We use frequency-resolved spectroscopy to examine the energy spectra of the prominent low frequency QPO and its harmonic in GX 339-4. We track the evolution of these spectra as the source makes a transition from a bright low/hard to hard intermediate state. In the hard/intermediate states, the QPO and time averaged spectra are similar and the harmonic is either undetected or similar to the QPO. By contrast, in the softer states the harmonic is dramatically softer than the QPO spectrum and the time averaged spectrum, and the QPO spectrum is dramatically harder than the time averaged spectrum. Clearly, the existance of these very different spectral shaped components mean that the time-averaged spectra are complex. We use the frequency resolved spectra to better constrain the model components, and find that the data are consistent with a time-averaged spectrum which has an additional low temperature, optically thick Comptonisation component. The harmonic can be described by this additional component alone, while the QPO spectrum is similar to that of the hard Comptonisation and its reflection. Neither QPO nor harmonic show signs of the disc component even when it is strong in the time averaged spectrum. While the similarity between the harmonic and QPO spectra in the intermediate state can be produced from the angular dependence of Compton scattering in a single region, this cannot explain the dramatic differences seen in the soft state. Instead, we propose that the soft Compton region is located predominantly above the disc while the hard Compton is from the hotter inner flow. Our results therefore point to multiple possible mechanisms for producing harmonic features in the power spectrum. The dominant mechanism in a given observation is likely a function of both inclination angle and inner disc radius.
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