stage is a pentagon shape with the back wall on stage not angled, side walls on stage angled of 40, that avoids the parallel effect as explained previously, and front walls on stage angled of 100. The risers are important because they allow the creation of the reflective surfaces inside the stage. They are designed considering the need of the clear 41

42 separation of the percussion/brass sections and string section and the need of visibility of the conductor. According to Barron, the distance in height between two musicians heads in two different risers should be at least 10 cm [6]. Moreover, the riser should be proportioned to the depth of the risers to allow the visibility of the conductor for each height. Consequently, they are designed as in Figure 4.3. Figure 4.3 Height and depth of risers for the visibility of the conductor Figure 4.3 shows the height and depth of risers that allow the visibility of the conductor for each musicians. As can be seen, each musicians, at 1 m height from every riser, can perfectly see the conductor. The first three risers have a depth of 1.3 m and mainly host woodwinds. The last riser has a depth of 2.6 m to host the percussion and brass instruments, which occupy a lot of space. The string section is always on the flat floor. Therefore, the height of the stage depends on these dimensions and they are 0.25 m, 0.55 m, 0.90 m and 1.30 m respectively. The enclosures of the stage are walls 2.2 m high with non-scattering surfaces. This height of the walls is preferred by the double basses in order to create more reflections near them and raise the level at low frequency. The reflective surfaces above the walls are added to reach the goal of more reflections in the string section; they are 1 m high and tilted of 10. The materials for each surface of the stage are showed in the Table C.1 of the Appendix C with the respectively absorbtion coefficients. Different materials are chosen for diverse elements of the stage. For the stage floor, it is used a material that includes the presence of the orchestra on the stage; for this reason, the absorbent coefficient is high. The risers are made of wood, hence they are reflective; they contribute to increase the amount of reflections inside the stage and to create a warm environment for the musicians. Different types of woods are chosen for the walls, depending on the considered configuration and the need of reflections in the stage. In the initial configurations, the walls-risers (reflective surfaces in the middle of the stage close to the string section) and the front walls are made of 25 mm of wood with air space (α=0.06 at 1000 Hz), and the back walls are 20% absorbent. In the final configurations, the walls-risers and the front walls are made of 22 mm of chipboard with 50 mm of cavity filled with mineral wool (α=0.05 at 1000 Hz), and the back walls are 30 % absorbent. The ceiling is permanently reflective and it is plasterboard on frame filled with mineral wool. Moreover, the stage is limited by surfaces with the material 100 % absorbent that allows ODEON to not lose rays during the simulations. Every surface has a transparent coefficient t = 0 and scattering coeffcient s = At the end, the layout of the orchestra is chosen. The Fürtwangler layout of the orchestra generates a balanced sound because of three reasons: the vicinity of the first and second 42

43 violins on the left side of the stage, the position of the cellos in front of the violas on the right side of the stage, and the position of the double basses near a wall. 4.4 Design steps and results The design of the stage described above (configuration 2B) is the first idea of design, and it arises from the review of the literature and from the existing concert hall stage designs. From this stage design, the study proceeds to investigate the variations in terms of ST early,d removing/adding/changing elements/features. At the end, the process leads to the final and acoustically most appropriate configuration Configurations from 2B to 0-rectangular shape This paragraph describes the process of the design from the configuration 2B to the configuration 0-rectangular shape. The process consists of removing elements/features to the initial configuration. The initial configuration is the 2B, which is described in detail in the previous Section 4.3. In the configuration 1B the reflectors above the walls are removed. In the configuration 0 the front walls are not angled compared to the horizontal back wall. In the configuration 0-empty stage the risers (and, consequently, the reflective surfaces close to the string section) are removed, maintaining just one risers in the rear part of the stage. Finally, in the configuration 0-rectangular shape, the shape of the stage is changed with a rectangular shape. 2B 1B 0 0-empty stage 0-rect. shape ST early,d (db) S1 percussion/brass S5 percussion/brass S4 woodwind S3 string S2 string S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 2B 1B 0 0- empty stage 0 rectangular Configurations shape Figure 4.4 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration from 2B to 0-rectangular shape

44 Figure 4.4 indicates the average results on the distance of the ST early,d for each source (Source 1-5) and for each configuration from 2B to 0-rectangular shape. The result of each source considers an average of the ST early,d value measured at each receiver. This is a rough average since the distances from sources and receivers are not the same and the average of the ST early,d is influenced by it. As described in the previous Section 4.2, the purpose is to reach a lower ST early,d value for the percussion/brass sections (represented by the average on the distances of the Sources S1 and S5), a medium ST early,d value for the woodwind section (represented by the average on the distances of the Source S4), and a higher ST early,d value for the string section (represented by the average on the distances of the Sources S2 and S3). The configuration 2B, already described above, appears in the graph. The results of the configuration 2B state the presence of a reflective environment in the string section as well as in the rear part of the stage where Source 1 (S1) and Source 5 (S5) are positioned. Even tough the average of ST early,d is appropriate (-13.3 db) for a stage, there is concentration of the reflections in the rear part of the stage. The first modification of the configuration 2B concerns the inclination of the reflective surfaces above the walls. The configurations 2A/2B/2C/2D considers the reflective surfaces above the walls (1 m high) with different inclinations. In the configuration 2A the reflectors above the walls are 5 tilted; in the configuration 2B the reflectors above the walls are 10 tilted; in the configuration 2C the reflectors above the walls are 15 tilted; in the configuration 2D the reflectors above the walls are 20 tilted. The different configurations are shown in the following Figure Configuration 2A Configuration 2B ST early,d (db) Log. (2A (5 )) Log. (2B (10 )) Log. (2C (15 )) Log. (2D (20 )) Configuration 2C Configuration 2D Distance (m) Figure 4.5 Models of configurations 2A/2B/2C/2D and logaritim trend of the ST early,d for the configuration 2A/2B/2C/2D depending on the distance Moreover, Figure 4.5 shows the logaritim trend of the ST early,d for the configuration 2A/2B/2C/2D depending on the distance. The difference between the configurations is noticeable. The ST early,d for the configuration 2A (5 ) is the lowest. Configurations 2B (10 ) and 2C (15 ) are comparable (almost equal). The results of the 2D (20 ), in which the ST early,d is lower than configuration 2B (10 ) and 2C (15 ), are somewhat unexpected; consequently, an 44

45 excessive inclination of the reflective surfaces above the walls does not have positive results in the stage. Because of the maximum effect of the reflectors above the walls, the configuration 2B is chosen. This configuration is compared with the configuration 1B showed in Figure 4.6, in which the reflective surfaces above the walls are removed. Figure 4.6 Model of configuration 1B As can be seen in Figure 4.4, the reduction of the ST early,d is constant for every source and at every distance, and it is at maximum 2.3 db. However, the ST early,d in the percussion/brass sections (Sources S1 and S5) decreases 0.2 db more than the ST early,d in the other sections of the orchestra. This difference is not appreciated by musicians because the value 0.2 db is too low compared to the Just Noticeable Difference 9 (JND) of most of the parameter [24]. Moreover, the ST early,d reduces at an average of db. Comparing configuration 2B and 1B, the results explains that the use of reflective surfaces above the walls behind the stage increases more the amount of reflections in the percussion/brass section. To create a closer environment for the string section, the effect of angling the front walls of the stage is investigated as in the previously described configuration 1B; in fact, the front walls are angled of 100 compared to the horizontal back wall. The issue is to understand which angle of the front wall is most suitable for the string instruments. The configuration 1A has a width of 16.0 m at the front and the front walls on stage are angled of 95 towards the back wall (5 towards the lateral straight direction); the configuration 1B has a width of 15.3 m at the front and the front walls on stage are angled of 100 (10 towards the lateral straight direction); the configuration 1C has a width of 14.4 m at the front and the front walls on stage are angled of 105 (15 towards the lateral straight direction). The models of these configuration are shown in Figure The Just Noticeable Difference (JND) is how much the value of the STsupport must change in order to notice a difference [?]. 45

46 ST early,d (db) Configuration 1A (5 ) Log. (1A (5 )) Log. (1B (10 )) Log. (1C (15 )) -14 Configuration 1B (10 ) Configuration 1 C (15 ) Distance (m) Figure 4.7 Models of the configurations 1A/1B/1C and logaritim trend of the ST early,d for the configurations 1A/1B/1C depending on the distance Figure 4.7 shows the models of the configurations 1A, 1B and 1C and the logaritim trend of the ST early,d for the same configurations. Comparing the three configurations, the difference in terms of ST early,d is small to acoustically appreciate the change. In fact, just 0.3 db of difference through the distance is relatively small compared to the JND. These results indicate that the inclination of the front walls is not important. The chosen configuration is the 1B (10 ) because it is an intermidiate situation between 1A (5 ) and 1C (15 ). Configuration 1A (5 ) is more suitable for the audience because the visibility is improved for them, and configuration 1C (15 ) is better for strings and woodwinds who have more reflections in their direction. In the configuration 0 the front walls are not angled compared to the horizontal back wall, as can be seen in Figure 4.8. Figure 4.8 Model of the configuration 0 46

