Guitar Fugue, "Authorized Version": Recognizing Perfection
Because of my musico-philosophical connection with the overtone series, I believe that it is a fact - and not my opinion - that so-called "common practice" techniques are an inevitable product of man's intuitive, intellectual, and philosophical interactions with the implications of the nature of sound. And, within the comon practice technical universe, sonata technique has been the ultimate attainment so far. But, for sheer erudition and purity, nothing can touch fugue writing: It is the ultimate musical challenge.
My main line of attack against post-common practice music is to point out the laws of musical motion derived from analyzing the implications of the overtone series: These are the opposite of rules foisted onto music; they are simply natural and inevitable deductions pertaining to the nature of musical motion, whether they be the circular transformations of harmony, the axial combinations of melodic trajectory, or the laws governing contrapuntal combinations. These things, properly defined and applied, are the quantum mechanics of music.
Ironically, it is the champions of post-common practice music who are often the ones guilty of burdening music with a bunch of man-made, artificial, and unnatural rules. Just trying to keep track of the plethora of rule-sets the various schools of atonality, stochasticism, aleatoric music have come up with makes one's head spin. It is no secret to readers of this blog that I think it's all just so much poppycock.
I liken these approaches to cheating at solitare or solo chess: There's no real-world penalty for doing such a thing, but neither is there any spiritual or emotional paycheck. To me, there can be no satisfaction in creating your own rule-sets, because there is no challenge there. Results of equal musical validity can be obtained by scattering the floor of one's study with staff paper and shaking a fountain pen over them: Just let the ink droplets be the notes, apply some overly-complex rhythmic formula, and you have something just as valid as the music of Schoenberg, Webern, Cage, Babbitt, or whomever the twentieth-century "dope of the moment" is. Where the laws of nature are absent, or the rules are the whim of the composer, there can be no perfection. Sorry, but I believe that to also be a fact, and not an opinion.
As far as absolute music is concerned, there is nothing more absolutely pure than a fugue. That is why there is nothing I like better than J.S. Bach's Art of Fugue, and nothing I enjoy more than fugue writing. As I've mentioned before, the first step in learning to write a fugue is learning to compose a fugue subject. There is no greater aid in that endeavor than to study Joseph Schillinger's Theory of Melody and Theory of Counterpoint books out of The Schillenger System of Musical Composition: That's how I "autodidactically" managed it. Of course, before this is even attempted, one needs to learn to proficiently write countrapuntal pieces that are not immitative in nature, which is a serious challenge all it's own. There are three keys to this: Miniatures, miniatures, and... miniatures.
When the laws of musical motion are learned and ascribed to, perfection is not an impossible goal: In fact, it is the inevitable end result. Through intellect and intuition, a good fugue subject in an appropriate idiom will compose itself. The end result will be that there will not be a note that could be changed without damaging the piece. Of course, different fugues can be composed on the same subject (And, believe it or not, the subject I'm working with here would work on the guitar in four vioces, but I'm nowhere near the virtuoso who would be required to play it, so that will have to wait for another day), but each decision throughout the process that is varied will lead to a series of further variations leading to a different form of perfection in the end. It is a difficult thing to explain, but one need only listen to and study Musical Offering and/or Art of Fugue to get what I'm straining for words to describe here.
My little Guitar Fugue in A minor has now nearly reached such a state of perfection (Versus the state of perfection, and I say "nearly" because I usually don't issue final pronouncements until I've actually performed a piece for a couple of years). The final key was figuring out the one-and-only solution to the arpeggiation of the harmonized version of the subject in the third episode that returns the fugue to the tonic. I probably put more work into those seven measures than the entire rest of the fugue (Well, that's an exageration, but it was very difficult to devine the proper formations).
Since there are no changes to the first three pages, here's the last page in it's final form:
Starting in measure 48, the third episode is a harmonized version of the answer in E minor, which is the subject in the home key of A minor. That's how I achieved the modulation: By treating it as the answer at the beginning, and the subject at the end. It is also on the same pitch level as the first statement of the subject back at the beginning of the fugue, and the last statements in the concluding stretto. Se est cool, non? (Pardon my French ;^)) The first and last notes of every measure of the episode are the subject: That part was easy to figure out, but the arpeggiation pattern wasn't.
The crux of the problem in this modulation is how to get rid of the F-sharp and introduce the F-natural. I solved that in measures 52 and 53, but before getting there, let me describe the "inevitabiltiy" of the arpeggiation pattern. First of all, the progression, starting in measure 48, is:
|| E minor, B major | E minor, A minor | D major, G major | C major, F#(d7) | B minor, E(7) | A minor, B(d) | A minor, E(7) ||
Because of the subject's head in measure 48, there are two patterns in this arpeggiation that are out of sync with each other. Looking at the first chord of each measure you can see that the arpeggiation alternates between 6/4 and 5/3 forms: This continues throughout all seven measures, and is only varied in the final one. The second pattern starts on the second chord of measure 49: The first two chords starting there are triads sharing the same 6/3 orientation, and then in measures 51 and 52, the patern is altered by the introduction of the fully-diminished chord on F-sharp to become seventh chords in 6/5 orientations, with a diminished fifth in the middle of the figure. The second pattern's evolution is out of sync with the first pattern because of the unique and inevitable figure in the second half of measure 48, but it is also in a 6/3 arrangement. This creates an effect that I find somehow trancendental or something.
