APPLICATION OF MODAL ANALYSIS TO MUSICAL BELL DESIGN
Behzad Keramati Nigjeh, Pavel M. Trivailo · 2002
Mathematical models of pitch multiplicity and virtual pitch have been developed and compared to human subjective responses to synthesized bell timbres, a range of musical chords and complex harmonic tones. A factor determined from results of human subjective tests can then be used to adjust for the listening attitude, where analytical listening favours hearing individual partials. The calculated and reported values of multiplicity for synthesized bell sounds were found to be higher than for complex harmonic tones with comparable fundamental tone frequencies 3 . The tone salience of individual pure tone or complex tone percepts is proportional to their calculated audibility 3 . The multiplicity and tone salience of European carillon bells calculated in this manner have been contrasted to a range of new harmonic bell designs with very low pitch multiplicity due to the tuning of the first seven partials to the harmonic series 6 .