Axial Fugue IV
I didn't remember to change the title before I took tonight's screen shots, but the piece just Axial Fugue in E now, because I have gotten both the low E and A strings in on the action, so the previous title just doesn't fit anymore. I have - believe it or not - four completely different versions of this on my desktop now; I've been doing a lot of work on it.
Tonight I just want to run quickly through the new exposition, as that is where the main changes are.
A couple of things I haven't pointed out previously: First of all, there are two versions of the subject in the initial fugal exposition. The first version has the melodic trajectory decending after it reaches do at the beginning of measure six. I'll be referring to this as the "subject form" of the theme. The second version has the melodic trajectory continuing to ascend after it reaches do in measure thirteen. I'll be calling this the "answer form" of the theme.
The second thing to notice is that there is no parallel movement between the answer form of the theme and countersubject one. This allows for doubling one or both melodies in thirds or sixths to get complex countrapuntal derivatives. I was aware of this when I wrote it, of course, but I have been primarily trying to work out the archetecture of the piece so far. There have been some derivitives presented, but now I'm starting to get more serious about figuring out which ones are playable on the guitar, and where to employ them. This has resulted in a few significant changes to the exposition, as you'll see shortly.
I have gone back to the arpeggiated fully diminished seventh chord in measure nineteen, but I'm still not positive which effect I like better; this or the arpeggio opening from the unison A. Aside from some shortened note durations to more accurately reflect what is possible on the guitar in measure twenty-six, there are no other changes to the first page.
The main change on page two is that I have exchanged the second thematic statement in C major for the one in C minor which previously appeared at this point in the varied repeat of the exposition. I did that for two reasons: It provides more contrast here, and the C major statement in this melodic inversion is the only one which allows for the countersubject to be presented in thirds. That just isn't possible in C minor with the E-flats.
In order to keep the bridge episode to the exposition's repeat, I had to modulate the phrase at the end to return to C major, and it turned out to be a necessity which added a nice effect. It's almost not noticible if you aren't paying attention.
Note also the small change in measure forty-six where there is now a G in the bass. That used to be an A, and this little change adds quite a bit of punctuation to the phrase which I like. I'll use that again later in the corresponding position in the varied repeat.
The repeat starts at measure sixty-one, and that has never changed... because it's perfect.
In measure seventy-nine I have also used a descending seventh chord arpeggio this time, but now it's a half-diminished seventh to anticipate the appearance of the A major statements. With the exception of a couple of shortened notes in measure eighty-six and the G replacing the A in the bass in measure one-hundred-six, these passages have not changed. However, the modulation at the end of measure one-hundred-seven is now to C major instead of the previous C minor version, so the E is a natural.
The top of the last page is where the action is now. As I mentioned, putting the C major version of this arrangement here allows for the countersubject in the lead to be harmonized in thirds, which the minor version would not allow on the guitar. I also use the subject form of the theme instead of the answer form now, which allows for a remodulation back to A for the new statements I've added because of the new episode starting on the second system. It is a shame that the A above the F-natural there is not physically playable, but it's just a tad out of reach with the F-natural in the bass.
I like the deceptive nature of the modulation in one-hundred-nineteen: It sounds like it's going to return to C major, but instead it goes to A minor. The "new" A minor statement has the harmonized countersubject in the bass, and this is also pretty much the only level and mode where this will work on the guitar. I just noticed the errant F-sharp in measure one-hundred-tewnty-two, which I'll have to repair: I just made these improvements tonight.
Using the answer form of the theme here allows for the episode at 127, which in turn allows for the new statement using the open low A-string at 132. This is an interesting statement, because the zero axis is functioning as the root, and the harmonized countersubject starts on the fifth, so it's melodically, intervallically, and modally inverted simultaneously.
The following episode on the bottom system is the answer I had been searching for for something unique to bridge the end of the exposition sections and the start of the development. Having triads going to diads and then unisons in the lead followed by the concluding decending run in the bass at the bottom of the guitar is quite nice.
