Sunday, February 26, 2006

Axial Fugue in E II (Updated)

Now we're getting somewhere.

One of the reasons I like to work a piece throught to a conclusion, and then re-work it from beginning to end, is that each time through, some idea I come up with later in the piece has implications for what should preceed it, so I get fresh ideas each time. Not only that, but through these re-dos I become very familiar with the materials, and I learn how they "want" to be related to one another.

For instance, in the coda last time through I introduced a decending chromatic line for the runup to the conclusion. You can't do something like that without preparing for it in some fashion (The line is like the do, ti, te, la, le, sol, la, ti do bass line in the coda of the Allegro of Beethoven's Ninth), and since I was looking for a different type of episode for the exposition and development areas, I decided to write them over ascending chromatic lines in the bass. This ends up working gloriously well. Of course, I have now also come up with a chromaticised version of the subject, so there is a whole new area of the development which needs to be written.

UPDATE: There is a lot of latent chromaticism in the initial settup of the piece that probably ought to be pointed out. The first statement of the subject alone has nine of twelve tones in it, since it uses both the ascending and decending forms of the melodic minor sol-do tetrachords, and the fugal exposition area as a whole has eleven of twelve, because the subdominant answer uses the ascending form and countersubject one the decending, which adds G-sharp and F-natural to the list. The only remaining unused tone, A-sharp/B-flat, appears within the first exposition area at measure fifty-four, so all twelve tones are used even before the three-voice texture is presented for the first time. That's one of the reasons I love the traditional minor tonality so much: If you are working with tonic/dominant or tonic/subdominant relationships in a fugue in minor, and use both ascending and decending forms of the sol-do tetrachords, it is actually an eleven-tone system with either the flatted second of the tonic or the subdominant as the only missing tone, depending upon which relationship is used.


Cool: Predator II is on, which I haven't seen in years.


This third version is starting to come much more into focus, as I've started editing out various repititions of material that doesn't need to appear in both two and three voiced versions, and also with respect to occurances of the three chromatic episodes, which don't need to appear every time either.

I went back to v1.2 for the first exposition area, which is the next shortest version at sixty-one measures. This is a big improvement from the 105 measure first expo of v2.0 as it gets things rolling toward the three voice statements much more quickly: Now the counter-exposition starts in measure sixty-two.

Another thing I have a better handle on now is the management of the melodic peaks for each section: The exposition's high-point is the F-natural in measure fifty (Just a semitone above the open E-string zero axis): That's almost exactly at the 80% point of the initial exposition area.

The counter-exposition proceeds exactly like that of v2 until I introduce the G-sharp in the bass at measure 107 to return the piece to A minor for the first chromatic episode. This eighteen bar interjection is exactly what this section has needed all along, and it prepares perfectly for the upcoming appearances of the Taneievian complex contrapuntal derivatives.

UPDATE: The length of this chromatic line - beyond the usual span of a tetrachord - is just long enough to get the listener disoriented, especially as the axis is destroyed.

Note also that the F-natural makes its second appearance in measure 118: This is still the high point of the piece so far.

The melodically inverted statement in C major now enters with more authority, and it establishes the new melodic peak of A in 129, which is at the 63% point of this particular section. After the transitional episode at 134, the following A minor statements are almost unique: The first one is a three voice version of the answer area of the initial fugal exposition, and the tripple inverted statement is totally unique within the piece, which is far more effective that in v2, where they were both just three-voice versions of things which had been heard before in the first exposition area. The final episode of the exposition at 160 also regains it's uniqueness and now more effectively prepares for the upcoming development.

Page one of the development is unchanged, but note that a new melodic peak is reached in 188 with the B natural.

Where the previous chromatic episode started on A and fell a fifth to E before proceeding with the chromatic line, this version starts off on the E. The previous episode was also under an E axis, and this one is under a B axis with the upper open E functioning as a secondary axis and then an actual third voice. Two of my students heard this piece today and pronounced this section "Awesome!" with which I agree. The turn-around figure in 216-217 is particularly nice. The final episode of this first development area that starts in measure 225 now has the lead voice doubled in thirds, which allowed for the melodic peak of B to be reiterated in 230, and also for the G-sharp to appear earlier, which brightens the triumphant entrance of the major mode here.


Hmmmm. Dances with Wolves; another flick I haven't seen in a coon's age. All right.


Again, there are no changes to the second statements of the development until the new episode appears again at 267 (It is so nice, I had to use it twice in this version). I used a V(4/3/b) to introduce it this time at the end of 266 (Which you could also call a French Augmented Sixth chord).

The modulation to upcoming key of E-flat major is set up for in the final measure of the page, but the F-natural (Which the F from the preceeding French Sixth set up) can't proceed down to E-flat because you simply run out of guitar at this point. The modulation works nonetheless, but this episode will probably end up being replaced by the new section with the chromaticised versions of the thematic elements.

UPDATE: Corrected the reference to the augmented sixth chord. Appologies to all nationalities involved. ;^)


I'd forgotten how nice the film score is in "Dances." Cinematography too.


At 283 the final thematic statement in E-flat occurs, and that leads to the unique bridging episode back to the recap which still has the melodic peak of the entire piece with the C in 294. This is now at exactly the 75% point of the piece, but the new section I'm planning for the development will demolish that and move the peak back to a better circa 66% point.

The recap statements are unchanged from v2. Then, the coda begins unchanged.

Nothing more to see here. Move along.


Bad horse. Bad horse.


Nothing has changed in these measures either.

The final chromatic episode is based on a decending line from A versus the previous two ascending versions, and functions as another interjection which has a nice feel to it. I changed the fllowing figures from diatonic falling and rising lines in E major to chromatic versions as a recollection of the minor mode until the final statement resolves the "issue."

At 390 measures of 2/4 with a tempo of 172 BPM the piece now runs about 4:35 with the final ritardando. I'm not sure how long the new development area with the chromaticised thematic elements will run, but I'm guessing it'll add at least another minute or so to the piece. At that point, I'll have to get serious about learning to play it, as I'm more than certain that the guitar will have its own ideas about how things should proceed.

Writing for solo guitar is like composing with a partner. I imagine writing for any solo instrument must be like that.

UPDATE: I am also coming up with some ideas to add some rhythmic variety to the piece - this is normally the last thing to occur to me anyway - and one of the ideas I have is for an episode in faster triplets which dissolves a la Beethoven, and the other is for a metric modulation to 6/8 wherein the eighth note remains a constant. Obviously, if I end up using those devices, a lot of re-writing will be involved. I really like the materials I'm developing here - it's really once-a-decade quality stuff for someone like myself - so I don't mind putting the time and effort in, because I know the end result will be worth it. Heck, it's already been worth it.

I have a little ditty for you to read through for me, hon.


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