Portuguese Catholic churches as reference acoustical models for heritage Catholic churches in Goa, India

ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 66 PORTUGUESE CATHOLIC CHURCHES AS REFERENCE ACOUSTICAL MODELS FOR HERITAGE CATHOLIC CHURCHES IN GOA, INDIA Menino Allan S. M. Peter Tavares and António P. O. Carvalho Laboratory of Acoustics, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal e-mail: [email protected] The architectural genres of the churches built in Goa (a Portuguese colony in India) during the 16th - 19th century period, are partial derivatives of the Portuguese style considering the affinity of the latter’s architecture and worship ambience with that of the Goan churches. Therefore reference ranges used for the normalization of the measured objective acoustical parameters in the Goan Catholic churches of values for Reverberation Time (RT) and Loudness (G) (both regarding the medium octave frequency bands of 500 Hz and 1000 Hz); Objective speech intelligibility parameters such as RASTI and D50; Objective music intelligibility parameters such C80, Center Time (TS) and Early Decay Time (EDT), were obtained through a regression on the total volume of the church of the reported measured values of the same in Portuguese churches. Reverberation Time was found to linearly relate with the total volume of the church (R2 = 0.42) with significant probability (p < 0.01). Mid-frequency Loudness (G) showed exponential decay of the first order with the total volume of the church (R2 = 0.76). A range was constructed using the standard deviation of the mean RT which would be the range of the optimal values of RT. A range of optimal values of Loudness was also constructed using the predicted value and the chi square value. If the measured value of Reverberation Time or Loudness belonged to their respective reference range of values then, their maximum normalized value was equal to 1. In case of RASTI, D50 and C80 the lower limit of the optimal reference range was fixed. The values of RASTI without the Sound Reinforcement System in the Portuguese churches were found to range from 0.22 to 0.56. The upper limit of this range was fixed as the lower limit of the optimal reference range for the normalization of the measured RASTI values. Thus if the measured value of RASTI belonged to this optimal reference range of 0.56 to 1 than the normalized value of RASTI was equal to 1. Definition for speech (D50) showed exponential decay of the first order with the total volume of the church (R2 = 0.56). Therefore, if the measured value of D50 belonged to its optimal reference range of values (0 - 1) then the normalized value was ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 67 equal to 1. Center Time for music (TS) showed a linear regression with the total volume of the church (R2 = 0.40) (p < 0.01). Early Decay Time (EDT) showed exponential decay of the first order with the total volume of the church (R2 = 0.41). If the measured values of TS and EDT were found to be equal to or less than this lower reference limit, then their respective normalized values were considered to be equal to 1. The values of the optimal reference limits were dependent on volume and therefore gave unique results for the different acoustical parameters in each sample church. _____________________________________________________________________________ 1. Introduction During the Portuguese era in Goa (1510 - 1961) a number of churches were built [1][2]. The architectural styles of these churches ranged from the Neo-Roman, Mannerist to the uniquely Goan IndoBaroque motif [3]. The genres of the churches in Goa, in a broad sense, can be considered as partial derivatives of the architectural styles of the churches in Portugal. The Portuguese churches (as represented in Figure 1) share architectural affinity (on the exterior and the interior) and similarity in functionality of the encompassed worship space (for the celebration of Catholic liturgy) with their Goan counterparts. Figure 1. The facade and the interior nave space of Basílica da Estrela, Lisbon, Portugal. The typical 18th century baroque wood altar pieces, paintings and the other many adorning wood artworks inside the churches in Portugal and Goa also indicate a similar acoustical utility. 