Acoustics of the Olympic Bell

[oakcroft13]

Fascinating discussion about the Olympic Bell, I would have posted earlier but have been away. I should preface my comments by saying that to produce a bell like this, and have it feature so prominently in an international event, is a huge success for those involved. My suggestions below as to the design of the bell cannot detract from this.

George Dawson:
> Somebody should have done a tonal by now??

Done by 9.15pm on Friday! The exact figures are as follows:
Partial, Frequency, Note, Cents from nominal
Hum, 61.7Hz, B+0, -2401.4
Prime, 123.5Hz, B+0, -1200.0
Tierce, 147.1, D+3, -897.3
Quint, 185.4, F#+4, -496.6
Nominal, 247.0, B+0, 0.0
III-mode*, 336.0, E+33, 532.7
Superquint, 368.5, F#-6, 692.6
Octave Nominal, 506.0, B+42, 1241.6
I-7, 656.2, E-7, 1691.5
I-8, 815.8, Ab-30, 2068.4
I-9, 982.3, B-9, 2389.9
* This partial is either III-2 or III-3 in Lehr's notation. It is particularly strong in this bell.

The claim that this bell is true-harmonic is certainly justified by these figures (hum, prime and nominal are in pretty exact octaves). Comparison of the figures before and after tuning suggest that very little metal was taken out of the bell, a compliment to designer and moulder. To tune partials this low to a fraction of a cycle per second is quite an achievement.

So what note do we hear when this bell is struck? The pitch perception of bells, and of most musical instruments with an identifiable note, is generated inside the ear or brain by a mechanism variously known as the missing fundamental effect or virtual pitch. If a musical tone contains reasonably strong partials with frequencies approximately 2f, 3f, 4f, 5f etc., then a pitch of approximate frequency f is heard. The presence or absence of a frequency f in the sound is not particularly relevant to what pitch is heard. The virtual pitch mechanism stops working if the frequencies are too high or too low. The exact range of frequencies varies from person to person, but virtual pitch is strongest when the lowest partial in the series (i.e. frequency 2f) is between 500Hz and 1500Hz. The series 2f, 3f, 4f etc. need only be approximate. In particular, if the frequencies are stretched out (typical of thinner bells), the pitch heard goes sharp, and if they are squeezed together (typical of thicker bells), the pitch heard goes flat.

In bells of middling size (nominals of 500Hz to 1500Hz), the nominal, superquint, octave nominal, I-7, I-8 etc. form a strong virtual pitch - the strike note. In the Olympic bell, the nominal is far too low (a whole octave) for the nominal and upper partials to form a virtual pitch for the average listener. However, the series III-mode, I-7 and I-9 are high enough to form a virtual pitch based on E, and this is the note heard by most people. As with many big bells, this 'secondary strike note' is a fourth above the nominal.

Peter Rivet:
> Perhaps ideally very big bells ought to have a slightly different profile?

Could the sound of the Olympic bell have been improved by changing its design? It is interesting to compare its tuning figures with Peter of Cologne, a bell of similar weight and note. The Cologne figures are as follows:
Hum, 62.8Hz, B+30, -2414.4
Prime, 127.6Hz, B+58, -1187.1
Tierce, 156.0, D#+5, -839.2
Quint, 184.5, F#-4, -584.6
Nominal, 253.3, B+44, 0.0
III-2^, 317.5, D#+35, 391.1
Superquint, 375.4, F#+25, 681.0
Octave Nominal, 509.0, B+53, 1208.1
I-7, 657.2, E-4, 1650.5
I-8, 804.2, G+44, 2000.0
I-9, 964.9, B-40, 2315.4
^ Loudest of the three partials between nominal and superquint.

In this bell, the tierce is very sharp, almost a major third, and the upper partials are much flatter than the Olympic bell. This is in all likelihood because the bell is much thicker in the soundbow, which pulls the tierce and the upper partials closer together around the nominal. In this bell, the secondary strike is formed from partials III-2, I-7 and I-9 and is D#, not E. The combination of the hum, prime and nominal (sounding 30 - 50 cents sharp of B), the tierce (sounding a little sharp of D#) and the secondary strike (sounding 35 cents sharp of D#) give the bell a warm major-third sound quite different from a bell with secondary strike a fourth above the nominal.

Regards,

Bill H