Writing Fugue Subjects as Canons II
The last time I posted on this topic I took the readers through the process I used to write the fugue subject for my string quartet. I posted all of the stages there, so I won't go through it all again, as it is actually quite a mechanically simple process.
That subject and its canonic stretto are at the octave, of course, but it has occured to me that a subject and an answer - either tonal or real - could be composed as a double canon. So, that is what I did here, choosing to use a tonal version of the answer.
Since my Fuga da Camera series progresses through all of the traditional chamber ensembles - string trio, wind trio, string quartet, wind quartet, string choir, wind choir, and chamber orchestra - I decided to replace the Irreducible Fugue that has been the wind quartet piece with a full-blown fugue to better balance with the magnum opus-sized string quartet fugue. The two subjects even share some of the same flavor now, and I'm tickled pink with this one.
As you can see, I used do to sol to open up the subject, so that was naturally answered tonally by sol to do. Under the sol-do progression ti to le was a natural, which yeilded fi to me in the second bar of the answer. Here's where it gets weird, as the second statement of the subject is entering at this point in the bass voice: The resulting interval is a tritone, which implies a V(4/2)/V. I really, really like this effect though, so I not only allowed for it, I actually accented it with a doubled "seventh" in the interior voice, which then progresses to the root of the sonority.
At this point, the resolution of the V/V is interrupted by an implied I(6/4) in the second half of the measure, which then finally resolves to the primary dominant acrtoss the bar line. This is a really neat effect.
The root of the dominant in measure four is trippled, which is kind of uncomon in harmony, but is no big deal in counterpoint. But it's what happens in the second half of that measure that is so interesting to me: There is a severe dissonance on the downbeat - which is not mitigated one iota by the rest in the tenor voice - that has the tonic, the leading tone, the dominant, and the natural submediant degree all competing with each other. It does not resolve to the deceptive motion at the submediant sonority until the final eighth note in the alto voice, and then only very briefly in a highly syncopated rhythmic environment. I like this kind of slippery harmony in countrapuntal textures because it adds so much color and interest.
Across the bar line into measure five we get the V(4/2)/V again, and I was thrilled to discover I could continue the dotted-eighth/sixteenth rhythm into a descending chromatic tetrachord at that point. Of course, this produced another chromatic descending tetrachord in the answer at sol, fi, fa, mi, me, re and this is where I had to make just one adjustment that broke the canon a single quarter note early: Me has to progress up to fa at the end of measure six to avoid a forbidden parallel, but it sets up the final cadences perfectly.
Baroque and probably even classical-era composers probably would not have allowed for so much unprepared ("Under Prepared"?) harmonic dissonance, but I have not broken any countrapuntal laws here, only some stylistic rules.
Remember, Counterpoint can be reduced to a single law: "Only imperfect consonances can proceed in stepwise parallel motion." All else are just rules that describe style, and therefore taste. I like how the dissonance accumulates during the first half of this phrase, and then abates gradually to a beautiful cadence at the end. And remember, this is the conclusion of the fugue, so the listener will be very familiar with the materials by this point, so it ought not be too jarring.
Another image from the golden era of commercial aviation.
That subject and its canonic stretto are at the octave, of course, but it has occured to me that a subject and an answer - either tonal or real - could be composed as a double canon. So, that is what I did here, choosing to use a tonal version of the answer.
Since my Fuga da Camera series progresses through all of the traditional chamber ensembles - string trio, wind trio, string quartet, wind quartet, string choir, wind choir, and chamber orchestra - I decided to replace the Irreducible Fugue that has been the wind quartet piece with a full-blown fugue to better balance with the magnum opus-sized string quartet fugue. The two subjects even share some of the same flavor now, and I'm tickled pink with this one.
As you can see, I used do to sol to open up the subject, so that was naturally answered tonally by sol to do. Under the sol-do progression ti to le was a natural, which yeilded fi to me in the second bar of the answer. Here's where it gets weird, as the second statement of the subject is entering at this point in the bass voice: The resulting interval is a tritone, which implies a V(4/2)/V. I really, really like this effect though, so I not only allowed for it, I actually accented it with a doubled "seventh" in the interior voice, which then progresses to the root of the sonority.
At this point, the resolution of the V/V is interrupted by an implied I(6/4) in the second half of the measure, which then finally resolves to the primary dominant acrtoss the bar line. This is a really neat effect.
The root of the dominant in measure four is trippled, which is kind of uncomon in harmony, but is no big deal in counterpoint. But it's what happens in the second half of that measure that is so interesting to me: There is a severe dissonance on the downbeat - which is not mitigated one iota by the rest in the tenor voice - that has the tonic, the leading tone, the dominant, and the natural submediant degree all competing with each other. It does not resolve to the deceptive motion at the submediant sonority until the final eighth note in the alto voice, and then only very briefly in a highly syncopated rhythmic environment. I like this kind of slippery harmony in countrapuntal textures because it adds so much color and interest.
Across the bar line into measure five we get the V(4/2)/V again, and I was thrilled to discover I could continue the dotted-eighth/sixteenth rhythm into a descending chromatic tetrachord at that point. Of course, this produced another chromatic descending tetrachord in the answer at sol, fi, fa, mi, me, re and this is where I had to make just one adjustment that broke the canon a single quarter note early: Me has to progress up to fa at the end of measure six to avoid a forbidden parallel, but it sets up the final cadences perfectly.
Baroque and probably even classical-era composers probably would not have allowed for so much unprepared ("Under Prepared"?) harmonic dissonance, but I have not broken any countrapuntal laws here, only some stylistic rules.
Remember, Counterpoint can be reduced to a single law: "Only imperfect consonances can proceed in stepwise parallel motion." All else are just rules that describe style, and therefore taste. I like how the dissonance accumulates during the first half of this phrase, and then abates gradually to a beautiful cadence at the end. And remember, this is the conclusion of the fugue, so the listener will be very familiar with the materials by this point, so it ought not be too jarring.
Another image from the golden era of commercial aviation.
posted by Hucbald at 12:27 PM
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