Sonata One in E Minor for Solo Guitar: IV - Fugue
You can download the PDF scores and MIDI to MP3 conversions of all four movements of Sonata One here.
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UPDATE: Since I first wrote this post in a single marathon session, I left some things out, of course. Scroll down for the updates at the appropriate places.
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Fugue writing is by far my favorite compositional endeavor. Nothing else even comes close. I view it as the ultimate compositional challenge in general, and on the guitar - where imitative counterpoint is about as non-idiomatic as one can get - it's even lightyears beyond this.
I remember the first fugue I heard performed on the guitar quite vividly: It was Bach's A minor fugue for lute (Originally in G minor) performed by Christopher Parkening. This was in about 1978, and my teacher Jackie King turned me on to it. The first words out of my mouth were, "It sounds so logical!" I immediately went out and bought everything Christopher Parkening had recorded to that point: In The Spanish Style, In the Classic Style, and Parkening Plays Bach. To this day, I don't think anyone of the strict Segovia tradition guitarists is anywhere near where Parkening is at: His effortless command of the instrument, as evidenced by the exquisite nuances in his interpretations, is simply unmatched. None of the more recent virtuoso pioneers have this quality to their playing either: Kazuhito Yamashita's tone is quite strident by comparison, for example, despite his super-powerful playing.
Later, when I was attending Berklee College of Music in Boston, I had the amazing good fortune to have a counterpoint teacher named Chris Frigon. Though I was interested in becoming a famous rock guitarist at the time, Chris' class - a required course I admittedly dreaded when I registered for it - was a revelation in many ways. His seriousness about the subject and obvious command of it impressed me deeply: Chris was probably the first real highly educated musician I ever encountered of the traditional pedagogical line. And, what a line it was too:
1) Johann Sebastian Bach
-Taught-
2) Wilhelm Friedman Bach
-Who Taught-
3) Franz Joseph Haydn
-Who Taught-
4) Ludwig van Beethoven
-Who Taught-
5) Carl Czerny
-Who Taught-
6) Theodore Leschetizky
-Who Taught-
7) Edwine Behre
-Who Taught-
8) Chris Frigon
-Who Taught-
9) Hucbald
Is that cool, or what?
Though nothing came of it at the time, I had the idea to really master counterpoint in the back of my mind from that point forward, and a few years later - around 1986 - when I was in NYC, I started stopping by the Joseph Patelson Music House across from Carnegie Hall every payday to buy a counterpoint book. I became positively absorbed by the subject.
Some of the books I bought and studied during that time were: Riemann's History of Music Theory, Tenney's History of Consonance and Dissonance, Mann's The Study of Fugue, Gedalge's Treatise on Fugue, Zarlino's The Art of Counterpoint, Fux' The Study of Counterpoint, Rameau's Treatise on Harmony, and Taneiev's Convertible Counterpoint in the Strict Style. You get the idea: I wanted to know what just about everybody thought about the subject (And, there were other books by Benjamin, Kennan, Jeppesen, Piston and others I got as well).
This lead almost immediately to me writing just a bunch of studies for solo guitar, and eventually I abandoned the rock guitarist lifestyle and returned to school and a master's program in traditional theory and composition.
My first fugal works were for solo organ since my fiance at the time (then wife, now ex-wife) was a Lutheran Music Minister and virtuoso organist. I really wanted to write fugues for the guitar, but all of the subjects I came up with wouldn't "fit" on the guitar: This problem plagued me for over a decade.
It wasn't until 2005 that I came up with a new class of subject that was stately - as the Musical Offering and Art of Fugue subjects are - and also fit on the guitar. This subject is what became the three imitative movements of Sonata Zero.
Immediately after finishing Sonata Zero I had the idea to do a guitar transcription if the Organ Fugue in D Minor that is usually attributed to Bach: Just noodling around with it I figured out that the repeated note subject and answer at the fourth would work perfectly on the guitar in E minor, which would employ the open B and E strings. This exercise made me certain of at least two things: 1) There is no way that J.S. Bach is the author of this fugue, and 2) The original fugue was written by some unknown virtuoso lutenist. I am absolutely positive about that.
For a bit about the scholarly debate on this subject, you can start at the Wikipedia entry here.
While the opening Tocatta may indeed have been originally for the violin, this fugue was originally for the archlute, and was not written by J.S. Bach. It simply fits all too well on the guitar, and there is no real counterpoint in it: The countersubject, such as it is, merely makes parallel thirds or sixths with the melodic trajectory of the subject. This would be exactly the kind of thing a lutenist whose counterpoint was shaky would have come up with.
Since I liked the premise of the D Minor Organ Fugue, but not the lame execution of that premise, I decided to use the same premise, only make it a real contrapuntal tour de force. So, I composed a better subject and a real countersubject to it, and I used Sergi Taneiev's techniques from Convertible Counterpoint in the Strict Style so that the original combination would yeild derivatives at different intervallic distances.
This is easier than it sounds: If there is nothing but contrary and oblique motion between the subject and countersubject, both lines can be doubled in thirds - or sixths, but I don't use that here, because it wouldn't work out on the guitar - and so many possibilities exist.
