Sunday, February 19, 2006

Tri-Axial Fugue in E

I came up with a cute bromide today. I think I'm going to start telling it to my students: "You don't have to know what you're doing to start composing a piece of music, but you do have to figure it out before you finish." What brought that to mind was the situation concerning the key relationships in this fugue. I was originally thinking of it as being in A, but some unseen and irresistable force kept dragging the thing toward E. Then the lighbulb went off above my noggin: The three axes the piece is based around are the open E, B, and G strings of the guitar; that spells an E minor triad. Duh.

Needless to say, knowing what key the piece is in made coming up with an ending a bit easier. ;^)

It also helped me to tighten up the organization of the previous sections. A lot of little things, but important ones. This would represent v1.0 alpha of the fugue, and as always with a guitar piece of mine, it really won't be finished until I learn how to play it. I have just a ton of ideas that I've developed, tested, and rejected, and some of them are quite nice, but for this first "completed" version I wanted to make it as short as possible. It's still 295 measures long, but at one point it was over 325, and that was without the recap and coda. This might sound long, but in 2/4 at 172 BPM that only comes to 3.4 minutes.

First change to page one would be the title, and then the key signature. The first episode is now a measure longer. This allowed me to converge on a singularity at A, and then arpeggiate out of it. This both better completes the first theme/key area (This is a sonata-process fugue, remember), as well as sowing seeds for later developments. These last two measures of the episode now prefigure the sequential figuration that comprises episode three and its subsequent derivatives.

At measure twenty the second theme/key area begins, which exposes A minor and its relative major of C. Since it's a fugue, it's monothematic, so most of the contrast is accomplished via regional variations, but the variations in the nature of the subject vis-a-vis the function of the zero axis as either the fifth or the third (And eventually the root in the coda) also plays a role.

The second episode on the bottom system builds up some energy and accomplished the modulation to C.

At the top of page two is the first statement in C with the open E-string zero axis functioning as the third of the tonic of the moment. That statement leads organically into the third episode, which has now been prefigured by episode one.

At the second statement in C the open G-string is the zero axis and is functioning as the fifth, which means the subject is back in its original form.

The fourth episode is the joint between the exposition and the upcoming varied repeat of it. At the time of the previous post it was unique, but now it reappears in a variant at the corresponding seam between the end of the development and the recapitulation.

One of the things I figured out about this piece is that it's not just a struggle between tonic and subdominant levels, but also between major and minor modes. As a result, the varied repition of the exposition now starts off with a fugal counter-exposition in Emajor/A major. This is really the only way it can be. The original expo has the most naturally related keys: E minor, A minor, and C major, while this one will have the less naturally related keys oriented around the same axial plan; E major, A major, C-sharp minor, and C minor. This plan allows for an increasing interest level to develop.

On the top system of the third page is the major mode version of the original first episode, and it has also been lengthened by a measure to get the same singularity/arpeggio effect. Then comes the octave inversion of the subject and countersubject one, followed by a more radically modulating version of the original second episode. This relationship between A major and C-sharp minor is "upside down" compared with the major/relative minor relationship at this point in the original expo.

After the C-sharp minor thematic statement, an even more radically modulating version of the original third episode appears to get the piece to C minor. I love these modulations and the emotional contrasts they elicit (Ha! The Aviator is on and they are using the orchestrated version of "Bach's" fugue in D minor as the background music. I love funny synchronicities). The C minor statement ends the page.

The episode at the top of page four is the joint between the end of the varied repeat of the exposition and the development area. I'm still not sure about his episode because I think something unique belongs here, but it works so darned well. The last major bad-ass fugue I wrote had a similar "issue" and it wasn't until a couple of months after I had "completed" it that the solution came to me, and that - literally - ended up making the piece. Can't rush the muse, I guess.

The development now begins with a minor mode version of the climax over a tonic pedal (Which is the open low E-string of the guitar) with countersubject one in the lead. This is actually pretty easy to play and sounds gorgeous, but not nearly as joyous as the upcoming major mode variant.

Each individual thematic statement now has its own truncated version of the original first episode, and it was the sheer overwhelming weight of the E pedal points which started me scratching my head over what tonic level this piece was actually in. It was somewhere around this point that I finally figured it out.

Like the original exposition, this first section of the development area presents the most naturally related keys: E minor, G major, and E minor again, while the upcoming repeat of the axial scheme presents the more remote relationships; E major, G-sharp minor, and E-flat major. Therefore, both the expository and developmental areas are bipartate in layout.


"Fastest man on earth." Great line. Too bad I won't have occasion to use it. I really love my Formac Studio TVR: It allows me to have a small TV screen in the lower right hand of my monitor at all times. I have my Satellite piped right into my computer. Anyway...


The second truncated version of the original first episode here accomplishes the modulation to G major, and that statement completes the fourth page.

The episode at the top of page five is a three-voice version of the third episode from the original exposition, and it re-modulates the fugue back to E minor for the first statement in which the open B-string zero axis is the third.

After that a three-voice version of the original second episode makes an appearance, and I put it over the open E pedal to increase the tension level as much as I could in preparation for the triumphant appearance of the main climaxes in E major/A major.

The E major version of the climax has countersubject two included in it, which was not in the minor mode version, and the A major version has an alternating E pedal to prefigure the final versions of the subject in the coda.

It's impossibe to describe the sonic athmospheres I created with these climaxes in this development section, but I'll post PDF and MIDI files on my FileShare page later tonight or tomorrow so you can listen to it if you want.

Page six begins with the truncated version of the original first episode that effects a modulation to G-sharp minor, where the B as third makes its second and final appearance. Then the three-voice version of the original third episode appears that takes the piece down for the E-flat major statement. This is a very strange passage. I dig it.

After the E-flat major thematic statement the second appearance of a variant of the fourth episode appears to bridge the gap between the end of the development and the recap. The C in this episode is the melodic peak of the piece in its current version, but I have some additional episodic passages in mind that will take the piece to the E above that C (At least).

The recap begins just as the varied exposition did, but with the statements now in E and A minor.

The final appearance of the A tonal level begins the next-to-last page, and it is followed by a truncated version of the original first episode which returns the piece to E minor for the beginning of the coda: Only the previous two thematic statements are recapitulated.

The guitar's low E string makes it's initial appearance here with a melodically inverted version of the subject with the zero as tonic, also for the first time. After the corresponding episode the high E-string answers - also being zero as tonic - (More orchestrated D minor fugue in The Aviator... too funny), and its episode changes mode and prefigures the conclusion of the fugue. Here the four bars are repeated once: At the end they will appear three times.


Amazing airplane crash scene! (Yup: Guy thing. Daring-do, massive destruction, and torrents of fire: How can you beat that?)


Last page (Whew!) Here we have the concluding E major statements which are otherwise just like the previous E minor statements, followed by the concluding episode which winds the piece down. Now...


I wimped out an put a lower saddle on the fretted Glissentar. It works! The higher tension B and E strings don't buzz like the stockers did. I can play it just fine now, so I'm going to play it at tomorrow's gig.

I need to practice some. Or, perhaps I'll watch some of the Olympics.

I love the Winter Olympics.


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