Abstract:

Ringing of changes on tower bells (the ``exercise'') involves acoustics, in the tuning of the bells, sound insulation, and propagation from the tower. Muscular power is required to ring, though even young girls can ring the light (treble) bells. At the same time husky teenagers ring the heavy tenors---all can join in. In England, 16th-century ringers developed the techniques to sound their bells (tuned diatonically) sequentially, using a rope and wheel to swing them through almost a full circle, mouth vertical. The period lengthens toward the balance point, and by using the rope to change the energy, the order in which the bells sound may be changed. Each bell is tuned for the strike note, the hum note (about an octave below), and partials a third (the tierce) and a fifth (quint) above. Methods such as ``plain bob major,'' ``superlative surprise maximus,'' or ``grandsire caters'' organize the ``changes'' (possible permutations of the bells rung). Mathematics is required to compose peals (5000 different changes) which are true (no repeats). Ringing in America died out after the Revolutionary War, but in the last 30 years, at least 25 new towers have been built here, and several pre-Revolutionary rings refurbished.