[r-t] FW: A compositional question I am hoping a change-ringing theorist could help with! (re-sending)
Philip Earis
Earisp at rsc.org
Wed Jun 9 10:44:13 UTC 2010
From: Mark Simos <msimos at berklee.edu<mailto:msimos at berklee.edu>>
Date: June 6, 2010 1:20:28 PM EDT
To: ringing-theory at bellringers.net<mailto:ringing-theory at bellringers.net>
Subject: A compositional question I am hoping a change-ringing theorist could help with! (re-sending)
Dear Ringing Theory Community:
I was doing some Internet searching this morning into the vast world of change-ringing theory hoping to find some help for a compositional problem I have. I am a songwriter and composer, and teach at Berklee College of Music. I should say at the outset I am not a change-ringer or versed at all in the theory or practice (beyond getting intrigued years ago by The Nine Tailors like so many others). Nonetheless I have been aware of the practice for some time, and I feel I have an intuitive sense for the kinds of patterns that change-ringing theorists might be able to spot, in contrast to mathematicians coming from a purely abstract perspective. If any of you had a spare minute to look over my little problem and suggest some directions for research I would be very grateful. (I am not a subscriber to the ringing-theory list and would probably be more of a nuisance than a contributor!)
Recently I have been working on some pieces involving sequences of modal chord changes which are not unlike ringing changes or rows in nature. These sequences involve 6 triads on different roots, always avoiding the dimished triad. For the Lydian mode, for example, the six triads would be 1Maj, 2Maj, 3min, 5Maj, 6min, 7min (skipping the diminished triad on #4). I have been studying the properties and musical qualities of various permutations of such 6-chord sets. 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 - so, a total of 14 rows:
ROW RETROGRADE
132675 157623
136752 125763
137562 126573
153672 127635
167352 125376
172563 136527
175236 163257
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. Also, one could deal with these rows more abstractly (as ABCDEF); I've preserved the roots of the chords above to keep the connection with the musical consequences a little fresher in my mind.
My question is this: I've arranged the rows above in a reasonably systematic, but not particularly musical ordering. I would like to work on compositions that 'tour' these rows in an overall sequence (a row of rows) that create the kind of musically engaging patterns that the more musical of change-ringing methods sometimes produce. Am I missing something? Is there an ordering that takes us through these patterns via some sort of 'method' that produces ONLY these sequences, ALL these sequences, and does not repeat (e.g., is "true") any of the sequences until the set is exhaustively visited?
Philip Earlis has already kindly explained to me the concept of 'jumping' in change-ringing, and has suggested that there is certainly no jump-free ordering of the above rows. I can see possible method-like swaps between individual pairs of rows above, but not for the set as a whole. E.g., allowing for more than one swap at a time, then:
172563 can reach, without jumping...
175236
... but so far that's about the only such neighbor I've found. So clearly any 'method' (taken in the broader sense of a regular or algorithmic procedure for moving from one row to the next) will have to involve jumping. Since my application is not change-ringing that is not a non-starter for me. I am hoping that the sequence would create some audible transition effects however.
In other words, I am trying to work backward from a relatively small set of permutations to find a plausible 'method' which could order them. I don't know that this is a problem that typically comes up in change-ringing theory, as it may not correspond to any practical concerns in bell-ringing. But perhaps you can see why I thought a change-ringing theorist's perspective might be a useful take on the problem.
PS - On a somewhat related note, I am also wondering if there is a traditional of MODAL changes in ringing; most sets of bell appear to be tuned to the diatonic major scale, but with such a scale you can treat tones other than the lowest as an implied tonal center. So, are there Dorian, Mixolydian, or heaven forfend Phrygian peals?
Again, I know this is an imposition from a total stranger but if the problem interests you at all I'd be grateful for any insights or suggestions you might have. Thanks for your attention.
All the best,
Mark Simos
Assistant Professor, Songwriting
Berklee College of Music
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