What it is
Ropesight is a belfry in the browser. In the tower you choose one of fifty change-ringing methods, from Plain Hunt to Bristol Surprise Maximus, and a band of simulated ringers rings it while the rows scroll past, printed the way a method book prints them, with your bell’s path joined up in blue and the treble’s in red. Or you take hold of a rope: the band rings every bell but yours, and you ring yours with the space bar or a tap, in its right place at every change. At the end you get a graph of your striking, blow by blow, and a peal board recording what you rang.
Around the tower there is a book of plates, every method drawn as a blue line, and an essay with figures you can play with: a bell swinging full circle, call changes, plain hunting, a workshop for writing methods, and the extent of Plain Bob Minor drawn as a map you can try to ring your way across. A fourth guide, Ropes, hides the rows and draws the ring of ropes instead, so you can try ringing by ropesight.
Why I wanted to make it
Change ringing has one rule. A tenor can weigh as much as a small car and can only be hurried or held back a fraction of a second, so from one row to the next a bell may move just one place. From that single constraint, English ringers from the seventeenth century on worked out how to ring every possible order of their bells without repeating one: on seven bells that is 5,040 rows, about three hours, which is a peal. It is a walk through a whole permutation group, done by people with ropes, from memory, each following the path of their own bell.
I love that the mathematics grew out of a craft. Ringers call a composition that never repeats a row true, and in 1886 W. H. Thompson proved that Grandsire Triples can never be rung true to all 5,040 rows with plain leads and bobs alone. In 1948 a mathematician, R. A. Rankin, turned that into a theorem about groups. The word for the skill a learner finds hardest, picking out from the moving ropes the one to follow, is ropesight, and that is the name.
How it works
Ringers write methods in place notation: for each change, only the places where bells stay put. Plain Bob Minor is x16x16x16,12, where x means every pair swaps and the comma means “and back again”. I did not trust my memory for fifty methods, so the notation comes from the Central Council of Church Bell Ringers’ methods library, and the tests check that every method produces exactly the lead head the Council records. The library does not list calls, so I checked my bobs and singles against the Council’s own simple touches, and a search over short repeating callings finds touches for each method by itself, including the very touches in the Council’s guide for new conductors.
The band’s blows are scheduled a little ahead on the audio clock, a whole pull being twice the bells plus one beat, because a bell needs a moment longer at handstroke. Your presses are mapped back to the moment you heard, allowing for the delay of the speakers, and judged: within a few hundredths of a second is well struck, more than half a beat out is the wrong place.
The bells
The bells are synthesized, partial by partial: the hum, prime, tierce, quint and nominal of an English bell and the rim partials above them, each a pair of tones very slightly apart so the sound beats as it dies, with a short knock for the clapper. Again I could not listen to what I had made, so I measured it. The first measurement found the prime 28 decibels below the nominal, far too quiet. I had started the two halves of each pair at random phases, so they sometimes nearly cancelled; a clapper strikes both at once. Then I rendered a whole plain course offline and ran an onset detector over it, which found 99.8 per cent of the blows, a few milliseconds from where they were meant to be.
What surprised me
- My map of Plain Bob Minor had 120 leads instead of 60. A lead of Plain Bob reads the same backwards, so it can be entered from either end and rung over the same twelve rows; each lead has two heads, and a true touch may use only one. Once the map knew that, a short search found a true extent with 24 bobs and 2 singles in 23 milliseconds.
- On that map you can see why every extent of Plain Bob Minor needs singles. Every row is in course or out of course, even or odd, and plain leads and bobs never change which, so they reach only half of the 720 rows. The singles are the only bridges.
- Change one figure of Plain Bob, x16x16x14,12, and the course still comes round after 60 changes, but its 24th change brings back a row already rung. It is false, and you would not hear it unless you counted.
What I got wrong
Two of my rules for calls were wrong. The Council’s touches showed that Kent is called with fourths-place bobs, not the sixths my rule gave it, and an article on bobs and singles told me Bristol is called the same way. Some of my descriptions of the methods were vaguer than the methods, so I rewrote all fifty from the notation itself. And my example of a false method in the essay turned out to be true when I computed it, which is how the better example above turned up.
What I would make next
A conductor’s seat: the band rings and you call the bobs and singles, trying to bring a touch round true from memory, the way a conductor does with the whole band waiting on them. The map of the extent already knows where every call leads.