  Ratios of multiplicity moments, H_q (cumulant over factorial moments
K_q/F_q), have been observed to show an oscillatory behaviour with respect to
order, q. Recent studies of e^+e^- annihilations at LEP have shown, moreover,
that the amplitude and oscillation length vary strongly with the jet resolution
parameter y_{cut}. We study the predictions of the perturbative QCD parton
cascade assuming low non-perturbative cut-off (Q_0\sim \Lambda_{QCD}\sim few
100 MeV) and derive the expectations as a function of the cms energy and jet
resolution from threshold to very high energies. We consider numerical
solutions of the evolution equations of gluodynamics in Double Logarithmic and
Modified Leading Logarithmic Approximations (DLA,MLLA), as well as results from
a parton MC with readjusted parameters. The main characteristics are obtained
in MLLA, while a more numerically accurate description is obtained by the MC
model. A unified description of correlations between hadrons and correlations
between jets emerges, in particular for the transition region of small y_{cut}.
