[HN Gopher] The Sound of Bells - The acoustics, sound, tuning an...
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The Sound of Bells - The acoustics, sound, tuning and history of
church bells
Author : belkarx
Score : 105 points
Date : 2022-05-10 15:03 UTC (7 hours ago)
(HTM) web link (www.hibberts.co.uk)
(TXT) w3m dump (www.hibberts.co.uk)
| enriquto wrote:
| 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.
| nonrandomstring wrote:
| 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.
| crustycoder wrote:
| 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.
| sitkack wrote:
| 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
| hprotagonist wrote:
| The pitch perception work alone is probably a few degrees, if
| you get deeper into it.
| Someone wrote:
| > 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.
| cpp_frog wrote:
| 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.
| nomel wrote:
| > Surface of revolution is okay
|
| But surface, by definition, has no concept of thickness,
| right? Surely there's a better term?
|
| > 'solid' would mean its interior is completely filled.
|
| I think the easiest way to define a bell would be the
| difference of two solids of revolution (front surface, back
| surface). What do you call the difference of two solids of
| revolution?
| cpp_frog wrote:
| I meant it from a numerical analysis/differential
| geometry perspective (the reason I attached the
| reference). While not being strictly a surface, it _is_
| characterized by a mid-surface, and a thickness _t_.
| After having that information, for each point in the mid
| surface, a normal vector is drawn and scaled by a
| magnitude of _t_ /2 in both directions of the normal,
| giving a thickness of _t_ to the object that, I should
| have made it clearer, is not a surface but characterized
| by one.
| enriquto wrote:
| I don't think that a bell is correctly modelled as a
| shell of variable thickness. The inner surface is smooth,
| and the outer surface has _ridges_. These ridges are
| apparently important to the timbre, thus it may be more
| appropriate to consider it as a solid volume of arbitrary
| shape. Of revolution, if you want to stay with a one-
| dimensional model.
| crustycoder wrote:
| Nah, the mouldings are entirely decorative. And bells are
| tuned by taking off material on a lathe at various
| positions on the inside of the bell.
|
| https://funwithbells.com/nigel-taylor/
|
| https://www.youtube.com/watch?v=JEJkMalMVv4
| enriquto wrote:
| Wow, it's good to know, thanks for the clarification!
| Someone wrote:
| > 'solid' would mean its interior is completely filled.
|
| I disagree. Mathematically, I wouldn't know how to define a
| solid other than "anything with a volume".
|
| Certainly, a bell, when defined as a surface of revolution,
| doesn't have an interior in a mathematical sense
| (https://mathworld.wolfram.com/Interior.html), does it?
|
| There's the convex closure, but that would, for the
| prototypical bell, add volume 'outside' the bell, too.
|
| Also, I think varying wall thickness in bells for centuries
| was the only known way to tune them. https://en.wikipedia.o
| rg/wiki/Pieter_and_Francois_Hemony#Lif...:
|
| _"When struck, a bell produces a number of partials which,
| if imprecisely tuned, can create an unpleasant sound and
| which prevents it from harmonizing in accordance with other
| bells. To address this problem, the Hemony brothers gave
| their bells a particular profile and thickened it in
| certain places. The bells were then tuned by hollowing
| ridges from specific parts of the inner wall until the
| first few partials were acceptably in tune."_
|
| (Aside: if you want your work to be used for centuries,
| becoming a professional bell caster seems a good bet)
| a1369209993 wrote:
| > 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.)
| cpp_frog wrote:
| 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.
| elijahwright wrote:
| I read a few pages of this and found it most enjoyable. The sheer
| nerdiness of tuning bells and improving them - it's great!
| pradn wrote:
| 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 wrote:
| 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. :)
| pradn wrote:
| It's an unforgettable 40 minutes. So lucky to have seen it on
| the big screen the first time I saw the film.
| scarecrowbob wrote:
| 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 wrote:
| 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"
| pradn wrote:
| Yes, exactly. The father also died of a plague before they
| came to the son, if I recall.
| h2odragon wrote:
| Thanks for sharing your joy in bells. That's an awesome
| collection of knowledge.
| rwmj wrote:
| If you just like the sounds of church bells, the BBC has you
| covered:
|
| https://www.bbc.co.uk/programmes/b006sgsh
| [deleted]
| jhallenworld wrote:
| 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 wrote:
| That book (that section specifically) has one of the best "slow
| realization that you're in trouble" processes I've read.
| jFriedensreich wrote:
| why would he name his software wav"anal" when there even is a
| concept of "rim partials". this is hilarious.
| WalterBright wrote:
| 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.
