Mathematical Impressions: Change Ringing

Change ringing, in which a band of ringers plays long sequences of permutations on a set of peal bells, is a little-known but surprisingly rich and beautiful acoustical application of mathematics.
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[@admg1340]

Who is here because they are reading "The Nine Tailors" by Dorothy Sayers? :)

[@gabymeares6189]

Aaron Cole I just finished it and felt I needed to learn more!

[@christinemcintosh6467]

Reading the book for the second time, and needed to fathom the complexities of the changes, and also to hear each of them - thanks to all on KZbin who make this possible!

[@mariekevanoostende]

Yes! 😂

[@thissweethour]

Yup!

[@pauliina5199]

Me! 😄

[@Art4ArtsSakeVideo]

I have been a virtual fan of change-ringing since reading Dorothy L. Sayers' mystery novel "The Nine Tailors." This makes it much clearer how it all works. Now I'd like to find a video that gets into Triple Bob Major and a touch of Grandsires Doubles (altho' I bet I've forgotten the proper names of the rings!)...

[@davros_adl8155]

Treble Bob Major & Grandsire Doubles

[@edfelstein3891]

So here's how little I knew up until a few minutes ago -- I thought those carillon peals were entirely random. I had no idea there was such a complex formula that went into the playing. Color me impressed!

[@mashiroikaze]

Did a search on Change Ringing to see a good explanation of it, and noticed the thumbnail seemed a bit...familiar. Watched the first minute and went, "Hey! That's where *I* learned to ring!" I recognized a few of the people in the video as well - that was really cool.

[@NonTwinBrothers]

Awesome! These old George Hart videos truly are classics

[@mrs.wsomnibusiclass1713]

That would be me! I read Nine Tailors years ago but next week my students will begin reading it. I plan to show this video to them, with many thanks to those who put it together!! Americans generally have no idea about change ringing! Thank you for making this available! 😊

[@phyllispetras3821]

Very interesting!!!Thank you! I just read the mystery The Nine Tailors!~!!!

[@Lorelcom]

The Nine Tailors is what brought me here as well! I also looked up the novel on Wikipedia and read, to my chagrin: "In a letter discussing the book, Sayers said 'I wrote [the novel] without ever having seen bells rung, by brooding over Troyte on Change-Ringing and trying to translate its technical descriptions into visual effects. That ... "came out" beyond expectation.'"

[@amycortez3289]

I just began reading The Nine Tailors & wanted to learn more about change ringing.

[@michellesenft1517]

Can you sing this too

[@lynndanielson2688]

I'm reading Nine Tailors too, and came here.

[@MrJas321]

.....I'm here because I just read the Nine Tailors and I wanted to know what all that sounded like. I've heard this kind of bell-ringing before but never knew what it was called.

[@Lorelcom]

What a wonderful, informative video! Thanks for making/posting it.

[@lunaticonthegrass111]

A very nicely made video, with a great explanation of bell music.

[@shaleine01]

Fantastic video! We are preparing a recording of William Byrd's "the bells" and will be using the insights of your video for inspiration.

[@hortondlfn1994]

This is fascinating! Makes me want to live in a town where I could be on a bell ringing team.

[@aambrioso]

Nice, instructive video. But I don’t understand how the pulling action we see the ringers doing corresponds to changes in the sequence of bells sounded. Perhaps someone can recommend a other video that explains this.

[@gailremp3628]

Lovely ... I Enjoy bell choir and I can do some changing. But this is just phenomenal. Thank you for posting this video.

[@Steven_Rowe]

I think this is a good video. No doubt change ringing is good for mindfulness. Its really impossible to think of anything else . Never rang at Washington but they sound lovely. its not only the bells vut the tower that makes them sound nice. A tower is to bells what an accoustic guitar is to the strings it has.

[@elliottswanson9307]

Brilliant vid on change ringing. It can also be done with hand bells!

[@nerdiconium1365]

Wait, the truncated octahedron graph has a Hamiltonian loop! Wholy simple permutation permutation Batman!

[@feynman6756]

Woah... so you could cycle _every_ permutation of 4 items and only swap one pair on each change!

