Stedman on Even Numbers

Before we look at ringing Stedman on an even number of bells, let's just recap the basics of Stedman, as rung on an odd number of bells. Then we will look at applying this knowledge to find our what happens on an even number of bells.

Stedman is a principle, so there is no hunt bell. It is constructed of sixes, i.e. blocks of six rows, in which the front three bells ring (the extent of) Plain Hunt on 3, while the back pair(s) of bells double-dodge. The Plain Hunt may be rung right (i.e. with the leading handstroke then backstroke), giving what is referred to as a Quick Six, or wrong (i.e. leading back and hand), which gives a Slow Six. Here are examples of Quick and Slow sixes, both Doubles and Triples.

Quick Slow

If you were to just ring Quick Sixes, you would get Cloister; if you were to ring just Slow Sixes, you would get Erin. But in Stedman, the sixes are alternately Quick and Slow. In the example below, the sixes are, respectively, quick, slow, quick and slow.

Here is a plain course of Stedman Doubles, with the sixes marked by lines. Note that, although each six is composed of plain hunting, because of the way they are joined up, you get points as you change from slow to quick sixes and vice versa. Each of the place bells starts part-way through a quick six.

The blue line contains two (identical) sections of dodging, alternating with two (different) front works. The Slow Work is the complicated section, in the middle, lasting for 5 sixes. The Quick Work happens at the end of the line, as shown here, where the treble goes in to lead right, before heading up to dodge again straight away. This section is just 1 six long. Each of the back-work sections takes 2 sixes.

In Triples, the front-work (both quick and slow) is just the same, but, as well as double-dodging in 4-5, there is double-dodging in 6-7, both up and then down. The backwork then lasts for 4 sixes.

In both cases, the back-work lasts for an even number of sixes, which is why, having completed that, each bell arrives at the next section of the front-work at the opposite type of six. In the Doubles example above, the treble first leaves the front at a quick six, then gets back to the front at a slow six. Then, for the next bit of back-work, it leaves the front at a slow six and returns at a quick six. This is why the two types of front-work alternate.

(It also explains the rules for which way you go back in after Bobs and Singles, depending on whether you've spent an odd or an even number of sixes at the back, but I don't want to go into that now...)

Now, we can look at Stedman on an even number of bells.

We still need alternate quick and slow sixes. But each six has to have a bell staying at the back for the whole six rows, while those underneath it do their double-dodge. So the back-work looks like these examples:

The crucial thing is that the back-work now lasts for an odd number of sixes. And this will be true for Royal, Maximus and beyond, too.

So what does this mean for which way you go in to your front-work? If you left the front at a slow six, you will find that, after the back-work, you get back to the front at a slow six. Equally, had you left at a quick six, you would return again at a quick six. So, each bell in the plain course will either only do quick work or only do slow work. The alternating types of front work have gone - at least until you have some calls.

For instance, here are the lines for 5 and 6 in Stedman Minor. The 5 only goes in slow, while the 6 only goes in quick.

Notice, however, that their lines are not the same length. The path of the 5th takes 8 sixes, i.e. 48 rows, while that of the 6th takes just 4 sixes, or 24 rows. So we get a Differential method, where different bells ring their blue lines a different number of times, before rounds is reached.

In Minor, bells 1 and 6 only do the quick work and have to ring their blue line twice, while bells 2, 3, 4 and 5 only do the slow work and ring their blue line just once.

Feel free to pause here, and work out for yourself how many changes their are for Stedman Minimus, Major, Royal and so on...

In Minimus, the treble is actually the only bell to go in quick, so the method becomes an Alliance method, rather than a Differential Principal. The treble's blue line is only 2 sixes long, while all the other bells go in slow each time, having a line taking 6 sixes. The plain course is 36 changes long.

In Major, the quick bells are 1, 6 and 7, each having a blue line of 6 sixes. 2, 3, 4, 5 and 8 are slow bells, with a blue line of 10 sixes. The lowest common multiple of 6 and 10 is 30, so the plain course is 30 sixes long, i.e. 180 changes. Every bell has to repeat their blue line in the plain course; the quick bells ring their line 5 times, while the slow bells ring theirs 3 times.

This is where it gets even more interesting! In almost every other case, the same method on a greater number of bells has a longer plain course. So far, we've had 36 changes of Minimus, 48 changes of Minor and 180 changes of Major...

But for Stedman Royal, the plain course is just 144 changes.

I'm sure there are hours of fun for the number theorists out there, but I will just conclude by commenting that on 20 bells, the plain course is very nearly a quarter peal, at 1188 changes.