Ancient Greek / Roman odeia were semi-enclosed theaters that currently survive without their original roof sections. The work compares the acoustics of the well-preserved Herodes Odeion in its current open-air form to a detailed acoustic model reconstruction of its original roofed version and illustrates the significant differences in acoustics between the two spaces. It is shown that in their original state, the odeia had acoustics appropriate for music performances in contrast to their current open-air form that have acoustic properties appropriate for speech reproduction, similar to the larger open-air theaters of the time which were used specifically for ancient drama performances.