47 According to the Figure 4.4, the ST early,d continues to decrease. The trends of the previous configuration are maintained, but the ST early,d is lower for every source. The ST early,d decreases of 0.8 db in the percussion/brass sections (Sources S1 and S5) and 0.5 db in the string section (Sources S2 and S3). Moreover, the ST early,d at the woodwind section (Source S4) decreases more compared to the other sources. Removing the inclination of the front walls reduces the average ST early,d, reduces the visibility from the string to the percussion/brass section, and reduces the amount of reflections and the sound pressure level. Considering that the most common aspect of the stage is usually the fan-shaped shape opened to the audience, its effect on the ST early,d values is investigated. In the configuration 0 - fan shape, the front walls are splayed of 10 towards the outside and opened to the audience, as shown in the Figure 4.9. STearly,d (db) -13 Log. (0) Configuration Log. (0-fan shape) Configuration 0 -fan shape Distance (m) Figure 4.9 Models of the configurations 0 and 0-fan shape and logaritim trend of the ST early,d for the configurations 0 and 0-fan shape depending on the distance As can be seen in Figure 4.9, the ST early,d of configuration 0 - fan shape is lower than the value for the configuration 0. At large distances the difference is more visible since most of the reflection are not in the stage anymore, but are directed into the audience. Consequently, the configuration 0 - fan shape is more suitable for the audience, and the best configuration for the musicians seems to be the configuration 0. By removing the risers of the configuration 0, the configuration converts in the configuration 0-empty stage in Figure Consequently, the initial main idea of reflective walls inside the stage close to the string and woodwinds sections is detached. 47

48 Figure 4.10 Model of configuration 0-empty stage Considering the Figure 4.4, the ST early,d increases mostly for the percussion/brass section (Sources S1 and S5) of 1.2 db. The ST early,d in the woodwind section (Source S4) decreases of 1.3 db. The separation between string section and percussion/brass sections in the configuration 0, thanks to the installation of the risers, is positive since it reduces the comunication between these two parts, and consequently, reduces the amount of reflections in the percussion/brass section. The following graphs explains the differences between the configuration 0 and 0-empty stage in more details (Figure 4.11). ST early,d (db) Distance (m) ST early, Log. (S1 percussion/brass) d (db) Log. (S5 percussion/brass) -11 Log. (S2 string) -12 Log. (S3 string) -13 Log. (S4 woodwind) Distance (m) Figure 4.11 ST early,d depending on the distance for every source position for the configuration 0 and 0-empty stage and the source-receiver positions for the first stage design. Figure 4.11 shows the results in terms of ST early,d depending on the distance for every source position for the two configurations 0 and 0-empty stage. As can be seen, the ST early,d in the configuration 0 - empty stage decreases mostly at small distances for every source position because of the fusion of the two parts of the stage. In the configuration 0 - empty stage, the trend of the ST early,d for the string section and in particular for the violin at the source position Source S2 is completely opposite since there are less reflective surfaces. At small distances the ST early,d for the string section (Source S3-cello) decreases. At large distances, the ST early,d for the percussion/brass sections (Source S1) increases compared to the configuration 0, deteriorating the communication between strings (since S1 and S5 should be higher than S2 and S3). 48

49 In the configuration 0, the peak of the ST early,d in the woodwind section (Source S4) at 1 m distance is noticeable. This can be explained by the fact that all the steps are reflective and are at the same height of the source. As a result, they contribute to increase the numbers of reflections. In addition, these reflections are doubled because of the symmetric plan and the symmetry of the risers. In general, the graphs maintain the same ST early,d at large distances. In conclusion, removing the risers create a double effect: one at small distances and one at large distances. At small distances, the ST early,d decreases and at large distances increases. Therefore, the overall ST early,d decreases with an average of db. The pentagon shape of the configuration 0-empty stage is designed trying to avoid the problem of the parallel effect and image shift, visible in the results of ST early,d of the configuration 0-rectangular shape (Figure 4.12). Figure 4.12 Models of configuration 0-rectangular shape In the Figure 4.4, in fact, the average of ST early,d for the configuration 0-rectangular shape considerably decreases. In addition, the S2 and S3 (string section) diminishes more than S1 and S5 (brass/percussion sections). In conclusion, the best configuration seems to be the 2B since the ST early,d reached is the highest compared to the other configurations. The configuration 2B integrates all the elements/features that the orchestra needs and that are common to use. Therefore, the general architectural guidelines from the literature are appropriate to reach a higher average value of the ST early,d. However, these general guidelines do not allow to reach lower ST early,d values for the percussion/brass sections and higher value for the string section. Consequently, the configuration 2B must be improved Configurations 2B, 3 and 4 This paragraph describes the process of the design from the configuration 2B to the configuration 4. The process consists of changing the design of the reflective surface in the middle of the stage close to the string section. The initial configuration is the 2B, which is 49

50 described in detail in the previous Section 4.3. In the configuration 3, the reflective surfaces inside the stage are replaced by real walls inside the stage. In the configuration 4, a different shape for the reflective walls inside the stage is proposed: the risers as reflective surfaces are placed in a circular configuration. 2B 3 4 STearly,d (db) S1 percussion/brass S5 percussion/brass S4 woodwind S3 string S2 string S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 2B 3 4 Configurations Figure 4.13 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 2B, 3 and 4. Figure 4.13 indicates the average results on the distance of the ST early,d for each source (Source 1-5) and for each configuration 2B, 3 and 4. The result of each source considers an average of the ST early,d value measured at each receiver as in the process described in the previous Paragraph The ST early,d value to reach is lower for the percussion/brass sections (represented by the average on the distances of the Sources S1 and S5), medium for the woodwind section (represented by the average on the distances of the Source S4), and higher for the string section (represented by the average on the distances of the Sources S2 and S3). The configuration 2B, already described in Section 4.3, appears in the graph. The average ST early,d for this configuration is appropriate (-13.3 db) for the overall orchestra. However, the ST early,d for the percussion/brass sections (Sources S1 and S5) is higher than the value for the string section (Source S2 and S3). 50

51 Figure 4.14 shows the model of the configuration 3. In this configuration, the reflective surfaces inside the stage are replaced by real walls inside the stage. These walls are 0.30 m higher than the surfaces of the configuration 2B. The material of the middle walls changes compared to the configuration 2B and it is even more reflective (0.06 at 1000 Hz). The materials of the configuration are shown in Table C.2 of the Appendix C with their absorption coefficients. Figure 4.14 Model of configuration 3 The change in the ST early,d, as illustrated in Figure 4.13, is insignificant. The ST early,d is lower in correspondence of the string section (Source S3) and of the woodwind section (Source S4), and is higher for the percussion/brass sections (Source S5). This could be explained by the fact that there are more reflections in the percussion/brass sections created by the 0.30 m of the wall. Moreover, at large distances the configuration 3 has less reflections than the configuration 2B, even though the number of reflective surfaces are more. In fact, this configuration separates the strings from the percussions and brasses and creates two separate stages. Configuration 2B remains the best options because of the high results of ST early,d and the average of it of -13 db. With the previous configurations, sound rays cannot reach the other side of the stage, but they can just contribute to increase the reflections and the sound pressure level in the same side part of the string. This is extremely inconvenient for the ensemble conditions. A possible solution to the problem is provided with the configuration 4, in which is proposed a different shape for the reflective walls inside the stage: the risers as reflective surfaces are placed in a circular configuration. Figure 4.15 shows the model of the configuration 4. 51

