Angular correlations between unidentified charged trigger (t) and associated (a) particles are measured by the ALICE experiment in Pb-Pb collisions at sNN=2.76TeV for transverse momenta 0.25<pTt,a<15GeV/c, where pTt>pTa. The shapes of the pair correlation distributions are studied in a variety of collision centrality classes between 0 and 50% of the total hadronic cross section for particles in the pseudorapidity interval |η|<1.0. Distributions in relative azimuth δφ≡φt-φa are analyzed for |δη|≡|ηt-ηa|>0.8, and are referred to as "long-range correlations". Fourier components Vnδ≡〈cos(nδφ)〉 are extracted from the long-range azimuthal correlation functions. If particle pairs are correlated to one another through their individual correlation to a common symmetry plane, then the pair anisotropy Vnδ(pTt,pTa) is fully described in terms of single-particle anisotropies vn(pT) as Vnδ(pTt,pTa)=vn(pTt)vn(pTa). This expectation is tested for 1≤n≤5 by applying a global fit of all Vnδ(pTt,pTa) to obtain the best values vn{GF}(pT). It is found that for 2≤n≤5, the fit agrees well with data up to pTa~3-4GeV/c, with a trend of increasing deviation as pTt and pTa are increased or as collisions become more peripheral. This suggests that no pair correlation harmonic can be described over the full 0.25<pT<15GeV/c range using a single vn(pT) curve; such a description is however approximately possible for 2≤n≤5 when pTa<4GeV/c. For the n=1 harmonic, however, a single v1(pT) curve is not obtained even within the reduced range pTa<4GeV/c. © 2012 CERN.