Clarity and Definition in Mudejar-Gothic Churches

1 Clarity and Definition in Mudejar-Gothic Churches M. Galindo, T. Zamarreño, S. Girón Departamento de Fisica Aplicada, Escuela Técnica Superior de Arquitectura, Universidad de Sevilla, Avenida Reina Mercedes, 2, 41012 Sevilla, Spain (Received 19 April 1999 and accepted 1 June 1999) ABSTRACT This paper studies the C80 and D50 objective acoustic indices in relation to source-receiver distance for five different octave bands inside Mudejar-Gothic churches. This type of church, eight examples of which we have studied in the city of Seville, is characterised by good acoustic conditions as far as this can be indicated by reverberation times. This article aims to supply more data on these values and to explore the dependence of these measurements on receiver position. Finally, the experimental results have been compared with expected results derived from a semiempirical analytical model proposed. 1. INTRODUCTION Mudejar-Gothic churches were probably built between the thirteenth and fifteenth centuries and they were made of brick, a material more widely available than stone on the Iberian peninsula. All these churches have similar architectural features: three naves with Moorish-style trussed roofs and a vaulted presbytery. Sendra et al.1,2 have that the smaller size of these churches and, mainly, their wooden ceilings significantly improve their acoustics over their Gothic contemporaries. Besides being used for worship, which implies the use of speech and music, these buildings are sometimes deconsecrated and renovated and used as lecture halls, theatres, or auditoria, especially in small provincial towns that lack other public buildings for cultural activities. This paper reports the experimental results of clarity and definition indices at several locations in eight churches. Table 1 shows some significant data on these churches, and Figure 1 has a scale drawing of the ground plan and sections showing the architectural features of two churches. The analyses are performed in terms of both source-receiver positions and five octave bands with centre frequencies between 250 Hz and 4000 Hz. Reverberation time alone cannot predict acoustic quality in auditoria. Literature on acoustics supports the view that clarity or definition measurements determine acoustical quality of halls and auditoria. Little has been published on the effect of spatial variations on these objectives indices, and there is no evidence of an understanding of how these indices are related to other physical and acoustical properties of rooms. Apparently no one yet knows how to design a new hall so as to achieve the desired values of these parameters. The importance of the early reflection portion of a sound decay process in an enclosed space with respect to degree of clarity, reverberation, and spatial effect is well established, so it would be advantageous to have some simple equations to calculate these character- 2 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES istics at any reception point. After consulting the literature in this area, we perceived the difficulty of predicting these parameters without using expensive scale or computer models. The reason for this is that these parameters are very sensitive to changes in the early reflection sequence, which depends largely on the shape of the room, its surface treatments, and the relative location of the perception points. For example, Perloson et al.3 see the relevance of the C80 acoustic parameter for analysing the acoustic quality of a room and state that this parameter can also describe seat to seat variations. When Barron4 published C80 measurements under balcony overhangs in concert halls to establish the acoustic effect of these balconies, the values of this parameter at middle frequencies exceeded the predictions of his own revised theory5,6; the average increase is 2.6 dB. Pirn7 also establishes that clarity measurements at several distances in three music halls are inconsistent with the Barron or diffuse field predictions. Gade8 averages frequencies and positions for thirty-two famous European concert halls to assign each concert hall a C80 value (in addition to other acoustic parameters he assigns). Gade compares these results with the values derived from the classical diffuse field model; clarity shows the lowest correlation. Neither is it clear which frequency range interests us in the study of these parameters in rooms because Barron9 states that his model is valid only for comparing the average middle frequencies (500 Hz, 1 kHz and 2 kHz). Bradley10 measures a C35 clarity index at 1000 Hz as a function of distance. Marshall11 studies the C50 and C80 parameters from five positions in a large auditorium. He associates C50 with an early to late ratio for speech and therefore supplies weighted averages in the 0.5, 1, 2 and 4 kHz bands. Similarly he associates C80 with a descriptor of musical quality and calculates averages for the 0.5, 1 and 2 kHz bands. On the other hand, Jordan12 measures C80 in a number of prestigious European concert halls where the acoustic conditions for two octaves (0.5 and 1 kHz) have already been subjectively evaluated. Gade8 aims to study the acoustic data averaged for locations and frequencies for these thirty-two concert halls and establish a correlation with architectural design variables. Gade