Here I am walking from my neighbourhood towards Patrick’s Cathedral and then past it, ending at Aungier Street.

You can hear all the usual city sounds–birds, wind, cars, bikes, people walking by, bits of conversation. Same ingredients found in most other recordings I’ve made in this city. My mostly steady footsteps are present here, too. You can also hear the bells of Patrick’s Cathedral ringing changes.

This is something I love about where I live: I love change-ringing. Change-ringing is a kind of “algorithmic music” made with church bells. You need a set of bells hanging in your church, tuned to different notes of a scale (often a major scale), and then you need people to ring those bells. And you have to have those people ring those bells in a certain order. And then you have to have those people change the order in which they ring their bells, one by one. And they need to all know when the order changes, and they need to know how it changes–who switches place with who in the order.

To illustrate what I mean, say you have six people ringing six bells. Let’s suppose the person with the highest pitched bell rings first, then the second highest pitched bell, then the third, and so on. If our six change-ringers do this, they’ll have run a descending scale. We can notate it like this:

1 2 3 4 5 6

This is one sequence. We could repeat it, but we want to make it interesting. Let’s imagine that whichever bell is first in the sequence has to start to work its way, position by position, to become the last bell in the sequence. And meanwhile, whichever bell is last in the sequence must start making its way, position by position, to become the first in the sequence. And because we have six bells, we actually have six separate journeys occurring. At any given time, each bell is making its way either towards the top or the bottom of the sequence.

So, everyone needs to move either up or down in the sequence every time we repeat the cycle. And since we have a group of people doing this together, in real-time, and it is physically difficult work (ringing these bells takes a lot of practice and skill), we need a set of rules that everyone can learn so that, no matter what order the bells are rung in, no matter where we happen to be in the potentially long list of possible permutations of ringing-order, everyone can deduce what the next order ought to be. It would be impractical to memorize a hundred or more unique sequences, and then execute them in real-time. It is far easier to learn a few simple rules for how to swap positions. This is why we can call this algorithmic music: some starting conditions (our bells ringing in their original order 1 2 3 4 5 6) are fed into a simple set of rules for how to tweak those starting conditions, outputting a new set of conditions which will then become the input for the next transformation. Some starting ingredients + some rules generates new arrangements of sound. (We can for this reason also use the term “generative music”.)

There are lots and lots of rules that have been devised for swapping positions. One very simple one, called “Plain Hunt”, works by applying two alternating transformations to each sequence. Every time we reach the end of a sequence we either make three swaps or two swaps.

When we make three swaps we swap positions 1 and 2, 3 and 4, and 5 and 6. Like this:

seq. changes notes
one 1 2 3 4 5 6 our original order
two 2 1 4 3 6 5 three swaps

Now, if we were to apply this same transformation again, we would return to our original order. Not very interesting. But if we keep our first and last place bells where they are (after all, they were seeking those positions, so they may as well enjoy them!), we can make two swaps with our four “inner voices”. To summarize, we can keep the first and last positions the same, but swap the second with the third, and the fourth with the fifth. Like this:

seq. changes notes
two 2 1 4 3 6 5 see previous for how we got sequence two
three 2 4 1 6 3 5 two swaps on inner voices, outer voices stay

It turns out that these two rules, in alternation, are enough to generate 12 distinct “changes”. It looks like this:

seq. changes notes
one 1 2 3 4 5 6 our original order
two 2 1 4 3 6 5 three swaps
three 2 4 1 6 3 5 two swaps on inner voices, outer voices stay
four 4 2 6 1 5 3 three swaps
five 4 6 2 5 1 3 two swaps only for inners
six 6 4 5 2 3 1 three swaps
seven 6 5 4 3 2 1 two swaps only for inners. Reverse!
eight 5 6 3 4 1 2 three swaps
nine 5 3 6 1 4 2 two swaps only for inners
ten 3 5 1 6 2 4 three swaps
eleven 3 1 5 2 6 4 two swaps only for inners
twelve 1 3 2 5 4 6 three swaps
one 1 2 3 4 5 6 two swaps only for inners. Original order!

(Notice how each number leaves a “zig-zag” path. Choose one from the top row and follow it down with your eyes and you’ll see what I mean.)

This is a simple example. Some patterns of changes can yield hundreds of sequences. Change-ringers will sometimes attempt to see how long they can go ringing a certain pattern without someone messing up. If they make it far enough, they may commemorate the occasion with a plaque hung up in the ringing chamber below the belfry listing the date, the pattern, how many changes, and maybe even the names of the ringers. I used to spend a little time with change-ringers at the Old North Church in Boston, MA, USA. It was hard and fun.

What I love about change-ringing is that it takes simple ingredients, applies sometimes simple and sometimes complex transformations, and in so doing yields lots of unique and new combinations. If you program a computer to do it (which I’ve done) it can be entertaining but, once you know the algorithm, never surprising. The great thing about people is that they are fallible and mortal and susceptible to daydreaming and fatigue, and so there are glitches and hiccoughs and occasionally the whole set of changes breaks down. These events are always surprising, exciting, and maybe even funny if you and your companions have a good sense of humour. Listening to the bells ringing in this recording I love the moments where Someone rings their bell slightly early or slightly late. I love the surprise, and the reminder that a group of passionate enthusiasts are making this sound right now in the ringing chamber and probably chuckling to themselves about it. (Or maybe they’re exasperated that this is the umpteenth time today that so-and-so has made a goof–charming in its own way.)

The universe works like this too, I think. Dublin at least does. Same ingredients, same stuff day to day, same people on their same routines crossing paths with the same people on their same routines. A million of us, though, not six. And all the birds and rodents as well. And the insects of course. And the remaining trees, the grasses, the hedges and wildflowers and so on. The weather (a lot less steady and dependable than I think it used to be, or at least that’s my impression). So much stuff. So much stuff doing its thing. So many things and beings doing their things and being. It’s tempting to try and fit an algorithm to it, and I suppose that’s what economists and social scientists and the like are doing. But we know that there are glitches and that people and beings and things are fallible and susceptible to fatigue and flights of fancy. One could try to see how long they can keep the same set of changes going, both at a personal level and perhaps even at a broader social level. One should have a good sense of humour, because inevitably Someone or Something will goof it up.



Walking along the sidewalk, the fuzzy windshield of the recorder sticking up from below the bottom edge.

Figure 1: Walking down the sidewalk near Na Cuithí Dubha, recorder held out in front.

On the sidewalk, the windshield of the recorder sticking up from the bottom edge, looking down a narrow street. Patrick's Cathedral rising up in the distance.

Figure 2: Still walking, still holding the recorder, Ardeaglais Phádraig visible above the far end of the street.


Around Patrick’s Cathedral, Dublin 8
<2024-01-28 Sun>
Sony PCM-M10
Built-in mics on the recorder
2, Stereo
Other notes
Some light high-pass filtering to knock down some wind sound.