[r-t] Similar compositions

[Mark Davies]

I think this is an important and necessary undertaking. Without it, we 
certainly lose the concept of original authorship, but also the history 
of development of composition. As John and others have pointed out, it 
isn't necessarily easy, though, and beyond a certain point subjectivity 
plays a part. When are two compositions closely related?

This is something I think about all the time when checking compositions 
for the G&B Report. To me, if a composition is a pure rotation or 
reversal of another, it is the same composition. If two compositions 
differ only by the movement one or two blocks or Q-sets, then they are 
closely related, and the later is an arrangement of the earlier. Two 
compositions may also be related if small sequences of calls are 
replaced with an equivalent, e.g. 2W for MB. To take some examples:

1. Johnson's Variation is indeed an arrangement of Middleton's. The 
calling is rotated, and B substituted for 2M2W.

2. Starbuck's Yorkshire (https://complib.org/composition/10665) is an 
arrangement of Shuttleworth's 30-course block (W sM 2W 3M H). The basic 
calling, W sM 2WH, is identical, the compositions differing only in the 
position of the inserted blocks of three.

3. This Alan Reading composition of Bristol Max 
https://complib.org/composition/37065 is a variation of David Hull's 
peal https://complib.org/composition/36614. In Alan's version, sH 
replaces HsHH, a block ssM is removed, and another block HsHsMM inserted.

I suspect everyone will agree with me on (1) - what about (2) and (3)?

Clearly you have to stop somewhere. For instance, there are hundreds 
(possibly thousands) of one-part 5056 compositions for b-group methods 
based on the calling MBW padded with blocks of three. Are these all 
arrangements of each other? Probably so, but once the padding becomes 
sufficiently different it seems reasonable to accept them as novel 
creations.

I use human eye for spotting duplicates or prior variations of G&B 
compositions. To do this I try to identify some key feature that is 
invariant under rotation, reversal and block substitution. This may be 
something as simple as the number of call pairs I/V in a composition 
which uses those, or it may be a fundamental building block like 
Shuttleworth's W sM 2WH. I then scan the libraries for compositions 
which have this key feature. With lots of practice this can be done 
relatively quickly - five minutes or so. The benefit of this approach is 
that it can identify a wide range of variations as well as straight 
duplicates.

In terms of automation, that would be brilliant, and I applaud Graham 
for attempting it. Hashes are clearly useful for spotting duplicates, 
with some generality possible such as applying across different 
rotations or LH groups, however this technique is unlikely to be so 
helpful for finding variations. Alan's idea of using string distance 
bears merit, one problem being the algorithm is then O(N^2) rather than 
O(N), where N is the library size.

Ultimately it would be nice to train a neural network to do it...

MBD