Correlations of the acoustic fields of mudejar-gothic churches

BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 Pages 175–196 175 Correlations of the Acoustic Fields of Mudejar-Gothic Churches Miguel Galindo, Sara Girón and Teófilo Zamarreño Departamento de Física Aplicada II, Universidad de Sevilla, E. T. S. de Arquitectura IUACC, Avda. Reina Mercedes 2, 41012-Sevilla, Spain [email protected], sgir[email protected], [email protected] (Received 3 March 2008 and accepted 26 August 2008) ABSTRACT This paper studies the statistical correlations between monaural acoustic parameters with themselves and with architectural parameters from an acoustical survey undertaken in 12 Mudejar-Gothic churches in Seville, southern Spain. Objective room-acoustic parameters have been measured using impulse response analysis through a maximum-length-sequence measurement system in each church. Measurements cover time parameters (reverberation time, early decay time); levels (sound strength); energy-based parameters (centre time, clarity for speech, clarity, definition, early lateral energy fraction); and speech intelligibility (rapid speech transmission index) and the analysis takes into account both spatially averaged values and individual positions. The aim of the study is to identify the main architectural factors that have relevant influence on the acoustic fields of the churches, and the minimum number of room acoustic parameters which are able to describe adequately this acoustic field, thus the possible excess of information is evaluated. Significant correlations have been found that, in the best cases, correspond to fits using pairs of independent variables instead of one single variable. The best option to describe the six subjective attributes of sound perception in these buildings consists of three acoustic parameters formed by two different pairs plus the early lateral energy fraction. 1. INTRODUCTION Ever since the 1950s, a number of monaural and binaural acoustic parameters based on experiments has been established for the evaluation of room sound quality in order to know relevant details of the sound field that were not previously covered, apart from the reverberation time (Sabine 1923). This has given rise to a multivariable and multipositional study of a closed enclosure. The singular development of electronics and computer science has propitiated a great advance in building acoustics measurements (ISO 18233 [1]). In addition, these objective acoustic parameters are well correlated to the subjective judgments of music, speech and singing, giving rise to the consensus expressed in ISO-3382 [2] (currently under revision ISO/DIS 3382-1 [3]). From the very beginning, research has been aimed at identifying dependencies of acoustic parameters on geometric dimensions in order to enable spaces to be designed with appropriate variables for sound quality, as the general tendency to investigate the relationships between acoustics and architecture bears witness. At the same time, correlations between different acoustic parameters have also been studied in order to determine the number of strictly independent variables of the existing group. Hence in a precursor study in concert halls, Schroeder et al [4] studied the dependence of some acoustic parameters on hall volume and width. Later Gade [5,6], in a report concerning 11 European concert halls, showed the necessity of using at least one objective parameter per subjective aspect (reverberance/clarity, level and spaciousness) and employed statistical methods to determine the mutual connections between the room-acoustic parameters and their dependence on architectural design variables. A similar analysis was carried out by Pelorson et al [7] in 14 concert halls, and, more recently the study of Hidaka et al [8] correlated objective acoustical factors and architectural parameters in 18 European and Japanese chamber-music halls to reveal four orthogonal objective acoustic parameters (reverberation time, strength, initial time delay gap and binaural quality index) in their sound fields. In the specific area of worship buildings, Carvalho [9] published the statistical relationships between 6 objective acoustic parameters using averaged and total data in 41 Catholic churches of different styles in Portugal. Through linear and non-linear regression, this same author [10] later studied the relationships between 8 objective acoustical measures (lateral fraction was excluded) using averaged data with 13 architectural features of the churches. Higher