How to Compose Counterpoint (Imitation and Modulation 1)
This is part five of a series that progresses from Where to Begin through How to Progress, Using Larger Forms, and Using Three Voices. All of the examples so far have been non-imitative and none of them have had any modulations, however, so now we are ready for those subjects.
Philosophically, I simply do not think that small pieces have to modulate, and for the idiom of the guitar, specifically, modulations tend to complicate things significantly. As a result, I write a lot of miniatures that don't contain any modulations at all, though they may be quite chromatic, as you will have seen if you have followed this series of posts. Another issue I have with Baroque and Classical miniatures is that the modulations are so formulaic and predictable that they border on the manneristic: "Oh, it's a major key: We're going to modulate to the dominant," or, "Oh, it's a minor key: We're going to modulate to the relative."
I knew from my years of writing popular styles and jazz that modulations weren't required to write effective music, so I didn't want to get caught on that particular strip of flypaper. However, some idiomatic pieces do actually require modulations - fugues, sonatas, preludes &c. - so I saved those things for last in my musical evolution, at least in the area of contrapuntal guitar music.
Between the E-Axis Studies and the B-Axis Studies I found another vehicle that allowed me to create a large series of pieces that did modulate, and that vehicle was the figuration prelude. I've written fourteen out of the twenty-four so far, but since they are homophonic versus polyphonic, they don't fit in this particular series as examples. So, we are going to go forward to fugue today, and speak of the modulations as they arise. Since imitation and modulation are such deep subjects, I anticipate three installments on this topic.
A distinction should be made here between the idea of modulation and tonicization: A true modulation changes key for a section of the piece, while a tonicization just targets a secondary chord within a key for a fleeting moment. Therefore, almost any employment of a secondary dominant can be considered a tonicization, while a modulation is going to present some new material in a different key region, or previously heard material on a new level, and perhaps in a different modal gender. In really sophisticated music, like the songs of Schubert, for instance, the dividing line between what constitutes a modulation and what is merely a tonicization can become quite blurred, if I may be allowed the understatement.
A good composer doesn't just throw modulations into a piece willy nilly, but rather plans them out according to some logical formula of his own devising. Strict fugues actually make this process easier, as there are only the close keys - those differing by one accidental in the sharp or flat direction - to work with. Some fugues never modulate at all, in fact, as is the case with Contrapunctus I in Bach's Die Kunst Der Fuge. I dare you to call that a boring piece because it doesn't modulate. Some fugues do go to more remote keys, of course, but many of them I think ought to be strictly referred to as ricercares. Beethoven's Grosse Fugue for string quartet, for example. He subtitled it, "Sometimes researched, sometimes free," which would not have been necessary if he had just gone ahead and called it a ricercare, which implies much more freedom in that regard.
So, today's example is going to be a strict fugue I wrote for the guitar. This is far from the first fugue I ever composed, as I believe no less than five fugues preceded this one, as well as several canons and other imitative pieces. The problem I had was that I wanted to write a stately Art of Fugue kind of piece for the guitar - in miniature, of course - but there were no models for me. The kinds of subjects Bach used were fine for the keyboard, and I wrote a lot of subjects similar to his for organ and ensembles, but for the much more restrictive idiom of the guitar the were unwieldy, to say the least. Then, the subjects he used for lute and violin were too - there's no tactful way to say this - trivial, which is why his fugues for those instruments are so highly episodic. I was left then to come up with a new kind of subject that would work for the guitar, and that would have some weight to it that allowed for some interesting contrapuntal devices. I finally got the subject back in 1999, but it took seven years before the piece reached its final form. It's written on two staves, but this is a solo.
As you can see, the fugue is in A minor and the subject is 3.5 measures in length. There are no leaps in it at all, and after tonicizing the dominant degree, it just descends the scale to the tonic, where there is a brief tail figure that likewise tonicizes the tonic. The range of the subject is a minor sixth, and this is important: Subjects with wide ranges suck for the guitar. An octave is pretty much the outer limit, and that is really, really stretching it.
