The hum and the tierce in the chimed bell do not affect the initial sensation of pitch, despite the loudness of these partials.
But we have to remember that with strings, pipes and instruments generally the fundamental tone is accompanied by overtones, called also " upper partials," and beating within the dissonance range may occur between these overtones.
If we are to assume that the tones received by the ear are pure and free from partials, the loudness of the beattones would appear to show that Helmholtz's theory is not a complete account.
In a true-harmonic bell, with the main partials in octaves, the pitch is about an octave below the nominal.
It has a slightly flat hum and a strong, very flat prime and has large doublets on all its important partials.