Every
Bell Once

A tower bell can weigh a ton and a half and swings through a full circle. You cannot play a tune on it — by the time you have decided on a note it has already sounded. So in the seventeenth century English ringers stopped trying, and started ringing permutations: every bell exactly once per row, and from one row to the next a bell may move only one place.

Four centuries later there are 25,094 named ways to do it. This is all of them.

Central Council of Church Bell Ringers library of

I  ·  Eight ropes

Nothing here is a melody. Each of the eight bells sounds once, then the band swaps some adjacent pairs and they all sound again. Follow one bell down the line and you get the picture ringers have drawn by hand since the seventeenth century — the blue line. Follow all eight at once and you get what is actually happening in the tower: a plait.

Time runs left to right, one column per row. The vertical axis is the order the bells strike in: top is first, bottom is last. The treble — the lightest and highest bell, always numbered 1 — is in red. One working bell is in blue. That is the entire visual grammar, and the rest of this page uses nothing else.

II  ·  One place at a time

The constraint is physical. A ringer controls a bell by when they pull, and can nudge it a little earlier or a little later — enough to trade places with the bell next to it, and not enough to jump the one beyond. So the only legal move from row to row is to swap neighbours.

one place · allowed two places · not
Three successive rows. A bell may cross one line between them, never two.

That is the claim the whole tradition rests on, so this page checks it rather than repeating it. Every method in the library was rung out from its place notation, change by change, and every bell's displacement measured:

1

The largest distance any bell moves in any change, anywhere in the library. Not a mean, not a maximum-with-exceptions — the maximum, over changes and individual bell positions. There is no second-largest.

III  ·  The same red line

Methods have classes — Surprise, Delight, Treble Bob, Bob, Place, Alliance, Treble Place, Hybrid — and a ringer learning a new one asks its class first. You would expect the class to describe how the method sounds, or how hard it is. It does not. It describes what the treble does, and nothing else.

Here are the six commonest treble paths on eight bells, with how much of the library hangs off each:

One lead, treble only, on eight bells. Together these six account for of the 10,853 Major methods in the library.

The first one covers — of the Surprise, Delight and Treble Bob methods ever named on eight bells draw exactly that red line: the treble hunting up to the back of the tower and down again, dodging in each pair of places on the way. The thousands of methods built on it differ only in what the other seven bells do behind it. (The remaining are Little methods, where the treble turns round before it reaches the back — the fifth glyph above.)

Which makes a demonstration possible. Cambridge and Bristol are the two most-rung Surprise Major methods and they feel nothing alike; ringers argue about them. Take the working bell away and there is nothing left to argue about.

One lead of each, thirty-two changes. Second's place bell in blue, treble in red.
distinct hunt-bell paths in the whole library
of them on eight bells
class re-derived from notation

The library is enormous and its frame is tiny. Twenty-five thousand methods across nineteen stages use different hunt-bell paths between them.

And because the distinction really is mechanical, it can be recovered. The difference between Surprise, Delight and Treble Bob is whether an internal place is made at every point where the treble crosses between pairs of positions, at some, or at none. Applying that rule to the place notation alone, with no reference to the library's own label, reproduces the Council's classification for of the treble-dodging methods — . The twelve disagreements are all Treble Bob methods this page would call Surprise.

IV  ·  Twenty-five thousand

    Nothing is stored here but a name and a string of digits. Every line you have drawn on this page was rung out in the browser from that string, the same way the band rings it — apply the change, look at the row, apply the next one.

    The library records the place notation of methods in characters. Rung out in full they come to digits of numbers: the notation is the compression, and it has been for four hundred years.

    V  ·  Everything at once

    So here is the whole treble-dodging library on eight bells in one picture: the second's place bell's path through one lead of methods, drawn on top of each other and shaded by how many took each line. The solid strokes are the shapes nearly every method makes; the faintest are where one or two have gone and nobody followed. The gaps are the shapes four hundred years of ringers have never wanted.

    Each hairline is one method.

    The Council will not accept a method that duplicates one already named, and the rule holds exactly: of 25,094 methods, the number that ring an identical lead to another is

    0

    But it is a close-run thing, and the margin is often a single change. methods — better than one in five of the library — ring an identical lead to at least one other method right up to the very last change, and become a different method only there. They fall into groups, the largest holding . A ringer who nods off for one blow cannot tell you which one they just rang.

    VI  ·  Who named them

    A method belongs to whoever first rings a peal of it, and they get to name it. The library's earliest dated performance is ; its most recent is . Nearly all of it is modern — a naming boom that ran from the 1960s and peaked in the 2000s.

    First recorded performance of each method, one tick per year.

    It is not evenly spread. A few bands, in a few towers, are responsible for thousands of them — light rings of bells where a band can ring a peal of something untried in three hours and go again next week.

    Most names are English places: villages, hills, castles, railway halts. Reverse and Double and Little are structural prefixes. But methods are named after a lighthouse and begin Beinn, which is Gaelic for a mountain.

    Once a band has a theme, they tend to finish it. The single busiest day in the library's 342-year record is , when one band rang new methods at — , and every one of them named after a Billie Eilish song.

      They are not the first. Somebody, at some point, worked their way through the complete studio discography of Pink Floyd on four bells, in order, and the library holds all fifteen.

        Beyond that, a name only has to be unclaimed.