The answer starts in measure five, it is tonal, and it begins by tonicizing the tonic and then descends the scale. You'll note all the parallel thirds: This is idiomatic for the guitar. Because the answer starts on the tonic, it ends in a half-cadence to an implied V(6/3) in nine, which allows the final entry of the subject to begin on a highly desirable I(6/4) sonority, and the D-sharp actually momentarily creates a diminished triad sound. Looking for cool harmonic juxtapositions like this is a big part of the job of writing counterpoint, and total awareness of these details adds an element of craftsmanship to the work. Bach and Beethoven both filled their music with nifty minutiae like this, and I picked this stuff up by analyzing in detail every momentary vertical sonority in some of their works. It was a serious chore, but it was well worth it.
You'll notice that the parallel thirds are between the lower two voices this time. This is not particularly idiomatic, but as you can tell from the fingering, it isn't overly daunting to execute either.
At thirteen the first modulatory episode starts, and I just used a modified retrograde of the subject's tail figure to achieve it. Note the idiomatic parallel thirds in the top two voices. The harmony in thirteen is i, of course, and thirteen has an implied ii(d5). Then, I just modified the sequence in the bass to get the, la, ti, do, sol of the upcoming dominant region with, me, re, do, ti in the lead and the new, fa in the middle voice. This gives the V(m7) of the new key on the final eighth note, and we're there in three measures flat.
Bach was fond of lengthy episodes - especially in his younger days - and his episodes are sublimely beautiful, but my approach is far more minimalist. It's a shame the term "minimalist" has been used to describe the repetitive music of Philip Glass et al because it is really fitting of my approach. I'm interested in economy of means and expression, not lengthy perorations, and if you look at Bach's last works, he cut down on the episodic material there as well. Beethoven became almost ascetic in his spareness in some of the movements of the late string quartets, and it is from there that I take my queues.
Now that we have reached the dominant level and the key of E minor, you can see here in the first middle entries the contrapuntal device this subject is set up to exploit: Suspension chains (Or, syncopation chains, if you prefer). I modified the first counter-subject so that instead of parallel thirds, we now have a series of 4-3 suspension resolutions in measure seventeen into eighteen. I repeat this 4-3 device at twenty into twenty-one under the answer (Now on the original tonic level: Tres cool, non?), and the lowest voice on the second system is free.
In the third system I inverted the subject in the bass and have the syncopations in the lead, so we get a rising chain of 11-10's at twenty-five into twenty-six. The inverted subject leads into a half cadence in twenty-eight, so the second modulatory episode has an extra measure in it to turn us around to the tonic. Aside from a slight elaboration in the lead, this episode is the same as the previous one, so it seems to be taking us to, "the dominant of the dominant," but that would be out of bounds for a strict fugue. So...
I used the traditional deceptive motion to "modulate" to the relative of the dominant, which is perfectly legit, even in the most rigorous of fugues. See how looking for the most economical means can lead to some great ideas? I could have composed an entirely new episode and just modulated in the same old boring way, but this arrival comes as a surprise after hearing just a mildly varied form of the first episode.
Since suspension chains are this subject's raison d'etre this set of middle entries starts off with a 2-3 chain. I'm adding some sixteenth note action to build up to the third episode in the final measures, as you can see, and the second system presents the 7-6 posibilities. I present the 7-6's again over an inverted form of the subject in the third system, and the 2-3's again in inversion in the bottom system. Finally, I give a run of four sixteenths to lead to the final episode at the end of the page, and it appears from the V(m7)/I that we are going to stay in the key of G major.
Wrong! The previous D(m7) allows for another deceptive motion, this time by whole step instead of half step, and to E minor this time versus G major previously: We're back in E minor... or so it appears.
Believe it, or not, this episode is actually the original subject in augmentation. If you look at the first and last notes of every measure, you can see this clearly: I've just ornamented it with harmonic figuration and put it all over a dominant pedal, the open low E string of the guitar. As my mom would say, "That's the bee's knees!" LOL! Notice that I don't shed the F-sharp until measure fifty-three, at which point the modulation to A minor becomes apparent.
The recapitulation is a stretto, of course, but a unique one: Every voice starts out on the same pitch, which is the open high E string of the guitar, and then descends to take its place in turn.
None of this is overly difficult to play, and I ought to be performing it within the next year or so, but I just have so many pieces on the to do list. At least I can see light at the end of the tunnel now. Coming up on four years ago I was looking at a list of nearly eighty pieces and saying... well... you know. LOL! Now I have less than ten left.