correlations were found in the non-linear case in both papers and it was also concluded that the most significant parameters to describe the acoustics of a church were the reverberation time, the clarity and the total sound level. The Portuguese report took into account other aspects such as an in-depth study of the speech intelligibility of the churches through RASTI measures and its relationships with architectural features [11,12], and the relationships of the subjective parameters with the objective measures and with architectural features [13]. Furthermore, Magrini et al [14] made a contribution along these lines by studying 10 churches in Italy of different styles and the correlation [15] between several room acoustic parameters and the church volume and volume/floor surface ratio. To conclude this review, it should be mentioned that Cirillo et al [16] studied the acoustic properties of a special typology of church in Italy, the Apulian-Romanesque. They found remarkable relationships [17] between reverberation times at mid-frequencies and geometric parameters only when similar mean absorption coefficients were involved; all the other room acoustic parameters presented poor correlations with architectural parameters. As for the correlations between acoustic parameters themselves, they highlighted an excess of information in the same way as did Carvalho, and proposed the early decay time, the sound strength and the interaural cross-correlation coefficient as the three acoustic parameters that characterize the acoustic field of this type of church. In this paper the experimental data obtained in the Mudejar-Gothic churches [18]; and which have been analysed from different points of view such as the distribution of omnidirectional acoustic energy [19], the distribution of speech intelligibility 176 Correlations of the Acoustic Fields of Mudejar-Gothic Churches BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 177 descriptors [20], and the directional energy parameter [21], have been collected together in order to examine the statistical correlations between acoustic and architectural parameters and between acoustic parameters themselves. 2. MUDEJAR-GOTHIC CHURCHES All these churches were built in the Middle Ages and have suffered restorations and adaptations throughout their existence due to several reasons (including earthquakes, fires, and deterioration). Their architectural style was the result of a unique Spanish artistic movement since it was influenced by both Islamic and Gothic Christian elements. The Mudejar-Gothic churches in Seville, all located in its historical centre, are morphologically characterized by this stylistic dualism: a vaulted Gothic apse and a body of three naves with a timber roof (collar beam in the main nave) of Moorish origin. Their brick walls are complemented with portals and a stone apse. The supports are also clearly Islamic, with quadrangular or sometimes octagonal pillars and with raised brick mouldings as decoration. Pointed, round or segmental arches rest on these supports. In order to complete the description of these religious spaces, Fig. 1(a) shows some photographs taken in Santa Marina, San Julián and San Marcos churches. Among other elements of particular interest, funeral chapels have been successively added to the side naves which, on some occasions, are housed in remaining sections of pre-existent mosques. Funeral chapels do not exist in San Julián, San Esteban and San Marcos churches. Figure 1(b) shows the ground plan for each church studied in this paper, with the source and receiver positions for measurements and the seating areas. These drawings are all on the same scale and presented in order of decreasing volume. The name of each church is accompanied by its abbreviation which is used in the tables throughout the paper. Figure 1. (a) Interior of Santa Marina church (left), San Julián church (centre) and San Marcos church (right). 178 Correlations of the Acoustic Fields of Mudejar-Gothic Churches Table 1 summarizes some geometric and architectural data of interest, obtained through measurement or building plans, and a brief description of the interior finishes for the twelve churches: Figure 1. (b) Ground Plan with the source (S) and receiver positions () for measurements, pew zone (shaded area), for the 12 churches. Vvolume, Llength, Wwidth, Haverage height, STtotal surface, SCcentral nave ground surface, SLlateral nave ground surface, SG=SC+SLtotal ground surface, (presbytery floor area not included), The church floors are of marble or ceramic material and the congregational seating area consists of wooden pews distributed in the main nave and also occasionally in the lateral naves (shaded area in Fig.1(b)). A complete description of the furnishings and other acoustical information on these temples can be found in Galindo et al [18]. 