I hope I did not lead you astray with my explanation about the Liberty Bell’s tuning using terms like overtone and partial. My apologies, dear reader. I give you a description of bell tuning below for the uninitiated, and I reveal the mystery of all mysteries at the end!
Bells are tuned unlike any other musical instrument. Most musical instruments from the western art tradition use either vibrating columns of air, such as woodwind and brass instruments in which the player blows air through a narrow pipe. Or they use vibrating strings, such as violins, cellos, guitars, and pianos. These instruments produce what is called the natural harmonic series. That means when you hear one of these instruments play a pitch, let’s say C, you are not hearing a pure C tone. What you are hearing are a combination of overtones of different pitches above that main pitch C.
Still with me? Here’s a graph showing the overtone structure for C. For you non-music readers out there, C is the very lowest note, the note that we hear the pitch at, and all the other notes above it are the overtones. Notice that they are spaced far apart in the beginning and then become closer together towards the top. Three out of the four first overtones are C, reinforcing the main C pitch.
So how is a bell overtone series different? When that bronze (alloy of copper and tin) vibrates, it produces this overtone series below (for a C bell). I should add the strong caveat that bells can be and are tuned to different overtone series, but this has become the most common overtone structure in the western hemisphere after centuries of bell casting. Another caveat is that this only shows the first five overtones of a bell—there are several more above these main five.
The pitch we hear the bell at is actually a C positioned at the second overtone, not the lowest note. Notice that the overtones are positioned closer together. Also, there are three Cs spread out over five partials, not four. And music readers will notice the minor triad formed by the middle three notes very prominently. The minor triad is often understood as sad or gloomy in music of the western art tradition.
The most amazing, mysterious thing about the sound of bells, though? Are you ready for this? The strike tone, or the main pitch that we identify in the bell, is not present in the bell sound!
Umm…what? Come again? How can the pitch that we hear the bell ringing at not be in the bell sound?
And the answer is…we’re not sure. We have some theories, but no conclusive answer at this point. It seems our best hypothesis is that our brain hears the higher partials and creates the strike note for us. In the overtone scheme above, the strike note coincides with the pitch of the second overtone, but not necessarily. The prime overtone and the strike tone are decidedly different things.
So the next time you hear a bell, just remember that your brain is doing some heavy-duty work in creating the bell’s pitch for you. Your brain is far more musical than you had ever imagined!