[r-t] Ringable Alternating Groups On Five Bells

[Andrew Johnson]

> From: Joe Norton
> I have used “REVERSE” to mean reflection, 
> as in the reverse method. I have used “BACKWARDS” to mean reversal, 
> as in reading the changes from last to first. 
Other possible terms could be 'retrograde' as I suggested yesterday
or 'inverse' or perhaps 'counter-'.

I notice that 'inverse' has been used in the name of a few methods
such as Inverse Little Bob Major
https://complib.org/method/28906
but CompLib indicates it is a true reverse of Little Bob Major, so
perhaps 'Reverse' would have been better even though there is no 
requirement to use the term.
Perhaps the composer felt that a reverse of a little method should
retain the treble path (or reverse it in the range of the treble
path if not front-back symmetric) but true reversal is a 
well-defined operation, but generating something like
-18-34,18 as a reverse isn't going to always work.

Actually now I see that CompLib defines inverse for non-palindromic
methods:
Union Triples: https://complib.org/method/12428
3.1.7.1.7.1.7.1.7.1.7.1.5.1
Reverse Union Triples: https://complib.org/method/34007
7.1.7.1.7.3.7.5.7.1.7.1.7.1

inverse of Union Triples:
Single Cambridge Cyclic Bob Triples: https://complib.org/method/10262
3.1.5.1.7.1.7.1.7.1.7.1.7.1
inverse of Reverse Union Triples:
Surfleet Reverse Bob Triples: https://complib.org/method/32713
7.1.7.1.7.1.7.5.7.3.7.1.7.1

Inverse is then reading the place notation backwards,
reverse is reading the place notation forwards, but flipping the
place notations from front to back of the change.

So from CompLib:
Union Triples:
Inverse         Single Cambridge Cyclic Bob Triples
Reverse         Reverse Union Triples
Double form     [Unrung] Double Union Differential Triples

Reverse Union Triples:
Inverse         Surfleet Reverse Bob Triples
Reverse         Union Triples

Surfleet Reverse Bob Triples 
Inverse         Reverse Union Triples
Reverse         Single Cambridge Cyclic Bob Triples

Single Cambridge Cyclic Bob Triples
Inverse         Union Triples
Reverse         Surfleet Reverse Bob Triples
Double form     [Unrung] Double Cambridge Cyclic Differential Triples

From Wikipedia: https://en.wikipedia.org/wiki/Retrograde_(music)
retrograde means play all the notes backwards, which I 
think for ringing is a combination of inverse and reverse.

Andrew Johnson





Unless stated otherwise above:
IBM United Kingdom Limited - Registered in England and Wales with number 
741598. 
Registered office: PO Box 41, North Harbour, Portsmouth, Hampshire PO6 3AU