Prominence threads are expected to be cold plasma condensations in a long magnetic tube. Because of this density inhomogeneity along the magnetic field, the ratio of the fundamental transverse mode period to twice that of its first overtone, P 1/2P 2, must differ from 1. We investigate the dependence of this ratio on the equilibrium parameters of prominence threads and its possible use as a diagnostic tool for prominence seismology. Using the low-beta plasma approximation, we follow the procedure of previous works to obtain the frequencies and spatial distribution of the modes. We also check the thin tube approximation and find it reasonably accurate. The period ratio P 1/2P 2 is found to be greater than unity, in contrast with coronal loops, for which the effect of inhomogeneities is to make this ratio smaller than 1. The ratio is very sensitive to the thread length, while the dependence on other parameters is less important for threads than for coronal loops. Hence, the period ratio can be used to obtain an estimation of the length of the supporting magnetic tube, since the thread length is known from observations. The obtained value of the tube length does not depend on other parameters, so their potential for prominence seismology may be great.