The Sound of Bells – The acoustics, sound, tuning and history of church bells

https://www.hibberts.co.uk/

by belkarx • 4 years ago

133 72 4 years ago

hibberts.co.uk

h2odragon• 4 years ago

Thanks for sharing your joy in bells. That's an awesome collection of knowledge.

enriquto4• 4 years ago

As if there was just material for a single PhD thesis! I would guess that the mathematical theory of bells is pretty much open. The shape of a bell (a solid of revolution) can be described by one function u:R->R. Given u, you can compute the vibration spectrum of the sound by standard methos. But if you are given a desired timbre, how to find u? Nobody knows. The most that we can do is optimization starting from a close solution candidate.

hprotagonist• 4 years ago

The pitch perception work alone is probably a few degrees, if you get deeper into it.

Someone2• 4 years ago

The shape of a bell (a solid of revolution) can be described by one function u:R->R

If you phrase it that way “surface of revolution” describes bells much better than “solid of revolution”.

I think “solid of revolution” is the better term, though. That allows you to model varying wall thickness. You’d need more than a function u:ℝ->ℝ to do that.

Also, I don’t a priori see why the shape of a bell would be limited to such functions. If the edge of a bell bends inwards into the bell and goes up a bit, I think I would still call it a bell, especially if it somewhat sounds like one.

Finally, rotational symmetry isn’t required for a bell. Your typical cow bell, for example, is elliptical or even rectangular (https://en.wikipedia.org/wiki/Cowbell_(instrument))

⇒ the design space is a lot larger than you indicate.

mbustamanter3• 4 years ago

Surface of revolution is 'okay', 'solid' would mean its interior is completely filled. What you're describing is an active area of research in numerical analysis (adjacent to my own MS thesis topic, buckling of shells).

That allows you to model varying wall thickness

That's mentioned in the first chapter of this book [0].

[0] The Finite Element Analysis of Shells – Fundamentals, Chapelle & Bathe

EDIT: I'm aware it is not a surface, but the notion is closer than that of a solid of revolution.

a1369209993• 4 years ago

You'd need more than a function u:ℝ->ℝ to do that.

Actually, if you normalize the bell height to 1, you can take u from 0 to 1 as the inner surface (tracing down from the top), and u from 1 to 2 as the outer (tracing back up from the bottom). I'm not sure that's mathematically convenient, but it does work. (You could also use a periodic function on 0..pi for inner and pi..tau for outer, which might be nicer math-wise and also allows you to say that the height (pi) is half of whatever the function's period is.)

mellavora• 4 years ago

I've got a fever, and the only prescription is more cow bell!

nonrandomstring• 4 years ago

This site is quite old and IIRC I had bachelors students building additive synthetic bells from the amazing data he's collected. Also great tales of acoustic archaeology, building bell sounds based on models from the foundry drawings and metallurgy data.

crustycoder13• 4 years ago

It's been around for a while but he's still active in the field (he recorded & analysed our bells a couple of years ago) and he's revamped the site fairly recently.

mbustamanter3• 4 years ago

Yes, it's a vibration of an elastic axisymmetric thin shell (surface of revolution, as you meantioned). Going deeper into the theory, to know or characterize the sound it makes one should have a model of free or forced vibration and find the eigenvalues of the resulting linear system. That system is typically (K-omega^2 M) U = F, where K is the stiffness matrix of the material, M the mass matrix, U the displacement matrix, F the force matrix and omega the frequency.

Now, to find the displacement given the eigenvalues (spectrum) is possible in a finite-dimensional setting, in infinite dimensions it's trickier. I'm sure there are approximation results of this kind, but not if there is an exact way.

sitkack• 4 years ago

If drums are bells, you should see how Nicolas Bras [1] modifies the sound by damping some of the nodes of the drum. Are you saying all bell are radially symmetric?

[1] https://www.youtube.com/watch?v=fXavtyyyj34

crustycoder13• 4 years ago

Yes, Bill did. He's a really nice guy and the subject of bell tuning has been of academic interest for a very long time, because they don't produce a single note and the note you "hear" isn't produced by the bell at all. See for example Nobel Laureate Lord Rayleigh's paper of 1890, linked to on Bill's site.

krumbie• 4 years ago

That is fascinating. I thought that bells had one or a couple dominant / loud frequencies that would mostly determine pitch, and the rest would just mix in to change the timbre but not the main percept. I always found the sound of melodies played with bells kind of uncomfortable because there is too much going on, too many different frequencies interfering with each other.

crustycoder13• 4 years ago

For literally centuries European bell tuning was all done by rule of thumb, with results varying from to sublime to abysmal. It was all finally figured out by Canon Simpson in 1895/6 who described the relationship between the 5 main components of a bell's strike note - the hum, prime, tierce, quint and nominal.

https://www.hibberts.co.uk/building-a-bell-sound/

jmmcd• 4 years ago

Bells is also one of the sub-themes in the Polifonia EU-funded research project (disclaimer, I'm involved in a different theme). It's more about documentation of historical bells in open/linked data, rather than acoustics.

