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Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s√=13 TeV by the ALICE Collaboration. The yields of particle pairs at short-(Δη ∼ 0) and long-range (1.6<|Δη|<1.8) in pseudorapidity are extracted on the near-side (Δφ ∼ 0). They are reported as a function of transverse momentum (pT) in the range 1<pT<4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-pT leading particles and jets for varying pT thresholds. The results demonstrate that the long-range "ridge" yield, possibly related to the collective behavior of the system, is present in events with high-pT processes. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement, in particular for the pT and event-scale dependencies.