3. MEASUREMENT TECHNIQUES The procedures employed have been those established in ISO 18233 [1], ISO 3382 [2] and IEC 60268-16 [22] standards, and all measures were carried out in unoccupied churches. Temperature and relative humidity have been monitored during the measurements. The range of variation in all churches was 22.6-27.4 °C for the BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 179 Table 1: Significant data of the churches VLWHS TSC+SLV/SG Church (m3)(m) (m) (m) (m2)(m) (m3/2)Finish (*) MN 10708 34 19 15 4517 250+279 20.24 (v), (-), (s), (w), 3si OM 8180 29 16 16 3760 194+219 19.81 (pp), (mc), (p), (w), 2do LO 7040 24 24 16 3346 132+267 17.64 (pp), (wc), (p), (w), 2do VI 6915 26 18 11 3656 144+180 21.34 (pp), (-), (f), (w), 2do, 1si JU 6226 27 15 13 3321 187+150 18.47 (pp), (wc), (f), (w), 1do GI 6200 22 15 14 3249 170+148 19.50 (pp), (wc), (f), (w), 2do PE 6180 20 17 16 3035 123+154 22.05 (pp), (wc), (p), (t), 2do AN 5955 23 15 11 3380 132+154 20.82 (pp), (-), (f), (w), 2do, 1si ES 4746 20 14.5 14 2691 141+134 17.26 (v), (-), (p), (w), 1do, 1si MC 4623 26 17 10 3041 144+226 12.49 (d), (-), (s), (r), 2si CA 4362 22 15 12 2474 121+102 19.56 (pp), (-), (p), (w), 2do IS 3947 26 14.5 11 2547 133+144 14.25 (pp), (mc), (f), (w), 1si *Lateral wall: v=visible brick; pp=plastered and painted; d=directly painted brick. Baseboard: mc=major chapel; wc=whole church. Decoration: s=scarce; f=fair; p=profuse. Ceiling: w=wooden framework in three naves; t=tiles substitute the wooden board in the laterals; r=rough ceramics substitute the wooden boards in the central nave. Inner doors: si=single; do=double. temperature, 35.7-65.7 % for the relative humidity and 101.7-102.5 kPa for the atmospheric pressure. Monaural impulse responses (IR) and other room responses to stationary signals have been measured to determine the following parameters for each frequency band between 125-4000 Hz in all receiver positions: •reverberation time (T) •early decay time (EDT) for the evaluation of reverberation characteristics, •sound strength (G) to explore the sound level distribution within the measuring area, •centre time (Ts), •clarity for speech (C50), clarity (C80) and definition (D50), as energy-based parameters related to the early-to-late or early-to-total sound energy ratio, •early lateral energy fraction (LF) to study the spatial impression phenomena in these places, and finally, •the RASTI index to evaluate the intelligibility from the degradation of the modulation transfer function. All these objective descriptors assess the perception of music, speech and singing in these religious places. The IR has been obtained using MLS (Maximum Length Sequence) signals generated and analysed by the analyser MLSSA from DRA laboratories. The omnidirectional source (B&K 4296) was placed at the most usual point of location of the natural source: the altar at a height of 1.70 m from the floor. The microphone (omnidirectional B&K 4190 1 /2-in or multipattern Audio-Technica AT4050/CM5) was located at the approximate height of the head of a seated person ~1.20 m, in a predetermined number of positions distributed in the central nave and the lateral naves, ranging from 12 reception points for Santa Catalina church to 23 for Santa Marina (Fig. 1(b)). The calculation of sound strength uses the emission of a stationary signal, related the level produced by the source, at 10 m distance under free field conditions. The equivalence of these results with those obtained by MLS signals has been also published elsewhere [18]. The RASTI values used in this paper have been obtained using the B&K 3361 system, which uses the modulated stationary noise technique. The equivalence of these results with those obtained through the MLS spectrum has also been proved in previous published work [18]. To characterize the acoustics of each church, the following multi-octaved band average indices have been calculated: •clarity and centre time as a direct average of the values at frequencies of 500, 1000, and 2000 Hz, •clarity for speech and definition as a weighted average as Marshall [23] proposed: , (1) •reverberation time, early decay time and sound strength as a mean of the corresponding values at mid-frequency 500 and 1000 Hz bands, and •early lateral fraction as a direct average of 125, 250, 500, and 1000 Hz octave bands [3]. CCHzCkHz C av50 50 50 50 015 500 025 1 035=++.