Thursday, November 10, 2011

Exemplar 6: Doctor of Able Polyphonists

You have to read this blog from the beginning to have any hope of, "getting it."

The highest level within the guild as I currently have it laid out is Doctor of Able Polyphonists, though a level of Professor between Honorable Grandmaster and Doctor is a possible addition. Whereas the three Master levels are of peers and there is no huge barrier to advance from Master to Esteemed Master and then Honorable Grandmaster, advancing to Doctor is different: Nothing but an epic contrapuntal work will do, it has to demonstrate profound mastery, and it has to have at least one unique aspect - preferably more.

The exemplar for this level is a Ricercare for solo guitar that has a lengthy story behind it. Back in 2005 I decided to transcribe the D Minor Organ Fugue that is usually attributed to J.S. Bach for solo guitar. In E Minor, it worked perfectly with the subject and answer using the open B and E strings as the played zero axes. Where I ran out of room was in the bass, as a seven string guitar with a low B would be needed to pull off the transcription really well. That's when it hit me: The D Minor Organ Fugue was originally a work for baroque lute - which had more courses than the guitar has strings - and Bach did not compose it. This is obvious to me because, 1) there is a parallel perfect fifth in the exposition and, 2) the countersubject - such as it is - just makes parallel thirds or sixths with the subject and answer: IOW, there is no counterpoint. I don't believe Bach would have done anything like this, but it is exactly what you would expect from a lute virtuoso with a shaky understanding of counterpoint.

In any event, the idea is a good one, but the execution was lame, so I decided to improve upon it. As I was thinking about how to do that, I noticed that an old Schillinger-inspired open-string study I had written back around 1987 had a melody and counterpoint that contained nothing but contrary and oblique motion: If there is nothing but contrary and oblique motion in a contrapuntal combination, then both voices can be doubled in parallel thirds or sixths, and all six resulting combinations will be technically correct (This is something I got from studying Sergi Taneiev's Convertible Counterpoint). So, this piece is the culmination of twenty years of working with Schillinger's axes of melody concepts, and Taneiev's vertical-shifting counterpoint techniques.

The answer and counter-answer in this piece are note-for-note exactly like the A section of that old study, with the exception of the sixteenth-note ornaments, so I actually added the subject statement before it to get the fugal part of the exposition. As for the version with both parts doubled in thirds, that full combination is saved for the recapitulation, and it only works in A major. This set the piece up as an epic struggle between minor and major with major winning out at the end.

Formally, the piece is a combination of both the fugal and the sonata processes: Basically, a monothematic sonata with a fugato as the opening theme.

There are also some unique modifications of the theme that owe their existence to the idiom of solo guitar: In order to modulate with relative freedom, I had to maintain the use of open strings, so the zero-axis of the subject and countersubject - the repeated notes - had to change function from perfect fifth to major or minor third and also the root of whatever the key of the moment was. This technique enabled me to create a gigantic piece of musical architecture, as you shall see, with constant variation of aspects of the thematic material, while keeping it all idiomatic to the guitar.

Here is the sound file:

Ricercare in E Minor

And the score with the required structural and thematic analysis, and commentary:

The subject is 7.25 measures in length, and the first zero-axis is the fifth of the key of the moment, so the open B string is employed. The answer is at the fourth above, and the zero-axis is still the fifth, so the open E string is employed there. Since the subject and answer create an antecedent-consequent phrase group that does not return to the original tonic, a release episode was needed. This first one stays in the secondary key of A minor. The first middle entries at 10, then, are still on the subdominant level, with the parts inverted, and the zero axis is still the fifth (And not an open string, so this is pretty difficult to execute). The final measure of the subject provides the motif for the sequential episodes, and the first one beginning at 27 modulates the piece to C major.

So then, for this C major statement, the open E string is employed as the zero-axis again, but now it is functioning as the major third of the key of the moment, versus the previous fifth. The resulting sequential episode is different, and this one does not modulate, it just shifts genders to C minor when I introduce E-flat in the last measure. This sets up an inverted statement in C minor in which the zero-axis is the fifth again, and the open G string is used for the first time. At 55 the sonata exposition is concluded with a different kind of episode that is heard only before fugal expositions: We'll hear a different version of it before the recapitulation. The counter-exposition at 61 is the first time since the beginning that the home key of E minor has appeared. This time the subject is as it was in the beginning, but there is a countersubject below and a drone on the open E string above.

The answer and counter-answer are also the same as before, but now there is a second counter-answer that effectively doubles the melodic trajectory of the answer in thirds. This is part of the progressive unveiling of the full combination. Release episode two is exactly the same as before, but it changes gender to A major at the end. The inverted statement at 80 is also the same with the exception of being now in the major mode. These additional sharps enable the following sequential episode to modulate to C-sharp minor, versus the previous C major. That means the final statement on the page at 94 is in C-sharp minor, with the open E string now functioning as the minor third of the key of the moment.

