How to Compose Counterpoint (Using Three Voices)
I briefly considered re-titling this series, "How to Compose Counterpoint for Guitar," but the examples thus far will work for keyboard as well, so I decided against it. I'm sure guitarists will find these posts if they search that term anyway.
We started with Where to Begin using a microscopically small ternary miniature in two voices as an example, then we learned How to Progress through a series of small pieces adding implied secondary dominants, augmented sixths, and whatnot, next came Using Larger Forms, in which I gave an example of a compound ternary Scherzo, but everything thus far has been in two voices, so now we're ready for three.
One of the fortunate things about being a composer of counterpoint for the guitar is that two-voice counterpoint is completely idiomatic for the instrument. On the keyboard, two-part polyphony sounds rather naked and spare - incomplete even - but on the guitar it is completely full and satisfying. Unfortunately, however, three contrapuntal voices on the guitar compounds the technical execution significantly, and restrictive idiomatic concerns can become nightmarish. As a result, I was writing my first three-voice pieces for organ and trio ensembles long before I tried it on the guitar.
In order to crack that particular cosmic egg, I had to come up with at least a quasi-idiomatic approach to three voices on the guitar, and it finally happened with one of the last G-Axis Studies that I wrote, G-Axis Study No. 3 in E-flat Major. While any of the eighteen Axial Studies could be considered incipient three-part counterpoint due to the repeated zero axes, for the sake of this series of posts, we'll leave the repeated notes out of our calculations in that regard.
This then, is the first fruits of three-voice polyphony that I came up with for the guitar.
Obviously, three flats is a very, very uncommon key for guitar music, and I learned something valuable about that issue as well: The zero axis of G is the major third of the tonic E-flat major triad here, so this really shouldn't be such a daunting key. I also ended up with pieces in C minor and G minor in this series - where the open G string is functioning as the fifth and the tonic of the keys, respectively - so there are a lot more nice possibilities for flat keys than most composers of guitar music have heretofore realized. Guitar recitals get boring to me very fast because the vast preponderance of traditional guitar literature is in the same old, boring, predictable keys.
Next, you'll notice that this particular Axial Study does not have an interlude between the A and B sections - it is the only one of the eighteen so configured - and so the form is a much more normative, A, A', B, A, A', B, A''. This texture is inherently much more interesting, so it just wasn't required to have the interlude.
Since, in these G-Axis Studies, the zero axis is not bound to the melodic trajectories as was the case with the E-Axis Studies and B-Axis Studies - and since there are two strings above the G to work with here - I was able to start the piece off with the simple idea of just doubling the melodic trajectory in thirds. This is quite idiomatic to the guitar.
The three measures of the top system create a simple, I, vii(d5), vi(m7) progression that is really just the result of contrary contrapuntal motion, but in measure four we arrive at a ii chord with M9 and P11 suspensions, which gave me the opportunity to create a V(m7)/V in the second half of that measure. After the V triad at the beginning of measure five, then, I was able to create a V(m7) targeting the tonic using a major ninth as a lower neighbor to the third, and then after the tonic triad (diad, actually) I was able to create a V(m7)/IV at the ned of measure six using the same major ninth as lower neighbor device, only this time in the top voice.
At the beginning of the third system, the IV chord is also a diad, and it becomes a V(4/2)/I in the second half of measure seven, which then "resolves" to a I(6/4) sonority before I introduce the tritone to make it the V(m7)/I which leads to the repeat of the A section. The second ending just creates a triad on the dominant degree to lead into B.
You'll notice I had to let the bass rest in measures five and seven. This is simply the result of it being physically impossible to hold them there due to the idiom: The bass notes remain implied. This is a very pretty A section, and it has a logical inevitability to it that suggests that it has existed forever; it was just left to me to discover it.
I reduced the number of essential voices to two for the first measure of the B section, so this piece has an element of "free-voiced-ness" to it: Later I'll use four essential voices for the climax. Measure eleven begins with a ii(6/4) sonority which becomes the traditional French Augmented Sixth in the second half. I call this chord a V(4/3/b)/V, of course. measure twelve gives us the major triad on the dominant degree, and then I sequentially repeat the formula starting on a iii(6/4) triad in measure thirteen. The resulting "French Sounding" sonority is this time a V(4/3/b)/vi, which gives an indication of how ridiculous the traditional nomenclature for these chords is: They are just altered secondary dominants.
