Remember those countless years ago when the bells of St. Paul’s Cathedral in London pealed out for Prince Charles’ and Princess Diana’s wedding? I sure don’t; I was a toddler. My mom says she watched it, though, so I might have caught some glimpses of it.
You can hear the full range of the twelve bells on William Hibbert’s website. These bells were cast in 1878 by the Taylor bell foundry in Loughborough, England. It is a splendid peal of bells. Unlike carillon bells, bells in peals ring out together in mathematical patterns to create a wash of sound, rather than a distinct melody.
A peal of twelve bells is large, and that range of bell sizes creates a problem. To put it in vague terms—they are difficult to tune together. And why’s that? The profiles of bells are not actually consistent across a wide range, and changes in the profiles affect the partials. Smaller bells are usually cast with thicker walls so that they ring louder to hold their own against the larger, louder bells. So higher bells cannot be tuned in quite the same way as lower bells with the same results. Thanks to the thesis of William Hibbert, we now know that the strike tones of bells in the middle range are affected a lot by the tuning of the nominal partial (which is the fifth note from the bottom shown below—C) and other upper partials above the nominal. Below are the bell partials for a bell with a strike note of middle C.
(The minus sign above one F and the plus sign above the other indicates that these two partials are very flat and sharp, respectively.) Hibbert’s finding applies to bells from those with strike notes at B just below middle C up to G an octave and a half above. This is the middle range for many carillons, chimes, and peals.
His discovery does not apply so well to bells outside of this range, however, and as of yet we do not have a satisfactory explanation for the strike notes in the upper range of bells. Curiously, if a bell founder tunes bells in the upper range as he or she would for the lower and middle range, the high bells can actually sound flat. That means if the bell founder tunes the five lowest bell partials shown above to perfect equal temperament tuning, the strike note for those high bells may still sound a little too low, or flat. This may have to do with the flat upper partials in these high bells due to their thicker walls. Hibbert’s experiments suggest a correlation between one of the flat upper partials and a flat strike tone in the high bells, but there’s no conclusive evidence on what produces the perceived flat strike tone.
So what are bell founders supposed to do? This is a conundrum in large peals that span large to small bells—how can they all get in tune? Click back next time to find out, when the St. Paul’s peal will give us the answer.