Philosophically, I simply do not think that small pieces have to modulate, and for the idiom of the guitar, specifically, modulations tend to complicate things significantly. As a result, I write a lot of miniatures that don't contain any modulations at all, though they may be quite chromatic, as you will have seen if you have followed this series of posts. Another issue I have with Baroque and Classical miniatures is that the modulations are so formulaic and predictable that they border on the manneristic: "Oh, it's a major key: We're going to modulate to the dominant," or, "Oh, it's a minor key: We're going to modulate to the relative."
I knew from my years of writing popular styles and jazz that modulations weren't required to write effective music, so I didn't want to get caught on that particular strip of flypaper. However, some idiomatic pieces do actually require modulations - fugues, sonatas, preludes &c. - so I saved those things for last in my musical evolution, at least in the area of contrapuntal guitar music.
Between the E-Axis Studies and the B-Axis Studies I found another vehicle that allowed me to create a large series of pieces that did modulate, and that vehicle was the figuration prelude. I've written fourteen out of the twenty-four so far, but since they are homophonic versus polyphonic, they don't fit in this particular series as examples. So, we are going to go forward to fugue today, and speak of the modulations as they arise. Since imitation and modulation are such deep subjects, I anticipate three installments on this topic.
A distinction should be made here between the idea of modulation and tonicization: A true modulation changes key for a section of the piece, while a tonicization just targets a secondary chord within a key for a fleeting moment. Therefore, almost any employment of a secondary dominant can be considered a tonicization, while a modulation is going to present some new material in a different key region, or previously heard material on a new level, and perhaps in a different modal gender. In really sophisticated music, like the songs of Schubert, for instance, the dividing line between what constitutes a modulation and what is merely a tonicization can become quite blurred, if I may be allowed the understatement.
A good composer doesn't just throw modulations into a piece willy nilly, but rather plans them out according to some logical formula of his own devising. Strict fugues actually make this process easier, as there are only the close keys - those differing by one accidental in the sharp or flat direction - to work with. Some fugues never modulate at all, in fact, as is the case with Contrapunctus I in Bach's Die Kunst Der Fuge. I dare you to call that a boring piece because it doesn't modulate. Some fugues do go to more remote keys, of course, but many of them I think ought to be strictly referred to as ricercares. Beethoven's Grosse Fugue for string quartet, for example. He subtitled it, "Sometimes researched, sometimes free," which would not have been necessary if he had just gone ahead and called it a ricercare, which implies much more freedom in that regard.
So, today's example is going to be a strict fugue I wrote for the guitar. This is far from the first fugue I ever composed, as I believe no less than five fugues preceded this one, as well as several canons and other imitative pieces. The problem I had was that I wanted to write a stately Art of Fugue kind of piece for the guitar - in miniature, of course - but there were no models for me. The kinds of subjects Bach used were fine for the keyboard, and I wrote a lot of subjects similar to his for organ and ensembles, but for the much more restrictive idiom of the guitar the were unwieldy, to say the least. Then, the subjects he used for lute and violin were too - there's no tactful way to say this - trivial, which is why his fugues for those instruments are so highly episodic. I was left then to come up with a new kind of subject that would work for the guitar, and that would have some weight to it that allowed for some interesting contrapuntal devices. I finally got the subject back in 1999, but it took seven years before the piece reached its final form. It's written on two staves, but this is a solo.
As you can see, the fugue is in A minor and the subject is 3.5 measures in length. There are no leaps in it at all, and after tonicizing the dominant degree, it just descends the scale to the tonic, where there is a brief tail figure that likewise tonicizes the tonic. The range of the subject is a minor sixth, and this is important: Subjects with wide ranges suck for the guitar. An octave is pretty much the outer limit, and that is really, really stretching it.
The answer starts in measure five, it is tonal, and it begins by tonicizing the tonic and then descends the scale. You'll note all the parallel thirds: This is idiomatic for the guitar. Because the answer starts on the tonic, it ends in a half-cadence to an implied V(6/3) in nine, which allows the final entry of the subject to begin on a highly desirable I(6/4) sonority, and the D-sharp actually momentarily creates a diminished triad sound. Looking for cool harmonic juxtapositions like this is a big part of the job of writing counterpoint, and total awareness of these details adds an element of craftsmanship to the work. Bach and Beethoven both filled their music with nifty minutiae like this, and I picked this stuff up by analyzing in detail every momentary vertical sonority in some of their works. It was a serious chore, but it was well worth it.
