[r-t] 1-part tenors together atw compositions of 23-spliced major

[Roddy Horton]

Mark has done an exceptional job here and it reminded me to dig out some old
papers from a similar project I looked at sometime in 1980s.
With 7 and 3 being factors of 21, I was looking for 7 lots of 3 course
blocks which would allow all the work for 21 methods with tenors together.
It would effectively be a 3 part with different methods rung in each part.
The remaining length would be filled with padding from the selected 21
methods.

I found one series of suitable blocks and put them together as follows:-

5280 Spliced Surprise Major (21 methods)

         Methods
M  W  H  Part 1      Part 2         Part 3
-----------------------------------------------
   -     BCDE/ABC    IJKL/HIJ       123456/3   
   -     DEFG/LMN    KLMN/2         456712/EFG 
-        HIJ/MNHI    3/712345       ABC/FGAB    
-  -     JKL/A/DEF   6/H/KLM        CDE/34567/4   
   -     GABC/X      NHIJ/X         567123/X     
   -  -  YX/BCD/     YX/IJK/        XY/1/  
      -  XYX/        XYX/           XYX/
      -  MNHIJKL/    7123456/       FGABCDE/
-  -  -  EFG/K/FGA/  LMN/4567/MNH/  2/D/7/ 
-----------------------------------------------
A to N - Group B lead heads.
1 to 7 - Group F lead heads.
X - any of 1 to 7
Y - any of A to N

All The Work tenors together 164 com.

I then started a search to find suitable methods to slot into the
composition and this was done by extracting all the then rung Group B and F
methods (Groups B and F were selected simply because these two groups
contained the most methods, hopefully increasing the chances of a successful
search) and running a search program to try them all.
It kept running into a brick wall at about 16 or 17 methods each time and
after a number of months I gave up. I discussed this little idea with John
Leary and he suggested that I design new methods to fit the composition but
I had moved on to other things and never took that up. Some years later at
Stephen and Fiona Wheeler's wedding I was sitting next to PABS and the
conversation got around to composition and I seem to recall him saying that
he had had a similar idea and also got to about the same brick wall at the
same place.

What Mark has done is well beyond where I was going and he has done a superb
job in crafting new methods to fit the composition - that in itself is no
mean feat. Hats off to you Mark.

Roddy