[r-t] Queens and Tittums

[Philip Earis]

Richard Pullin:
"May I remind and inform that Queens and Tittums are transpositions of each other... Either Tittums came about because of this, otherwise it's plain but amazing coincidence"

The link between Queens and Tittums is indeed very well known.  I think your hypothesis that "tittums came out because of this" is both a simplification and an over-interpretation.


What is more interesting is how this effect has been used in ringing to generate neat effects. Eg a three-part peal composition of Stedman triples, with Tittums and Queens at the part-ends.

5,040 Stedman Triples
Philip A B Saddleton 
 2314567  1 2 3 4 5 6 7 8 9 0 
 2376145          -     - - s |  
 2375164  - - - - - -   - -   |  
 4375126  - -   - -   - - - - |  
 4275631    - -     - -   - - |  
 1435627  - -   - -   -     - |  
 1423765  -   -   - - - - -   |  
 7413652    -   - -   - -   - |  
 7453216  -   -   - - - - - - |  
 7253146      - - - - -     - |  
 6243571  -       - - - - - - |  
 5246137    - -   -     - -   |  
 5216734  - -     -   - -   - |  
 5316427    - -     - -   - - |  
 4315762    - -   -     - -   |A 
 4361752  -   - - - -   - -   |  
 4325716  - - - - - -   -   - |  
 4312756  -   - - - -   - -   |  
 6312745  - -   - -   - - - - |  
 5314726  - -   - -     - -   |  
 5364712  -   - - - - - -   - |  
 5316742  -   - - - -   - -   |  
 5316274    - -   - - - - - - |  
 5213467    - -     -   - -   |  
 5716432  - - - - - -     - - |  
 5746231    - -   - - - -   - |  
 5746123    - -   - - - - - - |  
 5716243      - - - - - -   - |  
 5216374    - -     - - s - - |  
 2314567         2A               


The transposition gets even more interesting on ten bells, producing what I call the "magnificent six", ie:

1234567890 (rounds)
----------
1357924680 (queens)
1594837260 (reverse tittums)
1987654320 (reverse rounds)
1864297530 (reverse queens)
1627384950 (tittums)
1234567890 (rounds)


This effect has been exploited in royal compositions (eg see http://ringing.8bit.co.uk/nextgen.html), as well as coupled with a cyclic 9-part transposition to produce a stonking peal of Erin Caters:

5076 Erin Caters
Alexander E. Holroyd

 123456789
 ---------
 738495162   (a)
 975318642   (b)
 198765432   (b)
 615948372   (b)
 468135792   (b)
 345678912   (b)
 ---------
9-part

(a) =  s1.s6.s9.10.s12.13 (14 sixes)
(b) =  s1.6.s9.10.14.15 (16 sixes)


Parts of the transposition on ten can also be used in more conventional compositions.  Eg see the emails to this list on 30 January 2006, where David Hull used the short linking block (1.2.4) in Bristol Royal to transpose between the magnificent six:

5120 Bristol Surprise (no.11)
 234567890
 43652        M
 357924680    SM.SW.W.S3rds.SH
 627384950    1.2.4    (4)
 023547698    1.2.4.S8 (8)
(543267890)   S7.8.12
(24356)       SW
(56342)       SM.W
 34562        SM.SW.W.M
 53462        H
 65432        W
 23456        7ths.S7ths.SM

 20.1.2006
 First rung at Birmingham St Paul 21.1.2006


This effect was used by Rob Lee to incorporate the cyclic transpositions too in a Bristol Royal composition:

5220 Double Coslany/10440 Bristol:
 
            234567890
---------------------
1, 2, 4     864297530
1, 2, 4     594837260
      4     602374859
2, 3, 4     972640853
2, 3, 4     342907856
s1, s8, 9   345678902
---------------------
 
9 part. Contains the 54 cycles of rounds, queens & tittums and reverses thereof.

I think there's plenty of scope for further development on this plan.


 

  

________________________________________
From: Richard Pullin [mailto:grandsirerich at googlemail.com] 
Sent: 14 February 2007 07:52
To: ringing-theory at bellringers.net
Subject: [r-t] Queens and Tittums

May I remind and inform that Queens and Tittums are transpositions of each other.
You can see that by looking at the below transpositions:
 
12345678
13572468
15263748
12345678
 
or:
 
12345678
15263748
13572468
12345678
 
Either Tittums came about because of this, otherwise it's plain but amazing coincidence. 
 
From Richard Pullin. 
 


DISCLAIMER:

This communication (including any attachments) is intended for the use of the addressee only and may contain confidential, privileged or copyright material. It may not be relied upon or disclosed to any other person without the consent of the RSC. If you have received it in error, please contact us immediately. Any advice given by the RSC has been carefully formulated but is necessarily based on the information available, and the RSC cannot be held responsible for accuracy or completeness. In this respect, the RSC owes no duty of care and shall not be liable for any resulting damage or loss. The RSC acknowledges that a disclaimer cannot restrict liability at law for personal injury or death arising through a finding of negligence. The RSC does not warrant that its emails or attachments are Virus-free: Please rely on your own screening.