Friday, May 19, 2006

Happy "Blogversary" to Me/Palindromic Variations



Well, here I am: One year, 196 posts, 5,601 visitors, 8,035 page views, and 1,295 profile views later. Not impressive traffic, actually, but that was never the point of the blog. MMM has always been and will continue to be an autodidactic aid which allows me to organize my thoughts. As a result of that, lots of things - such as the B's 9th analysis and the Taneiev transcription - will be taken up and abandoned as suits my personal goals. The Beethoven project lead to a nice sonata process piece, and the Taneiev project lead to the Axial Fugue for Solo Guitar (An amazing piece, if I do say so myself, which you can download here). This is the purpose of study for me; to launch new pieces.

And so, I will continue in this vein.

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Today's piece is v2.0 of a variation set built around the Fuga: Reductio ad Absurdum theme, which I have blogged about previously and most recently here.

As I have mentioned before, this theme is a four voice fugue distilled out to it's irreducible essence: The subject and answer are a single note, and the four-measure exposition is presented in a series of quadrant rotations so that a compound double palindromic canon is created: Original, retrograde inversion, inversion, and retrograde is the sequence required to pull this off.

So, the theme is an antecedant/consequent phrase duplet as well. This means the two halves can be separated in a series of variations on the theme so that the entire variation set is a gigantic double palindromic canon!

Basically, the antecedent of variation one is the first phrase in the set, and the consequent of variation one is the last phrase in the set; the consequent of variation two is the second phrase in the set, and the antecedent of variation two is the next-to-last phrase in the set, and so on. Setting the piece up this way makes the canonic voices of the entire variation set read the same forwards and backwards. It's really cool, it's totally fractal, it's symmetrical, and I like it a lot.

For this initial experiement I wrote pairs of variations: The first is "straight ahead" and it's pairing contains 4-3 suspension chains. The first set is in 4/4 time, the second pair is in 3/4 time, the third pair is in 2/4 time, and then there are three in 3/8 time. The third 3/8 variation is necessary to get a "keystone" at the top of the arch, and it has 2-3 suspension chains in it.

This simple mechanical variation scheme nonetheless yeilds fascinating results.

What has captivated me the most are the rhythmic implications. Over my twenty some-odd years of contrapuntal writing, I have never employed the retrograde or retrograde-inversion orientations of any theme I've come up with. The few times I've tried it, the results were sucky, to say the least. Well, as I've discovered, the problem is non-retrogradable rhythm/melody combinations, with rhythm being a prime culprit (Truth be told, I don't care for Bach's experiments with "crab" canons and other retrogrades because it seems he's just forcing them to work, and not particularly tactfully at that).

Dealing with this situation is forcing me to concentrate on rhythm as I never have before. For decades I've been looking for a unique and systematic approach to rhythm - as well as a crucible in which to pulverize it - and so I've finally found it. I was never really convinced of Schillinger's symmetrical resultants of interference, but in this context breaking up the entecedents and consequents of those rhythms works quite well. As usual, I use them freely, the musical result always trumping any rigorous systematic approach.

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So, here it is: (If you would like to download an MP3 and a PDF of the score, they are here, as usual). These are so simple and self-explanitory that I will present them without further comment.



















This particular theme is going to be one of those which takes months or even years to come to full fruition, but it sure has got me thinking more than anything I've come up with in the past few years.

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Though the gold is a bit too "Liberace" for my taste, in a royal blue this would be nice embroidered on a comforter/pillowcase set. LOL!

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No need to wrap my present.

1 Comments:

Blogger Terminaldegree said...

Happy Birthday!

3:35 PM  

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