A brief overview of the workings of the human auditory system is followed by a review of literature concerning both the theories and experimental investigations of human pitch perception. The application of these theories to the inharmonic complex tones produced by bells is discussed, and further experiments using bell sounds are reviewed. A methodology for psychoacoustic experiments with specific reference to those investigating pitch perception of inharmonic complex tones is presented. This methodology is then implemented in an experimental investigation of pitch perception of ringing and chiming bell sounds. A pitch matching experiment using ringing and chiming sounds from four bells aimed to determine perceived pitch differences between ringing and chiming bells. This experiment was inconclusive because insufficient data was collected. Known experimental results, such as the inability of non-musicians to match the pitches of sounds with different timbres were confirmed. Spectral analyses of the stimuli were performed. The presentation of stimuli at a low level of sensation is questioned, as this might have prevented pseudo high frequency noise resulting from stronger upper partials in the ringing sound from being audible, and hence the pitch differences between ringing and chiming bells would not be observed.