You'll notice that the parallel thirds are between the lower two voices this time. This is not particularly idiomatic, but as you can tell from the fingering, it isn't overly daunting to execute either.
At thirteen the first modulatory episode starts, and I just used a modified retrograde of the subject's tail figure to achieve it. Note the idiomatic parallel thirds in the top two voices. The harmony in thirteen is i, of course, and thirteen has an implied ii(d5). Then, I just modified the sequence in the bass to get the, la, ti, do, sol of the upcoming dominant region with, me, re, do, ti in the lead and the new, fa in the middle voice. This gives the V(m7) of the new key on the final eighth note, and we're there in three measures flat.
Bach was fond of lengthy episodes - especially in his younger days - and his episodes are sublimely beautiful, but my approach is far more minimalist. It's a shame the term "minimalist" has been used to describe the repetitive music of Philip Glass et al because it is really fitting of my approach. I'm interested in economy of means and expression, not lengthy perorations, and if you look at Bach's last works, he cut down on the episodic material there as well. Beethoven became almost ascetic in his spareness in some of the movements of the late string quartets, and it is from there that I take my queues.
Now that we have reached the dominant level and the key of E minor, you can see here in the first middle entries the contrapuntal device this subject is set up to exploit: Suspension chains (Or, syncopation chains, if you prefer). I modified the first counter-subject so that instead of parallel thirds, we now have a series of 4-3 suspension resolutions in measure seventeen into eighteen. I repeat this 4-3 device at twenty into twenty-one under the answer (Now on the original tonic level: Tres cool, non?), and the lowest voice on the second system is free.
In the third system I inverted the subject in the bass and have the syncopations in the lead, so we get a rising chain of 11-10's at twenty-five into twenty-six. The inverted subject leads into a half cadence in twenty-eight, so the second modulatory episode has an extra measure in it to turn us around to the tonic. Aside from a slight elaboration in the lead, this episode is the same as the previous one, so it seems to be taking us to, "the dominant of the dominant," but that would be out of bounds for a strict fugue. So...
I used the traditional deceptive motion to "modulate" to the relative of the dominant, which is perfectly legit, even in the most rigorous of fugues. See how looking for the most economical means can lead to some great ideas? I could have composed an entirely new episode and just modulated in the same old boring way, but this arrival comes as a surprise after hearing just a mildly varied form of the first episode.
Since suspension chains are this subject's raison d'etre this set of middle entries starts off with a 2-3 chain. I'm adding some sixteenth note action to build up to the third episode in the final measures, as you can see, and the second system presents the 7-6 posibilities. I present the 7-6's again over an inverted form of the subject in the third system, and the 2-3's again in inversion in the bottom system. Finally, I give a run of four sixteenths to lead to the final episode at the end of the page, and it appears from the V(m7)/I that we are going to stay in the key of G major.
Wrong! The previous D(m7) allows for another deceptive motion, this time by whole step instead of half step, and to E minor this time versus G major previously: We're back in E minor... or so it appears.
Believe it, or not, this episode is actually the original subject in augmentation. If you look at the first and last notes of every measure, you can see this clearly: I've just ornamented it with harmonic figuration and put it all over a dominant pedal, the open low E string of the guitar. As my mom would say, "That's the bee's knees!" LOL! Notice that I don't shed the F-sharp until measure fifty-three, at which point the modulation to A minor becomes apparent.
The recapitulation is a stretto, of course, but a unique one: Every voice starts out on the same pitch, which is the open high E string of the guitar, and then descends to take its place in turn.
None of this is overly difficult to play, and I ought to be performing it within the next year or so, but I just have so many pieces on the to do list. At least I can see light at the end of the tunnel now. Coming up on four years ago I was looking at a list of nearly eighty pieces and saying... well... you know. LOL! Now I have less than ten left.
posted by Hucbald at 8:27 PM
2 Comments:
The harmony in thirteen is i, of course, and thirteen has an implied ii(d5).
Small correction: You mean of course that the implied ii(d5) is in measure fourteen, not thirteen.
Great articles! I've enjoyed reading them immensely.
Good catch!
I really appreciate your comment. Most of these posts are done to keep my analytical juices flowing, but it's very nice to hear that someone else appreciates them.
Are you the reader from Bethesda I see in the Sitemeter stats? I used to live in Adelphi, and I hung out at Uncle Jed's Roadhouse quite a bit.
Cheers,
George
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