  We present a new spectral-timing technique for phase-resolved spectroscopy
and apply it to the low-frequency Type B quasi-periodic oscillation (QPO) from
the black hole X-ray binary GX 339-4. We show that on the QPO time-scale the
spectrum changes not only in normalisation, but also in spectral shape. Using
several different spectral models which parameterise the blackbody and
power-law components seen in the time-averaged spectrum, we find that both
components are required to vary, although the fractional rms amplitude of
blackbody emission is small, ~1.4 per cent compared to ~25 per cent for the
power-law emission. However the blackbody variation leads the power-law
variation by ~0.3 in relative phase (~110 degrees), giving a significant break
in the Fourier lag-energy spectrum that our phase-resolved spectral models are
able to reproduce. Our results support a geometric interpretation for the QPO
variations where the blackbody variation and its phase relation to the
power-law are explained by quasi-periodic heating of the approaching and
receding sides of the disc by a precessing Comptonising region. The small
amplitude of blackbody variations suggests that the Comptonising region
producing the QPO has a relatively large scale-height, and may be linked to the
base of the jet, as has previously been suggested to explain the binary orbit
inclination-dependence of Type B QPO amplitudes.
