We have analysed archived Ginga data on the Z source Sco X-2 (GX349+2). We present the first detailed investigation of its X-ray fast-time variability, as a function of position in the Z track. During the two-day observation over the period 5-7 March 1989, the source was in the so-called flaring branch, and the lower part of the so-called normal branch. We found broad peaked noise with a centroid frequency and width of ~4-7 Hz and ~6-12 Hz respectively. The peaked noise was strongest in the lower flaring branch, with a maximum fractional rms amplitude of ~3 %. We conclude that it is not a manifestation of atoll source high frequency noise, as had been suggested, and compare it with the power spectral features seen in other Z sources. We find that the peaked noise is markedly different to the quasi-periodic oscillations found in the normal and flaring branches of Sco X-1; however it bears some resemblance to that seen in the flaring branch of Cyg X-2 at low overall intensities.