In the D Minor Organ Fugue, the subject's repeated note, or Zero Axis as Joseph Schillinger called it, is always functioning as the fifth of the mode of the moment, but two other possibilities exist: The zero axis can also function as the root or third of the mode of the moment. I used those possibilities too, and I don't think any composer has ever employed this strategy to vary a fugue subject before. By doing this, I was able to modulate to a host of keys, some of which are quite remote from the tonic, while still using the open strings of the guitar for the zero axes.
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It is worth noting that, to this point, the opening Tocatta ended on an E tonic with a Picardy third in it, which I deliberately did not confirm as a modal shift by using a fully diminished seventh chord in the final cadence. Then, the Sonata is in A minor, which is where the answer is in this fugue, and it ended plaintively in A minor, even though there was an A major section within it. The Scherzo was in the relative major of G, but the second phrase of it was in G minor, and it ended on a blurry G(6/9) chord, and so now we are set up for the final battle between major and minor.
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On the top system is the subject, which has all of the most perfect dimentional attributes that a subject can contain: It is an odd number of measures in length at seven, and it is also fractional with the eighth note anticipation. Odd is better than even, and fractional is better than whole: There is almost nothing worse than a four measure fugue subject, which makes Bach's Motto Theme from The Art of Fugue a monumental anomaly.
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UPDATE: I should have also noted that the original subject contains all nine notes of the nonatonic minor system, and it has the range of a ninth as well.
*****
In the original subject and answer, the zero axis is functioning as the fifth of the mode of the moment, just like in the D Minor Organ Fugue's opening. One of the things I have done is to carefully manage all of the appearances and disappearances of the axes: The melodic trajectory of the subject merges smoothly into the counter-answer into measure eight, and - via the sixteenth note figure im measure seven - the zero axis also merges into the answer's melodic trajectory. There are no "loose ends" in this fugue.
On the second system is the answer at the subdominant level, and it is accompanied by the main counter-answer. As you can see, there is nothing but contrary motion between the answer and counter-answer from measure to measure, and oblique motion within the measures (Except at the end, where there is contrary motion with the lower quarter notes). This means both the melodic trajectory of the answer and the counter-answer could be doubled in thirds and all resulting contrapuntal relationships would be correct. This fugue is a progressive realization of those possibilities.
On the third system is the first episode, which I call a "release area." and this one does not modulate. As you can see in the final measure of it, the zero axis on E descends to merge smoothly with the upcoming counter-answer, the melodic trajectory merges into the bass line's A, and then the lower voice is free to begin another statement of the answer.
The octave inversion statement beginning in measure twenty does not use an open string for the zero axis: This is the only place in the fugue where I had to do that, so it is quite difficult to execute, but the fugue wouldn't work without it. We're still in A minor here, but this statement of the answer and counter-answer sets up the modulation to C major I want. Well, need, actually.
On the bottom system starting at measure twenty-seven is the first of the second type of episode, which I call sequential episodes, since they grow out of the final measure of the answer/counter-answer or subject/counter-subject. In measure thirty-three we have modulated to C.
As you can see, we are now in C major, but the zero axis is still the open E string, which means it is functioning as the major third here. This also means that the counter-subject (This is the subject form, with the descending trajectory at the tail of the subject, with the rising quarters in the counter-subject, which we get here for the first time) is a third closer to the subject in this statement: This is Taneiev's Convertible Counterpoint at work.
In the sequential episode starting on the second system, notice that the melodic trajectory fragments above always merge into unisoni with the bass line at the start of every measure, and the zero axis on E becomes an E-flat before continuing down to merge with the next counter-answer statement. This means we have not modulated, but we have changed the gender of the mode to C minor.
The C minor statement is in an octave inversion again, and it employs the open G string as the zero axis for the first time. That means it is functioning as the fifth again.
At fifty-five we get the third type of episode, which I call a concluding episode, because it concludes the exposition and the development to lead into the counter-exposition and the recapitulation later. At the end I've put a double bar line, because this is the end of the exposition.
As you can see, this is a combination of fugal process and monothematic sonata process.
On the bottom system the counter-exposition begins with the subject exactly as at the beginning of the piece, but now there is a drone on the high E string, the zero axis is on the open B string (as before), and the counter-subject is now in the bass. That makes the exposition a two-voice deal and the counter-exposition a three voice kind of thing: The recapitulation will be four voices, revealing the entire original contrapuntal combination. Note again how I'm careful to merge the axes and trajectories: The open low E at fifty-five is merely an octave transposition.
Here we get the answer, counter-answer one, and counter-answer two for the first time. Though counter-answer two does not follow the trajectory of the answer throughout - the voices actually cross in measure seventy-one - it does effectively double the trajectory in thirds, which is a further revelation of the original combination.
The release area episode on the second system is exactly like its counterpart in the exposition until the end, where a C-sharp is introduced to change the mode to A major. The sharps in A major will allow me to modulate to C-sharp minor at the end of the following sequential episode. So the third system is just like the earlier A minor statement except for the mode.
