A simplified clarinet was modeled as a closed--open tube of uniform cross section with an open tonehole lattice near its open end. The tube had a length of 50 cm and a diameter of 1.5 cm. The tonehole lattice consisted of five identical toneholes spaced at 2.8-cm intervals. Each tonehole was 0.8 cm in diameter and had an effective length of 1.3 cm. The open end of the tube and each of the toneholes was treated as a simple source, and a corresponding source strength (volume velocity) was calculated at frequencies of interest. The far-field radiated pressure was calculated at a constant radius in a plane that included the tonehole lattice. The pressure was calculated at angular positions from 0 deg (open end) to 180 deg (closed end) for normal mode frequencies. (Circular symmetry about the tube axis was assumed.) Significant directional patterns were seen for frequencies above 2000 Hz. Experiments were performed on a similar structure to measure the directivity and for comparison with the calculations.