The spectroscopic properties of discotic hexa-alkylthiotriphenylenes are studied in solution and thin films and compared to those of hexa-alkyloxytriphenylenes. The solution properties are analyzed in the light of CS-INDO-CIPSI quantum chemistry calculations. The absorption maximum is assigned to the degenerate S-0 --> S-4 transition, The fluorescence of the neat phases is attributed to weakly bound excimers, The phase transition leading from ordered to disordered columnar stacks induces an increase in the oscillator strength of the S-0 --> S-1 transition and favors excimer formation. The influence of structural disorder on the properties of the delocalized states is rationalized by using various approximations within the frame of the exciton theory; three models for the calculation of the exciton coupling (point dipole, extended dipole, atomic transition charge distribution) are tested, short and long range interactions are considered, and the introduction of a dielectric constant is discussed. The best agreement between experimental and calculated absorption maxima is obtained using the atomic charge transition model. Off-diagonal disorder is correlated to structural disorder by changing the orientation and the position of the molecules within the aggregate. The case of degenerate molecular states is compared to that of nondegenerate ones. Orientational disorder has a dramatic effect on the energy and the localization of the upper eigenstate when molecular states are nondegenerate. Conversely, the properties of degenerate eigenstates are quite insensitive to orientational disorder. The magnitude of the off-diagonal disorder induced by positional disorder largely depends on the model used in the calculation of the exciton coupling. The results of the numerical calculations are in agreement with the small change observed in the neat phases absorption maxima upon a quasi one-dimensional melting of columnar stacks.