Wednesday, March 01, 2006

Axial Fugue in E Minor for Solo Guitar: "Final"

I put the word "final" in scare-quotes because this is as far as I can take the piece without actually learning to play it, and I want to get on with that phase now. Though I've been playing the guitar for over thirty-five years, I still need to actually learn to play a piece before I consider it finished, as the process of actually getting a piece under my fingers invariably leads to many new ideas and revisions of existing ones.

There are just so many places this piece could go beyond where it is now: As I've been drifting off to sleep the past few weeks playing the piece in my head it has taken me on some fantastic voyages. Learning to play it will allow me to explore those of which the guitar will be comfortable with.


Yes, I feel like crap today, but I'm so pumped about getting this fugue out of the way (I'm tired of blogging about it, truth be told) that I believe I'll get through this epic post OK. It's 5:00PM now, so we'll see just how long this takes.


For this final post on this piece for the time being, I have included formal and thematic analyses in the score which will make it easier to see what's going on. It's a little cramped since I put six systems on each page, but I didn't want to end up with any more than ten pages if I could help it, and I just managed to cram it all in. For the guitar score with fingerings, I'll go back to five systems per page and let it sprawl out to twelve pages.

An overview of the form listing the thematic statements by key region and axial orientation along with the chromatic episode placements displays the orginization of the fugue:

Sonata Exposition: Two-Vioce; 61 mm

E minor (Ax=5), A minor (Ax=5), A minor (Ax=5), C major (Ax=3), C minor (Ax=5)

Varied Exposition Repeat: Three-Voice; 105 mm

E minor (Ax=5), A minor (Ax=5), A major (Ax=5), C-sharp minor (Ax=3), (Ch. Ep. 1), C major (Ax=5),

A major (Ax=5), A major (Ax=1)

Sonata Development: 141 mm

E minor (Ax=5), A minor (Ax=5), G major (Ax=3), (Ch. Ep. 2), E minor (Ax=3)

E major (Ax=5), A major (Ax=5), G-sharp minor (Ax=3), (Ch. Ep. 3), E-flat major (Ax=3)

Recapitulation: Four-Voice; 18 mm

E major (Ax=5), A major (Ax=5)

Coda: 76 mm

E minor (Ax=1), E minor (Ax=1)

E major (Ax=1), E major (Ax=1), (Ch. Ep. 4)

As you can see, in the original sixty-one measure exposition the axes are all functioning as the fifth of the momentary tonic triads (Ax= 5) with the exception of the C major statement, where it is functioning as the third (Ax= 3). This pattern is repeated exactly with the modes exchanged after the three-voice fugal exposition of the 105 measure varied repeat, and then it is extended with a bit of development and the exposition areas end with the zero axis functioning as the root for the very first time.

The 141 measures of development are set up in two parts as well: The first starting on the tonic minor and the second on the tonic major. The i/I and iv/IV statements both use the fifths of their respective triads as the zero axes, and then the following two statements use the thirds as the axes.

In the recapitulation we get the four voice statements, and here the fugal exposition is in the major modes for the first time. The concluding coda has everything resolved with the zero axes functioning as the root throughout. The only bit of unfinished business concerns the mode, and the major eventually wins out, of course.

I really like this structural plan: It's highly organized and presents a lot of contrast.

These pages are now pretty much self-explanitory, so I'll keep commentary to a minimum. The sonata sections are labeled in a bold 24 point font, whereas the fugal elements are labeled in a bold 18 point font. The thematic elements are labeled in a bold 14 point font, and the key regions are labeled in a bold underlined 14 point font. Finally, the axial functions in the thematic statements are in parenthesises: I didn't label all of them because there wasn't room for some, but I did manage to label all of the ones where the axis is functioning as something other than the fifth, which are the more unusual and interesting statements anyway.

All of the episodes are labeled in relation to their appearance in the exposition areas, and where they are varied in any way other than by key that is indicated as well. Therefore, the unique episodes just get sequentially increasing numbers.

Episode four is the first of the chromatic episodes, and I have labeled all of those as well.

I didn't label all of the complex contrapuntal derivatives - figuring those instances where the subject was varied over or under countersubject one would be obvious (Though this is a slightly different type of complex counterpoint than the Tanievian type) - but I did label the instances where CS 1 is doubled in thirds. Though episode five is a melodic inversion of episode three, it is unique within the piece, so I gave it its own number.

For the climactic statements in the development I have given each statement its own truncated version of episode one, the second of which allows for modulations due to its open-ended nature.

In the last version of this piece, there were two versions of episode six. Now it is unique.

The final new element for the piece is episode seven, which has the chromatic elements in the lead, and which leads up to the melodic high point of the piece. I set this up over an E pedal point with a descending diatonic minor do-sol tetrachord repeating above. The third repeat the decending tetrachord is chromaticised, so you have chromatic against chromatic. Many CP books frown on this, but if it's set up properly - as I've done here - it's quite effective.

The interval progression between the two chromatic lines starting in measure 275 is quite interesting: P5, d7, M7, m9, and A9. In measure 278 this finally resolves out to a P11 and a i6/4 chord. It's a nifty little contrapuntal passage. After the decending augmented arpeggio in 280, the second phrase of the episode begins with lengthened runs.

The second run of the new phrase also has chromatic against chromatic in 286 and 287. After the P8, M9 progression in 285 it proceeds (In octave reduced form): d4, A4, m6, A6, and then P8 into 288. I love augmented sixths! Then the melodic peak of the piece occurs in 289 on the A that is only a whole step below the highest note on the standard classical guitar. This is actually pretty easy to play since it's over an open A in the bass and an open B axis in the midfield. This section could be expanded ad infinitum, and so I look at it right now as just a place holder until I learn the piece to this point, which - as I say - will involve many revisions during that process.

Nothing has changed in the coda, but the labels ought to make it more immediately understandable.

One thing I'd like to point out here is that in the concluding episode there is a decending chromatic line in the middle ground. This almost universally implies a minor mode. However, in measures 390, 394, and 398 the bass has a major third which contradicts this. It's a really cool little bit of cognitive dissonance that isn't resolved until the final phrase changes to a diatonic line harmonized in thirds that is completely in the major mode. I like the effect a lot.

At 403 measures of 2/4 at 172 BPM the piece runs about 4:40. The melodic peak is at the 72% point, which is pretty near the ideal mean, but I expect this to change some as I revise the piece during the memorization process. In any event, at least I won't have to blog about it again for a while.

7:00 PM: Two hour post.

Don't get any ideas.


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