We evaluate using a range of ab initio and density-functional approaches the vibrational frequencies, including correction for diagonal anharmonicity, of the lowest triplet state of pyrazine T-1(B-3(3u)); less extensive calculations are also performed for the ground state, three excited singlet states, and five other triplet states. The results indicate that CASSCF-based methods are cumbersome to apply to molecules of this size, with no practicable CASSCF methodology producing a continuous potential energy surface for T-1. While CASPT2 (and also MRCI) methods can correct for erroneous CASSCF state energies, they are not capable of removing the effects of erroneous CASSCF conical intersections. Density-functional schemes, and in particular B3LYP, provide the best qualitative and quantitative results, with the time-dependent approximation to density-functional theory providing results comparable with those from direct evaluation. An overview of vibronic coupling theory is presented and used to demonstrate the relative strengths and weaknesses of these Born-Oppenheimer calculations compared to the traditional diabatic vibronic coupling calculations of Fischer. In particular, for T-1(B-3(3u)), the current assignments of the strongly vibronically active modes upsilon(4), upsilon(5), and upsilon(10a), are readily verified, vibronic activity is predicted for upsilon(12), the anomalous behavior of upsilon(16a) and upsilon(16b) is reproduced, and upsilon(8a) is reassigned.