[r-t] Stedman Triples and Camapanalogia

[Richard Johnston]

On 15 Jan 2020 at 11:00, ringing-theory-request at bellringers.org 
wrote:

>  [r-t] Stedman Triples and Camapanalogia
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Andrew Johnson:
> In the Christmas issue of The Ringing World, issue 5669/5670, p.1246 
> (subscriber link: https://bb.ringingworld.co.uk/issues/2019/1246)  I wrote
> an article examining whether Fabian Stedman ever extended Stedman Doubles
> (the Principle on Five) to triples.
> 
> J Armiger Trollope, Jasper Snowden, Ernest Morris and Clavis were of the
> opinion it wasn't extended to seven bells by the composer.
> 
> I pointed that in Campanalogia (1677), p.168, Fabian Stedman says:~
> ~Tis 
> plainly demonstrable, that [t]he Principle upon five may go 420 triples 
> upon seven, which is a twelfth part; 840 which is a sixth part; or 1260 
> which is a fourth part of the whole, and the utmost period of triple 
> changes. And then by making four extreams it may go 5040, the complete 
> peal.TM
> 
> Who agrees or disagrees that this shows Fabian Stedman did extend the 
> method to triples?
> 
> What was the extension? In the article I proposed some ideas, but none 
> were completely satisfactory.

Thanks - I found it interesting.

I didn't want to be prejudiced by your article, so I looked back at 
Camopanalogia, to see whaty I got by looking at the immediate and 
larger context, and not thinking too hard.

I cae to  much the same conclusions and for the same reasons as you 
on p1246.

The only additional point is that on page 131 of Campanalogia, 
Stedman doubles is written out with the conventional start at the 
middle of a quick six, which makes it likely that his triples would 
be written out the same way and that the parting change 5, needed to 
get a 5 part, occurred at the middle of the quick six.  

I don't think the fact that not all the bells do the same work would 
have bothered him, as many other contemporary method/compositions 
were like that. 

Looking at the sophistication level (i.e they are not static or 
tedious) of the other 7 bell methods, and the elegance of stedman 
doubles, suggests to me that it is more likely that Stedman's triples 
extension was probably our stedman triples rather than doubles with 
30 dodges behind.  But I admit either is possible.  

I didn't find your later proposals convincing - they seem more .
contrived, and plain hunt on 5 does not exhaust the possibilities in 
the elegant way plain hunt on 3 does.

I think it probably significant that the triples version was not 
pricked out, perhaps suggesting that he thought of it at a late stage 
in production of the book, and so just squeezed it in.  Consequently, 
he may well have underestimated the difficulty of obtaining true 
compositions especially as regards a 5040, so I don't think failure 
to find one as a 4 part using an extreme is significant.  He may have 
done no more than sketched out a few transformations.

My conclusions?  Yes he did have a stedman triples extension, and it 
is more likely than not that it was the one we use now, but otherwise 
the doubles version with dodges behind.   And, it got overlooked by 
later authors because it was not pricked out.

Richard Johnston