In the fourth system you can see how the modulation works out: We're at C-sharp minor by the end, instead of C major as before. This means the bottom system is exactly like the earlier C major statement in that the open E is the third of the mode of the moment, but now it's the minor third of C-sharp minor versus the major third of C. See how cool this is?
One of these accumulated sharps has to be shed, of course, and that's what the sequential episode at the top of page four allows: We're back to A major by the end of it.
On the second system begins the first of the fourth type of episode, which I call a chromatic episode because they are all over chromatic lines in the bass. Note that I left out the sixteenths at the end of measure one-hundred-six leading into it: I didn't want that rhythm to clash with the new placement in the chromatic episode... yet. This episode is nineteen measures long, and it acts as a release from the constant fugal struggle we've endured so far, and it also modulates to C major by the end.
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UPDATE: I should have pointed out that, after all the painstaking management of the axes and trajectories up to this point, the C-sharp is abandoned for the first of the chromatic bass line episodes at measure one-hundred-seven. This creates a tension throughout the episode that is not resolved until measures 124-125 where the C-sharp resolves up to D and then the D progresses down to C-natural to effect the modulation.
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The C major statement of the answer at one-twenty-six has the main counter-answer doubled in thirds for the first time, and it is in octave inversion as well: This was the C minor statement last time, and the open G zero axis is again the fifth of the mode.
The counter-exposition is longer than the exposition was, and all of the statements are now new. The sequential episode at the top was the concluding episode last time, and we modulate to A major by the end of it. The answer/counter-answer statement at one-hundred-forty has the counter-answer doubled in thirds again, but in the original octave arrangement.
Our old reliable release area episode keeps us in A major, and sets up the first appearance of the inversus form of the subject, which also has the low A string zero axis functioning of the root of the mode for the first time as well. The inversus form of the counter-answer is also doubled in thirds.
This leads to a properly unique sequential episode to lead into the development areas: It's inverted, and you get triad, diad, and monad as the trajectories merge. A second double bar line signals the beginning of the development.
The development is in two sections, just like the exposition and counter-exposition. Also like them, I modulate to closer keys the first time through, and follow the same pattern but modulating to the more remote keys the second time.
We begin with an answer statement on the same level as the original subject, but now the main counter-answer is in the lead voice, and there is a tonic pedal in the bass. This passage is only possible because the low E pedal and the zero axis B are open strings.
Since this is an answer form, we get a new version of the release area episode on the second system, and this modulates us to A minor.
The A minor statement on the third system has the answer and counter-answer two, but above an alternating pedal using the open low A and E strings: It's actually pretty easy to play.
In the release area episode starting at one-hundred-eighty-four, we get a modulation to G major. Note the chromatic movement of the D-sharp in measure 186 into the D-natural in 187: This is a setup for the next time, where the notes will be reversed. Since the bottom system is in G major and the zero axis B is the major third, that means the next time we get here it will be G-sharp minor with the B as the minor third. Shiny!
The final statement on the page is the subject form with a drone G in the lead, and the counter-answer below.
The sequential episode at the top is further developed with the G in the lead coming down to D-sharp at the end for the return to E minor. Next time, this episode will start out with a G-sharp in the lead, of course.
At two-hundred-one we get the second of the chromatic bass line episodes, and I again avoided the sixteenths at the end of two-hundred so as not to clash with the episode's rhythmic figure at this point. Note that between the low F-sharp and the D-sharp in the lead at two-undred we have a major sixth: I'll make that an augmented sixth with an F-natural next time, to set up the final development statement in E-flat major.
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UPDATE: Again, a tension is created when the A is abandoned at measure two-hundred. It is not picked up and absorbed into the bass line until the G in measure 207, so the suspense only lasts half of this particular episode.
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This chromatic bass line episode does not modulate this time, however, getting us to the E minor statement that starts on the fourth system. here, the open G zero axis is the minor third of the mode, the open B is a drone above, and the counter-answer is in the lead; all over a tonic pedal in the bass.
From 216 into 217 I have technically gotten myself a parallel stepwise dissonance between the F-sharp in the bass and the open G that launches the new answer statement. First it's a minor ninth, and then a major ninth, though, and since the answer immediately goes up to the minor third, I gave myself this single licence. Since it's a ninth, and the entire piece is based on nine and twenty-seven, it seemed appropriate.
The sequential episode on the bottom system is the most dramatic yet, and it leads to the exuberance climax of the piece with the appearance of the key of E major for the first time on the next page. You can see how I took the sixteenth duplets, expanded them in the previous episode at the end, and then added even more in the last measure of the page. A double bar signals the end of the first half of the development.
Here we have E major for the first time, and the combination is like the previous appearance of E minor at this point, except for the fact that counter-answer two is now present. You need to employ the right hand c finger to execute this passage, and yes, it's a bitch to play, but it is technically possible.
The release area episode on the second system takes us to A major this time, otherwise it is the same as before.
OK, *big sigh* the statement at measure two-hundred-forty-two has a pedal underneath that is alternated with the counter-answer above. You really don't need the c finger here, but it would help. And, as for myself, I plan to use funk bass technique to slap the low E's... but that's just me. ;^) This passage can be simplified by playing the counter-answer line as quarter notes versus the half notes here.