( ).().(220254 50 kHz C kHz). ( )+ 180 Correlations of the Acoustic Fields of Mudejar-Gothic Churches 4. ANALYSIS OF THE POSITION-AVERAGED DATA This section deals with the results of analysing the set of data from the churches by linear and non-linear regression methods. The aims of the analyses are to reveal the dependencies of room acoustic parameters on architectural variables. Throughout this section, frequency (as described in section 3) and position-averaged values will be discussed since the design aspects are related to the overall features of the churches. 4.1. Correlations with one geometric variable Table 2 summarizes the results of the 9 monaural acoustic parameters analysed in each church. These acoustic variables are shown in Table 3 linearly correlated with the 7 geometric variables specified in the heading of Table 1 plus the mean height/width, BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 181 Table 2: Spatially averaged room-acoustic parameters in each church Church T (s) EDT (s) TS(ms) G (dB) C80(dB) C50av(dB) D50 (%) LF (%) RASTI MN 3.09 3.12 213 7.88 −3.03 −4.48 30.0 17 0.38 OM 2.74 2.85 208 7.89 −3.36 −5.51 25.3 17 0.40 LO 2.29 2.38 172 7.04 −2.42 −4.17 29.2 21 0.47 VI 2.48 2.49 190 8.30 −2.87 −5.14 26.2 14 0.42 JU 2.28 2.15 152 8.37 −1.29 −2.56 35.2 17 0.49 GI 2.28 2.33 167 7.48 −2.14 −3.70 31.3 18 0.45 PE 2.06 2.00 148 9.47 −1.74 −3.79 32.9 18 0.47 AN 2.00 1.97 151 9.22 −2.32 −5.48 29.7 23 0.45 ES 2.02 1.88 136 8.50 −0.83 −3.18 34.0 17 0.43 MC 3.25 3.59 269 11.5 −5.77 −8.21 16.3 16 0.35 CA 1.61 1.56 104 9.15 1.10 −1.76 42.7 20 0.60 IS 2.22 2.41 189 9.33 −4.05 −6.54 20.0 20 0.42 Table 3: Linear correlation between acoustic parameters and geometric parameters R2< 0.25 are excluded and those with R2> 0.50 in bold. Underlining means P < 0.05 Parameters W L H H/W STSG=SC+SLVV/SGV/ST T--- 0.75 --- --- 0.76 0.84 0.76 --- 0.52 EDT --- 0.48 --- --- 0.28 0.56 --- --- --- TS--- 0.39 --- --- --- 0.43 --- 0.27 --- G--- --- 0.29 --- --- --- --- --- 0.33 C80 --- --- --- --- --- --- --- 0.31 --- C50 --- --- --- 0.27 --- --- --- 0.29 --- D50 --- --- --- --- --- --- --- 0.35 --- LF --- --- --- --- --- --- --- --- --- RASTI --- --- --- --- --- 0.27 --- 0.28 --- H/W, and volume/total surface, V/ST, ratios. Their most significant dependencies are represented by the inclusion of the coefficient of determination, R2. Correlations for which R2<0.25 are excluded and those for which R2>0.5 are written in bold. The significant Pvalues have also been indicated by underlining their corresponding R2 value. It can usually be concluded that the independent variable can be used to predict the dependent variable when P<0.05. Only eleven correlations achieve this condition, giving T as the best estimated acoustic parameter. These results show the following features: -The best linear regression fits were found to be between the church floor surface area and reverberation time T, and between the church floor surface area and early decay time EDT, whose results are expressed in eqns (2 - 3). (2) (3) -No parameter is correlated with the church width. -The early lateral energy fraction LF has no significant dependence on the church architectural parameters. -The omnidirectional energy-based acoustic parameters centre time Ts, clarity C80, clarity for speech C50, and definition D50 present some noticeable correlations with the ratio V/SG. -In the same way, the sound strength G shows only a weak dependence on the height H and the V/STratio. This is a logical result because the averaged values for these churches are approximately constant (see column G in Table 2) and hence G (frequency and spatially averaged) can be considered as a typological constant parameter. The standard deviation (1.17 dB) is approximately the JND for this parameter. -Finally, speech intelligibility seems to be affected by the church floor surface area. In Fig. 2, as an example of the whole set of results, the regression calculated between the RASTI index and the V/SGratio is shown. Although the correlation is poor it can be seen that most points are in the 95% confidence interval. From all the linear tests carried out it is also possible to emphasize the following trends: -Reverberation times increase with church length, total surface area and floor surface area. -Early decay times increase with church length and floor surface area. -Centre time increases with church floor surface area. -Clarity, clarity for speech and definition decrease as the width of the churches increase. Other dependencies are not clear. EDT S S CL =⋅+⋅ + −− 669 10 513 10 13 ..