nevertheless concluded that C80 is strongly affected by room geometry. Concerning the acceptable values of these parameters and tolerance intervals, we must emphasize that literature on acoustics has much more information for the clarity index than for the definition index in spite of the close correlation between them. In this sense, Marshall11 proposes –2 dB– +2 dB as an acceptable range, and Jordan12 proposes not to exceed 4–7 dB for the maximum variation of C80 from one point to another in a room. 2. MEASUREMENTS DETAILS All measurements were made in unoccupied churches and no corrections for occupancy were applied because our main aim is to analyse the behaviour of this architectural typology. The furniture consisted in wooden pews with low absorption, which may suggest greater attenuation depending on the degree of occupation because of an increase in audience plane absorption. All the churches are basically symmetrical about a central axis, and receiver positions were distributed uniformly throughout the audience seating area. In Figure 1 we show the ground plan, the longitudinal section, and the cross section of Santa Marina and San Marcos churches. CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES 3 Figure 1. Ground plan with its reception points (top), longitudinal (middle) and cross section (bottom) of Santa Marina (left) and San Marcos (right) churches. Two types of measurements were carried out: impulse measurements and steady-state measurements. The steady-state sound levels in these places were obtained using a reference source (B&K 4205) placed on the altar. These results have been published elsewhere13 and will be discussed later. Impulsive signals were generated by firing a blank cartridge from a 9 mm pistol at the place where the source would be located in normal use. At each reception point the microphone signal was recorded using a Sony PC 204 DAT. In all cases, omnidirectional B&K 4165 microphones were used with their respective preamplifiers and polarization sources from the same manufacturer. The first stage of the analysis is laboratory processing of the signals using a B&K 2133 analyser to find reverberation time T in the bands of interest with Schroder’s integrated impulse method.14.15 The second stage of the analysis requires the conversion of individual 4 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES analogue recordings to a “wav” file using a PC Sound Blaster AWE34 sound card at a sampling frequency of 44.1 kHz. Afterwards, these data were processed with the MATLAB language to separate the range of interest (50–80 ms) and obtain the indices. 3. THEORETICAL MODELS The acoustical indices are defined as follows by Reichardt16 (1975) for music and Thiele17 (1953) for speech: (1) where g(t) is the impulse response and t = 0 coincides with the arrival time of the direct sound to the observation point. These indices can be determined in broadband or in octave band after having been filtered from the impulse response signal. In the classical diffuse field model, there are no variations in sound level while we are within the reverberant field. In music auditoria or concert halls, however, levels generally do continue to decrease with increasing distance beyond the critical distance. Therefore, Barron et al.,5,9,18 to predict total pressure levels and early to late sound/energy ratios (as clarity and definition), divide the acoustic energy received at each point into three components, all of which depend on source-receiver distance r: direct sound d, reflected sound in the first t ms er, and late reflected sound with a delay greater than t ms l, t = 80 ms for clarity and t = 50 ms for definition. So we would write for C and D: æd + erö æ d + erö C = 10 logç––––– ÷ , D = 100%ç––––––– ÷(2) è l ø è d + r + lø In a recent paper on sound pressure levels measured in these Mudejar-Gothic churches, Sendra et al.13 proposed some modifications to Barron’s equations for d, er and l to take into account measured attenuation in the reverberant field in this type of spaces. This modified model also maintains the same separation of energy as Barrons model as well as the exponential decay distance dependence for early and late acoustic energy, but it introduces in these exponentials some <bi> coefficients reached through nonlinear regression from the experimental values for each octave band i and averages them for all churches. Thus for the i octave band we would have: (3) This study13 clearly shows on one hand the acceptable correlation that exists for acoustic levels measured at different source-receiver distances and the theoretical behaviour expected, and on the other the discrepancy with Barrons premises. These last commented discrepancies are shown graphically in Figure 2, that is reproduced of our previous work.13 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES 5 Figure 2. Sound pressure level L–L0 (dB) (L0, direct level under free field conditions at 10 m) versus source-receiver distance (m) for the different octave bands in Santa Catalina church. 