BELFRY
The acoustics, measured
Strike a real bell and you do not get one pitch. You get a handful of tones that have almost nothing to do with one another — and the exact distances between them are the entire reason your body knows it heard a bell.
Every sound in BELFRY was put through a spectrum analyser. This page shows what came back, and the method used to get it.
Pick a bell and strike it. The seven coloured lines are where each classical partial should fall if that bell were perfectly cast — the same colours used on the bell diagram further down. The trace is the real sound coming out of your speaker, and the bell fills with its own spectrum as it rings.
Where the seven come from
A bell is a shell, and a shell can flex in many independent patterns at the same time. Each pattern has its own frequency and its own place on the bell where it moves most. That is why a founder can tune the partials separately: thinning the metal in one zone lowers one partial and barely touches the others.
Tap a zone or a partial to see the pairing. These are the zones a bell tuner actually cuts, on a vertical boring lathe, taking off a few hundredths of an inch at a time and re-measuring after every pass.
What "full spectrum" means here
An oscillator makes whole-number harmonics — 1, 2, 3, 4 — because that is the mathematics of a vibrating string or an air column. A bell's ratios are 0.5, 1, 1.2, 1.5, 2, 3, 4. The 1.2 in particular has no place in a harmonic series at all; it is a minor third, and nothing that oscillates in whole numbers will ever put a tone there.
You can approximate a bell by summing sine waves at those exact ratios, and people do. What is harder to reproduce is that each mode decays at its own rate — the hum outlasts the nominal by many seconds — so the colour of the sound changes continuously as it rings.
Strike a bell eight times and you are not hearing eight sounds. You are hearing one continuous, changing texture, because each strike lands on the decaying tail of the last and their partials interfere.
That interference is where the shimmer and the slow beating come from. It only happens if the partials are genuinely there and genuinely inharmonic — two tones an exact octave apart do not beat, two tones at 1.2 do.
The measurements below are simply what is in the recordings. They are published here with the method so that anyone who wants to check them can.
The three you can strike above
Each of these is a recording of a physical bell, so the mode structure is whatever the founder put there — not a design decision made afterwards. Two of the three carry all seven traditional partials. The third carries five, with a tierce a little sharp, which is what an ordinary parish bell usually measures.
Filled dots are partials found within 3% of the ideal ratio. The full table for all nineteen voices is further down, with the frequency of every partial in hertz.
A bellfounder does not tune a bell by making it louder or cleaner. They put it on a lathe and shave bronze from the inside until seven separate vibration modes land at seven traditional distances from each other. It takes days, and it is done by ear against a tuning fork.
Ratios relative to the prime. A founder who lands all seven has cast what is called a true-harmonic bell — and that is what the tierce at exactly 1.2 does: a minor third, which is why every church bell on earth sounds solemn rather than cheerful. It is not a mood. It is a measurement.
The note you think you hear when a bell is struck is usually not in the sound at all.
It is called the strike note. The hum, the nominal and the superquint sit roughly an octave, two octaves and so on apart — a pattern your hearing reads as the upper harmonics of a note an octave below the nominal. So it supplies that note, confidently, whether or not anything is playing it.
On a well-tuned bell the prime happens to sit at that same frequency, so there is energy there too. On a badly-tuned one there is nothing at all — and you still hear the note. That is the part no microphone can show you.
A synthesised “bell” tone has no partial structure, so there is nothing for your ear to build a strike note from. It sounds like a notification, and it goes thin the moment two of them overlap.
BELFRY’s bells carry the real mode structure, which is why counting eight of them at eight o’clock sounds like a tower and not like a phone.
Each square is one of the seven classical partials, in order — hum, prime, tierce, quint, nominal, superquint, octave nominal. Filled where the partial was found within 3% of where it should be.
| Voice | The seven partials | Prime | Strike note | Verdict |
|---|
Big Ben carries all seven, and it is close to perfect: hum 0.500, tierce 1.201, quint 1.498, nominal 2.000, superquint 2.998, octave nominal 4.001. Within measurement error those are not approximations of the ideal ratios — they are the ideal ratios. Cast in 1858, tuned by ear, and it still holds up against a spectrum analyser a century and a half later.
The Singing Bowl scores two of seven, and that is the correct answer. A bowl is not a bell. Its modes fall near 1 : 2.7 : 5.4 : 8.9 — the vibration of a shallow shell, not a bell profile. It is doing exactly what a bowl does, which is why it beats and shimmers instead of tolling.
Each recording was decoded to 44.1 kHz mono. A four-second window was taken starting 150 ms after onset, so what is analysed is the bell ringing rather than the hammer landing. Hann taper, zero-padded, transformed. Peaks located by three-point comparison, refined by parabolic interpolation, thinned so no two sit within 1.2% of each other, and everything below −58 dB discarded.
A very dense spectrum — a gong, say — has enough peaks that some will land near an ideal ratio by chance. A high count on an inharmonic instrument is suggestive, not conclusive.
The result that carries real weight is a complete and tight series like Big Ben’s. Coincidence does not produce that.
Ring it
Nineteen bells, recorded from real instruments, with their mode structure intact.
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