The release area on the fourth system now takes us to G-sharp minor, as I mentioned it would, and so we get that super-remote key area on the bottom system: Five freaking sharps!
Here's the sequential episode I mentioned earlier that starts with G-sharp in the lead. It sheds four sharps in its six measures, and there's the F-natural in the bass making the augmented sixth with the D-sharp above at the end there. This leads into a literal repeat of the earlier chromatic bass line episode (And I again avoid the clashing sixteenth placements)... until the very last measure: There you can see how I use the sixteenth note run to make the modulation to E-flat major this go-round, and the F-natural reappears, so the earlier setup is complete.
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UPDATE: As before, the abandoned A in 265 is picked up by the bass at the G in 272.
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Since the guitar only goes down to E-natural, I was able to avoid the parallel ninths this time by just abandoning the bass line. However, the F-natural does finally resolve to E-natural at the beginning of the next page.
The E-flat major statement is quite a challenge, since the B-flats are not an open string, and this leads to the second appearance of the concluding episode - no developed a bit - which returns us to the recapitulation.
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UPDATE: Note three flats. The most remote keys are four sharps to the sharp side, and four flats to the flat side: a total difference of nine accidentals including the original key.
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The high C-sharp in measure two-hundred-ninety-four is the pitch climax of the piece, and it comes at... the 72% point!
Here's the recap, and we are now starting in E major and have four primary voices. The subject statement has an open E drone in the lead, the subject below, counter-subject two for the third voice, and counter-subject one in the bass. For the answer statement we have the fully revealed original combination: The answer is in the lead, counter-answer two is below that, and counter-answer one doubled in thirds is below, but I managed to get the funk bass pedal on E in here too. This is an extreme passage that would take a Christopher Parkening or a Kazuhito Yamashita to play. Again, it can be simplified by playing counter-answer one as quarter notes throughout.
This fully formed original combination is what I composed first - without the bass drone, of course - and it only works in this octave and in the major mode which set the whole fugue up for me. I didn't think of the funky bass pedal until after I wrote out the development sections.
After the release area episode, which is a measure shorter now and returns us to E minor, we get the inversus using the low E string as the zero axis root for the first time. Since this is the answer form, it leads to another short release area episode which keeps us in E minor. Note that the inversus really doesn't work well in the minor mode: Raised sixth and seventh degrees are required while the inverted answer's trajectory is descending. It would work much better in the major mode... which is the point.
Now we get a statement of the subject in E minor, but with the high E string zero acis being the root for the first time. This requires a modification of counter-subject two.
In the second system the key of E minor attempts to "hijack" the fugue by ending it early with the first appearance of the ending episode (Versus the earlier concluding episodes, which just ushered in the counter-exposition and recapitulation). This has a descending chromatic tetrachord for three measures, followed by a return to the tonic through the raised sixth and seventh degrees. Beethoven used this figure at the conclusion of the first movement of the Ninth Symphony.
The figure repeats with me, re, do in the bass of the fourth measure each time, and it really does sound like the piece is building to an ending.
At the last possible second, E major interrupts and does the inversus statement in this preferrable form, followed by its major mode release area.
The major mode version of the subject with the root as the zero axis follows, and this too is a more satisfying arrangement of the material. At the end of this statement of the subject, however, the final chromatic bass line episode appears, and I let the sixteenth rhythms clash, because I have to: This episode is not coming out of a sequential episode, but a thematic statement! Note that this is also the first chromatic bass line episode that is built on a descending chromatic line, and that the E that begins it is abandoned. With all of the axes and trajectories so well managed throughout the fugue, this is noticible to an astute listener.
Well, that E is picked up at the return of the ending episode on the fourth system: A nice bit of tension.
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UPDATE: The above mentioned tension is a part of a pattern I have created previously, of course.
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This ending episode is different, however, because the fourth measure has MI, re, do instead of ME, re, do as before: The chromatic descending tetrachord implies a minor ending, but the mi, re, do figure implies a major ending. This is the final conflict.
The conflict is finally resolved on the second system where the chromatic tetrachord gives up and becomes diatonic to the key of E major, and in parallel thirds, which leads up to the twenty-seventh statement: The trajectories of the subject and counter-subject in augmentation harmonized with the axes of B and E.
As Emeril would say, "BAM!"
Twenty-seven thematic statements, twenty-seven episodes, and ten keys (Nine keys other than the original tonic).
That's how Adam got into trouble, right there: It all makes sense now; Eve was a redhead.
Holy mackerel: This post took over four hours!
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UPDATE: Since I first wrote this post in a single marathon session, I left some things out, of course. Scroll down for the updates at the appropriate places.
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Fugue writing is by far my favorite compositional endeavor. Nothing else even comes close. I view it as the ultimate compositional challenge in general, and on the guitar - where imitative counterpoint is about as non-idiomatic as one can get - it's even lightyears beyond this.