After the measure of vi in fourteen, I repeat the sequence yet a third time, only now, since it is the third time, I vary the formula: The bass rises a third this time, and the chromatic alteration of the A from A-flat to A-natural makes the chord a II, which you can think of as a modal interchange from the Lydian mode. As for myself, I was just shooting for the V(4/3/b)/I that appears in the second half of the measure (Or, the French Augmented Sixth of One, if you still need to think of it that way).
At sixteen we get the expected measure of the tonic triad, and then I retain the E-flat as a pedal point for the next two measures, which are the climax of the piece. The sonority at the beginning of measure seventeen is actually a ii(4/2) in fully open position. What does fully open mean? The chord spelling reads precisely from top to bottom: F, A-flat, C, and E-flat. This is way gnarly! In the second half of seventeen, that sonority becomes a doubly-augmented fourth augmented sixth, which is a V(A4/3/b)/I (Over a tonic pedal) in my modern terminology, and that resolves to a root position tonic triad. This would have been a I(6/4) chord, as expected, if not for the tonic pedal point: See why I used that device? I didn't want to have to "resolve" a 6/4 sonority into a dominant harmony here, I wanted the tonic to be a fully resolved arrival. I wonder if any other composer has ever done this. I can't recall ever seeing it before, but the literature is vast.
Measure nineteen has a m6-d5 over the A-natural for a V(6/5)/V effect - and I again reduce to two voices - then, measure twenty consists of a V to vi deceptive motion, which leads to the fully diminished vii in second inversion (vii(6/d5)), which functions as a ii(d5) in the second half of that measure, and then we get the V(m7)/I in twenty-two to return us to the A section.
There is no variation in the repeats, and the A'' prime section just has a new and final ending where the zero axis G raises to A-flat to make the final dominant seventh resolution to a close position E-flat triad possible.
The climax of this piece is very, very difficult to execute. In fact, it is nearly impossible on a standard non-cutaway classical guitar, but it is manageable for a virtuoso... which I'm not. LOL! This is one of the reasons I don't play non-cutaway guitars anymore. So much of what I write is real, actual guitar music versus lute (or whatever) transcriptions, so I use the entire range of the thing. This was one of the last pieces that I re-memorized, so it's not quite in my set yet - I've been working on it for about a year - but it is close. One thing for sure, and that is that this is quite an interesting guitar piece.
We started with Where to Begin using a microscopically small ternary miniature in two voices as an example, then we learned How to Progress through a series of small pieces adding implied secondary dominants, augmented sixths, and whatnot, next came Using Larger Forms, in which I gave an example of a compound ternary Scherzo, but everything thus far has been in two voices, so now we're ready for three.
One of the fortunate things about being a composer of counterpoint for the guitar is that two-voice counterpoint is completely idiomatic for the instrument. On the keyboard, two-part polyphony sounds rather naked and spare - incomplete even - but on the guitar it is completely full and satisfying. Unfortunately, however, three contrapuntal voices on the guitar compounds the technical execution significantly, and restrictive idiomatic concerns can become nightmarish. As a result, I was writing my first three-voice pieces for organ and trio ensembles long before I tried it on the guitar.
In order to crack that particular cosmic egg, I had to come up with at least a quasi-idiomatic approach to three voices on the guitar, and it finally happened with one of the last G-Axis Studies that I wrote, G-Axis Study No. 3 in E-flat Major. While any of the eighteen Axial Studies could be considered incipient three-part counterpoint due to the repeated zero axes, for the sake of this series of posts, we'll leave the repeated notes out of our calculations in that regard.
This then, is the first fruits of three-voice polyphony that I came up with for the guitar.
Obviously, three flats is a very, very uncommon key for guitar music, and I learned something valuable about that issue as well: The zero axis of G is the major third of the tonic E-flat major triad here, so this really shouldn't be such a daunting key. I also ended up with pieces in C minor and G minor in this series - where the open G string is functioning as the fifth and the tonic of the keys, respectively - so there are a lot more nice possibilities for flat keys than most composers of guitar music have heretofore realized. Guitar recitals get boring to me very fast because the vast preponderance of traditional guitar literature is in the same old, boring, predictable keys.
Next, you'll notice that this particular Axial Study does not have an interlude between the A and B sections - it is the only one of the eighteen so configured - and so the form is a much more normative, A, A', B, A, A', B, A''. This texture is inherently much more interesting, so it just wasn't required to have the interlude.