52 Figure 4.15 Model of configuration 4 As illustrated in Figure 4.13, the change between configurations 2B and 4 is slightly visible. The two configurations seems to have some advantages and disadvantages. In the configuration 4, the reflections decrease at large distances and increase at small distances, slightly improving the condition of the string section. However, with the configuration 4 the area for the string section diminuishes compared to the configuration 2B because of the presence of the curved wall-risers inside. In addition, the curved walls could likely create a focus effect directioning the sound in just two specific point of the string section and not distribuiting the sound in all the stage. The configuration 4 could be better for the direction of the sound from one string sections to the other on the opposite side, but the expected positive effect is not visible because the walls are too short (except for the last one that is 1.30m) compared to the height of the string source and receiver (1 m from the floor). The best configuration seems to be also in this case the 2B Configurations 2B and improvements This paragraph describes the process of the design that leads to an improved configuration of the configuration 2B. The process consists of removing/adding elements and changing materials of the stage in order to reach the purpose of different values of ST early,d depending on the instruments. The initial configuration is the 2B, which is described in detail in the previous Section 4.3. In the configuration 2B improvement 1, the tilted reflectors at the back of the stage are removed and the materials are changed. In the configuration 2B improvement 2 only the materials are changed, while the geometry of the previous configuration is maintained. In the configuration 2B improvement 3, the shape of the ceiling is adjusted. In the configuration 2B improvement 4, the string instruments are positioned in a pit composed by two risers. 2B 2B improv. 1/2 2B improv. 3 2B improv. 4 52

53 STearly,d (db) S1 percussion/brass S5 percussion/brass S4 woodwind S3 string S2 string S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 S1 S5 S4 S3 S2 2B 2B improv. 1 2B improv. 2 2B improv. 3 2B improv. 4 Configurations Figure Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 2B improvement 1, 2B improvement 2, 2B improvement 3 and 2B improvement 4. The configuration 2B presents more reflections in the highest part of the stage (percussion/brass sections). The result is that the level and the loudness of percussion and brass is high. The configuration 2B improvement 1 aims to provide a solution to this problem (Figure 4.17). Figure 4.17 Model of configuration 2B improvement 1 Removing the tilted reflectors at the back of the stage and leaving only the front ones, choosing materials for the front walls and for the reflective surfaces in the middle of the stage even more reflective than before (materials in Table C.3 of the Appendix C), the ST early,d is improved. As can be seen in the Figure 4.16, even though also for string and woodwind sections (Sources S2, S3 and S4) the ST early,d is lower than before, the decrease of percussion/brass sections (Sources S1 and S5) is more (almost 2 db). 53

54 The configuration 2B improvement 2 is geometrically equal to the configuration 2B improvement 1; the material for the front walls is more reflective than before, and the material for the walls in the back of the stage is more absorbent. Details of the materials are indicated in the Table C.4 of the Appendix C. Figure 4.16 shows that, adjusting the materials for the front walls and for the wall-risers, the ST early,d for the percussion/brass sections (Sources S1 and S5) decreases and the ST early,d for string section (Sources S3 and S2) increases. The configuration 2B improvement 3 maintains the same materials of the configuration 2B improvement 2 adjusting the shape of the ceiling. The back portion of it is tilted of 65 towards the horizontal (Figure 4.18). Figure 4.18 Model of configuration 2B improvement 3 In the Figure 4.16, the ST early,d at string source (S1) and at woodwind source (S4) maintains the same values. According to the directivity studies of Meyer, the ceiling should be tilted in the rear part of the stage trying to push away the reflections from the percussion/brass sections directly into the audience [4]. The results cannot show this aspect, but the ST early,d for the percussion/brass sections (Source S5) decreases by 1.1 db. To avoid the problem of the loudness of percussions and brass towards the strings, one solution is to increase the distance between them. Consequently, in the configuration 2B improvement 4, a pit for the string section is created. The string instruments are positioned in two risers that go down, incrementing the surface areas of the reflective walls inside the stage. The variation is presented in Figure

55 Figure 4.19 Models of configuration 2B improvement 4 The effect of the walls inside the stage is incremented because they are higher than before. This effect is visible in the Figure 4.16 with the decrease of the ST early,d for percussion/brass sections (Sources S5 and S1) of almost 0.5 db. The ST early,d for the string and woodwind section (Sources S2, S3 and S4) decreases, but the average ST early,d is still high and it is -15 db Influence of scattering coefficient All calculations above are achieved assuming flat surfaces. The scattering coefficient can be introduced by adding in walls diffuser (as QRD diffuser) or irregularities or using wrinkled/rough surfaces. If the scattering coefficient is introduced in the properties of the materials, the field should be more diffuse. Musicians can be surrounded by the sound because of the reflections coming from different directions. The scattering coefficient is a property of the surfaces that does not influence the numbers of reflections, but their directions. In fact, the ST early,d should not be influenced by the scattering coefficient. Considering the configuration 2B, the scattering coefficient is added just in the enclosures of the stage (s=0.3) and in the ceiling (s=0.3). For the other materials used for the stage the scattering coefficient has the default value of 0.05 (the scattering coefficient is frequency independent). The results are likely equal; consequently, the expectations are confirmed by the results of the simulations. 55

56 STearly,d (db) S1 percussion/brass S5 percussion/brass S4 woodwind S3 string S2 string S1 S5 S4 S3 S2 S1 S5 S4 S3 S B Configurations 2B scatt. coeff. Figure 4.20 Average results on the distance of the ST early,d for each source (S1- S5) and for the configuration 2B and 2B with scattering coefficient. Figure 4.20 shows the average results on the distance of the ST early,d for every source positions between the receiver position of the stage configuration 2B and 2B with scattering coefficient. As can be seen, there is no difference between the values of the ST early,d. Consequently, the diffusion and the scattering should not be considered in this study because it does not influence the Stage acoustic descriptor ST early,d. The ST early,d, in fact, considers just the amount of energy of early reflections and not the directions of them. 4.5 Conclusions and further research The basic idea of stage design is to use reflective surfaces inside the stage close to the string section and to install elements/features based on the architectural guidelines. With this idea of stage design (configuration 2B), the average ST early,d is appropriate for musicians (-13.3 db) compared to the advised literature values (-14 db). As the results confirm, the audibility of the strings in the two opposite sides of the string section is improved. However, other elements of the stage configuration (2B) together with the use of reflective surfaces inside the stage increment also the reflections in the percussion/brass sections; in fact, the ST early,d is also high for these sections. Consequently, this element/feature alone is not enough to completely reach the goal. A large number of small other details, such as removal of some reflectors, adjusting of the materials and variations of the stage ceiling shape, are needed to create more reflections in the string section and less reflection in the percussion/brass sections. The results in ST early,d caused by material variations are less visible than geometrical changes (changing in width, depth, height of the stage) because of small changes in materials (from a less reflective material with absorbtion coefficient of 0.07 at 1000 Hz to a more reflective material with absorbtion coefficient of 0.05 at 1000 Hz). The variations in terms of adding 56

57 elements in the stage produce the main changes in the ST early,d parameter values. However, every variation produces contemporary improvements and worsening in different part of the stage and between the two different opposite sections of the orchestra (strings and percussions/brasses). Moreover, the ST early,d has a fundamental role in the description of the problem and in the definition of solutions. The use of it, to approach the goal, turns out to be positive compared to the use of ST early, because it is the only stage parameter that indicates the differences depending on the distance. 57

58 Chapter 5 Second stage design 5.1 Introduction This Chapter analyses a different approach to find a solution for stage design. A theoretical study of reflections is used to reach the optimal stage design best suited for musicians and for the strings in particular. 58

59 5.2 Method The approach used in this study is different than the previous one. The design of the stage does not arise from the literature backgroud or investigating the existing concert hall stages, but it emerges from a theoretical analysis. This analysis is based on the research of the correct positions of reflective surfaces on the stage for each instruments section. The basic idea is to consider each couple of instruments sections, and optimize the ST early,d parameter values between them using reflective surfaces. The goal is to understand how the ST early,d can change using different position or size of the reflective surface and to appreciate the differences in the results. After this step, all these reflective surfaces, obtained from each couple of instruments, are placed together generating a stage. Finally, using the same source-receiver positions of the different couples in the theoretical study, the stage is adjusted trying to optimize the ST early,d parameter for the overall orchestra. This study is structured in two parts: the first part considers omnidirectional sources, and the second part considers the directivity of one instrument for each section of the orchestra. Each model is modeled using the software SketchUp 2016 in order to create a 3D model, considering just the inner surfaces of the stage only. The simulations of the models are studied using the software ODEON Combined in which it is necessary to set source-receiver positions, materials, room properties and parameters definitions and to perform Jobs to obtain the RIR and parameter results. Source and receiver positions The source-receiver positions are set as in Figure 5.1. Timpani Trombone Oboe Violin Cello Figure 5.1 Source-receiver positions and the distances between each other 59