() TSS CL =⋅+⋅ + −− 858 10 426 10 13 ..() 182 Correlations of the Acoustic Fields of Mudejar-Gothic Churches When non-linear correlations are calculated, the number of significant correlations increases notably and the coefficients of determination improve in relation to those obtained in the linear relationships. Table 4 summarizes the results obtained where in all cases the best results correspond to third-order functions (cubic (+) in Table 4, or inverse, unmarked). There are two exceptions: a third-order logarithm type, y=y0 +a1n x+b(1nx)2+c(1nx)2, ((ln), in Table 4); and an exponential decay, y=a exp (b/ (x+c)), ((exp), in Table 4). Again the significant Pvalues have been indicated by underlining their corresponding R2value. There is an increase in the number of correct estimations in relation to linear estimations, where T is again the best estimated BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 183 V/SG (m) 12 14 16 18 20 22 24 RASTI 0.2 0.3 0.4 0.5 0.6 Linear Regression 95% Confidence Interval Measured Figure 2. RASTI values as a function of the V/SGratio. Table 4: Coefficients of determination R2 > 0.25, (R2 > 0.50 in bold) in non-linear correlations; almost all are third-order functions: cubic (+) or inverse, with two exceptions ln and exp, respectively. An underlined value means P < 0.05 Parameters W L H H/W STSG=SC+SLVV/SGV/ST T 0.47+0.79 0.60+--- 0.79 0.88+0.94 --- 0.69 EDT 037 0.51 0.69+0.38 0.35 0.63 --- 0.51+0.74 TS0.29 0.46 0.73+0.44 --- 0.54+--- 0.57+0.71 G--- --- 0.52 0.51 0.321n --- 0.59 0.54 0.38+ C80 --- 0.38 0.67+0.44+--- 0.44 --- 0.52+0.69 C50 --- 0.30 0.74+0.49+--- 0.27 --- 0.56+0.60+ D50 --- 0.33 0.66+0.49+--- --- --- 0.56+0.68 LF 0.32 --- --- 0.45+0.29 0.41+--- --- --- RASTI --- 0.33 0.68+0.35+--- 0.45exp --- 0.50+0.71 (17) (18) (19) According to all the tests carried out, the best correlation for LF corresponds to the tandem of dependant variables T, RASTI; (R2=0.39). This is the only parameter that cannot be obtained with enough accuracy when starting from the other acoustic parameters (see Table 7), and hence its estimations are the worst. In the studies conducted in Portuguese churches by Carvalho [10] to investigate similar correlations, it was shown that the acoustic particularities of worship places were described starting from a set of three monaural acoustic parameters. In his studies early lateral acoustic energy was not considered which in general (for concert halls and churches) appeared as an independent parameter. Four parameters would be needed therefore to characterize the inside acoustic field. The results obtained in this case proved that only three parameters are necessary: two room acoustic parameters in order to determine the others, plus the early lateral energy fraction, LF. As it has been pointed out, Cirillo et al [17] also found the same result, working on a common typology, while Carvalho [10], who studied churches which correspond to different eras and architectural styles, needed one more independent parameter. The common typology, together with the constancy in the shape, seem to be RASTITC S =+ + −⋅ − 0 4083 0 0010 0 0238 3 5197 10 80 9 .. . . TTCR S 2 80 22 0 0016 0 89+=.;. D CT 50 05 10 6508 96514 91 6024 50 2 =−−     +− .e .. . 22 5539 59383 2 2 1 . .; ()        R CTCT S50 80 6 6 1759 0 0353 1 7338 1 2493 10=− + + + ⋅ − .. . . SS CR 2 80 22 0 0316 0 91−=.;. 190 Correlations of the Acoustic Fields of Mudejar-Gothic Churches 1.0 0.8 0.6 0.4 0.2 0.0 20 15 10 5 0.0 0.1 0.2 0.3 0.4 0.5 LF G (dB) RASTI Measured Adjusted Figure 5. 3D plotted graph of RASTI as a function of G and LF acoustic parameters. decisive factors in the reduction of the number of descriptor parameters of the acoustics in these enclosures. Furthermore, in the Mudejar-Gothic churches, the range of geometric values (church width, height and length) presents a great uniformity, a fact that seems to propitiate the dependencies obtained. In addition, several combinations of pairs of parameters exist which allow the acoustic behaviour to be described, especially those formed by the tandem (TS, C80) or (EDT, D50). In most cases, the correlations correspond to paraboloid surfaces with a coefficient of determination R2≥0.80 in all cases. Specific correlations that correspond to Lorentzian and Gaussian surfaces exist. The two tandems presented show great