## 3 Results and Discussion
### Characterization of the Historic Study Case
#### 3.1.1 Formal Characters of Rural Historic Buildings: Clusters
The graph of Figure 9, referred to cluster 1, shows how the consonant buildings are characterized by values of \(\delta\) generally near 0 for all the parameters. Only in two cases there are slight deviations for one parameter: building n. 3 for residential use deviates for \(\delta\)HL1 and the building has a slender upward shape corresponding to cluster 2 features, with which the building has an asssonance; in the second case (no. 53), instead, the building is multifunctional and has positive \(\delta\)BFO1 indicating that has a greater amount of openings in the perimeter surface. As for dissonances, it may be noted that these can be due to \(\delta\) positive for a single parameter, or for pairs of parameters or even for multiple parameters simultaneously, even for all five. In cluster 1 the following cases were identified:  
* positive for a single parameter (3/54 on the sample total), found either for \(\delta\)HW\({}_{1}\) (41) or for \(\delta\)HL\({}_{1}\) (9-see abacus in Figure 10), therefore dissonance with respect to cluster 1 is due to a perception of the building very slender in the landscape;
* \(\delta\) positive for pairs of parameters (13/54 on the total sample): when it comes to positive \(\delta\)HW\({}_{1}\) and \(\delta\)HL\({}_{1}\), the buildings have closed and compact volumes but can appear either stretched upwards, with \(\Delta\)HW\({}_{1}\) and \(\Delta\)HL\({}_{1}\) positive (5), or flattened to the ground with negative \(\Delta\)HW\({}_{1}\) and \(\Delta\)HL\({}_{1}\) (No. 40-see the abacus of Figure 10 which represents a tool recess); when the dissonance is for EV1 and EW1 the \(\delta\) are positive and the buildings have \(\Delta\)EV\({}_{1}\) and \(\Delta\)EW\({}_{1}\) negative i.e., they give the perception of open volumes (No. 8, 38);
* \(\delta\) positive for multiple parameters (22/54 on the total sample): the building has dissonance for all formal characters both in proportions and in permeability and volume opening characters (see nr. 17 in Figure 10). Also, for cluster 2 there may be asssonances for all parameters, or cases of asssonance in which \(\delta\) is positive for a single parameter, confirming what can be observed in cluster 1. In particular, minor \(\delta\)HW\({}_{2}\) deviations occur for the functional residential class, where for 2 cases out of 5 of asssonance \(\delta\)HW\({}_{2}\) is positive with \(\Delta\)HW\({}_{2}\) negative, resulting in a more flattened form on the soil (nr 3 and 9). In the case of mixed-function buildings (class C), the asssonance is recorded despite the presence of  
Figure 10: Abacus of asssonances and dissonances (in red the \(\delta\) parameters with positive value). parameters with slight deviations, so with \(\delta\)BFO\({}_{2}\) positive (nr. 53, as in the case of cluster 1 previously discussed), or with the pair \(\delta\)HL\({}_{2}\) and \(\delta\)EW\({}_{2}\) (see nr.51 in Figure 10). For cluster 2, the same formal differences can be observed according to the number of parameters showing dissonance:  
* for single parameter (3/54 on the total sample) there are dissonances as for \(\delta\)HW2 in residential buildings (nr. 1 see abacus in Figure 10) and for mixed functions (nr. 52). * for pairs of parameters (16/54 on the total sample): for most cases of dissonances involving pairs of parameters (14/54 cases) these are the parameters related to the buildings form HW and HL (with \(\delta\) values greater than 0.200). Given the corresponding negative values of \(\Delta\)HW and \(\Delta\)HL, the buildings have very flattened and elongated shapes in the landscape (e.g., nr. 26 a cellar building where both processing and storage of the wine is carried out) and with specialized production functions.