60 Figure 5.1 shows the source-receiver positions and the distances between them. These sourcereceiver positions are placed based on the most common positions of one instrument per section (considering the string section divided in two part correspondent to the opposite side of the stage) of the orchestra in the Fürtwangler layout of the stage. The violin and the cello sources (S1 and S2) are placed at 16 m distance between each other in the opposite side, representing the two opposite part of the string section. The woodwind instrument (S3) is placed in the centre of the stage (representing the woodwind section), at 6 m distance from the string instruments. The brass instrument (S4) is positioned on the right side at 8 m from the string instruments and 8 m from the percussion instrument at the opposite side (S5). The height of the sources is 1 m from the stage floor for the violins, 1.25 m from the stage floor for the woodwind instrument, and 2 m from the stage floor for the percussion/brass instruments. The receivers R1, R2, R3, R4, R5 are located in the same positions of the sources. In addition, certain receivers (R6, R7, R8, R9, R10) are positioned 1 m in front of the each source in order to calculate the ST early. In the first part of the study, the sources and the receivers are omnidirectional. In the second part of the study, the sources have the directivity of one instrument for each section. S1 has the directivity of a violins for the string section, S2 has the directivity of a cello for the string section, S3 has the directivity of an oboe for the woodwind section, S4 has the directivity of a trombone for the brass section, and S5 has the directivity of timpani for the percussion section. For each source, the gain is set as 11 db and the Electrical Input power is adjusted in order to obtain the total power of the directive source equal to the same omnidirectional source. Materials The model is composed by surfaces and stage floor 100% reflective. The stage is delimited by surfaces that are 100% absorbent and make sure that, in the simulating fase, no rays are lost. Parameter calculation The setting of the ODEON file is the same as explained in Section 3.2. Jobs At the end of the preparation of the file, ODEON requires the creation of Jobs. The Jobs allows the calculation of every parameter associated to the model. In one Multiple Job, the parameter are calculated considering just one source (from 1 to 5) and every receiver (from 1 to 10). In addition, ODEON calculates also parameters for Jobs composed just by one source and one receiver, because of the need to look at the reflectogram and, consequently, at the reflections created between the source and receiver considerated. Purpose To judge the acoustics of the stage, just the ST early,d parameter is needed from the extended list of parameters that ODEON provides. The ST early,d values should vary between -11 and -17 db to reach a respectable acoustics. In particular, as already described in the Section 1.4 of the Chapter 1, the ST early,d should vary between -11 and -14 db for the string section (Sources S1 60

61 and S2), between -14 and -16 db for the woodwind section (Sources S3), and between -15 and -17 db for the brass/percussion section (Sources S4 and S5). 5.3 First part: omnidirectional sources The first part of the study considers omnidirectional sources. The sources are the violin (V), the cello (C), the woodwind instrument (W), the brass instrument (B) and the percussion instrument (P). The change in the ST early,d parametes values is studied for each couple of instruments: V-C and C-V, V-W and C-W, V-B and C-B, V-P and C-P, W-V and W-C, W-B and W- P, B-V and B-C, B-W and B-P, P-V and P-C, P-W and P-B Theoretical study The first goal is to understand how the acoustics of the stage is influenzed by surfaces positioned in the stage, and what is the proper position of these surfaces to reach significant ST early,d values. For each couple of instruments, the preliminary configuration is composed by a 100% reflective surface of 100*100 m 2 that is the stage floor, surrounded by a box of 100% absorbent walls, and a source and a receiver; in this way, the stage is an open stage without any enclousers as illustrated in Figure 5.2. Figure 5.2 Premilinary configuration theoretical study with violin and viola positions Results of this configuration for each couple of instruments indicate an extremely dry acoustics environment with low ST early,d values, which vary from -50 db to -80 db as average in the frequencies depending on the couple considered (in theory ST early,d for this configuration should be -, but the influence of the scattering of the boundary in ODEON produces a real value). To find the correct position of the surface in order to reach a higher ST early,d value, this surface (2*2 m 2 ) should be placed in the range of distances 1.7 m 9.5 m from the source/receiver. The ST early,d considers the amount of energy in the time interval 10/103-delay ms and, hence, is possible to find the distance. This range derives from the following calculation. 61

62 dd = 0.01 ss 340 mm ss = 3.4 mm dd = (0.103 dddddddddd)ss 340 mm ss 16 mm = ss 340 mm 340 mm ss ss = 19 mm where the delay=distance between source-receiver/velocity of the sound. The two values (3.4 m and 19 m) represent the double distance between source and surface (from source to surface and from surface to source). Consequently, the range of distances from the source/receiver is 1.7 m 9.5 m. If the surface is placed at 9.5 m from the source-receiver, the ST early,d is almost doubled in every instruments couple case. As a result, just a little reflective object inside a completely absorbent environment creates a considerable effect. Moreover, according to Wenmaekers et al., the source and the receiver must be kept at least 2 m (this value confirms the 1.7 m of minimum distance from the source found) from any stage boundary, since in this way, the ST early,d will not be influenced by reflections in the time interval 0-10 ms [8]. Consequently, the range of distance in which the surface can be positioned is between 2 and 9.5 m. The closer to the source-receiver is the surface, the higher ST early,d is generated. The best position seems to be 3 m behind the source-receiver position as it can be seen in the Table 5.1 for the case of the couple violin-viola as an example. Table 5.1 ST early,d of different configurations of the couple violin- viola ST early,d (average on the frequencies) db Preliminary configuration Reflective surface 9.5 m behind the source Reflective surface 1.7 m behind the source Reflective surface 3 m behind the source Reflective surface in the middle of source-receiver position at 11 m distance from the line source-receiver Table 5.1 shows the differences in terms of ST early,d for different positions of the reflective surface for the couple violin- viola. The models of the configurations in the Table 5.1 are shown in the Figure The value should be - because there are not surfaces in the configuration. The value derives from ODEON considering the scattering of the boundary on. 62

63 Figure 5.3 Different positions of reflective surface for the couple violin- viola: 19 m behind the source, 0.34 m behind the source, 3 m behind the source and 11 m distance from the line source-receiver As can be seen in the Table 5.1 and in the Figure 5.3, the most significant result is presented when the surface is placed 3 m behind the source. If the surface is placed 3 m behind the receiver, the result should be the same because of the symmetrical model, and because of the same distance between source and receiver and reflective surface. However, ODEON does not present the same result; the cause of these different values is unknown. In this study, an average of the results in both directions is taken. In addition, if the surface is placed in the middle of the source-receiver, the result is still significant but less than the previous case. Equal results are obtainable for the other couples of instruments in the orchestra. If other surfaces are added to the model, the ST early,d will continue to rise. The ST early,d values that should be reached adding reflective surfaces, are different depending on the couple of source-receiver considered. From the strings to every other instruments the ST early,d values should vary from -11 to -14 db. From the woodwinds to every other instruments the ST early,d values should vary from -14 to -16 db. From the brasses/percussions to every other instruments the ST early,d values should vary from -15 to -18 db. Figure 5.4 illustrates the number of reflective surfaces needed to reach the optimal ST early,d for each couple of instruments. 63

64 Figure 5.4 Number of surfaces and elipses used to find the correct position of the reflective surfaces. In order the couples are Violin-Cello, Violin-Woodwind, Violin-Brass and Violin-Percussion and vice versa. As can be seen, for each couple the reflective surfaces are placed around the source and the receiver following ellipse shapes. Considering source and receiver positions as the two foci of an ellipse and considering the ellipse properties, any reflective surface tangent to the ellipse creates equal angles with the lines that connect the two foci [10]. Consequently, every reflective surface tangent to the ellipse defines a reflection from the source to the receiver (where the angle of incidence is equal to the angle of reflection) improving the comunication between them. For the strings, many surfaces are added since the ST early,d should be the highest and since the distance between each other is longer than the other couples. Using in three dimensions a rotated ellipse, known as an ellipsoid, (adding, consequentely, reflectors above the stage) the goal can be reached. Since the sources are omnidirectional and are positioned symmetrical between each other, most of the configurations can be used several times and symmetrically. For each couple of instruments, the reflective surfaces are positioned 3 m behind source/receiver and in the middle of source-receiver position at certain distances depending on the couple. 64

65 Table 5.2 shows a summary of ST early,d reached, number of surfaces used and number of ellipses used for every case studied. Violin is indicated with V, Cello with C, Woodwind with W, Brass with B and Percussion with P. Table 5.2 ST early,d reached, number of surfaces used and number of ellipses used for every case studied Optimal ST early,d ST early,d reached N. surfaces used N. ellipses used V-C -11/ V-W C-W -11/ V-B C-P -11/ V-P C-B -11/ W-V W-C -14/ W-B W-P -14/ B-V P-C -16/ B-W P-W -16/ B-P -16/ Definition of the stage and adjustments Figure 5.5 shows the concept of the stage design (configuration 0) generated by the union of all the surfaces from the study of every instruments couple. Figure 5.5 Configuration 0: union of all the surfaces from the study of every instruments couple 65