6 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES Those facts led us to believe this could also happen with the objective acoustic clarity and definition indices, with the subsequent possibility of predicting their values in this architectural typology with no other premises than their geometry and Ti.19 Based on Equations (2) and (3), we obtain for clarity a sa function of source-receiver distance r: (4) Likewise for the definition: (5) where V is the volume and Ti is the reverberation time for octave band i. Considering Equations (4) and (5), we must emphasize that both functions C(r) and D(r) show a minimum at the same value of r (r¢ = 2TÖ<bi>). Also in Barron’s revised theory, a very moderate minimum would be obtained for CB and DB, in this case at a reception point distance r¢B = 50 T in which T is again the reverberation time, in other words, the deader the room, the shorter the distance. Both r¢ or r¢B are usually located outside the room and, according to the data of <bi> (see Table 1), it can be expected that r¢<r¢B. Nevertheless, r values can be found within the limits of the deadest churches, as occurs in San Vicente church at 2 kHz (r¢ = 28 m) and at 4 kHz (r¢ = 23.3 m) or Santa Catalina church at 4 kHz (r¢ = 24.2 m). Finally, it must be said that this minimum does not appear when we use these expressions to predict the stationary pressure levels. 4. EXPERIMENTAL RESULTS AND DISCUSSION Figure 3 shows the behaviour of C80 (dB) on the left and D50 (%) on the right as a function of source-receiver distance r (m) between 250 Hz–4000 Hz for the eight churches studied. The same graphics show the theoretical curves of these parameters obtained through Equations (4) and (5), with <bi> calculated as mentioned above. The experimental data are too far out to be fitted by the application of simple diffusefield theory, so the theoretical curves obtained by this classical model are not shown to avoid confusion in the figures. CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES 7 Figure 3. Clarity (dB) and definition (%) versus distance r (m) in four churches: Santa Marina, San Vicente, San Julián and San Gil at each octave band. Symbols: measured data. Solid and dotted lines: theoretical models. 8 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES Figure 3 cont. Clarity (dB) and definition (%) versus distance r (m) in the last four churches: San Pedro, San Marcos, Santa Catalina and San Isidoro at each octave bands. Symbols: measured data. Solid and dotted lines: theoretical models. CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES 9 Table 1 Significant data on Mudejar-Gothic churches Santa San San San San San Santa San Param. Marina Vicente Julián Gil Pedro Marcos Catalina Isidoro <bi> V (m3) 8696 6915 6226 6200 6108 4763 4362 3947 S (m2) 3988 3290 2984 2931 2758 2671 2251 2270 dmx (m) 36 33 27 24 22 29 26 27 ra (m) 2.76 3.87 2.40 3.03 3.46 2.02 3.12 2.50 a0.09 0.19 0.09 0.14 0.18 0.07 0.18 0.12 T1 (s) 3.62 1.71 3.57 2.49 1.76 4.01 1.50 2.13 T2 (s) 3.96 1.81 3.89 2.48 1.98 3.95 1.72 2.21 T3 (s) 4.00 1.82 3.81 2.50 1.99 4.01 1.75 2.30 T4 (s) 3.57 1.68 3.34 2.35 1.87 3.57 1.67 2.14 T5 (s) 2.62 1.40 2.44 1.87 1.56 2.58 1.45 1.76 Tbroad 3.92 1.73 3.74 2.45 1.94 3.90 1.59 2.22 b10.05 0.06 0.05 0.07 0.04 0.10 0.05 0.06 0.06 b20.13 0.08 0.11 0.13 0.09 0.14 0.12 0.11 0.11 b30.09 0.07 0.06 0.10 0.07 0.10 0.08 0.08 0.08 b40.13 0.10 0.13 0.14 0.11 0.15 0.12 0.12 0.12 b50.13 0.10 0.13 0.13 0.11 0.20 0.11 0.12 0.12 bbroad 0.13 0.08 0.12 0.11 0.10 0.14 0.08 0.10 0.11 The most significant geometric and acoustic parameters of the churches analysed are listed in Table 1: volume V, interior surface S, maximum source-receiver distance dmx, acoustic radius ra, mean estimated absorption coefficient a, measured reverberation times for the octave bands between 250 and 4000 Hz and in broadband Ti, and adjustment parameters bi and <bi>. After considering the results, we would like to point out: The parameters at each receiver are relatively disperse. Bradley20 also observed this in his paper on the R index (Running Liveness, reverberant to early sound ratio), obtained from the response to the impulse in concert halls with similar reverberation times. This author uses averages for the 250–500 Hz and 2–4 kHz frequency ranges. Parameter C80 has a spatial and spectral pattern similar to those obtained by Lam21 at frequencies of 125 Hz and 1 kHz when he studies the physical scale models of rectangular and fan-shaped auditoria. In the 4 kHz band, a unique increase in both indices is usually seen in the theoretical model. This increase is mainly due to the fact that there is a sharp drop in reverberation times in this octave in all churches because of air absorption at these frequencies (see Table 1). This increase matches the experimental results for most churches. Greater attenuations over distance than allowed by the model are observed, especially for the deadest churches, as shown in the graphs for San Vicente and Santa Catalina churches. The C80 early to late ratio undergoes changes of sign at different frequencies at the same reception point. This also occurs with the same frequency at different positions within the 16 CLARITY AND DEFINITION IN MUDEJAR-GOTHIC CHURCHES tics fields in Mudejar-Gothic churches, 137th regular meeting of the Acoustical Society of America 2nd convention of the EAA: Forum Acusticum, Berlin, Germany, 14–19 March 1999. 23. Vela, A. (1996). Análisis de diferentes métodos de evaluación de la calidad acústica de un local: aplicación al teatro Gayarre de Pamplona, Tesis Doctoral, Universidad de Valencia, Spain. 24. Lochner, J.P.A. and Burger, F. (1964). The influence of relfection on auditorium acoustics, J. Sound Vib., 1: 426.