Carillon

Left: the bell cut through its axis, to scale, with the chosen partial’s shape (exaggerated, slowed down); dashed: its nodal circles, ● the clapper at the strike height. Right: seen from below, the lip’s 2m lobes and nodal meridians, the doublet’s two axes (heavy side ━), the clapper’s strike point ▲ and the listener ◆. Below: that partial’s level as you hear it over the last 8 s; an uneven bell makes it beat. Pick a partial in the table.

Stems: the bell’s partials as you hear them now (live after a strike; before, as the model predicts). Curve: the pitch strength of subharmonic summation, each partial counted as the 1st, 2nd, 3rd … harmonic of every candidate pitch. Its peak, the strike note (red), sits an octave below the nominal, where the nominal, superquint and octave nominal (near 2 : 3 : 4) agree, whether or not a partial is there.

The upper partials of a bell die fast, the hum lasts longest. From far away, air absorption takes the top off first.

The upper partials vanish within moments while the hum, the lowest line, rings on and on; from further away the top goes sooner still.