[@jasonburnet9181]

There are only change ringing bells in: England, USA, New Zealand & Australia England has over 5000 towers with change ringing bells because that's where originates from. USA only has about 30 towers with change ringing bells. Australia has around 10 towers N.Z has 5

[@Steven_Rowe]

Ther is more than 10 towers in Australia. Check the dove guide ther are 5 peals alone in the city of Sydney alone not including the suburbs My dad was,a vell hanger for Whitechapel till 1972 He installe St Marys Cathedral in Sydney in 1986 I knew the man who installed Washington Cathedral bells, his name was Bill Theobald Got to ring here one day wouldclove to ring a peal of Steman Caters

[@AshleyMonck]

Dordrecht in South Holland has a light ring of 8

[@Steven_Rowe]

Ashley Monck they have also done change ringing in Italy by English bands even though the bells are not technically change ringing bells

[@JohnSmith-ku1dr]

+Ringer Jason Wales also has many towers, so do Scotland, Ireland and Northern Ireland

[@contraposaune]

and canada! It's easier to say that change-ringing exists in english speaking territories.

[@theodorranebo2909]

Can change ringing be done with electric motors instead of bellringers?

[@thierrypauwels]

You show a beautiful polyhedron for a set of 4 bells. Does such a shape also exist for more bells ? I guess for 5 bells you need a shape in 4-dimensional space ?

[@johnr9526]

A nicely put togther video. It's a shame the bells ringing sequences were slowed down (even though the sound was left at normal speed). This makes it more diffcult for non-ringers to see what it really looks like.

[@singlesideman]

Not once were prime number ratios mentioned - that's ultimately what this is all about...

[@carolynmcpherson2667]

What does "moves more than one position" mean?

[@omarjensen8520]

Are there any Change ringing CD's available? If so, where can I find them?

[@borbetomagus]

+Omar Jensen Try -- 'Change Ringing from St Mary Redcliffe, Bristol' (Saydisc CDSDL243) 'Bells of the Cotswolds' (Saydisc CDSDL290) 'Church Bells of Kent' (Saydisc CDSDL302) 'Church Bells of England' (Saydisc CDSDL378) Or possibly -- 'Change Ringing on Handbell' (Saydisc CDSDL310) Amazon has audio samples from these recordings, so you can get the one you'd prefer. I'd probably get the first one. You also might enjoy this -- /watch?v=yLMiK-TMyPI

[@tuatara77]

When the person says that change ringing can be done up to a dozen(12) that isn't true because in England there is a church with 16 bells

[@Steven_Rowe]

Armadillo Hero77 your right but ithink 12 is the norm. Actual there are 3 16s Birmingham, Dublin and Swan Bells in Perth . Lets face it you can change ring on handbells and 24 has been done. Personally I dont like the sound of 16.... 12 is good but I actually think i like 10 the best

[@mashiroikaze]

I don't know about in Europe, but there are few places in the US with more than 8, and Trinity in NYC is the only location in the US with 12. The 10 at the National Cathedral are the heaviest set in North America.

[@ringeradam4575]

and the only other twelve in North America is Toronto Cathedral

[@johnr9526]

I'm so sorry, I take back what I said in the last comment. My computer is doing something odd from time to time! I played it again and all was fine.

[@rashayellow560]

math for fun- now, I'm actually convinced

[@michellesenft1517]

Can you sing lettin go in this disposition i mean ABC

[@deeremeyer1749]

In any "permutation" where a player "stays in place" besides where he/she is "leader" is not a "permutation" since having the same "leader" and a "follower" in the same position in successive "permutations" would be a "pattern". The "leader" would ring on the "1-count" and the non-moving "follower" would ring on the "X-count" in two consecutive "permutations" which is NOT a "different permutation" since a PATTERN PRECLUDES "PERMUTATIONS". There are no "patterns" POSSIBLE with "three bells" and if the SAME RULES APPLY TO ADDING BELLS, you have to prevent "non-moving" ringers in order to have "permutations". And as long as each player is a "bell" rather than a "ringer" and can only fill TEN POSITIONS TOTAL and will only "LEAD" TEN TOTAL UNIQUE PERMUTATIONS WHERE EACH RINGER "MOVES" AFTER EACH "PERMUTATION", JUST LIKE EACH OF THREE BELLS CAN ONLY FILL EACH OF THREE POSITIONS TWICE WHILE ALLOWING THE OTHER TWO BELLS THEIR TURN AS "LEADER", WITH TEN BELLS EACH BELL CAN ONLY "LEAD" NINE TIMES IF EACH OF THE NINE OTHER BELLS ARE GOING TO GET THEIR TURNS AS "LEADER" AND AFTER BEING "LEADER" EACH BELL OCCUPIES EACH OF THE NINE OTHER AVAILABLE POSITIONS NO MORE THAN 9 TIMES PRIOR TO MOVING. THE "EASY" WAY TO "QUICKLY" PLAY EVERY POSSIBLE COMPLETELY UNIQUE PERMUTATION IS TO SIMPLY HAVE EACH PERSON "LEAD" TEN "PERMUTATIONS" AT ONE BELL WITH EVERYBODY ELSE MOVING TO A DIFFERENT BELL AFTER EACH PERMUTATION UNTIL ALL THE NINE "FOLLOWER" HAVE RUN ALL NINE "FOLLOWING" BELLS BEFORE EVERYONE "TAKES ONE STEP" TO HIS/HER RIGHT AND WHOEVER IS THE NEW "LEADER" BEGINS THAT SHORT, SIMPLE AND "QUICK" PROCESS OVER AGAIN.

