  Measurements of the double-differential $\pi^{\pm}$ production cross-section
in the range of momentum $100 \MeVc \leq p < 800 \MeVc$ and angle $0.35 \rad
\leq \theta < 2.15 \rad$ in proton--beryllium, proton--aluminium and
proton--lead collisions are presented. The data were taken with the HARP
detector in the T9 beam line of the CERN PS. The pions were produced by proton
beams in a momentum range from 3 \GeVc to 12.9 \GeVc hitting a target with a
thickness of 5% of a nuclear interaction length. The tracking and
identification of the produced particles was performed using a small-radius
cylindrical time projection chamber (TPC) placed inside a solenoidal magnet.
Incident particles were identified by an elaborate system of beam detectors.
Results are obtained for the double-differential cross-sections at six incident
proton beam momenta (3 \GeVc, 5 \GeVc, 8 \GeVc, 8.9 \GeVc (Be only), 12 \GeVc
and 12.9 \GeVc (Al only)) and compared to previously available data.
