Context: TRACE 171 A° observations of transverse loop oscillations on May 13, 2001 have been studied by De Moortel & Brady (2007). They found hints of 3 periodicities present in this event.Aims: The aim of this article is to improve the analysis, and measure the periodicities more accurately in order to do coronal seismology.Methods: We create multiple (x,t)-slices across the loop, and determine the oscillatory parameters within those slices. We then use statistical methods to reduce the errors on the measured oscillations parameters.Results: We find two populations with a clearly distinct period. The population at the loop top has a period of 895 ± 2 s, while the population in the loop leg has a period of 452 ± 1 s. The fact that the ratio of these two periods is roughly 2 and the geometry of the problem suggests that two harmonics are observed. In the residues, we confirm the presence of a 3rd harmonic with period 309 ± 15 s using two separate data analysis techniques. The three periods are then used to do a seismological estimate of the loop expansion and the density scale height.