  This study presents special cases of inconsistent pairwise comparisons PC
matrices and analysis of their eigenvalue-based inconsistency index using
mathematical methods. All studied special cases of PC matrices are Toeplitz
matrices with only three different entries $1$, $x$, and $1/x$. A new type of
circulant pairwise comparisons matrix has been introduced. Although this class
of PC matrices may be perceived as restricted, it is general enough to cover
numerous levels of eigenvalue-based inconsistency index from the lowest to the
highest. Both exact mathematical expressions and estimations, where the exact
expression was impossible to find, are provided