[@thierrypauwels]

You say that with 4 bells there are over 10000 sequences of permutations, and this sounds plausable. Yet, I read somewhere that with 4 bells there are only 11 methods possible, and that it can be proved. Does that mean that to be a method there are more requirements than the ones shown at 03:02 ?

[@ralphgifford1821]

There are only 24 possible permutations with 4 bells. 1*2*3*4=24. The big numbers start turning up after 6 and more bells. Examble: 5 Bells 1*2*3*4*5=120; 6 bells is 1*2*3*4*5*6=720 and so on.

[@KempBrinson]

"Does that mean that to be a method there are more requirements than the ones shown at 03:02 ?" Yes, sort of. There are some more rules. I am not a total expert, so I may slightly misspeak on something, but here is something of an explanation. What you likely read is not quite what you remember. What you likely read was that there are "only 11 STANDARD 4-bell methods." The word "standard" is very important. So, what is a "standard" method? First, one of the bells, the highest pitch bell, rings a very simple line. It simply hunts its way from the front of the sequence to the back over and over again, like this: (position numbers given) 1 2 3 4 4 2 1 1 2 3 4 4 3 2 1... - this is called "plain hunt," and methods in which the highest pitch bell plain hunts are called "plain" methods -- and all the "standard" methods are "plain" methods. There are methods where none of the bells ring plain hunt, or the highest pitch bell rings a simple line, but not one quite this simple. These are not "standard" 4-bell methods. Second, the line that the other bells ring is a little more complicated, but ALL OF THEM RING THE EXACT SAME LINE/SEQUENCE, they just start in a different place on that line. Another way of saying that is that if you have memorized the path of the #2 bell, then you have also memorized the path of the 3 and the 4, you just start in a different place on the pat. There are ways of ringing all the permutations where the other three bells do not ring the same line. These are not "standard" methods. Third, the when the bells do this, at least in 4 bells, you end up ringing all the possible permutations on 4 - i.e. 24 changes. There are some methods where it might get back to the start without having traversed all the permutations, i.e., the method may be only 16 changes long, with an extra special change needing to be inserted to get all 24 permutations. Some methods are 48 changes long and hit each permutation twice. These are not "standard" methods. Finally, for the purposes of counting how many "standard" methods there are, we don't count methods that are simply the mirror image, the reverse, or a "rotation" of another method. These inversions and rotations are not "standard" methods, either. Therefore, if we count only methods where: 1. The highest pitch bell plain hunts. 2. All the other bells ring the same line as each other, starting from a different point. 3. The method is exactly 24 unique changes long before it repeats. And... 4. The method is not a trivial variation of another method on the list. ...then, with these criteria, there are, indeed only 11 "standard" 4-bell methods. However, there are LOTS of other ways besides these 11 standard methods, that obey the rules set forth in the video, to traverse the 24 permutations. And that is likely what the video was referring to.

[@peterclark1041]

Yes and that is why theoretically more than 40k options for crew order in a rowing eight!! Mind you in this case weight height and talent will help decide order of rowing!!

[@thierrypauwels]

@@ralphgifford1821 There are only 24 changes with 4 bells, but there are many many more sequences of these permutations that are possible. Theoretically 1*2*3*...*24. But these include a lot of impossible transitions because a bell would have to move more than one position from one change to the next.

[@SarylSaku]

Anyone here from the opening ceremony of EGMO 2020?

[@geyserite]

Is it just me or does the narrator sound like Philip Zimbardo?

[@singlesideman]

This is basically where I live...

[@paecar21]

interesting...

[@josefadul550]

Compare discussion in www.lulu.com/shop/jose-a-fadul/faduls-encyclopedia-of-bells/paperback/product-22070278.html

[@sartajjamalchowdhury3643]

Pink Floyd - High Hopes intro !!

[@albertnortononymous9020]

Sartaj Jamal Chowdhury Yeah lol permutations of one bell😂

[@meddemongalaxy691]

It’s about the evil matter calling the bad spirits