I'm going to have to do some work on the recap now, and then I have some interludes to add to the development. I'll probably be working on this piece for weeks or months before I'm finished with it.
You definitely do not want me to get a hold of that feather duster.
Tonight I just want to run quickly through the new exposition, as that is where the main changes are.
A couple of things I haven't pointed out previously: First of all, there are two versions of the subject in the initial fugal exposition. The first version has the melodic trajectory decending after it reaches do at the beginning of measure six. I'll be referring to this as the "subject form" of the theme. The second version has the melodic trajectory continuing to ascend after it reaches do in measure thirteen. I'll be calling this the "answer form" of the theme.
The second thing to notice is that there is no parallel movement between the answer form of the theme and countersubject one. This allows for doubling one or both melodies in thirds or sixths to get complex countrapuntal derivatives. I was aware of this when I wrote it, of course, but I have been primarily trying to work out the archetecture of the piece so far. There have been some derivitives presented, but now I'm starting to get more serious about figuring out which ones are playable on the guitar, and where to employ them. This has resulted in a few significant changes to the exposition, as you'll see shortly.
I have gone back to the arpeggiated fully diminished seventh chord in measure nineteen, but I'm still not positive which effect I like better; this or the arpeggio opening from the unison A. Aside from some shortened note durations to more accurately reflect what is possible on the guitar in measure twenty-six, there are no other changes to the first page.
The main change on page two is that I have exchanged the second thematic statement in C major for the one in C minor which previously appeared at this point in the varied repeat of the exposition. I did that for two reasons: It provides more contrast here, and the C major statement in this melodic inversion is the only one which allows for the countersubject to be presented in thirds. That just isn't possible in C minor with the E-flats.
In order to keep the bridge episode to the exposition's repeat, I had to modulate the phrase at the end to return to C major, and it turned out to be a necessity which added a nice effect. It's almost not noticible if you aren't paying attention.
Note also the small change in measure forty-six where there is now a G in the bass. That used to be an A, and this little change adds quite a bit of punctuation to the phrase which I like. I'll use that again later in the corresponding position in the varied repeat.
The repeat starts at measure sixty-one, and that has never changed... because it's perfect.
In measure seventy-nine I have also used a descending seventh chord arpeggio this time, but now it's a half-diminished seventh to anticipate the appearance of the A major statements. With the exception of a couple of shortened notes in measure eighty-six and the G replacing the A in the bass in measure one-hundred-six, these passages have not changed. However, the modulation at the end of measure one-hundred-seven is now to C major instead of the previous C minor version, so the E is a natural.
The top of the last page is where the action is now. As I mentioned, putting the C major version of this arrangement here allows for the countersubject in the lead to be harmonized in thirds, which the minor version would not allow on the guitar. I also use the subject form of the theme instead of the answer form now, which allows for a remodulation back to A for the new statements I've added because of the new episode starting on the second system. It is a shame that the A above the F-natural there is not physically playable, but it's just a tad out of reach with the F-natural in the bass.
I like the deceptive nature of the modulation in one-hundred-nineteen: It sounds like it's going to return to C major, but instead it goes to A minor. The "new" A minor statement has the harmonized countersubject in the bass, and this is also pretty much the only level and mode where this will work on the guitar. I just noticed the errant F-sharp in measure one-hundred-tewnty-two, which I'll have to repair: I just made these improvements tonight.
Using the answer form of the theme here allows for the episode at 127, which in turn allows for the new statement using the open low A-string at 132. This is an interesting statement, because the zero axis is functioning as the root, and the harmonized countersubject starts on the fifth, so it's melodically, intervallically, and modally inverted simultaneously.
The following episode on the bottom system is the answer I had been searching for for something unique to bridge the end of the exposition sections and the start of the development. Having triads going to diads and then unisons in the lead followed by the concluding decending run in the bass at the bottom of the guitar is quite nice.
I'm going to have to do some work on the recap now, and then I have some interludes to add to the development. I'll probably be working on this piece for weeks or months before I'm finished with it.
You definitely do not want me to get a hold of that feather duster.
posted by Hucbald at 12:27 AM
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