[r-t] Terms of truth

Joe Norton strainsteamford0123456789+ringingtheory at gmail.com
Sat Jul 11 12:49:00 UTC 2015

I have a question about the names given to various classes of "truth" in 
a block. I've been working on some code to do various things with regard 
to proving, generating etc. of different kinds of blocks. I have given 
names to various properties relating to truth of given blocks, but I was 
wondering if people use more standard names for them.

I think it is well understood that the term "true" means that no row is 
repeated in a block.

If I want to describe a block on n bells that contains all of the n! 
rows at least once each, I call the block "complete". I'm not sure if 
there is a more widely used term for this.

If a block on n bells contains each possible row exactly m times each, 
for some integer m, then I call the block "balanced". For example a 240 
of Doubles that contains each row exactly twice.

Then there is a slightly less "true" sort of truth which exists in, say, 
quarter peals of Minor. If we have a 1260 of Minor, I would regard it as 
"true" if every possible row exists at least once and at most twice. 
More generally this can be expressed as: a block is complete (all 
possible rows are present) and the maximum and minimum number of 
occurrences of any two rows does not differ by more than one. I don't 
have any name for this.


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