I remember the first fugue I heard performed on the guitar quite vividly: It was Bach's A minor fugue for lute (Originally in G minor) performed by Christopher Parkening. This was in about 1978, and my teacher Jackie King turned me on to it. The first words out of my mouth were, "It sounds so logical!" I immediately went out and bought everything Christopher Parkening had recorded to that point: In The Spanish Style, In the Classic Style, and Parkening Plays Bach. To this day, I don't think anyone of the strict Segovia tradition guitarists is anywhere near where Parkening is at: His effortless command of the instrument, as evidenced by the exquisite nuances in his interpretations, is simply unmatched. None of the more recent virtuoso pioneers have this quality to their playing either: Kazuhito Yamashita's tone is quite strident by comparison, for example, despite his super-powerful playing.
Later, when I was attending Berklee College of Music in Boston, I had the amazing good fortune to have a counterpoint teacher named Chris Frigon. Though I was interested in becoming a famous rock guitarist at the time, Chris' class - a required course I admittedly dreaded when I registered for it - was a revelation in many ways. His seriousness about the subject and obvious command of it impressed me deeply: Chris was probably the first real highly educated musician I ever encountered of the traditional pedagogical line. And, what a line it was too:
1) Johann Sebastian Bach
-Taught-
2) Wilhelm Friedman Bach
-Who Taught-
3) Franz Joseph Haydn
-Who Taught-
4) Ludwig van Beethoven
-Who Taught-
5) Carl Czerny
-Who Taught-
6) Theodore Leschetizky
-Who Taught-
7) Edwine Behre
-Who Taught-
8) Chris Frigon
-Who Taught-
9) Hucbald
Is that cool, or what?
Though nothing came of it at the time, I had the idea to really master counterpoint in the back of my mind from that point forward, and a few years later - around 1986 - when I was in NYC, I started stopping by the Joseph Patelson Music House across from Carnegie Hall every payday to buy a counterpoint book. I became positively absorbed by the subject.
Some of the books I bought and studied during that time were: Riemann's History of Music Theory, Tenney's History of Consonance and Dissonance, Mann's The Study of Fugue, Gedalge's Treatise on Fugue, Zarlino's The Art of Counterpoint, Fux' The Study of Counterpoint, Rameau's Treatise on Harmony, and Taneiev's Convertible Counterpoint in the Strict Style. You get the idea: I wanted to know what just about everybody thought about the subject (And, there were other books by Benjamin, Kennan, Jeppesen, Piston and others I got as well).
This lead almost immediately to me writing just a bunch of studies for solo guitar, and eventually I abandoned the rock guitarist lifestyle and returned to school and a master's program in traditional theory and composition.
My first fugal works were for solo organ since my fiance at the time (then wife, now ex-wife) was a Lutheran Music Minister and virtuoso organist. I really wanted to write fugues for the guitar, but all of the subjects I came up with wouldn't "fit" on the guitar: This problem plagued me for over a decade.
It wasn't until 2005 that I came up with a new class of subject that was stately - as the Musical Offering and Art of Fugue subjects are - and also fit on the guitar. This subject is what became the three imitative movements of Sonata Zero.
Immediately after finishing Sonata Zero I had the idea to do a guitar transcription if the Organ Fugue in D Minor that is usually attributed to Bach: Just noodling around with it I figured out that the repeated note subject and answer at the fourth would work perfectly on the guitar in E minor, which would employ the open B and E strings. This exercise made me certain of at least two things: 1) There is no way that J.S. Bach is the author of this fugue, and 2) The original fugue was written by some unknown virtuoso lutenist. I am absolutely positive about that.
For a bit about the scholarly debate on this subject, you can start at the Wikipedia entry here.
While the opening Tocatta may indeed have been originally for the violin, this fugue was originally for the archlute, and was not written by J.S. Bach. It simply fits all too well on the guitar, and there is no real counterpoint in it: The countersubject, such as it is, merely makes parallel thirds or sixths with the melodic trajectory of the subject. This would be exactly the kind of thing a lutenist whose counterpoint was shaky would have come up with.
Since I liked the premise of the D Minor Organ Fugue, but not the lame execution of that premise, I decided to use the same premise, only make it a real contrapuntal tour de force. So, I composed a better subject and a real countersubject to it, and I used Sergi Taneiev's techniques from Convertible Counterpoint in the Strict Style so that the original combination would yeild derivatives at different intervallic distances.
This is easier than it sounds: If there is nothing but contrary and oblique motion between the subject and countersubject, both lines can be doubled in thirds - or sixths, but I don't use that here, because it wouldn't work out on the guitar - and so many possibilities exist.
In the D Minor Organ Fugue, the subject's repeated note, or Zero Axis as Joseph Schillinger called it, is always functioning as the fifth of the mode of the moment, but two other possibilities exist: The zero axis can also function as the root or third of the mode of the moment. I used those possibilities too, and I don't think any composer has ever employed this strategy to vary a fugue subject before. By doing this, I was able to modulate to a host of keys, some of which are quite remote from the tonic, while still using the open strings of the guitar for the zero axes.
*****
It is worth noting that, to this point, the opening Tocatta ended on an E tonic with a Picardy third in it, which I deliberately did not confirm as a modal shift by using a fully diminished seventh chord in the final cadence. Then, the Sonata is in A minor, which is where the answer is in this fugue, and it ended plaintively in A minor, even though there was an A major section within it. The Scherzo was in the relative major of G, but the second phrase of it was in G minor, and it ended on a blurry G(6/9) chord, and so now we are set up for the final battle between major and minor.
