“But Cambridge forty-eight, for many years, was the greatest peal that was rang or invented” (Tintinnalogia p.2)
In Duckworth’s Tintinnalogia, published in 1668, he gives the full text of “three old peals on five bells, which (though rejected in these days yet) in former times were much in use” (p.15-17). I am interested in these three as rare testimony of the state of change ringing in its true infancy in the early to mid 17th century.
The first of Duckworth’s three “peals” is “the Twenty all over”. This is a simple but musically satisfying set of changes where each bell hunts in turn from the front to the back. There is a kind of repeating rotation of the melody as each comes into last place, which is upset again as the next leaves the front. He gives the verbal instruction that it can also be done in reverse, by hunting each bell down to the front instead. We do this one fairly often in St Salvator’s tower in St Andrews.
The second is “An eight and forty”, which is harder to call and to keep track of. The fourth and fifth alternately hunt to the front, and an extreme change is made while they lead. Because they alternate in running in and back out, either the four or the five is always left in fifths place, which gives a curiously doleful effect to the music. We do this one less often just because it is slightly harder to ring.
The third of Duckworth’s obsolete notations is “Cambridge eight and forty”. Unlike with the other two, he does not explain the method by which it is organised, just the notation of the numbers. And I have not yet managed to understand the method.
John C. Eisel, in his chapter in Volume 1 of Change ringing the history of an English art (ed. J Sanderson, CCCBR 1987), says “the basic idea seems to be that while one bell leads for six changes, another lies behind for six changes, and the three bells in the middle execute the three possible changes, although the idea is not completely carried through”. Not completely – more like not very well at all, with blocks of five, and inconsistent switches on the front and back and opposite rotations of the middle sixes. Eisel also reproduces an early 17th century manuscript which gives the Cambridge 48, and with the tracks of certain bells partially outlined a little like a modern “blue line”. but the tracks are incomplete, varying, and fail to highlight every point of importance.
Paul Cattermole also reproduces the same manuscript page in his book Church bells and bell-ringing, a Norfolk profile (Boydell 1990, p.23). But he doesn’t have much to say about the actual method, talking about the manuscript and its writers instead.
I did wonder if Duckworth had it garbled, but the Norfolk manuscript version seems to show they are genuine. Will the lines drawn on them prove useful for understading their structure? Or are they just like my scribblings on a photocopy of Duckworth’s page, vain attempts to “get” it?
Perhaps I just have to learn the sequences by rote…
In the meantime here is my MIDI realisation.
Each row is repeated twice, at a tempo of 120bpm, based on the comment in Stedman’s Campanologia (1677) p.4 “720 changes every hour”, i.e. 12 changes per minute. 11 strikes per change, is 132 beats per minute. I should do a blog post about performance practice implications of these throwaway comments in the two 17th century ringing books.
If you are still reading the comments I can point you towards understanding the structure of the lines drawn. They are very much a way to understanding the structure. The problem is the complete set of lines is not there, if it were you would see it makes a visually very interesting and highly structured pattern.
I came across you page while trying to search for the sound of the bells. The midi was cool. I have never considered what a generated sequence of numbers sounds like before.
I do math and computers and while working out a problem I read a footnote relating the problem to the Cambridge 48. This pattern is from a part of math called combinatorics and in computer science an area called combinatorial searching.
I never leave a real name or email. I will fill it with dummy information. I will check back here shortly to see if you accept the post.
Thanks, yes please do explain if you see a structure in the pattern. I would be comparing it to how the structures of the other two “old peals on five bells”. They both have memorable sequences of changes which means that after memorising the principle or the structure it is not hard to call them while ringing. I have never done that with the Cambridge 48 because I don’t see a memorisable system to the changes.
If you have annotated diagrams you can email them to me and I can upload them to insert into your comment.
I will try to put something together for you. It will take a few days. I don’t know how much help it will be for memorization, there is a very well defined pattern but I suspect it would be difficult. That being said I understand musicians can play vast amounts of highly complicated music from memory, so perhaps what seems difficult to me might not be so difficult for you.
Do you have any experience with any programming language or any friends who do? I could send you the algorithm in just about any programming language you wanted.
I have diagrams of the patterns in a textbook, I will try get get them scanned in the next few days.
OK… it should fit into established norms of change-ringing and how the permutations are described in change-ringing world. I am aware of the close parallels with change-ringing and group theory; but most change ringing nowadays uses “double changes” i.e. between each two adjacent rows, it is normal for two pairs to swap, e.g. you might go from 12345 to 21354.
You’ll see that the Cambridge 48 uses exclusively single changes, hence it goes 12345, swap 1 and 2 to get 21345, then swap 4 and 5 to get 21354.
The way I would describe that in ringing terms, is something like this:
make 2 lead
Hunt 5 in to seconds place, out to 4ths place, in to 2nds place, and then out to the back.
Then hunt 4 in to seconds, out to 4ths, and in to 2nds…
I would expect this simple set of instructions to repeat regularly (perhaps with triggers to switch to a different instruction for a bit). you’ll see that the other 2 tracks in the manuscript outline a bell hunting between seconds and fourths place for a bit, but I don’t see what the “triggers” are to tell you when to start hunting, which bell hunts, and how you know when to swap the bell in 1sts or 5ths place. These are the things I need to know to be able to memorise the entire sequence and call it out loud in real time as instructions to the ringers as they ring.