Tuning of bells by a linear programming method

A carillon bell is tuned by the removal of metal from the inner surface of the bell. Van Heuven [Acoustical Measurements on Church-Bells and Carillons (De Gebroeders van Cleef, ’s-Gravenhage, The Netherlands, 1949), Chap. IV] determined a set of tuning curves and derived a set of equations that relate the amount of metal removed to the relative alterations in the partial frequencies. This paper uses these equations as constraints in the formulation of the tuning problem as a linear program. An example illustrates the procedure.