The recent detection of multiple harmonic standing transverse oscillations in coronal loops by Verwichte et al. is of special importance, as it allows one to obtain information on the longitudinal density variation in loops. Verwichte et al. detected the simultaneous presence of both the fundamental and the first-overtone mode in two coronal loops. Here we point out that the ratio of the period of the fundamental mode to the period of the overtone mode differs from 2 in loops with longitudinal density stratification. Conversely, the difference between this ratio and 2 can be used as a seismological tool to obtain information about the density scale height in loops.