Collision centrality dependences of the transverse momentum distributions of negative pions produced in p12C and p−12C collisions at 9.9 and 40 GeV/c, respectively, are investigated. The shapes and widths of the normalized transverse momentum distributions, as well as the average values of the transverse momentum of the negative pions, do not depend within the uncertainties on the collision centrality in p12C and п−12C collisions at 9.9 and 40 GeV/c in experiment, which is confirmed by the modified FRITIOF model calculations and minimum X2 fits of the experimental spectra with the two- and three-temperature Hagedorn model functions. Modified FRITIOF model calculations underestimate the average values of transverse momenta of the negative pions in experiment and do not reproduce the tail of the experimental transverse momentum distributions of the negative pions in both collision types. It is obtained that the transverse momentum distributions of the negative pions exhibit two temperature (two-slope) shapes in peripheral and central p12C collisions at 9.9 GeV/c in agreement with the early works on nucleus-nucleus collisions at incident energies of the order of a few GeV/c. However, the transverse momentum distributions of the negative pions in peripheral and central p−12C collisions at 40 GeV/c can be described well assuming the three temperature (three-slope) shapes of these spectra.