The dramatic increase in sensitivity, spectral coverage and resolution of radio astronomical facilities in recent years has opened new possibilities for observation of chemical differentiation and isotopic fractionation in protostellar sources to shed light on their spatial and temporal evolution. In warm interstellar environments, methanol is an abundant species, hence spectral data for its isotopic forms are of special interest. In the present work, the millimeter-wave spectrum of the $^{13}$CH$_3$OD isotopologue has been investigated over the region from 150$-$510 GHz to provide a set of transition frequencies for potential astronomical application. The focus is on two types of prominent $^{13}$CH$_3$OD spectral groupings, namely the $a$-type $^qR$-branch multiplets and the $b$-type $Q$-branches. Line positions are reported for the $^qR(J)$ clusters for $J = 3$ to 10 for the $v_{rm t} = 0$ and 1 torsional states, and for a number of $v_{rm t} = 0$ and 1 $^rQ(J)$ or $^pQ(J)$ line series up to $J = 25$. The frequencies have been fitted to a multi-parameter torsion-rotation Hamiltonian, and upper level excitation energies have been calculated from the resulting molecular constants.
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