[r-t] Pitman's 13440 change compositions
Philip Earis
pje24 at cantab.net
Wed Aug 9 18:23:57 UTC 2017
So for this #2 composition (unrung), the Sirilic musical analysis shows it
has 12 5678s off the front and 12 8765s at the back, and 9 8765s off the
front, more than would be expected in a "random" distribution of one third
of the rows in the extent.
The composition is also of course very far from being all the work, as the
distribution below shows.
13440 rows ending in 12345678
Touch is True
Odd Even Total
xxxx5678 = 0 + 24 = 24
xxxx6578 = 0 + 24 = 24
xxxx4678 = 0 + 24 = 24
xxxx6478 = 0 + 24 = 24
xxxx4578 = 0 + 24 = 24
xxxx5478 = 0 + 24 = 24
15263748 = 1 + 0 = 1
xxxxxx87 = 720 + 0 = 720
5678xxxx = 0 + 12 = 12
8765xxxx = 3 + 6 = 9
xxxx8765 = 0 + 12 = 12
xxxx5432 = 6 + 10 = 16
xxxx2345 = 6 + 8 = 14
CRU = 0 + 144 = 144
NumberLeads=420
[Rutland] 87 leads 2784 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 87 - - - - - - -
2: - 15 17 23 9 17 - 6
3: - 15 17 23 9 17 - 6
4: - 15 17 23 9 17 - 6
5: - 21 18 9 12 18 - 9
6: - 21 18 9 12 18 - 9
7: - - - - 36 - 51 -
8: - - - - - - 36 51
[Watford] 120 leads 3840 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 120 - - - - - - -
2: - 24 12 24 12 12 24 12
3: - 24 12 24 12 12 24 12
4: - 24 12 24 12 12 24 12
5: - 24 12 24 12 12 24 12
6: - 24 12 24 12 12 24 12
7: - - 60 - - - - 60
8: - - - - 60 60 - -
[Wembley] 87 leads 2784 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 87 - - - - - - -
2: - 11 11 6 15 6 17 21
3: - 11 11 6 15 6 17 21
4: - 11 11 6 15 6 17 21
5: - 9 9 9 21 9 18 12
6: - 9 9 9 21 9 18 12
7: - 36 - - - 51 - -
8: - - 36 51 - - - -
[Ealing] 60 leads 1920 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 60 - - - - - - -
2: - - 12 - 12 12 12 12
3: - - 12 - 12 12 12 12
4: - - 12 - 12 12 12 12
5: - - 12 - 12 12 12 12
6: - - 12 - 12 12 12 12
7: - - - 60 - - - -
8: - 60 - - - - - -
[Belvedere] 33 leads 1056 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 33 - - - - - - -
2: - 3 1 7 9 7 6 -
3: - 3 1 7 9 7 6 -
4: - 3 1 7 9 7 6 -
5: - - 3 6 3 6 3 12
6: - - 3 6 3 6 3 12
7: - 24 - - - - 9 -
8: - - 24 - - - - 9
[Belgrave] 33 leads 1056 changes
1pb 2pb 3pb 4pb 5pb 6pb 7pb 8pb
1: 33 - - - - - - -
2: - 7 7 - 3 6 1 9
3: - 7 7 - 3 6 1 9
4: - 7 7 - 3 6 1 9
5: - 6 6 12 - 3 3 3
6: - 6 6 12 - 3 3 3
7: - - - - 24 9 - -
8: - - - 9 - - 24 -
381 changes of method
> 13440 Spliced Surprise Major (6 Methods)
> Albert J Pitman 1961 p287
> 23456 M W H Methods
> -----------------------------------
> 43526 2 - RWMEMW/BW/R/
> 54326 - LEMWR/
> 35426 - RWMEL/
> 36524 2 - R/WB/WMEL/
> 45623 - - R/WMEL/
> 62453 - - LEMW/R/
> 46253 - RWMEL/
> 24653 3 - RWMEMW/BW/BW/R/
> 64523 2 - RWMEMW/BW/R/
> 56423 - RWMEL/
> 52364 2 - - R/WB/WMEMW/R/
> 35264 - RWMEL/
> 23564 3 - RWMEMW/BW/BW/R/
> 53624 2 - RWMEMW/BW/R/
> 46325 - - R/WMEL/
> 24365 - LEMW/R
> 34625 2 - RWMEMW/BW/R/
> 63425 - RWMEMWR/
> 65324 2 - R/WB/WMEL/
> 42356 - - - R/WMEMW/R/
> -----------------------------------
> 3 part.
> 3840 Watford, 2784 Wembley(M), Rutland,
> 1920 Ealing, 1056 Belgrave, Belvedere(L).
> 381 com, 144 cru's.
> ===
8 bells
peal=3(c1,c2,c3,c4,c5,c6,c3,c8,c1,c3,c11,c3,c8,c1,c5,c12,c1,c13,c4,c14)
c1=Z,B,+12,W,+14,R,+14
c2=L,+12,E,+12,M,+12,W,+12,R,+14
c3=R,+12,W,+12,M,+12,E,+12,L,+14
c4=R,+14,W,+12,B,+14,W,+12,M,+12,E,+12,L,+14
c5=R,+14,W,+12,M,+12,E,+12,L,+14
c6=L,+12,E,+12,M,+12,W,+14,R,+14
c8=z,B,+12,W,+14,B,+12,W,+14,R,+14
c11=R,+14,W,+12,B,+14,W,+12,M,+12,E,+12,M,+12,W,+14,R,+14
c12=L,+12,E,+12,M,+12,W,+14,R,+12
c13=R,+12,W,+12,M,+12,E,+12,M,+12,W,+12,R,+14
c14=R,+14,W,+12,M,+12,E,+12,M,+12,W,+14,R,+14
Z=R,+12,W,+12,M,+12,E,+12,M,+12,W,+14
conflict=
music="default","?87","5678?","8765?","?8765","?5432","?2345","?7568"
R="@R","[Rutland]",&-3-4-5-6-4-3-34-1
W="@W","[Watford]",&-5-6-5-36-4-5-34-1
M="@M","[Wembley]",&-5-6-2-36-4-3-6-3
E="@E","[Ealing]",&-5-4-56-36-4-5-4-5
B="@B","[Belgrave]",&-3-4-5-6-2-3-4-1
L="@L","[Belvedere]",&-5-4-56-36-4-5-36-7
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