ATLAS measurements of two-particle correlations are presented for √s̅ = 5.02 and 13 TeV pp collisions and for √{S_{NN}} = 5.02 TeV p + Pb collisions at the LHC. The correlation functions are measured as a function of relative azimuthal angle Δφ, and pseudorapidity separation Δη, using charged particles detected within the pseudorapidity interval |η| < 2, is studied using a template fitting procedure to remove a "back-to-back" contribution to the correlation function that primarily arises from hard-scattering processes. In addition to the elliptic, cos(2Δφ), modulation observed in a previous measurement, the pp correlation functions exhibit significant cos(3Δφ) and cos(4Δφ) modulation. The Fourier coefficients ν_{n,n} associated with the cos(ηΔφ) modulation of the correlation functions for n = 2-4 are measured as a function of charged-particle multiplicity and charged-particle transverse momentum. The Fourier coefficients are observed to be compatible with cos(ηφ) modulation of per-event single-particle azimuthal angle distributions. The single-particle Fourier coefficients v_n are measured as a function of charged-particle multiplicity, and charged-particle transverse momentum for n = 2-4. The integrated luminosities used in this analysis are, 64 nb⁻¹ for the √s̅ = 13 TeV pp data, 170 nb⁻¹ for the √s̅ = 5.02 TeV pp data, and 28 nb⁻¹ for the √{s_{NN}} = 5.02 TeV p + Pb data.