Strike notes and their pitches of some kinds of bells

Abstract

The strike notes of western church bells have been studied very long. This paper considers the bells that are different from church bells: (1) simple tubular bells called “wind chime”, (2) a downward-stretching tubular bell with hyperbolic surface, which the authors name “Gaudi bell” because Antoni Gaudi envisaged music of such bells coming from the belfries of the Sagrada Familia Church, and (3) a double Gaudi bell stretching downward and upward from the center with different lengths. Strike notes of these bells are yielded from the axial vibrations. However, their pitches do not necessarily correspond to the strongest spectrum (mode) of the bell vibrations. Aluminum tubular bells of our wind chime gave the “spectral pitch” determined by the spectral frequencies (around 1 kHz) of the fourth mode. On the other hand, our Gaudi bell (brass-made, 1.80 m, 50 kg) yielded the fourth mode at 750 Hz. However, many listeners perceived the pitch at 375 Hz. This is the “virtual pitch” based on the missing fundamental (mode frequencies higher than the 4th were 1082, 1450, 1842, and 2258 Hz). A double Gaudi bell (bronze-made, 0.342 + 0.260 m) gave the “spectral pitch” at 1125 and 2046 Hz.