Sunday, June 04, 2006

Reductio Fingerings II

Ha! This is my 200th post to MMM. Believe I'll celebrate with a brew or two. Anyway...


The Fuga: Reductio ad Absurdum theme is now going to become a series of compositional/technical studies for the guitar, and not a variation set as I had previously thought (Except for in the wind quartet version, of course).


I enjoy writing sets of closely related pieces, and have done a lot of it in the past. Previous sets I've written have included:

1) Six Studies on an E-Axis

Open string studies for guitar using the open high E-string in two-voice counterpoint.

2) Six Studies on a B-Axis

Ditto the above using the open B-string.

3) Six Studies on a G-Axis

Ditto with the open G-string.

4) Twelve Figuration Preludes

Homophonic studies for the guitar in five-part harmony. This will eventually be 24 studies, I think.

5) Three Lineal Studies

Another set I'm currently writing, which is linear compound lines based on four-part harmony using Schillinger circular transformation voice leading: Impossible on the guitar any other way. There will be between six and twelve of these eventually.

The Eighteen Axial Studies and Twelve Figuration Preludes make up the core of my set. MIDI and PDF files of them are here, if you'd like to download them.


For this set of irreducible four-voice fugues, the final set will number twelve, as you will see.

Here is the first one:

The variation tactic I'm taking for the set has two essential primary variables: That of mode, and that of time. I'm being Hucbaldian about the whole thing by using the terms tempus perfectum and tempus imperfectum as the ancients did, but the concept of modus perfectum/imperfectum is something that is modern, and relates to post-modal harmonic practice.

I only admit of two modes: major and minor. The so-called modal degrees can be inflected in whatever way the composer wishes. The perfect arrangement has major triads on the cardinal degrees of I, IV, and V. Conversely, the imperfect arrangement has minor triads on those degrees, and inflections must be used to get leading tone/dominant harmony effects at cadential points. These two approaches give the modern Ionian and Aolean modes (Which are not the same as the old Church Modes of the same names).


Logically, this one is now number two:


Both of these work out so that the music can remain in its pure form: No concessions were required to play them on the guitar.

When I came up with the original version, I said it was like a musical Mandelbrot set, but that isn't really an accurate analogy. Now that we are working with dualities, they remind me more of the classic thespian masks.

The joker in the middle can only be me.


Obviously the perfect/imperfect forms of mode and time can be mixed, which will yeild four variants. Since the fingerings for the major and minor will remain the same through the change in time signature, once first two are learned, the second pair are no problem. I'll be putting those together next.

Beyond the four versions I will have at that point, 4-3 and 2-3 syncopes can be introduced as well. That will add eight more variants for the total of twelve.


Not only will this exercise reveal some compositional truths to me, and not only will learning them help my guitar technique out, but additional possibilities for the guitar itself will become apparent. As logic would have it, I wrote nothing but two-part counterpoint for the guitar for several years before anything with three voices occured to me. Now, I have gotten to a four-part contrapuntal theme - something I didn't really expect would ever happen - and so new horizons are opening up. This joins nicely with the five-voice harmonic technique I had developed for the guitar back in my jazz days, and furthered with the Figuration Preludes when I switched over to traditional writing.


Even though the mistique of black holes may have vanished, the newly-categorized super-dense bodies will still be able to cause gravitational lensing, which this is an artist's rendition of. If there was a super-dense body between you and the Milky Way, it might look something like this.


I think women ought to have hips, don't you?

Hips like those would cause gravitational lensing all on their own.


P.S. I'm experimenting with my Smugmug display sizes because they reduced their default "Large" size so much that the music is hard to read. If your browser has any problems with the page, please comment or e-mail me. Thanks.



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