  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.