Sequential episode four then modulates to A major. Up to this point, everything in the counter-exposition has had a parallel precursor in the exposition, but at 107 a new element is introduced with the first of four interludes. This one is based on a rising chromatic line in the bass, and it is unique to the counter-exposition. After this much needed nineteen measure break from the primary thematic material, and inverted statement in C major appears at 126. This is like the previous statement in this configuration that was in C minor, but now the counter-answer is doubled in thirds.

These thirds lead to another unique version of the sequential episode that modulates to A major for a statement of the answer with the counter-answer again doubled in thirds, but this time in the original orientation. Release episode three is then like the previous two, but now it is in the major mode, and it turns around in the last measure to introduce the first of the melodic inversions of the subject at 152. When an inverted form is used in the bass, only the root will work as the zero axis, which is the open A string here. This results in a particularly gnarly sequential episode that modulates to E minor for the start of the development.

I begin the development section with an E minor statement of the answer for the first time - which is over an open low E-string pedal point - and this leads to a new inverted form of the release episode that modulates to A minor. That A minor statement of the answer has the melodic trajectory doubled in thirds by counter-answer two, and it is over an alternating tonic-dominant pedal which leads to what seems like it should be a regular release episode: That doesn't come to pass. Instead, there is a very surprising modulation to G major at the end. The G major statement is therefore an entirely new key, and having the open B string as the major third of the momentary key is therefore also a first.

Sequential episode seven - related to the rest, but unique, as they all are - then modulates to E minor for the second interlude. The interlude is marked 2A because there is a counter-development in this piece, and so there is a second version of this later. At 217 the answer statement in E minor uses the open G string as the minor third zero axis for the first time: In the counter-development, this will be in E-flat major. Sequential episode eight is very dramatic, and it moves the piece to E major for the counter-development.

The counter-development begins in the parallel mode of E major, and it contains counter-answer two as well this time. The answer at 242 is very ballsy, with the answer, counter-answer one, counter-answer two, and an alternating pedal in the bass. Release episode seven is like the corresponding previous version, but the surprise modulation is now to G-sharp minor. At G-sharp minor, the open B-string is now the minor third of the momentary key.

Sequential episode nine is a parallel to its antecedent, but with many more sharps to shed on the way to E minor, it is much more interesting. Interlude 2B is the same as the previous version until the last measure, where I use the sixteenth-note run to make a very fast and cool modulation to E-flat major. With the E-flat major statement, all parallels have been worked through, and the counter-development then concludes with the second of the sectional conclusion episodes. This one modulates to E major for the recapitulation.

This recapitulation is what I composed first. The subject statement has - top to bottom - a drone on the high E-string, the subject in E major, counter-subject two doubling the melodic trajectory in thirds, and then counter-subject one in the bass. Then the answer statement has - again, top to bottom - the answer in A major, counter-answer two doubling the trajectory of the answer in thirds, and then counter-answer one doubled in thirds in the bass. Release episode eight then modulates the piece to E minor for the melodically inverted statement with the low E-string as the zero-axis root. Basically, the major modes have just demonstrated their superiority by playing the full contrapuntal combinations, and E minor has a tantrum over it. The inverted release episode nine, then, does not modulate.

The subject statement in E major now has the zero axis as the root - the first time for that in a rectus statement - and that unique arrangement leads to a concluding episode at 331. In the drama that is unfolding, E minor is attempting to hijack the piece and end it early. E major interjects at the last possible eighth-note with an inverted statement of its own, proving again that the major mode handles the thematic material in a superior way. Release episode ten is a parallel with the previous version, but now in major.

The key of E major is also better with the rectus statement, and that leads to the final interlude. Whereas before all of the interludes had ascending chromatic bass lines in them, this last one has a descending chromatic bass, as is fitting near the conclusion. That final interlude then leads to the concluding episode, which is the same as before, with one exception: The bass notes in the final measures are now mi, re, do instead of the previous me, re, do: This is the final struggle between major and minor.

The minor mode finally gives up for good at 385, where everything becomes diatonic to major. That leads to the final thematic statement in the coda: The trajectory of the subject and primary countersubject in augmentation harmonized for six voices (Five voices in the fifth and sixth measures). An utterly triumphant ending (There will be some sort of finger-strumming figure there to end with dramatic flair).

If this epic fugue does not absolutely rock your world, there is only one explanation: You have no ability to understand the intricacies of fugue or even to properly listen to counterpoint. This is the greatest fugue ever composed for solo guitar, and the most high tech and mechanically efficient fugue ever composed by anybody.

As usual, if you disagree, you are welcome to prove it, but prove it you must.

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