https://polifonia-project.eu/

crustycoder13• 4 years ago

In the UK we have 61,626 documented bells (a lower bound) spread across 7,148 towers. https://dove.cccbr.org.uk

In the last year unaffected by COVID, there were 10,701 recorded performances and many more unrecorded ones and practices. https://bellboard.uk/

There are 23,397 Methods and 52,650 Compositions available, where a Method is roughly equivalent to a piece or song in traditional music terms. http://methods.ringing.org/intro.html

Veen2• 4 years ago

I used to enjoy listening to the church bell practice sessions on summer evenings when I lived by a church (not so much being woken on Sunday mornings though). Annoyingly, they eventually shortened and lessened the frequency of practice because newcomers to the village complained that their idyllic second home in the countryside was affected by "noise pollution"— something that has been a regular feature of village life since the bell tower was built in 1545.

lqet• 4 years ago

Very cool. I became fascinated with bells after watching this [0] documentary on how they are made a few years ago (it's in German, but that hardly matters, just watching the process is extremely interesting).

The whole process is a combination of extreme sophistication and extremely simple tools and materials, something that has become quite rare nowadays. And despite an exact calculation of the bell shape and thousands of years of trial and error, tradition, and experience (the foundry in the video has been owned by the same family for 300 years), the cast is still highly dangerous and it still regularly happens that the bell just doesn't come out right and cannot be saved - months of work for nothing.

I think that explains why on the day of the cast (which is just 1 or 2 times per year), everyone involved is extremely nervous. The bell founder and the customer all join in prayer, and the cast traditionally starts with "in God's name" [1].

[0] https://www.youtube.com/watch?v=OQ8ZZV5UjcI

[1] https://youtu.be/OQ8ZZV5UjcI?t=1918

crustycoder13• 4 years ago

The only remaining dedicated bell foundry in the UK is in Loughborough - https://taylorbells.co.uk/ You can visit :-)

niccl• 4 years ago

Little known fact: They made the AC/DC's original Hell's Bell for the Back in Black tour. Touring with 3,000 kgs of bell in a flight case made for some interesting experiences

dylan604• 4 years ago

Even with it being in German, I agree, I still enjoyed it. If you've ever made anything or seen a different thing made, you'll get the concepts of what they are doing. The scale of what they are making is impressive, as well as their jigs for building. Thanks for the link

nicwolff• 4 years ago

That mug-tapping demonstration in the "Doublets or warble in bells" page [0] is neat! I'll be looking for an opportunity to show that to someone, ask why they think it happens, explain pedantically, and yell "Science!"

[0] https://www.hibberts.co.uk/doublets-or-warble-in-bells/

itsoktocry• 4 years ago

An interesting podcast on bells form Planet Money:

When you've got two companies down the road from each other making the same thing, you can almost guess the history. Originally there was just one company, but something happened. Maybe someone got angry, somebody left, and they started a second business, a competitor.

Today on the show, the rivalry between two companies that make nearly all the world's handbells. And how they eventually made peace.

https://www.npr.org/2021/12/23/1067333584/bell-wars-classic

ortusdux• 4 years ago

I found this video by Matthias Wandel about two-toned bells very interesting:

https://www.youtube.com/watch?v=eMgmJEaYs70

pradn3• 4 years ago

Tarkovsky's Andrei Rublev has an extended sequence where a bellmaker's young son agrees to pour a bell for a local lord. You see the entire process of making the mould and pouring the metal. It has a town-fair atmosphere. But at the end, there's tremendous pressure on the young bellmaker to have the bell ring properly and have no cracks. And it does. The protagonist, the lapsed monk Andrei Rublev, regains his faith, seeing the result of the young bellmaker's hope.

aeolis_mons• 4 years ago

One of my favorite sequences in any movie. I will never forget the visuals of workmen sweltering in front of flaming portholes in the bell's cast. Enduring a little inferno, to create the sound of heaven! Thank you for reminding me of it. :)

pradn3• 4 years ago

It's an unforgettable 40 minutes. So lucky to have seen it on the big screen the first time I saw the film.

scarecrowbob• 4 years ago

I can't recall as it has been a number of years, but my impression was that the young bell maker was lying about his father having given him the "secret" to making the bell, hence the anxiety about the success of the project. Am I misremembering that, or was I just not reading it correctly?

gregsadetsky• 4 years ago

That's exactly it -- https://www.villagevoice.com/2018/08/20/the-secret-of-andrei...