| lqet wrote:
| 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
| dylan604 wrote:
| 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
| crustycoder wrote:
| The only remaining dedicated bell foundry in the UK is in
| Loughborough - https://taylorbells.co.uk/ You can visit :-)
| niccl wrote:
| 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
| nicwolff wrote:
| 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 wrote:
| 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
| elric wrote:
| Somewhat tangential; there's a company, clock-o-matic, that makes
| hardware and software to play carillons (or single bells)
| programatically using MIDI files.
| crustycoder wrote:
| 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 wrote:
| 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.
| crustycoder wrote:
| 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/
| raymondgh wrote:
| "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?
| crustycoder wrote:
| I wouldn't worry, if that was the intent, I think it backfired
| ;-)
| skocznymroczny wrote:
| I thought it's clickbait because I expected that the text of
| the thesis was etched on the bells somehow.
| misterprime wrote:
| Nice joke, Dad.
| belkarx wrote:
| 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
| twangist wrote:
| 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.
| belkarx wrote:
| I mean ... they continued their work on bells, and appear
| to have done (and continue to do) a fair amount of work
| concerning them
| enriquto wrote:
| > 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.
| WhyOhWhyQ wrote:
| '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
| pvg wrote:
| You should still stick to original titles like the site
| guidelines ask
| belkarx wrote:
| Ah, apologies. I will keep that in mind in the future
| dang wrote:
| Thanks! We've changed the title above to the page title
| now.
|
| The submitted title was "Someone wrote a PhD thesis on
| bells". Sometimes a title like that has the virtue of
| getting an obscure, interesting submission onto the front
| page. The sin is venial when the submission is
| particularly good (and mortal when it's dreck, which alas
| is more often the case.)
| blipvert wrote:
| I wrote a lot of my undergraduate dissertation on Bell's too.
| Maybe that's why I got such a poor degree.
| [deleted]
| jmmcd wrote:
| 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/
| crustycoder wrote:
| 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
| Veen wrote:
| 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.
| crustycoder wrote:
| The UK government did promise to reduce the grounds for
| noise complaints about church bells, on the grounds that
| normally they were there before the complainant arrived,
| and would still be there long after they were gone, but it
| appears it was like many government promises...
|
| https://www.churchtimes.co.uk/articles/2018/2-february/news
| /...
| trasz wrote:
| "The church bells had chimed unchallenged every 15
| minutes since 1779."
|
| Over _all the night_. Seriously, this appears to be quite
| a rational complaint.
| Veen wrote:
| It was hardly a surprise, though. They must have known
| about the bells before they bought the property.
| clort wrote:
| My sister lives about 100m from such a church tower
| (which has 5 300yr old bells). Its not really as
| intrusive as one might imagine..
| crustycoder wrote:
| There's usually two different things going on in UK bell
| towers - bell ringing which involves ringing the bells
| full-circle using the internal clappers, and clock
| chiming which uses external hammers driven my the clock.
| The clock chiming is much quieter than change ringing.
|
| Ours only chimes on the hour but it's going 24/7 and is
| very close to the surrounding houses (~40m) some of which
| are uphill and directly in line with the bells. I had to
| go in today to fettle it as it wasn't chiming and someone
| had posted on the village FB group that they were missing
| it. That's a fairly regular occurrence, most people
| people like hearing them, even through the night. Any
| complaints we get are when the clock stops.
|
| It is possible to modify clocks to stop them chiming
| overnight, although ours is still in its entirely
| mechanical 1883 form, including me having to wind it
| every week.
| trasz wrote:
| If people want this, then it should be fine. To me, in
| case described in the article above the bells were to
| stay because of the church and tradition, not because the
| citizens wanted them.
| crustycoder wrote:
| It's usually one miserable git who complains, most people
| who buy houses next to big sticky up things at the end of
| religious building are smart enough to figure out what's
| in them.
| ortusdux wrote:
| I found this video by Matthias Wandel about two-toned bells very
| interesting:
|
| https://www.youtube.com/watch?v=eMgmJEaYs70
| Cenk wrote:
| Thesis PDF here: https://oa.mg/work/10.21954/ou.ro.0000add2
| crustycoder wrote:
| 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 wrote:
| wow. had no idea bell-ringing was so... pathological
| crustycoder wrote:
| Yeah, it's full of geeks :-]
| rwmj wrote:
| I think you mean campanological.
| crustycoder wrote:
| Ooh no, don't ever call bellringers that, unless you want
| to cause grave offence. Campanologist is a name for wussy
| academics, bellringers ring bells. And drink beer ;-)
| bsedlm wrote:
| 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
| rpmisms wrote:
| 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...
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(page generated 2022-05-10 23:00 UTC)