similarity since the first and second member of each pair are highly correlated to each other (see Table 7, TSwith EDT, and C80 with D50). In each pair its first member takes the clarity of the enclosure into account subjectively, while its second member, which corresponds to early-to-late or early-to- total energy ratios, carries information about the musical clarity or about the definition of speech. In any case the pairs of independent variables that serve from base to determine the remaining acoustic parameters (bearing in mind the exclusion of LF), correspond to parameters which are very sensitive to position. Another discussion of the results is conducted through a comparison of the independent acoustic descriptors found in this paper with those in pieces of work of the same nature carried out in concert halls and churches. This comparison is shown in Table 8 where the association of each subjective attribute of sound perception with the corresponding objective parameter has been deduced from Barron′s[24] study for music and the widely accepted criteria for speech intelligibility. Although a strict comparison is not possible due to the variety and omissions of parameters measured in the separate studies certain features may be highlighted: All results indicate that spatial impression is an independent attribute. Furthermore, having taken all 6 attributes into account by means of the measured parameters, the number of independent acoustic variables (3) in the present work on Mudejar-Gothic churches coincides with that of Cirillo’s work on Apulian-Romanesque churches consisting of BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 191 Table 8: Minimum independent parameters. Results from Carvalho (C), Cirillo (Ci), Gade (G), Hidaka (H), Pelorson (P), and present work (Pr1, Pr2)* Subjective Objective C Ci G H P Pr1 Pr2 Reverberance T †--- --- --- --- Reverberance/Clarity EDT, TS--- ††† Clarity C80 †--- --- --- --- †--- Level G †† --- --- Spatial Impression LF, IACCENA ††† Speech Intelligibility RASTI, C50, D50 --- --- NA NA --- † (*) Not available (NA). Churches (†), concert halls ( ). buildings of the same typology. Nevertheless, in the present study (in both 3-parameter proposals) level never appeared as an independent variable in spite of being one in all the other analyses in churches and concert halls. Finally, it should be pointed out that the study of mixed correlations which uses one geometric parameter and one room acoustic parameter as independent variables has been omitted. Although it is certain that good correlations would be achieved, the inclusion of one room acoustic parameter supposes that the in situ impulse response must be obtained, for which no improvement could be supposed regarding the use of two room acoustic parameters as independent variables. Meanwhile, correlations which involve reverberation time, volume and source-receiver positions are possible in each church, in fact an analytical model based on these variables and on measured clarity results is able to predict definition, clarity for speech, centre time and sound strength19 and rapid speech transmission index20 values as a function of source-receiver distances; the spatial distribution of lateral energy fraction21 values has also been discussed from the point of view of this analytical model in these temples. 6. CONCLUSIONS This paper studies the statistical correlations found between monaural acoustic parameters with geometrical variables and with acoustic parameters themselves in a survey of 12 Mudejar-Gothic churches in the city of Seville in southern Spain. Measurements were taken between the 125-4000 Hz octave band in multiple locations in each church, and both linear and non-linear regression have been used in the analysis. The acoustic parameters were spectrally averaged according to the most widely accepted way in order to qualify room acoustic quality and the correlations have been tested between the spatially averaged values in the room (each church is characterized by a single value) and with the full set of positional data. The best correlations between position-averaged parameters and the geometric parameters correspond to non-linear functions, where the geometric values are used as independent variables (one or two variables). The functions correspond to third-order polynomials. It has been impossible to establish a minimum group of architectural parameters to describe all room acoustic parameters because none of the architectural characteristics studied is related to the