*****
On the top system is the subject, which has all of the most perfect dimentional attributes that a subject can contain: It is an odd number of measures in length at seven, and it is also fractional with the eighth note anticipation. Odd is better than even, and fractional is better than whole: There is almost nothing worse than a four measure fugue subject, which makes Bach's Motto Theme from The Art of Fugue a monumental anomaly.
*****
UPDATE: I should have also noted that the original subject contains all nine notes of the nonatonic minor system, and it has the range of a ninth as well.
*****
In the original subject and answer, the zero axis is functioning as the fifth of the mode of the moment, just like in the D Minor Organ Fugue's opening. One of the things I have done is to carefully manage all of the appearances and disappearances of the axes: The melodic trajectory of the subject merges smoothly into the counter-answer into measure eight, and - via the sixteenth note figure im measure seven - the zero axis also merges into the answer's melodic trajectory. There are no "loose ends" in this fugue.
On the second system is the answer at the subdominant level, and it is accompanied by the main counter-answer. As you can see, there is nothing but contrary motion between the answer and counter-answer from measure to measure, and oblique motion within the measures (Except at the end, where there is contrary motion with the lower quarter notes). This means both the melodic trajectory of the answer and the counter-answer could be doubled in thirds and all resulting contrapuntal relationships would be correct. This fugue is a progressive realization of those possibilities.
On the third system is the first episode, which I call a "release area." and this one does not modulate. As you can see in the final measure of it, the zero axis on E descends to merge smoothly with the upcoming counter-answer, the melodic trajectory merges into the bass line's A, and then the lower voice is free to begin another statement of the answer.
The octave inversion statement beginning in measure twenty does not use an open string for the zero axis: This is the only place in the fugue where I had to do that, so it is quite difficult to execute, but the fugue wouldn't work without it. We're still in A minor here, but this statement of the answer and counter-answer sets up the modulation to C major I want. Well, need, actually.
On the bottom system starting at measure twenty-seven is the first of the second type of episode, which I call sequential episodes, since they grow out of the final measure of the answer/counter-answer or subject/counter-subject. In measure thirty-three we have modulated to C.
As you can see, we are now in C major, but the zero axis is still the open E string, which means it is functioning as the major third here. This also means that the counter-subject (This is the subject form, with the descending trajectory at the tail of the subject, with the rising quarters in the counter-subject, which we get here for the first time) is a third closer to the subject in this statement: This is Taneiev's Convertible Counterpoint at work.
In the sequential episode starting on the second system, notice that the melodic trajectory fragments above always merge into unisoni with the bass line at the start of every measure, and the zero axis on E becomes an E-flat before continuing down to merge with the next counter-answer statement. This means we have not modulated, but we have changed the gender of the mode to C minor.
The C minor statement is in an octave inversion again, and it employs the open G string as the zero axis for the first time. That means it is functioning as the fifth again.
At fifty-five we get the third type of episode, which I call a concluding episode, because it concludes the exposition and the development to lead into the counter-exposition and the recapitulation later. At the end I've put a double bar line, because this is the end of the exposition.
As you can see, this is a combination of fugal process and monothematic sonata process.
On the bottom system the counter-exposition begins with the subject exactly as at the beginning of the piece, but now there is a drone on the high E string, the zero axis is on the open B string (as before), and the counter-subject is now in the bass. That makes the exposition a two-voice deal and the counter-exposition a three voice kind of thing: The recapitulation will be four voices, revealing the entire original contrapuntal combination. Note again how I'm careful to merge the axes and trajectories: The open low E at fifty-five is merely an octave transposition.
Here we get the answer, counter-answer one, and counter-answer two for the first time. Though counter-answer two does not follow the trajectory of the answer throughout - the voices actually cross in measure seventy-one - it does effectively double the trajectory in thirds, which is a further revelation of the original combination.
The release area episode on the second system is exactly like its counterpart in the exposition until the end, where a C-sharp is introduced to change the mode to A major. The sharps in A major will allow me to modulate to C-sharp minor at the end of the following sequential episode. So the third system is just like the earlier A minor statement except for the mode.
In the fourth system you can see how the modulation works out: We're at C-sharp minor by the end, instead of C major as before. This means the bottom system is exactly like the earlier C major statement in that the open E is the third of the mode of the moment, but now it's the minor third of C-sharp minor versus the major third of C. See how cool this is?
One of these accumulated sharps has to be shed, of course, and that's what the sequential episode at the top of page four allows: We're back to A major by the end of it.
On the second system begins the first of the fourth type of episode, which I call a chromatic episode because they are all over chromatic lines in the bass. Note that I left out the sixteenths at the end of measure one-hundred-six leading into it: I didn't want that rhythm to clash with the new placement in the chromatic episode... yet. This episode is nineteen measures long, and it acts as a release from the constant fugal struggle we've endured so far, and it also modulates to C major by the end.
