[r-t] FW: A compositional question I am hoping a change-ringing theorist could help with! (re-sending)

[Ian Partridge]

Hi Mark,

Philip is right that there is no "jump-free" ordering of the
permutations you have listed.  However, as you say, since your
application is not change-ringing that is not necessarily a problem.

Personally I am most interested in this part of your message:

"Out of the 720 possible permutations of such a six-chord row I have
found a particularly interesting set of seven progressions; as the
musical properties which define this set are reversible, the
retrograde of each row is also in the set" ...

"If my reckoning is correct these are the only sequences out of the
720 permutations that share the property of interested in, but that is
not really germane to the puzzle that is stumping me."

What musical properties are these?  Could you explain how you have
selected these permutations from the 720 on offer?

As regards non-Ionian change-ringing performances, this is rare but
does happen.  The most common example is where a bell tower has a
diatonic set of 10 or 12 bells, but chooses to ring a Dorian subset of
them.  For example, if a set of 10 bells were tuned to Ionion C major,
where the highest pitched bell sounds an E, a 10th above the lowest
pitched (a C), then ringers might choose to instead ring a Dorian 8,
omitting the top and bottom notes of the 10.  Because of the minor
sound of the Dorian mode, when this is used it is generally for
funerals, Remembrance services etc.  But as I say, it is rare in any
case.

You may be interested to learn that non-modal ringing does take place
- VERY occasionally.  I was privileged to ring in what we believe to
be the first ever peal on a set of chromatic bells - you can see the
details of the performance at
http://www.campanophile.com/view.aspx?78331  The notes of the bells
were (descending):  A flat, G, G flat, F, E, E flat.  The effect was
very eerie, and quite mesmeric.

Ian