66 Considering the positions of the reflective surfaces chosen, most of the reflective surfaces are placed in front of the percussion/brass and string sections. The configuration 0 provides a ST early,d value for each couple of instruments different than the ST early,d value of the each separated couples configurations. Consequently, the configuration 0 must be adjusted to improve the comunication between the source-receiver. In fact, in these conditions, the direct sound between sources and receivers is stopped by surfaces inside the stage and in particular inside the string section. In addition, the source of the woodwind (Source S3) is not counted in the calculation because of the presence of a surface in the same position. This distorts the results, the sound and comprimises the acoustics. To adjust the stage and the ST early,d value, the following process is used. The process consists of removing/ adding/moving reflective surfaces to the configuration 0. In the configuration 1, the risers are added, some surfaces are removed or modified in size in order to allow the trasmission of the direct sound. The configuration 2 maintains the same geometry of the configuration 1, but the materials are changed. In the configuration 3, the surfaces in front of the string section are positioned under the floor with a proper inclination (10 ) rendering the floor acoustically transparent and adding an underneath floor 2 m under the transparent floor. In the configuration 4, more reflective surfaces are added under the floor and the distance between the transparent floor and the underneath floor is shorter. In the configuration 5, reflective surfaces above and under the lateral walls are added, and the underneath floor is put closer than before to the transparent one. 1/ ST early,d (db) S1 string S2 string S3 woodwind S4 brass S5 percussion S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 Separated configurations Configurations Figure 5.6 Average results on the distance of the ST early,d for each source (S1- S5) and for the separated configurations and the configuration 1, 2, 3, 4 and 5. 66

67 Figure 5.6 shows the average results on the distance of the ST early,d for each source (S1- S5) and for separated configurations and the configuration 1, 2, 3, 4 and 5. The ST early,d for the Separated configurations is the appropriate value for each source that there should be on stage. Unifying all the surfaces leads to a ST early,d too low and not equal to the value of the parameter calculated separately for each configuration. Therefore, the adjustment are needed. In the first adjustment (configuration 1), the risers are added, the surfaces at the back of the woodwind section are shorter than before, surfaces in the middle of the string and the woodwind are removed and surfaces at the back of the stage are moved creating the shape shown in the Figure 5.7. The materials are the same as the models of the single couples of instruments. Figure 5.7 Model configuration 1 The stage shows positive results in terms of ST early,d in Figure 5.6. The ST early,d in the string section (Sources S1 and S2) is higher that the other and ST early,d in the percussion/brass sections (Sources S4 and S5) are lower with a minimum of ST early,d of -18 db, quite low. The average of the ST early,d for string section (Sources S1 and S2) is almost -13 db, while the average for percussion/brass sections (Sources S4 and S5) is db. The stage should be adjusted with the purpose to reach a ST early,d for the brass/percussion sections of -15/-17 db. In the second adjustment (configuration 2) the materials are changed compared to the material of the theoretical study (100% reflective for every surface). The list of materials used is indicated in the Table C.4 in Appendix C. The material of the stage floor considers the presence of the orchestra. The surfaces in front are made of wood with 22 mm chipboard with 50 mm cavity filled with mineral wool (less reflective than before with α=0.05 at 1000 Hz). The surface on the back are 10% absorbent. The risers are made of wood. The surfaces above the stage (reflectors) are plasterboard on frame with empty cavity (less reflective than before with α=0.03 at 1000 Hz). The study is not theoretical any more, but it can be associated to a real stage. The change of materials produce a decrease of the ST early,d of 1.2 db for the string and 67

68 woodwind sections (Sources S1, S2 and S3) at every distance and 1.5 db for the percussion/brass sections (Sources S4 and S5) at every distance. In the third adjustment (configuration 3), the stage changes completely. The problem is that the surfaces in front of the string section are in the middle of the audience section. The main idea is to position these surfaces under the floor with a proper inclination (10 ) and to render the floor acoustically transparent. Moreover, an underneath floor is added 2 m under the transparent floor. The material of the underneath floor considers the presence of the orchestra inside the stage. Another changed element is the back walls of the woodwind section shorter by 0.4 m. The model of the stage is illustrated in the following Figure 5.8. Figure 5.8 Model of configuration 3 According to the Figure 5.6, The ST early,d decreases more with the configuration 3. The ST early,d in the woodwind section (Source S3) maintains the trend, while ST early,d in the string section (Sources S1 and S2) diminishes at large distances. The ST early,d in the percussion/brass sections (Sources S4 and S5) decreases at small distance of 0.5 db and at large distances of almost 1.5 db as can be seen in the graph in the Appendix D of th configurations. The purpose of reaching a ST early,d of -11/-14 db for strings, -14/-16 db for woodwinds and -16/-18 db for brasses/percussions is not possible with this configuration. Rendering the floor transparent and lowering the real floor produce less reflections, since the distances of the reflections from the floor increase. A solution to avoid this reduction of the ST early,d is to add surfaces under the transparent floor trying to create again the same ellipse for the string section and to put the underneath floor closer (at just 1.25 m) to the transparent one as can be seen in the Figure 5.9 (configuration 4). 68

69 Figure 5.9 Model of the configuration 4 The results are slightly better than the configuration 3 as can be seen in Figure 5.6. The average of the ST early,d in the string/woodwind sections (Sources S1, S2 and S3) increases, conserving the same values in the percussion/brass sections (Sources S4 and S5). In the fifth adjustment (configuration 5), reflective surfaces above and under the lateral walls are added, and the underneath floor is put closer to the transparent one (at just 1.00 m) as can be seen in Figure Figure 5.10 Model of the configuration 5 The ST early,d increases of 1.2 db in the string section (Sources S1 and S2), while the increase in the percussion/brass sections (Sources S4 and S5) is just 0.8 db. This improvement is visible in the Figure

70 5.3.3 Conclusions first part of the study For the first part of the study, a theoretical approach is used. This theoretical approach consists of the research of the appropriate positions of the reflective surfaces on a stage for each couple of sections (one instrument per section). With this different approach and design (configuration 0), the obtained ST early,d does not entirely accomplish the goal of different values of it for the different orchestra sources. In fact, a totally reflective environment is provided for the percussion/brass sections. Moreover, the design consistes of adding reflective surfaces also in front of the stage obstructing the visibility for the audience. The new idea of design (to introduce reflective surfaces under the floor and render the floor acoustically transparent) improves two aspects of the stage: the need of reflections for the string section and the need of visibility from the audience point of view. With this new stage design, the ST early,d accomplishes the goal previously described. However, the ST early,d for the string instrument source should be increased more to definitely optimize it at maximum. 5.4 Second part: sources with directivity The second part of the study considers the sources with their directivity. The sources are Violin (V) and Cello (C) for the two sides of the string section, Oboe (O) for the woodwind section, Trombone (Tr) for the brass section and Timpani (Ti) for the percussion section. In this case, the change in the ST early,d parameter values is also studied for each couple of instruments: V-C and C-V, V-O and C-O, V-Tr and C-Tr, V-Ti and C-Ti, O-V and O-C, O-Tr, O-Ti, Tr-V and Tr-C, Tr-O, Tr-Ti, Ti-V and Ti-C, Ti-O and Ti-Tr Theoretical study In this case the goal is different: to determine the position of reflective surfaces on a stage in a way to increase the ST early,d values from string to every other instrument, but not viceversa, considering the influence of the directivity of the instruments. For each couple of instruments, the initial conditions are the same as explained in the first part of the study: a 100% reflective surface of 100*100 m 2 as the stage floor, a box of 100% absorbent walls, and a source and a receiver. Results of this configuration for each couple of instruments indicate an extremely dry acoustics environment with low ST early,d values, which vary from -50 db to -80 db as average in the frequencies depending on the couple considered. To find the correct position of the surfaces in order to reach a higher ST early,d value, the same calculation and considerations of the first part of the study (Section 5.3.1) are used. However, the position of the reflective surfaces is not the same and the number of reflective surfaces is increased. In fact, the directivity of the instruments highly influences the number of reflective surfaces needed as well as their position on the stage. 70