*****
UPDATE: I should have pointed out that, after all the painstaking management of the axes and trajectories up to this point, the C-sharp is abandoned for the first of the chromatic bass line episodes at measure one-hundred-seven. This creates a tension throughout the episode that is not resolved until measures 124-125 where the C-sharp resolves up to D and then the D progresses down to C-natural to effect the modulation.
*****
The C major statement of the answer at one-twenty-six has the main counter-answer doubled in thirds for the first time, and it is in octave inversion as well: This was the C minor statement last time, and the open G zero axis is again the fifth of the mode.
The counter-exposition is longer than the exposition was, and all of the statements are now new. The sequential episode at the top was the concluding episode last time, and we modulate to A major by the end of it. The answer/counter-answer statement at one-hundred-forty has the counter-answer doubled in thirds again, but in the original octave arrangement.
Our old reliable release area episode keeps us in A major, and sets up the first appearance of the inversus form of the subject, which also has the low A string zero axis functioning of the root of the mode for the first time as well. The inversus form of the counter-answer is also doubled in thirds.
This leads to a properly unique sequential episode to lead into the development areas: It's inverted, and you get triad, diad, and monad as the trajectories merge. A second double bar line signals the beginning of the development.
The development is in two sections, just like the exposition and counter-exposition. Also like them, I modulate to closer keys the first time through, and follow the same pattern but modulating to the more remote keys the second time.
We begin with an answer statement on the same level as the original subject, but now the main counter-answer is in the lead voice, and there is a tonic pedal in the bass. This passage is only possible because the low E pedal and the zero axis B are open strings.
Since this is an answer form, we get a new version of the release area episode on the second system, and this modulates us to A minor.
The A minor statement on the third system has the answer and counter-answer two, but above an alternating pedal using the open low A and E strings: It's actually pretty easy to play.
In the release area episode starting at one-hundred-eighty-four, we get a modulation to G major. Note the chromatic movement of the D-sharp in measure 186 into the D-natural in 187: This is a setup for the next time, where the notes will be reversed. Since the bottom system is in G major and the zero axis B is the major third, that means the next time we get here it will be G-sharp minor with the B as the minor third. Shiny!
The final statement on the page is the subject form with a drone G in the lead, and the counter-answer below.
The sequential episode at the top is further developed with the G in the lead coming down to D-sharp at the end for the return to E minor. Next time, this episode will start out with a G-sharp in the lead, of course.
At two-hundred-one we get the second of the chromatic bass line episodes, and I again avoided the sixteenths at the end of two-hundred so as not to clash with the episode's rhythmic figure at this point. Note that between the low F-sharp and the D-sharp in the lead at two-undred we have a major sixth: I'll make that an augmented sixth with an F-natural next time, to set up the final development statement in E-flat major.
*****
UPDATE: Again, a tension is created when the A is abandoned at measure two-hundred. It is not picked up and absorbed into the bass line until the G in measure 207, so the suspense only lasts half of this particular episode.
*****
This chromatic bass line episode does not modulate this time, however, getting us to the E minor statement that starts on the fourth system. here, the open G zero axis is the minor third of the mode, the open B is a drone above, and the counter-answer is in the lead; all over a tonic pedal in the bass.
From 216 into 217 I have technically gotten myself a parallel stepwise dissonance between the F-sharp in the bass and the open G that launches the new answer statement. First it's a minor ninth, and then a major ninth, though, and since the answer immediately goes up to the minor third, I gave myself this single licence. Since it's a ninth, and the entire piece is based on nine and twenty-seven, it seemed appropriate.
The sequential episode on the bottom system is the most dramatic yet, and it leads to the exuberance climax of the piece with the appearance of the key of E major for the first time on the next page. You can see how I took the sixteenth duplets, expanded them in the previous episode at the end, and then added even more in the last measure of the page. A double bar signals the end of the first half of the development.
Here we have E major for the first time, and the combination is like the previous appearance of E minor at this point, except for the fact that counter-answer two is now present. You need to employ the right hand c finger to execute this passage, and yes, it's a bitch to play, but it is technically possible.
The release area episode on the second system takes us to A major this time, otherwise it is the same as before.
OK, *big sigh* the statement at measure two-hundred-forty-two has a pedal underneath that is alternated with the counter-answer above. You really don't need the c finger here, but it would help. And, as for myself, I plan to use funk bass technique to slap the low E's... but that's just me. ;^) This passage can be simplified by playing the counter-answer line as quarter notes versus the half notes here.
The release area on the fourth system now takes us to G-sharp minor, as I mentioned it would, and so we get that super-remote key area on the bottom system: Five freaking sharps!
Here's the sequential episode I mentioned earlier that starts with G-sharp in the lead. It sheds four sharps in its six measures, and there's the F-natural in the bass making the augmented sixth with the D-sharp above at the end there. This leads into a literal repeat of the earlier chromatic bass line episode (And I again avoid the clashing sixteenth placements)... until the very last measure: There you can see how I use the sixteenth note run to make the modulation to E-flat major this go-round, and the F-natural reappears, so the earlier setup is complete.
*****
UPDATE: As before, the abandoned A in 265 is picked up by the bass at the G in 272.