"The boy, named Boriska [...] claims that before his father died, he revealed to him the secret of casting a bronze bell"

"Amid his tears, Boriska reveals that his father never imparted to him the secret of bell making"

pradn3• 4 years ago

Yes, exactly. The father also died of a plague before they came to the son, if I recall.

raymondgh• 4 years ago

“Someone wrote a PhD thesis on bells” is a clickbait title. It implies the value of the content is merely the surprising or shocking concept that the content even exists. But looking at the page, that’s not what the content is about. It’s an earnest study into bells. Are we meant to point and laugh?

crustycoder13• 4 years ago

I wouldn't worry, if that was the intent, I think it backfired ;-)

skocznymroczny• 4 years ago

I thought it's clickbait because I expected that the text of the thesis was etched on the bells somehow.

misterprime• 4 years ago

Nice joke, Dad.

belkarx3• 4 years ago

I agree, title was a bit clickbait but I was surprised that one would dedicate their life to something that specific. Hyper-specialization at its finest, and the passion is something I can appreciate

pvg• 4 years ago

You should still stick to original titles like the site guidelines ask

twangist• 4 years ago

The doctoral candidate didn't "dedicate their life" to the topic, merely wrote a thesis on it. So, just an intense part of their life. Perhaps they'll remain focused on bells, perhaps not. Probably all PhD theses are 'hyper-specialized', unless they're surveys by an author who won't be continuing as an academic researcher. It's not surprising that people would want to understand these complex inharmonic sounds we've been making for centuries.

WhyOhWhyQ• 4 years ago

'Bells' are pretty un-specific as far as specialization goes. The average person actually knows what a bell is. The PhD theses in mathematics are likely far less applicable and far more specific. Check out the titles on arxiv and let me know if you think any of these are less specific than 'bells'.

https://arxiv.org/list/math/new

enriquto4• 4 years ago

Hyper-specialization at its finest

Don't be so sure. At least for mathematicians, the "bell" may be just an excuse to make the subject cool. Many of the underlying problems are very general. For example, the inverse spectral problem (vibration modes of a complex shape) is the basis of the interaction between proteins, enzymes, and the huge molecules of cell walls. At the cell scale, Brownian motion shakes everything in all possible frequencies, but molecules can only vibrate at a specific set of frequencies (their spectrum). The act of "matching" different molecules happens when they have some common frequencies, often with localized modes of vibration.

You may think that you are just modeling church bells, but everything that you do has immediate application to the understanding of some organic chemical interactions, which are a deep mystery yet.

blipvert• 4 years ago

I wrote a lot of my undergraduate dissertation on Bell’s too. Maybe that’s why I got such a poor degree.

bsedlm• 4 years ago

There's a russian artist who's made a couple of albums about "singing bronze". He plays the bronze plates, they sound a lot like bells.

https://www.youtube.com/watch?v=vsZ5RIZrNKw

jFriedensreich• 4 years ago

why would he name his software wav”anal” when there even is a concept of “rim partials”. this is hilarious.

Cenk• 4 years ago

Thesis PDF here: https://oa.mg/work/10.21954/ou.ro.0000add2

jhallenworld• 4 years ago

Here is my bell related science-fiction recommendation: Doomsday Book by Connie Willis.

"The drop had been scheduled for noon. If she had come through on time and Probability was right about the slippage, it would be six o'clock in the evening, which was too late for vespers. And if it were vespers, why did the bell go on tolling?

It could be tolling for mass, or for a funeral or a wedding. Bells had rung almost constantly in the Middle Ages—to warn of invasions or fires, to help a lost child find its way back to the village, even to ward off thunderstorms. It could be ringing for any reason at all."

InitialLastName• 4 years ago

That book (that section specifically) has one of the best "slow realization that you're in trouble" processes I've read.

elric• 4 years ago

Somewhat tangential; there's a company, clock-o-matic, that makes hardware and software to play carillons (or single bells) programatically using MIDI files.

rpmisms• 4 years ago

Grew up in a long tradition of bell-ringing. It's amazing, and even more so in person.

https://www.youtube.com/watch?v=qbn_Fzcxw3o&ab_channel=petya...

elijahwright• 4 years ago

I read a few pages of this and found it most enjoyable. The sheer nerdiness of tuning bells and improving them - it's great!

crustycoder13• 4 years ago

The bells studied in the PhD thesis are primarily used for English Change Ringing, which started in the early 1600s and the compositions played on them (methods) are based on mathematics, specifically Group Theory, rather than being tunes in the normal sense - the aim is to ring all the possible permutations of the bells.

The Mathematics of Bell Ringing https://www.youtube.com/watch?v=44jXUo6KaVs

Performances (Peals) consist of 5040 changes (sequences), have a strict set of rules and take around 3 hours 15 minutes to complete, and must be rung entirely from memory, with no written aids.

In the early 1960s a CS algorithm for efficiently enumerating permutations was published, the Steinhaus–Johnson–Trotter algorithm. It's in Knuth, for those who have access to a copy. Unfortunately for them, it had been known by English Change Ringers as Plain Changes, since around 1621.

allisvancity• 4 years ago

wow. had no idea bell-ringing was so... pathological

crustycoder13• 4 years ago

Yeah, it's full of geeks :-]

rwmj2• 4 years ago

I think you mean campanological.

rwmj2• 4 years ago

If you just like the sounds of church bells, the BBC has you covered:

https://www.bbc.co.uk/programmes/b006sgsh

WalterBright• 4 years ago

The sound of European church bells is so lovely and charming. No recording can do it justice.

On the other hand, the American church predilection for electronic bells is an abomination.

My desk telephone has real bells in it for the ringer. It's from the 1950s, naturally.

The Sound of Bells – The acoustics, sound, tuning and history of church bells

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