The detailed excitation functions for 13C(α,α) elastic scattering and the additional TTIK measurements were analyzed using the R matrix approach. The analysis covered the excitation region in 17O from 8.6 up to 11.2 MeV. Information on single particle widths of the levels in the 17O nucleus and shell model calculations are in good agreement. A comparative analysis of the α-cluster structures of 16O and 17O nuclei indicates their common underlying nature. However, the structure in 17O is more complex. In particular, each α-cluster level with spin J in 16O corresponds to several levels with spins J=±1/2 in 17O. Unexpectedly, the reduced-width-weighted centroids of the higher-spin members of these doublets always lie at lower excitation energies in 17O.