  The results of the measurements of the double-differential production
cross-sections of pions in p-C and $\pi^\pm$-C interactions using the forward
spectrometer of the HARP experiment are presented. The incident particles are
12 GeV/c protons and charged pions directed onto a carbon target with a
thickness of 5% of a nuclear interaction length. For p-C interactions the
analysis is performed using 100035 reconstructed secondary tracks, while the
corresponding numbers of tracks for $\pi^-$-C and $\pi^+$-C analyses are 106534
and 10122 respectively. Cross-section results are presented in the kinematic
range 0.5 GeV/c $\leq p_{\pi} <$ 8 GeV/c and 30 mrad $\leq \theta_{\pi} <$ 240
mrad in the laboratory frame. The measured cross-sections have a direct impact
on the precise calculation of atmospheric neutrino fluxes and on the improved
reliability of extensive air shower simulations by reducing the uncertainties
of hadronic interaction models in the low energy range.