The pattern conspires to take care of the F-sharp "problem" in measure 52, where the lowest voice of the pattern progresses from f-sharp, to G-sharp, and then to A across the bar line. Then, and only then can the F-natural be introduced in the second half of measure 53. The final two measures create an inevitable cadential modulation to the A minor chord at the beginning of measure 55, which is in a necessarily imperfect form (No tonic octave on the top and bottom), and is also at the only pitch level that is possible to prepare for the final stretto entries of the subject starting on E.
It is also worth looking at the inevitability of the top line in the arpeggiation. Measure 48 has the B at the top, which is just below the pitch climax of the piece - which was the C back in measure 47 - and this pitch is reiterated three times before decending to A in the second half of measure 49: The second half of 50 gets us down to G, the second half of 51 to F-sharp (The E-flat is an augmented second, and so does not function linearly, but only harmonically), the second half of 52 to E, which is reiterated in measure 53 to prepare for the F-natural! See how this has to be "just so", and couldn't be any other way? After the introduction of the F-natural, that pitch has to be brought down to the C at the resolution point, and that explains the inevitability of the varied 6/4 chord at the beginning of measure 54. The little do, ti, do figure within the V(7) chord is, of course, the head of the subject (Well, answer, actually, on that pitch level).
When I think I have a piece like this perfected, one of the ways I test that is by destroying the idiom I composed it in. One of the nice things about being a twenty-first century composer is the technology: All I had to do to erase any traces that this was a guitar fugue was to transpose it up an octave and apply a variety of different sounds to it via QuickTime. Most standard QuickTime sounds suck (Although there are nice HQ alternate Soundfont sets out there, and porting them into the Sounds folder in OS X is now simple, if you have a Mac), but the goofy little sound they call "Ocarina" actually sounds like the pure flute ranks of a pipe organ with even a hint of chiff. I love the way this fugue sounds with that sound in the higher octave! It really does make a nice little organ piece, which is kind of interesting.
As usual, updated PDF and MIDI files are on my .Mac FileShare page as O_STA_3.pdf/.mid, and if you want to hear the idiomatically destroyed version in the higher octave with the Ocarina sound, I put that there as well as P_GUITAR_FUGUE_Organ.mid.
Yes, yes: I said I needed to practice. My obsessive/compulsive nature simply would not let me go until I finished this fugue. I'm OK now... No, really! (My ex-wife never bought that either)
My main line of attack against post-common practice music is to point out the laws of musical motion derived from analyzing the implications of the overtone series: These are the opposite of rules foisted onto music; they are simply natural and inevitable deductions pertaining to the nature of musical motion, whether they be the circular transformations of harmony, the axial combinations of melodic trajectory, or the laws governing contrapuntal combinations. These things, properly defined and applied, are the quantum mechanics of music.
Ironically, it is the champions of post-common practice music who are often the ones guilty of burdening music with a bunch of man-made, artificial, and unnatural rules. Just trying to keep track of the plethora of rule-sets the various schools of atonality, stochasticism, aleatoric music have come up with makes one's head spin. It is no secret to readers of this blog that I think it's all just so much poppycock.
I liken these approaches to cheating at solitare or solo chess: There's no real-world penalty for doing such a thing, but neither is there any spiritual or emotional paycheck. To me, there can be no satisfaction in creating your own rule-sets, because there is no challenge there. Results of equal musical validity can be obtained by scattering the floor of one's study with staff paper and shaking a fountain pen over them: Just let the ink droplets be the notes, apply some overly-complex rhythmic formula, and you have something just as valid as the music of Schoenberg, Webern, Cage, Babbitt, or whomever the twentieth-century "dope of the moment" is. Where the laws of nature are absent, or the rules are the whim of the composer, there can be no perfection. Sorry, but I believe that to also be a fact, and not an opinion.
As far as absolute music is concerned, there is nothing more absolutely pure than a fugue. That is why there is nothing I like better than J.S. Bach's Art of Fugue, and nothing I enjoy more than fugue writing. As I've mentioned before, the first step in learning to write a fugue is learning to compose a fugue subject. There is no greater aid in that endeavor than to study Joseph Schillinger's Theory of Melody and Theory of Counterpoint books out of The Schillenger System of Musical Composition: That's how I "autodidactically" managed it. Of course, before this is even attempted, one needs to learn to proficiently write countrapuntal pieces that are not immitative in nature, which is a serious challenge all it's own. There are three keys to this: Miniatures, miniatures, and... miniatures.
