Vibrational frequencies and tuning of the African mbira

The acoustic spectrum of the mbira, a musical instrument from Africa that produces sound by the vibration of cantilevered metal rods, has been measured. It is found that the most prominent overtones present in the spectrum have frequencies that are approximately 5 and 14 times the lowest frequency. A finite-element model of the vibration of the key that takes into account the acoustic radiation efficiency of the various normal modes reveals that the far-field power spectrum is dominated by modes involving predominately transverse motion of the key. Modes involving longitudinal motion do not radiate efficiently, and therefore contribute little to the sound produced. The high frequencies of the dominant overtones relative to the fundamental make it unlikely that the tunings of the mbira that are used by expert musicians are determined by matching the fundamental frequencies of the upper keys with the overtones of the lower keys.