For realistic sources in a spherical, radially heterogeneous, anelastic earth, it is now possible to generate complete theoretical seismograms for direct comparison with the experimental records from the long-period instruments of the WWSSN. These synthetic seismograms for torsional waves contain all modes that exist for periods above 10 sec. All body-wave phases, as well as surface-wave arrivals, are obtained. A single, relatively short computer run yields all the required frequency-domain information for the necessary, 90-100 radial modes; the associated program is available for general distribution; simple, inverse Fourier transformation is used to obtain the time series. The initial, direct comparison of these complete theoretical seismograms with an experimental record from a standard long-period instrument of the WWSSN is exhibited.