early lateral acoustic energy. The architectural parameter resulting in the best fits is constituted by the V/STratio of the churches which gives a first indication of the trends of the acoustic parameters, except for the early lateral acoustic energy, as mentioned earlier. The correlations increase in number when two geometric parameters are used as independent variables and with much better results for the coefficient of determination. To describe the complete list of subjective acoustic attributes in these churches, three architectural parameters are necessary, consisting of the height, the width and the ground floor area, this last parameter involving the floor area of the central nave and lateral naves. However, in this case, the coefficients of determination are in the range between 0.56 and 0.69, and P< 0.05. This procedure was repeated by analyzing correlations exclusively between the room acoustic parameters. According to the statistical analysis (Pvalue), the acoustic parameters proved to be more robust variables than the architectural variables. The 192 Correlations of the Acoustic Fields of Mudejar-Gothic Churches relationships which involve pairs of parameters with third-degree polynomials, indicated the great dependence between them in almost all cases and has led to their study with two independent variables. These results also show the need for a set of three acoustic parameters to describe the acoustic behaviour of the churches studied, although in this case with a much higher coefficient of determination in the correlations than the one obtained in the tests with architectural parameters as independent variables. When taking the early lateral acoustic energy into consideration, the best cases correspond to the pair formed by the centre time and the clarity, or the early decay time and the definition. In concert halls, the number of parameters suggested for measurement when the 6 subjective attributes of sound are taken into account, are four or more (see Table 8) which are bound together with the perception of reverberation, sound distribution, clarity and spaciousness. An exception to this is Gade’s study where the number of essential parameters is also three but no single parameter related to speech intelligibility was included in the analysis (neither C50, nor D50 nor RASTI). In the churches included in Carvalho’s analysis on different style Portuguese churches, the spatial impression, which is always assumed as an independent parameter, increases the number of essential parameters for the evaluation of the 6 subjective attributes of sound to four (Table 8). Nevertheless, the conclusions drawn here for the Mudejar-Gothic churches are in accordance with those reached by Cirillo et al who also pointed out that only three parameters were essential to describe the acoustic field of Apulian-Romanesque churches. One possible explanation for this reduction in the number of independent variables is the common typology, the constancy in the forms and the small variation in the ranges of the geometric parameters. These features are thus associated to this reduction to the three subjective aspects in the Mudejar-Gothic church case: reverberance/clarity, clarity or speech intelligibility, and spatial impression. ACKNOWLEDGEMENTS The authors would like to express their gratitude to the priests and church management for allowing the measurements to be carried out. This work has been partially supported by the Spanish MCYT project BIA2003-09306-CO4-02. REFERENCES [1] ISO 18233 Acoustics-Application of new measurement methods in building and room acoustics 2006. [2] ISO 3382. Acoustics-Measurement of the reverberation time of rooms with reference to other acoustical parameters 1997. [3] ISO/DIS 3382-1. Acoustics-Measurement of room acoustic parameters. Part 1: Performance rooms. [4] Schroeder, M. R., Gottlob, D., Siebrasse, K. F., Comparative study of European concert halls: correlation of subjective preference with geometric and acoustic parameters, Journal of the Acoustical Society of America, 1974, 56 (4), 1195–1201. [5] Gade, A. C., Acoustical survey of eleven European concert halls- a basis for discussion of halls in Denmark, The acoustical laboratory, Technical university of Denmark, report 44. ISBN: 0 105–3027, 1989. BUILDING ACOUSTICS · Volume 15 · Number 3 · 2008 193 [6] Gade, A. C., The influence of architectural design on the acoustics of concert halls, Applied Acoustics, 1990, 31(1-3), 207–214. [7] Pelorson, X. 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