## 3 Results and Discussion
### Characterization of the Historic Study Case
#### 3.1.1 Formal Characters of Rural Historic Buildings: Clusters
Thus, stratum C is predominantly characterized by shapes defined within the landscape for the height-width-length proportions of the building (Figure 6. Stratum C). While stratum A buildings are completely enclosed, stratum C, although characterized by shape compactness and the closed volumes, includes cases with empty or partial portions of the perimeter openings (EV and EW other than 1), such as the presence of full height loggias, or partial ones with loggias only on the first floor (EV = 1 and EW \(\
eq\) 1). Relations between the Architectonic Characteristics of Historic Rural Buildings and Contemporary Ones: Continuity and/or Discontinuity  
The distances \(d_{ij}\) of every contemporary building from the centroids were represented in Figure 8.  
Figure 8 shows that about 52% of the contemporary building sample (28 out of 54 cases) have similarities with at least one of the three clusters of historic buildings, and in particular the assonances are distributed exclusively in the clusters 1 and 2, while the contemporary buildings are always significantly far from centroid of cluster 3. On the contrary, 29% of contemporary buildings have \(d_{ij}\) below 70 th percentile of \(d_{h}\) with cluster 1, while 22% with cluster 2: these cases were identified as assonances. There are two cases where \(d_{ij}\) is below that threshold for both clusters, respectively for a rural house (n. 3) and a building with mixed function (n. 53). Based on the Euclidean distances of contemporary buildings from the centroid of each cluster, Figure 8 also allows understanding of how the assonances of the clusters of the contemporary buildings of the study sample are distributed over the functional classes, illustrated in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Functional Class**} & \multicolumn{3}{c}{**Assonance with Cluster**} & \multirow{2}{*}{} \\  & **1** & **2** & **3** & \\ \hline A: contemporary & & & & Closed volumes and perimeter surfaces and building \\ rural houses & 20\% & 60\% & - & blocks slender upwards, with variable plan shapes. \\ \hline B: contemporary & & & & Diversity in terms of shapes and relationships with \\ farm buildings for & & & & the surrounding landscape due to the specific \\ production & 29\% & 9\% & - & functional and performance requirements [35]; \\  & & & & variable plan shapes, stretched in the landscape and \\  & & & & with compact and closed volumes; peaks of distances \\  & & & & from the centroids of clusters 1 and 2. \\ \hline C: contemporary & & & & Full volume buildings and shapes perceived as \\ buildings with two & 50\% & 33\% & - & stretched in the landscape \\ or more functions & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Distributions of the assonances of the clusters of the contemporary buildings of the study sample over the functional classes. Figure 6: Abacus of the physiognomic characters of the clusters and types of traditional rural buildings of the study sample. The abacus is divided into two sections: one shows the formal characters of the clusters of the historical buildings, the other the distribution of the historical topological sample with respect to the clusters. The second section shows the cases of buildings whose parametric values are closer to those of the barycenter of the cluster they belong to. Figure 7: _Cont_. Tables 8-12 show the delta values, while the graphs of Figure 9 show the deltas between component and corresponding 70 th percentile of the historical cluster, divided for each cluster. Figure 8: Radar diagram of Euclidean distances of the contemporary buildings form cluster centroids of historic sample buildings. (A) rural houses, (B) production buildings, (C) buildings with mixed functions. 70 th percentiles \(d_{i1},d_{i2},d_{i3}\) are 0.1768, 0.2752, 0.3353. respectively (dashed circles). Figure 7: Historical sample, graph for pairs of parameters (A) HW—HL; (B) EV—EW. The shape corresponds to the cluster, the colour to the stratum.