71 Figure 5.11 shows the directivity in plan at 1000 Hz and the directions of the sources considerated. Figure 5.11 Directivity in plan at 1000 Hz of the violin, the cello, the oboe, the trombone and the timpani, and direction of the sources in plan. Considering the couple violin - trombone, it is possible to appreciate the variance in the position of the reflective surfaces compared to the case of omnidirectional sources. In the case of omnidirectional sources, the reflective surfaces are 5 and they are positioned laterally and in front of the brass instrument (behind the string instrument). In the case of directive sources, the reflective surfaces are 4, and they are positoned only behind and laterally the trombone (brass instrument), since its directivity in that part is less expanded; as a result, the rays and the reflections from the violin to the trombone are stronger than the rays and reflections from trombone to the violin. The ST early,d is influenced by the intensity of the reflections and, consequently, is higher from the violin to the trombone and lower from the trombone to the violin. This is illustrated in the Figure Figure 5.12 Reflections intensity from violin to trombone and viceversa considering the directivity 71

72 In addition, it is possible to appreciate the variance in the number of the reflective surfaces compared to the case of omnidirectional sources considering the couple oboe - trombone. In the case of omnidirectional sources, the number of reflective surfaces needed is only 1. In the case of directivity sources, the number of reflective surfaces needed is 3, and they are positioned behind the trombone. In conclusion, the best position for the reflective surfaces seems to be 3 m behind the sources that needs less support for the acoustics. Also in this case, the reflective surfaces of each couple of instruments are placed around the source and the receiver following ellipse shapes. Figure 5.13 shows the ellipses considerated for each couple of instruments. Violin - Cello Violin Oboe and Cello - Oboe Violin Trombone and Cello - Timpani Violin - Timpani 72

73 Cello - Trombone Oboe Trombone Oboe Timpani Trombone - Timpani Figure 5.13 Ellipses for each couple of instruments. 73

74 2.4.2 Definition of the stage and adjustments Figure 5.14 Model of configuration 0 Figure 5.14 shows the concept of the stage design generated by the union of all the surfaces of every instruments couple. In this case, the reflective surfaces are in a larger quantity than for the first study and, mostly they are positioned at the back of the stage. As can be seen, all the surfaces that are positioned in the centre of the stage block the direct sound from sources and receivers. In addition, some surfaces are placed in the same position of the source. Consequently, the stage is adjusted to allow the production of the direct sound from each source to each receiver and to improve the ST early,d value. To adjust the stage, the following process is used. The process consists of removing/ adding/moving reflective surfaces to the configuration 0. In the configuration 1, the risers are added and most of the surfaces are removed or modified in size in order to allow the trasmission of the direct sound. In the configuration 2, the surfaces in front of the string section are positioned under the floor with an inclination of 10, rendering the floor acoustically transparent and adding an underneath floor 1 m under the transparent floor. The changes for the configuration 1 and 2 are described in detail below

75 STearly,d (db) S1 violin S2 cello S3 oboe S4 trombone S5 timpani S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 S1 S2 S3 S4 S5 Separated configurations 1 2 Configurations Figure 5.15 Average results on the distance of the ST early,d for each source (S1- S5) and for each configuration 1 and 2. Figure 5.15 shows the average results on the distance of the ST early,d for each source (S1- S5) and for separated configurations and the configurations 1 and 2. The ST early,d for the Separated configurations is the appropriate value for each source that there should be on stage. Unifying all the surfaces leads to a ST early,d too low and not equal to the value of the parameter calculated separately for each configuration. Therefore, the adjustment are needed. In this first adjustment the variations are shown in the Figure 5.16 and are listed below: - walls oboe timpani and oboe - trombone in the middle of the string section placed in a different ellipse at 2.5 m from the floor and 10 tilted; - lateral walls violin - cello placed in a smaller ellipse (0.3 m moved in the perpendicular direction); - lateral walls violin - cello shorter of 0.5 m; - removal of the wall violin - timpani from the woodwind section; - central wall violin - cello in the middle of the woodwind section placed under the floor in a smaller ellipse (3.50 m in the perpendicular direction) and 15 tilted; - walls violin oboe and cello - oboe shorter of 0.3 m; - floor transparent and floor 1.50 m under it; - risers for woodwind section 0.25 m high and for percussion/brass 2 m high. 75

76 Figure 5.16 Model of configuration 1 As can be seen in Figure 5.15, the configuration 1 states a lack of reflections in the string section and evidences a very reflective environment in the brass/percussion sections. The situation is opposite towards how it should be. The configuration 2 offers a solution to the problem. Some of the reflective surfaces are moved in different ellipses under the floor and above the stage (creating an ellipsoid), providing the same amount of reflections of the sound that they provides when the sourcereceiver couples are separated. In addition, some reflective surfaces are removed, since the integration of all the surfaces from different couples of instruments creates the possibility for one source to use surfaces that were supposed to be used by another couple in the theoretical study. Figure 5.17 Model of configuration 2 76

77 The model of the stage design is illustrated in the Figure 5.16 and the variations are described in detail in the following list: - walls violin oboe and cello - oboe on the front of the stage placed under the floor and 15 tilted; -floor 1.25 m under the transparent floor; -removal of the four walls in the middle of the string section; -walls violin - cello and cello - oboe in front of the stage placed under the floor and 15 tilted; -walls violin oboe and cello - oboe laterally the woodwind section halved; -wall violin - trombone lateral and behind the percussion section placed 2.40 m high from the floor and 10 tilted; -wall violin - trombone behind the percussion section placed 2.40 m high from the floor and 15 tilted; -wall violin - trombone behind the stage in the centre placed 5 m high from the floor and 40 tilted; -removal all the walls timpani - trombone and trombone - timpani ; -walls violin - timpani placed 5 m high, 1.2 m in a smaller ellipse and 40 tilted; -walls oboe - trombone and oboe - timpani behind the stage placed 1.7 high from the floor, 1 m high and 10 tilted; -wall lateral violin trombone and violin - timpani placed 2.5 m high and 10 tilted; -removal of the lateral walls violin - cello. According to the Figure 5.15, the ST early,d is improved, reaching not entirely, but almost the goal defined previously Conclusions second part of the study The approach used in this study provides a new stage design best suited for musicians since the ST early,d reaches the values defined in the goals. However, the approach used is limited at 5x5 couples of instruments. The complexity of the study can exponentially increase if it is executed considering the 100piece of a full orchestra. Moreover, the study is performed considering a problem evinced by the software version Combined of ODEON; it provides different reflectograms and different values of the ST early and ST early,d for the couple S1-R2 and the couple S2-R1, when these positions are exactly opposite between each other and the settings of the files are exactly the same. This problem should not be evinced because the reflection distances are equal in both the two sides. 77

78 Chapter 6 Conclusions and discussion The main goal of the study is to find possible solutions for design of concert hall stages, optimizing their physical descriptor ST early,d. In addition, another related goal is to optimize the ST early,d for the different sections of the orchestra and to solve the issues that musicians denounce mostly. Conclusions of this study are summarized in this Chapter, followed by a discussion of them. 6.1 Conclusions and discussion Two different approaches have been used to find possible solutions for stage design: The first approach consists of the investigation of a typical literature based design combined with a new feature of stage design: reflective surfaces positioned in the middle of the stage close to the string section. The results are positive because these reflectors create an appropriate reflective environment for the string section (average ST early,d db). However, the results indicate that this design of the stage (Configuration 2B) increments also the reflections for the percussion/brass sections, since the ST early,d in the rear part of the stage is also very high. Consequently, other features are studied to avoid this related problem; positive results are obtained changing materials and adding/removing elements on the stage. In particular: - Removing the reflective surfaces above the 2.2 m high walls only behind the percussion/brass sections provides positive results. Percussion and brass instruments do not need this additional support; - Adding the reflective surfaces above the 2.2 m high walls only in the front of the stage (in corrispondent to the string section) with an inclination less than 15 towards the musicians generates more reflections helpful for the string section. Negative results are found when these reflective surfaces are tilted more than 15 towards the musicians; - Changing from a reflective material to a more reflective material (from α=0.07 to α=0.05 at 1000 Hz) produces changes in the ST early,d of db; - Changing the shape of the ceiling trying to direct the reflection into the audience and not in the stage produce positive results. Therefore, the ceiling is an important surface in the stage; - The larger the area for reflective surfaces in the middle of the stage, the more is the support for the string. 78

