# Historically Based Room Acoustic Analysis and Auralization of a Church in the 1470s
## 4 Room Acoustic Analysis
### Acoustics in the Nave
It is found that the spatial variations can be explained well by the distance between source and receiver. Linear regression models for mid-frequency G and \(C_{80}\) to source-receiver distance are shown in Figure 15, and the \(R^{2}\)-values are presented in the caption. Except for sources in the gallery, more than 70% of the typical spatial variations in G and \(C_{80}\) can be explained by the source-receiver distance. In Figure 15, the results from within the gallery, within the choir, and the outlier found in Figure 14 are marked, and not included in the linear regression models. They deviate significantly from the pattern defined by the regression line, indicating that the assumption that these locations are governed by the acoustic properties of a certain subspace is accurate. However, no other measurement points show a similar deviation from the prediction. Thus, there are no indications that there are distinct acoustical subspaces in the reconstructed church except those already identified. Another pattern emerges in the evaluation of source-distance dependence, showing that the influence of distance varies depending on the location of the sound source. As shown in Figure 15a, \(C_{80}\) decreases as source-receiver distan  
Figure 15: (**a**) Mid-frequency \(C_{80}\) and (**b**) mid-frequency G as they vary with source–receiver distance; also shown are linear regression models estimating the influence of source–receiver distance for each source locations. \(R^{2}\) values for the models in subfigure (**a**): Source in the gallery: (\(R^{2}\approx 0.06\)), choir: (\(R^{2}\approx 0.78\)), and naive (\(R^{2}\approx 0.75\)). In subfigure (**b**), the corresponding values are gallery: \(R^{2}\approx 0.48\), choir: \(R^{2}\approx 0.98\), and naive: \(R^{2}\approx 0.92\). In subfigure (**b**), the regression line for a theoretical omnidirectional source in free field is also shown. Highlighted data points have been excluded from the regression lines. These correspond to configurations entirely within the gallery or choir and the outlier case when the source is in the gallery and the receiver below it. bearant field becomes more dominant. The linear regression quantifies the influence of distance for each source position. The effects of distance is most strongly seen when the sound source is located in the naive, by the high altar. Moving the sound source to the choir decreases this effect slightly. When the sound source is in the gallery, the effect is almost entirely gone, and clarity is not significantly affected by increasing the distance to a sound source in the gallery. This analysis is confirmed by a review of the \(R^{2}\)-values for the respective linear regression models. These indicate that only about 6% of the variations of \(C_{80}\) in the naive for sources in the gallery can be explained by the distance between receiver and source. The values are significantly higher for sources in the choir and naive. In Figure 15b, the distance dependence of G is examined and compared to the SPL decay of a free-field source. To facilitate comparison, the free-field condition is approximated with a linear regression model and is not normalized to the source's SPL at a distance of 10 m. As would be expected, the G decreases with increased source-receiver distance across all data series. However, the slope of the decays within the church are softer than that for the free field condition. This is due to the sustained reflections of the enclosed space. The G decay is fastest for the free field condition, followed by the source by the high altar. For sources in the choir, the effect is smaller and for sources in the gallery smaller still. These results indicate that the acoustic perception of sources by the high altar (P3 in Figure 9) strongly depends on the listener's position, which implies that the sound field created by such a source is less homogeneous. This may be explained by the lack of nearby reflecting structures around that source position, as compared to the choir and gallery.