This paper reports a systematic experimental and theoretical study of the second-order nonlinear optical properties of multichromophoric molecules that range from dipolar symmetry to three-dimensional octupolar symmetry. The four possible conformers of tetranitrotetrapropoxycalixarene (cone, pace, 1,2-air, 1,3-alt) were studied by nanosecond hyper-Rayleigh scattering and a newly developed time-resolved femtosecond hyper-Rayleigh scattering technique. The latter enables to correct for long-lived fluorescence contributions to the second harmonic scattering intensity. The depolarization ratios D-x/z prove the (partial) octupolar symmetry of the 1,2-alt and 1,3- alt conformers, and thus explain why their hyperpolarizabilities beta(FHRS) are of the same order of magnitude as those of the dipolar cone and pace conformers. The corresponding theoretical second-order nonlinear optical properties (both beta(FHRS) and D-x/z) were calculated using the conformations obtained from single-crystal X-ray diffraction, molecular mechanics (MM), and molecular dynamics (MD) calculations. In contrast with sum-over-state calculations presented in the literature, our theoretical method takes also into account octupolar contributions by linearly adding the NLO-properties of the separate chromophoric groups and using Bersohn's theory. The agreement between experimental and theoretical results is good both for the conformers having dipolar symmetry and for the conformers having (partly) three- dimensional octupolar symmetry. The 1,2-alt and 1,3-alt conformers of the tetranitrotetrapropoxycalixarene represent the first examples of multichromophoric molecules that have high hyperpolarizabilities beta due to 3D octupolar symmetry.