79 However, every variation produces contemporary improvements and worsening in different part of the stage and between the two different opposite sections of the orchestra (strings and percussions/brasses). The design of the stage should be compromised towards all the musicians of the orchestra. The second approach consistes in a developed theoretical study. Reflections between each instrument couple (one instrument for each section) of source- receiver are studied trying to find possible positions of reflective surfaces beneficial for them. The results indicate that considering both omnidirectional sources and directional sources, the strings need reflective surfaces in front of them. In addition, when the sources are omnidirectional, the position of the reflective surfaces is not so relevant, but these surfaces must be placed in one of the ellipses around the couple of instruments. Instead, when the sources are directional, the string instruments need reflective surfaces behind brass/percussion instruments increasing the reflections from string to percussion, but not vice versa. The idea of positioning the reflectors in different ellipses above the stage and under the floor with different inclinations produces positive results in terms of ST early,d, mostly for the percussion/brass sections. However, the results are not entirely positive for the string section, since the ST early,d does not reach the desired values. In fact, based on the purpose, the ST early,d for the brass/percussion section should vary between -15 and -17 db, and the obtained value is inside this range. The ST early,d for the string section should vary between -11 and -14 db, but the obtained value is not entirely inside this range. Moreover, results show that the directivity of the source has a large influence in the design of the stage. The results from the first stage design could be considered valid because architectural guidelines and common characterists are carefully taken into account during the design fase. For the second stage design some cautions must be considered. The approach is just theoretical and is limited at 5x5 couples of instruments of the orchestra. The method used would become extremely complex, if a full 100-pieces orchestra with 100x100 couples of instruments had been considered. In that case, the orchestra would be completely surrounded by surfaces with no possibilities of vision from the audience. Moreover, the method of the ellipses is developed using just a basic software for modeling as SketchUp and without an appropriate more precise software. In addition, ODEON gives also some limitations that influence the results of the first and second stage design. In fact, during the simulations, it provides different reflectograms with different values of the ST early and ST early,d for the couple S1-R2 and the couple S2-R1, when these positions are exactly opposite between each other, the model is symmetrical and the settings of the files are exactly the same. This problem should not be evinced because the reflection distances are equal in both the two sides. In conclusion, the use of the stage parameter ST early,d, instead of the ST early proposed by Gade, turned out to be helpful in understanding the change in the perception of the sound from the musicians point of view when some architectural feature are changed. 79

80 References [1] Gade, A. C Practical aspects of room acoustic measurements on orchestra platforms, In: Proc.14th ICA, Beijing. Paper F3-5. [2] Gade A.C Acoustical Survey of 11 European Concert halls a basis for discussion of halls in Denmark, Part 3, Report No. 44 from The Acoustic Laboratory Technical University of Denmark Building 352, DK 2800 Lyngby. [3] Beranek L. 1992, Music, Acoustics and Architecture, Wiley. [4] Meyer, J Akustik und musikalische Auff uhrungspraxis (Acoustics and the Performance of Music), 5th edn. Bergkirchen: PPVMEDIEN. [5] Dammerud J.J., Barron M Early subjective and objective studies of concert hall stage conditions for orchestral performance, 19 th International Congress on Acoustics, EPSRC, University of Bath. [6] Barron M Auditorium acoustics and architectural design, E & FN SPON, London [7] ISO : Acoustics Measurement of room acoustic parameters Part 1: Performance spaces. International Organisation for Standardisation (ISO), Geneva (CH), [8] Wenmeakers R.H.C., Hak C.C.J.M., Van Luxemburg L.C.J On Measurements of Stage Acoustic Parameters: Time Interval Limits and various Source-Receiver Distances, Acta Acustica united with Acustica vol. 98. [9] Dammerud J.J Stage Acoustics for Symphony orchestras in concert halls, Phd thesis for the degree of Doctor of Philosophy of the University of Bath. [10] Gade, A. C Musicians ideas about room acoustic qualities. Tech. rept. No. 31. Technical University of Denmark. [11] Gade, A. C Investigations of Musicians Room Acoustic Conditions in Concert Halls. Part I, II, Acustica. [12] Gade, A. C Practical aspects of room acoustic measurements on orchestra platforms, In: Proc.14th ICA, Beijing. Paper F3-5. [13] Beranek L How they sound, Concert and Opera halls, Acoustical Society of America, Woodbury [14] Heijnen P., Kivits M Akoestiek en comfort op podia (Acoustics and comfort on stages), Master project, Faculteit Bouwkunde, Technische Universiteit Eindhoven 80

81 [15] Akutek, [16] Beranek L Concert hall acoustics: Recent findings, Article in The Journal of the Acoustical Society of America [17] Wenmeakers R.H.C., Hak C.C.J.M Measuring impulse responses in a fully occupied concert hall using a tailor-made electronic musical composition proof of concept. Proceedings of the Institute of Acoustics, Vol. 37. Pt [18] Toyota Y., Oguchi K., Nagata M Acoustical Design of Walt Disney Concert Hall, Nagata Acoustics, Inc. US Office, Santa Monica, California, ICA [19] Philharmonie De Paris, Paris, France, 2015, Nagata Acoustics [20] Phiharmonie De Paris, Press Kit, Mécénat Musical Société Générale, Partenaire De La Musique Classique, Depuis 25 Ans [21] Van Luxemburg, L.C.J., Hak, C.C.J.M., Martin H.J. and Kok, B.H.M., Bijsterbosch, K.B.A. 2002, Casa da Musica, a new concert hall for Porto, Portugal, Audio Engineering Society Conference Paper,St. Petersburg, Russia [22] Gade A.C Acoustics in. Acoustics in Halls for Speech and Music, Part C/9, Springer New York, New York [23] Gade A.C Subjective and objective measures of relevance for the description of acoustics conditions on orchestra stages, International Symposium on Room Acoustics, Toronto, Canada [24] Bradley J.S A just noticeable difference in C 50 for speech. In Applied Acoustics 58 (2) [25] Linnea Gjers E Stage Acoustics in Concert Halls:a study of musicians' acoustical environment, Master of Science Thesis in the Master's Programme Sound and Vibration of the CHALMERS UNIVERSITY OF TECHNOLOGY, Gothenburg, Sweden 81

82 Appendix A Orchestra arrangements Generally a symphonic orchestra is composed by 100 members, but it can vary depending on the repertoire. It is composed by four instrument groups: strings, woodwinds, brasses and percussions. The strings are divided into 5 smaller groups: 16 first violins, 14 second violins, 12 violas, 10 cellos and 8 double basses. The woodwind section is typically composed by 2 flutes, 1 piccolo flute, 2 oboes, 1 cor anglais, 2 clarinets, 2 bassoons, 1 double bassoon. The brass section consists of 4 horns, 3 trumpets, 3 trombones, 1 tuba and the percussion section consists of 1 Timpani, 1 vibraphone, 1 harps and 1 piano [25]. According to Barron, the stage area for a full 100-member orchestra is 200 m 2 divided in: 1.25 m2 for upper string and wind instruments 1.5 m2 for cello and larger wind instruments 1.8 m2 for double bass 10 m2 for timpani, and up to 20 m2 more for other percussion instruments [6]. There are three seating arrangements for a symphonic orchestra: the American way, the Fürtwangler way, and the European way. These seating arrangements are used by the string section. The American arrangement is composed by the first and second violins placed together next to each other in the same side of the string section. On the other side of the string section, violas are positioned in front of the cellos. With this disposition, some musical passages are easier for first and second violins because of the visual contact and the improved synchronicity between them. At the same time, this arrangement contributes to create a monophonic effect; consequently, the audience perceives a predominance of low frequencies on right side of the stage. The Fürtwangler arrangement inverts the position of the violas with the cellos; the cellos are in front of the violas near the conductor. This configuration balances the emission of low frequency in the right side of the stage. The European arrangement divides the first from the second violins that are seated respectively on the left and on the right of the stage. This disposition creates a stereophonic effect because the first and the second violins are separated and the sound is not well merged. These arrangements are illustrated in Figure A.1. 82

83 American arrangement Fürtwangler arrangement European arrangement Figure A.1 Seating arrangements for symphonic orchestra 83

84 Appendix B Terminology The terminology of the Chapter 2 is explained in the following list and it is described in the Dammerud PhD thesis [9]: W rs = Average distance between side walls on stage (the distance between reflecting surfaces at the sides): a low value will indicate compensating reflections for players across the stage at significant level. This appears to contribute positively to avoid negative level and temporal masking effects, avoid perceived excess delay for the string players on opposite sides of the stage (precedence effect) and increase the spatial separation of reflected sound on stage (cocktail-party effect). A low value will also increase the sound level of double basses at low frequencies. H rb = Average height to reflector(s) over stage (the distance between stage floor and overhead surfaces reflecting brass instruments): a high value will indicate low levels of competing reflections from brass and percussion down towards woodwind and string players. This appears to contribute positively to avoid negative level and temporal masking effects. Overhead reflecting surfaces also appear as an important contributor to a build-up of reverberant sound on stage. A high value of Hrb could therefore also indicate good clarity of sound and that the reverberant sound from the main auditorium will take perceptual precedence over the reverberant sound within the stage itself. A high value could also indicate overall sound levels not being experienced as too high. P refl,area = Total area of suspended reflector(s) over stage P h,ceil = D = Average distance from stage front to rear wall on stage (the distance between the back end of the stage accessible to the orchestra and the average stage front): a high value will contribute positively regarding masking effects, like Hrb, but French horns players appear to prefer a reflecting surface behind them at moderate distance. A moderate value of D therefore appears as the best compromise. P elev = Height of stage front above main floor P volume = Hall volume behind stage front H rb/w rs: sincew rs should not be too large, and H rb not too small, a large value of H rb/w rs would indicate good acoustic conditions and partially monitor the different aspects monitored by W rs and H rb. D/W rs: similar to H rb/w rs. 84