2. Sample and Reference Churches A few sample Catholic churches (shown in Table 1) (representative of the diverse styles available in Goa) were chosen to be studied. Table 1. Primary details of the Churches surveyed. No CHURCH PLACE BUILT STYLE CH1 Capela do Monte Old Goa 1557 Mannerist CH2 Bom Jesus Basilica Old Goa 1594-1605 Jesuit Classic CH3 Our Lady of Pilar Pilar 1613 Mannerist CH4 Divine Providence Old Goa 1656-1661 Renaissance CH5 Holy Spirit Old Goa 1661-1668 Indo-Baroque CH6 Holy Trinity Benaulim 2005 Contemporary ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 68 The simple statistical data related to the volume and the acoustical parameters measured in the sample Goan churches and the referred Portuguese churches are provided in Table 2 and Table 3 respectively. Table 2. Simple Statistics in Goan churches. Simple Statistics of volume and acoustical measures in Goan churches Statistics VOLUME TS GD50 C80 RT (5001k Hz) EDT (5001k Hz) (m3) (ms) (dB ) 0 - 1 (dB) (s) (s) MINIMUM 2974 250 8.30 0.16 -5.03 3.02 3.51 MEAN 10106 279 11.88 0.21 -3.91 4.36 4.21 MAXIMUM 18858 294 16.79 0.27 -2.88 5.17 4.66 MEDIAN 7691 281 12.05 0.21 -3.75 4.48 4.51 STD_DEVIATION 7631 17 3.62 0.05 1.01 0.81 0.55 SKEWNESS 0 -2 0.35 0.13 -0.20 -1.36 -0.64 KURTOSIS -3 3 -1.47 -2.47 -2.92 2.41 -2.80 CONFIDENCE 6688 15 3.17 0.04 0.88 0.71 0.48 Table 3. Simple Statistics in Portuguese churches. Simple Statistics of volume and acoustical measures in Portuguese churches Statistics VOLUME TS GD50 C80 RT (5001k Hz) EDT (5001k Hz) (m3) (ms) (dB ) 0-1 (dB) (s) (s) MINIMUM 299 80 6.00 0.08 -10.00 1.20 1.06 MEAN 5772 250 13.66 0.20 -3.90 3.39 3.29 MAXIMUM 18674 577 21.90 0.46 2.50 8.14 8.07 MEDIAN 3918 242 13.70 0.17 -4.50 3.09 3.06 STD_DEVIATION 5161 117 3.59 0.10 2.89 1.64 1.60 SKEWNESS 1 1 0.31 0.90 0.29 1.14 1.23 KURTOSIS 0 1 -0.26 0.06 -0.47 1.47 1.82 CONFIDENCE 1580 36 1.10 0.03 0.89 0.50 0.49 Skewness - Measure of asymmetry, Positive: long right tail, Negative: long left tail Kurtosis - Measure of normality, Significance greater than zero: the variable is longer tailed than a normal distribution Confidence - Measure of confidence around the mean. The value obtained is used to construct a 95% confidence interval for the mean. The values of the mean and standard deviation in Portuguese churches in comparison with the values of the mean in the Goan churches justifies the selected Portuguese churches (within tolerable limits) as reference churches. 3. Purpose and Methodology The work presented below is part of a study to acoustically characterize the worship ambience of worship spaces [4][5][6]. The measured acoustical data for RT, EDT, TS, G, RASTI, D50 and C80 from 41 Catholic churches of Portugal was used as reference data [7]. Regression models for each parameter on Volume were tested and the regression analysis was done using Origin 6.1 ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 69 and Origin 8. These values of Portuguese churches are not all from “acoustically good” churches, hence, these reference values were considered only as standard (but not optimal) values. Thus the optimal reference range (= Prediction value ± 1 Standard Deviation) were calculated using the regression equations. The normalized value of RT or G was calculated using Equation 1. nY = 1 ∀ Ymeas ∈(Yref(LOW),Yref(HIGH)) Y Y 1nY ref Δ −= ∀ Ymeas ∉ (Yref(LOW),Yref(HIGH)) Y Y 1nY (LOW) ref Δ −= ∀ Ymeas < Yref(LOW) Y Y 1nY (HIGH) ref Δ −= ∀ Ymeas > Yref(HIGH) nY = 0 ∀ ΔY≥ Yref (1) Where, Ymeas is the measured value of either RT or G nY is the normalized value of either RT or G (Yref(LOW) , Yref(HIGH)) is the optimal reference values range for either RT or G Yref(LOW) = YregressionSD Yref(HIGH) = Yregression+ SD Yregression is the predicted value of either RT or G, obtained through the regression equations given in Table 4 SD denotes the standard deviation from the mean of Yregression. refmeas Y-YY =Δ ~ where denotes the absolute value. In case of RASTI, D50 and C80 the lower limit of the optimal reference range were fixed. The optimal reference range for RASTI was decided using measurements in the Portuguese churches. The values of RASTI without the Sound Reinforcement System (SRS) in the Portuguese churches were found to range from 0.22 to 0.56. Therefore the upper limit of this range was fixed as the lower limit of the optimal reference range for the normalization of the measured RASTI values in the present study. Thus the normalized value of RASTI (nRASTI) was calculated as follows: nRASTI = 1 ∀ RASTImeas ∈ [0.56, 1] 0.56 RASTI56.0 1nRASTI meas − −= ∀ RASTImeas < 0.56 (2) Where, RASTImeas is the measured value of RASTI. nRASTI is the normalized value of RASTI [0.56, 1] is the optimal range of values for RASTI The lower reference limit for optimal values of RASTI = 0.56 ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 70 The normalized value (nC80) was calculated as follows: nC80 = 1, ∀ C80 meas ≥ C80ref C C 1nC ref 80 80 80 Δ −= ∀ C80 meas < C80ref nC80 = 0, ∀ ΔC80 ≥ C80ref (3) Where, C80 meas is the measured value of C80 nC80 is the normalized value of C80 C80ref = C80regression = lower reference limit for optimal values of C80. C80regression is the predicted value of C80 obtained through the regression equation. (Table 4) ref 80 meas 8080 C-CC =Δ ~ where denotes the absolute value. The normalized values of D50 (nD50) was calculated as follows: nD50 = 1, ∀ D50meas ∈ [D50ref, 1] D D -D 1nD ref 50 meas 50 ref 50 50 −= , ∀ D50meas < D50ref (4) Where, D50meas is the measured value of D50 [D50ref, 1] is the optimal range of values for D50 nD50 is the normalized value. D50ref = D50regression = lower reference limit for optimal values of D50. D50regression is the predicted value of D50 obtained through the regression equation. (Table 4) The lowering of the values of TS and EDT was reported to improve the clarity of music. Therefore incase of TS and EDT the upper reference limit for optimal values was calculated. The normalized values were calculated as follows: nZ = 1, ∀ Zmeas ≤ Zref Z Z 1nZ ref Δ −= ∀ Zmeas > Zref nZ = 0, ∀ ΔZ ≥ Zref (5) Where, ‘Z’ denotes either TS or EDT. Zmeas is the measured value. nZ is the normalized value. Zref = Zregression = Upper reference limit for optimal values. Zregression is the predicted value obtained through the regression equations (Table 4). refmeas Z-Z Z =Δ where denotes the absolute value. 4. RESULTS The regression equations for RT, G, C80, D50, TS and EDT are shown in Table 4. ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 71 Table 4. Regression statistics of the Best Reference prediction equation Sr.No PREDICTION EQUATION R2 Adj R2 SD/Chi square F Statistic Prob>F 1 RT (s) = 2.20+ 2.06*10-4 VTOT 0.42 0.41 1.26 28.34 <0.0001 2 3762.49 -V MF e34.1067.9G += (dB) 0.76 3.28 3 C80 (dB) = -1.75 + -3.73*10-4 V 0.44 0.43 2.19 30.84 <0.0001 4 1534.89 -V 50 e29.014.0D += 0.57 0.0042 5 TS (ms) =166.99+ 0.01 V 0.40 0.39 92 26.37 <0.0001 6 EDT = 2.15 + 1.98*10-4 V 0.41 0.39 1.25 26.81 <0.0001 Thus on a scale of 0 - 1, the normalized values obtained for the different acoustical parameters in the Goan churches (using the counterpart acoustical data from the Portuguese churches as reference data) are shown in Table 5. Table 5. Normalized values (0 < nX > 1) of acoustical measures in Goan churches Churches Volume (m3) nRT nG [ MF ] nRASTI nD50 nC80 nTS nEDT CH1 2974 0.73 1.00 0.68 0.85 0.35 0.60 0.30 CH2 3457 1.00 1.00 0.73 0.99 0.70 0.85 0.76 CH3 18858 0.99 1.00 0.68 1.00 1.00 1.00 1.00 CH4 7691 1.00 1.00 0.76 0.87 0.77 0.94 0.76 CH5 17549 0.96 1.00 0.79 0.97 1.00 1.00 1.00 CH6 5761 0.26 0.95 0.51 0.97 0.73 0.61 0.24 5. Conclusion The acoustical data from the Portuguese churches was usable to construct a reference frame for the normalization of the counterpart acoustical measures in the Goan churches. Reverberation Time was found to linearly relate with the total volume of the church (R2 = 0.42) with significant probability (p < 0.01). Mid-frequency Loudness (G) showed exponential decay of the first order with the total volume of the church (R2 = 0.76) (p < 0.01). Definition for speech (D50) showed exponential decay of the first order with the total volume of the church (R2 = 0.56) (p < 0.01). Center Time for music (TS) showed a linear regression with the total volume of the church (R2 = 0.40) (p < 0.01). Early Decay Time (EDT) showed exponential decay of the first order with the total volume of the church (R2 = 0.41) (p < 0.01). The values of the optimal reference limits were dependent on volume and therefore gave unique results for the different normalized acoustical parameters in each sample church. References [1] J. Pereira, 2002. Churches of Goa, Oxford University Press, New Delhi. [2] J. Pereira and P. Pal, 2001. Ed., India and Portugal, cultural interactions, Marg Publications, Bombay. [3] J. Pereira, 2000. Baroque India; The Neo-Roman Religious Architecture of South Asia: a global stylistic survey, Aryan Books International, New Delhi. [4] M. A. P. S. Tavares, 2009. Acoustical Studies of Worship Spaces, Ph.D. thesis, Nagpur University, India. [5] M. A. P. S. Tavares, S. Rajagopalan and S. Sharma, 2007. Comparative Acoustical Studies of Two Goan Churches, Proceedings of the 19th International Congress on Acoustics, 2007, Madrid, Spain; J. Revista de Acústica, 38, 3. ACOUSTIS2013NEWDELHI, New Delhi, India, November 10-15, 2013 72 [6] M. A. P. S. Tavares, S. Rajagopalan S. J. Sharma and António P. O. Carvalho, 2008. Acoustic Characterization of worship ambience – Old Goa’s Capela do Monte, a comprehensive example, Proceedings of the 37th International Congress on Noise and Vibration, 2008, Shanghai, China, in08_0526. [7] A. P. O. Carvalho, 1994. Influence of Architectural Features and Styles on Various Acoustical Measures in Churches, Ph.D. thesis, University of Florida, Gainesville.