When the laws of musical motion are learned and ascribed to, perfection is not an impossible goal: In fact, it is the inevitable end result. Through intellect and intuition, a good fugue subject in an appropriate idiom will compose itself. The end result will be that there will not be a note that could be changed without damaging the piece. Of course, different fugues can be composed on the same subject (And, believe it or not, the subject I'm working with here would work on the guitar in four vioces, but I'm nowhere near the virtuoso who would be required to play it, so that will have to wait for another day), but each decision throughout the process that is varied will lead to a series of further variations leading to a different form of perfection in the end. It is a difficult thing to explain, but one need only listen to and study Musical Offering and/or Art of Fugue to get what I'm straining for words to describe here.
My little Guitar Fugue in A minor has now nearly reached such a state of perfection (Versus the state of perfection, and I say "nearly" because I usually don't issue final pronouncements until I've actually performed a piece for a couple of years). The final key was figuring out the one-and-only solution to the arpeggiation of the harmonized version of the subject in the third episode that returns the fugue to the tonic. I probably put more work into those seven measures than the entire rest of the fugue (Well, that's an exageration, but it was very difficult to devine the proper formations).
Since there are no changes to the first three pages, here's the last page in it's final form:
Starting in measure 48, the third episode is a harmonized version of the answer in E minor, which is the subject in the home key of A minor. That's how I achieved the modulation: By treating it as the answer at the beginning, and the subject at the end. It is also on the same pitch level as the first statement of the subject back at the beginning of the fugue, and the last statements in the concluding stretto. Se est cool, non? (Pardon my French ;^)) The first and last notes of every measure of the episode are the subject: That part was easy to figure out, but the arpeggiation pattern wasn't.
The crux of the problem in this modulation is how to get rid of the F-sharp and introduce the F-natural. I solved that in measures 52 and 53, but before getting there, let me describe the "inevitabiltiy" of the arpeggiation pattern. First of all, the progression, starting in measure 48, is:
|| E minor, B major | E minor, A minor | D major, G major | C major, F#(d7) | B minor, E(7) | A minor, B(d) | A minor, E(7) ||
Because of the subject's head in measure 48, there are two patterns in this arpeggiation that are out of sync with each other. Looking at the first chord of each measure you can see that the arpeggiation alternates between 6/4 and 5/3 forms: This continues throughout all seven measures, and is only varied in the final one. The second pattern starts on the second chord of measure 49: The first two chords starting there are triads sharing the same 6/3 orientation, and then in measures 51 and 52, the patern is altered by the introduction of the fully-diminished chord on F-sharp to become seventh chords in 6/5 orientations, with a diminished fifth in the middle of the figure. The second pattern's evolution is out of sync with the first pattern because of the unique and inevitable figure in the second half of measure 48, but it is also in a 6/3 arrangement. This creates an effect that I find somehow trancendental or something.
The pattern conspires to take care of the F-sharp "problem" in measure 52, where the lowest voice of the pattern progresses from f-sharp, to G-sharp, and then to A across the bar line. Then, and only then can the F-natural be introduced in the second half of measure 53. The final two measures create an inevitable cadential modulation to the A minor chord at the beginning of measure 55, which is in a necessarily imperfect form (No tonic octave on the top and bottom), and is also at the only pitch level that is possible to prepare for the final stretto entries of the subject starting on E.
It is also worth looking at the inevitability of the top line in the arpeggiation. Measure 48 has the B at the top, which is just below the pitch climax of the piece - which was the C back in measure 47 - and this pitch is reiterated three times before decending to A in the second half of measure 49: The second half of 50 gets us down to G, the second half of 51 to F-sharp (The E-flat is an augmented second, and so does not function linearly, but only harmonically), the second half of 52 to E, which is reiterated in measure 53 to prepare for the F-natural! See how this has to be "just so", and couldn't be any other way? After the introduction of the F-natural, that pitch has to be brought down to the C at the resolution point, and that explains the inevitability of the varied 6/4 chord at the beginning of measure 54. The little do, ti, do figure within the V(7) chord is, of course, the head of the subject (Well, answer, actually, on that pitch level).
When I think I have a piece like this perfected, one of the ways I test that is by destroying the idiom I composed it in. One of the nice things about being a twenty-first century composer is the technology: All I had to do to erase any traces that this was a guitar fugue was to transpose it up an octave and apply a variety of different sounds to it via QuickTime. Most standard QuickTime sounds suck (Although there are nice HQ alternate Soundfont sets out there, and porting them into the Sounds folder in OS X is now simple, if you have a Mac), but the goofy little sound they call "Ocarina" actually sounds like the pure flute ranks of a pipe organ with even a hint of chiff. I love the way this fugue sounds with that sound in the higher octave! It really does make a nice little organ piece, which is kind of interesting.
As usual, updated PDF and MIDI files are on my .Mac FileShare page as O_STA_3.pdf/.mid, and if you want to hear the idiomatically destroyed version in the higher octave with the Ocarina sound, I put that there as well as P_GUITAR_FUGUE_Organ.mid.
Yes, yes: I said I needed to practice. My obsessive/compulsive nature simply would not let me go until I finished this fugue. I'm OK now... No, really! (My ex-wife never bought that either)
posted by Hucbald at 12:50 AM
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