*****
Since the guitar only goes down to E-natural, I was able to avoid the parallel ninths this time by just abandoning the bass line. However, the F-natural does finally resolve to E-natural at the beginning of the next page.
The E-flat major statement is quite a challenge, since the B-flats are not an open string, and this leads to the second appearance of the concluding episode - no developed a bit - which returns us to the recapitulation.
*****
UPDATE: Note three flats. The most remote keys are four sharps to the sharp side, and four flats to the flat side: a total difference of nine accidentals including the original key.
*****
The high C-sharp in measure two-hundred-ninety-four is the pitch climax of the piece, and it comes at... the 72% point!
Here's the recap, and we are now starting in E major and have four primary voices. The subject statement has an open E drone in the lead, the subject below, counter-subject two for the third voice, and counter-subject one in the bass. For the answer statement we have the fully revealed original combination: The answer is in the lead, counter-answer two is below that, and counter-answer one doubled in thirds is below, but I managed to get the funk bass pedal on E in here too. This is an extreme passage that would take a Christopher Parkening or a Kazuhito Yamashita to play. Again, it can be simplified by playing counter-answer one as quarter notes throughout.
This fully formed original combination is what I composed first - without the bass drone, of course - and it only works in this octave and in the major mode which set the whole fugue up for me. I didn't think of the funky bass pedal until after I wrote out the development sections.
After the release area episode, which is a measure shorter now and returns us to E minor, we get the inversus using the low E string as the zero axis root for the first time. Since this is the answer form, it leads to another short release area episode which keeps us in E minor. Note that the inversus really doesn't work well in the minor mode: Raised sixth and seventh degrees are required while the inverted answer's trajectory is descending. It would work much better in the major mode... which is the point.
Now we get a statement of the subject in E minor, but with the high E string zero acis being the root for the first time. This requires a modification of counter-subject two.
In the second system the key of E minor attempts to "hijack" the fugue by ending it early with the first appearance of the ending episode (Versus the earlier concluding episodes, which just ushered in the counter-exposition and recapitulation). This has a descending chromatic tetrachord for three measures, followed by a return to the tonic through the raised sixth and seventh degrees. Beethoven used this figure at the conclusion of the first movement of the Ninth Symphony.
The figure repeats with me, re, do in the bass of the fourth measure each time, and it really does sound like the piece is building to an ending.
At the last possible second, E major interrupts and does the inversus statement in this preferrable form, followed by its major mode release area.
The major mode version of the subject with the root as the zero axis follows, and this too is a more satisfying arrangement of the material. At the end of this statement of the subject, however, the final chromatic bass line episode appears, and I let the sixteenth rhythms clash, because I have to: This episode is not coming out of a sequential episode, but a thematic statement! Note that this is also the first chromatic bass line episode that is built on a descending chromatic line, and that the E that begins it is abandoned. With all of the axes and trajectories so well managed throughout the fugue, this is noticible to an astute listener.
Well, that E is picked up at the return of the ending episode on the fourth system: A nice bit of tension.
*****
UPDATE: The above mentioned tension is a part of a pattern I have created previously, of course.
*****
This ending episode is different, however, because the fourth measure has MI, re, do instead of ME, re, do as before: The chromatic descending tetrachord implies a minor ending, but the mi, re, do figure implies a major ending. This is the final conflict.
The conflict is finally resolved on the second system where the chromatic tetrachord gives up and becomes diatonic to the key of E major, and in parallel thirds, which leads up to the twenty-seventh statement: The trajectories of the subject and counter-subject in augmentation harmonized with the axes of B and E.
As Emeril would say, "BAM!"
Twenty-seven thematic statements, twenty-seven episodes, and ten keys (Nine keys other than the original tonic).
That's how Adam got into trouble, right there: It all makes sense now; Eve was a redhead.
Holy mackerel: This post took over four hours!
posted by Hucbald at 6:27 AM
2 Comments:
I like your site Hucbald.
I saw you over at the Jawareport, and that's how I came upon it.
I play a little myself. I'm working on Bach's 3rd lute suite/cello suite (BWV 995 anyway) right now. Learning pieces always goes slowly for me. I'm always conflicted by another thing I like to do: rock climbing. Ruins the nails in short order.
I like Godin too. I've got a 1998 LGX. I like this model for its fretboard, different profile(radius and what not) from the later model. I'm in the process of refinishing it (nasty drop a while back, left a couple mean chips).
My classical is nothing much though-- maybe if I finish learning the Bach piece I could justify buying a nicer one. Or maybe instead of getting an expensive traditional classical I should look into those Godin Multiacs I see you holding there...
(Very beautiful women too.)
I play the Sarabande from the 3rd Lute Suite, and have Gavotte II on my "to do" list.
I'm not into rock climbing, but I do a lot of "guy" stuff: Archery, motorcycle maintanance, fishing, hunting... so, I use fake nails. When I mess one up, I replace it: If I want to shoot my bow or work on my bike, I just peel them off. I wasted years being paranoid about my nails. No more.
The cheapies seem to work the best. I use the Fing'rs Career Length or Kiss Natural Squares. Most Dollar Stores have them. I play enough that I need to replace them weekly, which has just become part of my Wednesday routine.
Cheers!
George
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