Summary: We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems \((\mathbf{Ku}=\lambda \mathbf{Mu})\). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution cost by adding zero-continuity basis functions, which decrease the matrix connectivity. As a result, rIGA enriches the approximation space and reduces the interconnection between degrees of freedom. We compare computational costs of rIGA versus those of IGA when employing a Lanczos eigensolver with a shift-and-invert spectral transformation. When all eigenpairs within a given interval \([\lambda_s,\lambda_e]\) are of interest, we select several shifts \(\sigma_k\in[\lambda_s,\lambda_e]\) using a spectrum slicing technique. For each shift \(\sigma_k\), the factorization cost of the spectral transformation matrix \(\mathbf{K}-\sigma_k\mathbf{M}\) controls the total computational cost of the eigensolution. Several multiplications of the operator matrix \((\mathbf{K}-\sigma_k\mathbf{M})^{-1}\mathbf{M}\) by vectors follow this factorization. Let \(p\) be the polynomial degree of the basis functions and assume that IGA has maximum continuity of \(p-1\). When using rIGA, we introduce \(C^0\) separators at certain element interfaces to minimize the factorization cost. For this setup, our theoretical estimates predict computational savings to compute a fixed number of eigenpairs of up to \(\mathcal{O}(p^2)\) in the asymptotic regime, that is, large problem sizes. Yet, our numerical tests show that for moderate-size eigenproblems, the total observed computational cost reduction is \(\mathcal{O}(p)\). In addition, rIGA improves the accuracy of every eigenpair of the first \(N_0\) eigenvalues and eigenfunctions, where \(N_0\) is the total number of modes of the original maximum-continuity IGA discretization.