Since, in these G-Axis Studies, the zero axis is not bound to the melodic trajectories as was the case with the E-Axis Studies and B-Axis Studies - and since there are two strings above the G to work with here - I was able to start the piece off with the simple idea of just doubling the melodic trajectory in thirds. This is quite idiomatic to the guitar.
The three measures of the top system create a simple, I, vii(d5), vi(m7) progression that is really just the result of contrary contrapuntal motion, but in measure four we arrive at a ii chord with M9 and P11 suspensions, which gave me the opportunity to create a V(m7)/V in the second half of that measure. After the V triad at the beginning of measure five, then, I was able to create a V(m7) targeting the tonic using a major ninth as a lower neighbor to the third, and then after the tonic triad (diad, actually) I was able to create a V(m7)/IV at the ned of measure six using the same major ninth as lower neighbor device, only this time in the top voice.
At the beginning of the third system, the IV chord is also a diad, and it becomes a V(4/2)/I in the second half of measure seven, which then "resolves" to a I(6/4) sonority before I introduce the tritone to make it the V(m7)/I which leads to the repeat of the A section. The second ending just creates a triad on the dominant degree to lead into B.
You'll notice I had to let the bass rest in measures five and seven. This is simply the result of it being physically impossible to hold them there due to the idiom: The bass notes remain implied. This is a very pretty A section, and it has a logical inevitability to it that suggests that it has existed forever; it was just left to me to discover it.
I reduced the number of essential voices to two for the first measure of the B section, so this piece has an element of "free-voiced-ness" to it: Later I'll use four essential voices for the climax. Measure eleven begins with a ii(6/4) sonority which becomes the traditional French Augmented Sixth in the second half. I call this chord a V(4/3/b)/V, of course. measure twelve gives us the major triad on the dominant degree, and then I sequentially repeat the formula starting on a iii(6/4) triad in measure thirteen. The resulting "French Sounding" sonority is this time a V(4/3/b)/vi, which gives an indication of how ridiculous the traditional nomenclature for these chords is: They are just altered secondary dominants.
After the measure of vi in fourteen, I repeat the sequence yet a third time, only now, since it is the third time, I vary the formula: The bass rises a third this time, and the chromatic alteration of the A from A-flat to A-natural makes the chord a II, which you can think of as a modal interchange from the Lydian mode. As for myself, I was just shooting for the V(4/3/b)/I that appears in the second half of the measure (Or, the French Augmented Sixth of One, if you still need to think of it that way).
At sixteen we get the expected measure of the tonic triad, and then I retain the E-flat as a pedal point for the next two measures, which are the climax of the piece. The sonority at the beginning of measure seventeen is actually a ii(4/2) in fully open position. What does fully open mean? The chord spelling reads precisely from top to bottom: F, A-flat, C, and E-flat. This is way gnarly! In the second half of seventeen, that sonority becomes a doubly-augmented fourth augmented sixth, which is a V(A4/3/b)/I (Over a tonic pedal) in my modern terminology, and that resolves to a root position tonic triad. This would have been a I(6/4) chord, as expected, if not for the tonic pedal point: See why I used that device? I didn't want to have to "resolve" a 6/4 sonority into a dominant harmony here, I wanted the tonic to be a fully resolved arrival. I wonder if any other composer has ever done this. I can't recall ever seeing it before, but the literature is vast.
Measure nineteen has a m6-d5 over the A-natural for a V(6/5)/V effect - and I again reduce to two voices - then, measure twenty consists of a V to vi deceptive motion, which leads to the fully diminished vii in second inversion (vii(6/d5)), which functions as a ii(d5) in the second half of that measure, and then we get the V(m7)/I in twenty-two to return us to the A section.
There is no variation in the repeats, and the A'' prime section just has a new and final ending where the zero axis G raises to A-flat to make the final dominant seventh resolution to a close position E-flat triad possible.
The climax of this piece is very, very difficult to execute. In fact, it is nearly impossible on a standard non-cutaway classical guitar, but it is manageable for a virtuoso... which I'm not. LOL! This is one of the reasons I don't play non-cutaway guitars anymore. So much of what I write is real, actual guitar music versus lute (or whatever) transcriptions, so I use the entire range of the thing. This was one of the last pieces that I re-memorized, so it's not quite in my set yet - I've been working on it for about a year - but it is close. One thing for sure, and that is that this is quite an interesting guitar piece.
posted by Hucbald at 10:27 PM
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