85 Appendix C Tables This Appendix contains all the Tables referred to the materials chosen in the different configurations. Table C.1 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design. Frequency (Hz) Floor risers: Orchestra with instruments on podium, 1.5 sq.m per person (Bobran, 1973) α Risers: Wooden floor on joists (Ingerslev, 1949) α Walls: 20% absorbent α Wall-risers 1: Wood, 25 mm with air space (Ref. Dalenbäck, CATT) α Walls in front 1: Wood, 25 mm with air space (Ref. Dalenbäck, CATT) α Walls in the back 1: 20% absorbent α Wall-risers 2: 22 mm chipboard, 50 mm cavity filled with mineral wool (Bobran, 1973) α Walls in front 2: 22 mm chipboard, 50 mm cavity filled with mineral wool (Bobran, 1973) α Walls in the back 2: 30% absorbent α Reflectors: 10% absorbent α Ceiling: Plasterboard on frame, 13 mm boards, 100 mm cavity filled with mineral wool (Fas α Absorbent walls: 100% absorbent α Table C.2 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design (configuration 3). Frequency (Hz) Floor risers: Orchestra with instruments on podium, 1.5 sq.m per person (Bobran, 1973) α Risers: Wooden floor on joists (Ingerslev, 1949) α Walls: 20% absorbent α Wall-risers 1: Wood, 25 mm with air space (Ref. Dalenbäck, CATT) α

86 Reflectors: 10% absorbent α Ceiling: Plasterboard on frame, 13 mm boards, 100 mm cavity filled with mineral wool (Fas α Absorbent walls: 100% absorbent α Table C.3 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design (configuration 2B improvement 1). Frequency (Hz) Floor risers: Orchestra with instruments on podium, 1.5 sq.m per person (Bobran, 1973) α Risers: Wooden floor on joists (Ingerslev, 1949) α Wall-risers 1: Wood, 25 mm with air space (Ref. Dalenbäck, CATT) α Walls in front 1: Wood, 25 mm with air space (Ref. Dalenbäck, CATT) α Walls in the back 1: 20% absorbent α Reflectors: 10% absorbent α Ceiling: Plasterboard on frame, 13 mm boards, 100 mm cavity filled with mineral wool (Fas α Absorbent walls: 100% absorbent α TableC.4 Absorbent coefficients of the materials chosen depending on the frequency for the first stage design (configuration 2B improvement 2). Frequency (Hz) Floor risers: Orchestra with instruments on podium, 1.5 sq.m per person (Bobran, 1973) α Risers: Wooden floor on joists (Ingerslev, 1949) α Wall-risers 2: 22 mm chipboard, 50 mm cavity filled with mineral wool (Bobran, 1973) α Walls in front 2: 22 mm chipboard, 50 mm cavity filled with mineral wool (Bobran, 1973) α Walls in the back 2: 30% absorbent α Reflectors: 10% absorbent α Ceiling: Plasterboard on frame, 13 mm boards, 100 mm cavity filled with mineral wool (Fas α Absorbent walls: 100% absorbent α

87 Table C.5 Absorbent coefficients of the materials chosen for the second stage design with omni-directional sources (configuration 2). Frequency (Hz) Floor: Orchestra with instruments on podium, 1.5 sq.m per person (Bobran, 1973) α Risers: Parquet on counterfloor (Bobran, 1973) α Surfaces in front 2: 22 mm chipboard, 50 mm cavity filled with mineral wool (Bobran, 1973) α Surfaces in the back: 10% absorbent α Surfaces above the stage: Plasterboard on frame, 13 mm boards, 100 mm empy cavity (Fasold & Winkler, 1976) α Absorbent walls: 100% absorbent α

88 Appendix D Graphs This Appendix contains the graphs of the ST early,d depending on the distance for every source position for each configuration studied. First stage design Configurations from 2A to 0-rectangular shape Configuration 2A Figure D.1 Model of the configuration 2A and ST early,d depending on the distance for every source position for the same configuration. Configuration 2B St early,d Log. (S1 percussion/brass) (db) Log. (S5 percussion/brass) -9 Log. (S2 string) -10 Log. (S3 string) -11 Log. (S4 woodwind) Distance (m) ST early,d (db) -9 Figure D.2 Model of the configuration 2B and ST early,d depending on the distance for every source position for the same configuration Log. (S1 percussion/brass) Log. (S5 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Distance (m) 88

89 Configuration 2C Figure D.3 Model of the configuration 2C and ST early,d depending on the distance for every source position for the same configuration. Configuration 2D ST early,d (db) Log. (S1 percussion/brass) Log. (S5 percussion/brass) Log. (S2 string) Distance (m) Figure D.4 Model of the configuration 2D and ST early,d depending on the distance for every source position for the same configuration. Configuration 1A Figure D.5 Model of the configuration 1A and ST early,d depending on the distance for every source position for the same configuration. 89 ST early,d Log. (S1 percussion/brass) (db) Log. (S5 percussion/brass) -9 Log. (S2 string) -10 Log. (S3 string) Log. (S4 woodwind) Distance (m) ST early,d (db) Log. (S1 percussion/brass) Log. (S5 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Distance (db)

90 Configuration 1B Figure D.6 Model of the configuration 1B and ST early,d depending on the distance for every source position for the same configuration Configuration 1C ST early,d (db) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (db) Figure D.7 Model of the configuration 1C and ST early,d depending on the distance for every source position for the same configuration Configuration 0 ST early,d (db) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) ST early,d Log. (S1 percussion/brass) (db) Log. (S2 string) -11 Log. (S3 string) -12 Log. (S4 woodwind) -13 Log. (S5 percussion/brass) Distance (m) Figure D.8 Model of the configuration 0 and ST early,d depending on the distance for every source position for the same configuration 90

91 Configuration 0 - fan shape Figure D.9 Model of the configuration 0- fan shape and ST early,d depending on the distance for every source position for the same configuration Configuration 0 empty stage Figure D.10 Model of the configuration 0- empty stage and ST early,d depending on the distance for every source position for the same configuration Configuration 0 rectangular shape ST early,d Log. (S1 percussion/brass) (db) Log. (S2 string) -11 Log. (S3 string) -12 Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) ST early,d (db) ST early,d Log. (S1 percussion/brass) Log. (S5 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Distance (m) Log. (S1 percussion/brass) (db) Log. (S2 string) -11 Log. (S3 string) -12 Log. (S4 woodwind) -13 Log. (S5 percussion/brass) Distance (m) Figure D.11 Model of the configuration 0- rectangular stage and ST early,d depending on the distance for every source position for the same configuration 91

92 Configurations 3 and 4 Configuration 3 Figure D.12 Model of the configuration 3 and ST early,d depending on the distance for every source position for the same configuration Configuration 4 Figure D.13 Model of the configuration 4 and ST early,d depending on the distance for every source position for the same configuration Configurations 2B improvement 1, 2, 3 and 4 Configuration 2B improvement 1 Figure D.14 Model of the configuration 2B improvement 1 and ST early,d depending on the distance for every source position for the same configuration 92 ST early,d (db) ST early,d (db) ST early,d Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) Log. (S1 percussion/brass) (db) Log. (S2 string) -9 Log. (S3 string) -10 Log. (S4 woodwind) -11 Log. (S5 percussion/brass) Distance (m)

93 Configuration 2B improvement 2 Figure D.15 Model of the configuration 2B improvement 2 and ST early,d depending on the distance for every source position for the same configuration Configuration 2B improvement 3 Figure D.16 Model of the configuration 2B improvement 3 and ST early,d depending on the distance for every source position for the same configuration Configuration 2B improvement 4 ST early,d (db) ST early,d (db) ST early,d (db) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) Log. (S1 percussion/brass) Log. (S2 string) Log. (S3 string) Log. (S4 woodwind) Log. (S5 percussion/brass) Distance (m) Figure D.17 Model of the configuration 2B improvement 4 and ST early,d depending on the distance for every source position for the same configuration 93