Dovetailing Harmonic Canons
Over the course of the las few posts, as I have presented all of the secondary dominant function harmonies - secondary dominant triads, secondary dominant sevenths, secondary diminished sevenths, secondary dominant seventh minor ninths, secondary dominant seventh diminished fifths, secondary augmented triads, secondary augmented sevenths, and substitute secondary dominants - I have given a few examples of harmonic canons. As I had hoped, these efforts have coalesced into a greater understanding of this technological approach, and have enabled me to develop a methodology for creating Dovetailing Harmonic Canons, which I am now prepared to present. Since I have not given an example of a Triadic Harmonic Canon to this point, we will start there.
In the above series of examples we return to the progression I initially employed to demonstrate secondary dominant seventh chords, and with which I composed an accompanied Harmonic Double Canon. The top staff shows the diatonic triadic transformations over a constant root bass.
Though the progression does not sound inherantly canonic in this form, the diatonic framework for the canon is nonetheless present, simply awaiting the composer's attentions to bring it out. This diatonic canon is extracted on the second staff, and all that needs to be done to make it a strict canon is to create minor triads over the dominant and tonic degrees in measures six and seven of that example by employing B-flat and E-flat respectively.
The third stave presents the canon with that aforementioned modification in conjunction with chromatically introduced leading tones for a series of secondary dominant triads. At this point, the canonic nature of the upper stratum becomes easily perceivable to the astute listener. I also introduced a secondary diminsihed seventh in the final cadence figuration - the vii d7/V - to smooth out the voice leading and also to show how these sonorities are employed in this two-strata texture: The texture changes from three real parts to four momentarily to introduce and resolve the secondary diminished seventh, and then it goes back to triads over a constant root bass line.
On the fourth staff, secondary augmented triads are introduced. Note that since the target chords are of the minor gender, the augmented fifth is notated enharmonically as a minor sixth and is tied across the barline to become the minor third of that target chord. I also introduced a dominant seventh on the final quarter note to demonstrate that there is the oportunity to change to a tetradic texture in the upper stratum at this point. Introducing the seventh in a new voice while tying the root over to become the fifth of the target chord will start a series of crosswise transformations and is a highly effective technique.
Then, on the fifth staff from the top, I have changed the canon to 3/4 time to get a surface rhythm of constant quarter notes, and have also introduced a modulation to the relative minor with a second secondary diminished seventh at the end just to point out that it is there.
As nice as that example is, a much more artful way to introduce the canonic elements is one-by-one with a Dovetail device, as I have demonstrated in the final example of the progression. Since the canonic voice is three measures long, the first time through is the diatonic version, then the leader introduces the raised leading tone figure at the first repeat of the canonic element and the followers continue with that in strict canon, and finally the leader introduces the enharmonic secondary augmented triad's minor sixth for the third repeat of the canonic figure, and it too is copied in strict canon by the following voices: The strictness of the canon is never compromised. Note that because of the length of the canonic voice, the progression's series of falling perfect fifths/rising perfect fourths must be extended all the way to B-flat to give the third and final following voice the oportunity to fully participate in the canon. This increasing distance from the original tonic coupled with the piling up of increasingly dissonant secondary dominant sonorities creates a highly effective and highly charged canon, despite the simplicity of it on it's face. It also presented me with the oportunity to use a very Medieval-sounding cadence to return to the tonic that is quite tasty in this context (The mediant degree is lowered and minor, the subdominant degree is a dominant seventh with no fifth, and the dominant seventh is missing it's leading tone, which combine to create a hollow and primitive sounding cadential figure).
The same proceedure can be followed with a tetradic upper stratum of seventh chords, as I have demonstrated before, and have recapitulated above. In this instance, since all the transformations are crosswise or delayed/interrupted crosswise transformations, all four of the voices do not share all og the canonic elements, rather a Harmonic Double Canon is created with two voice pairs.
After the top stave's transformation blueprint, I have extracted the diatonic canonic framework beneath. Again, just change the seventh chords on the dominant and tonic degrees to minor sevenths with B-flat and E-flat respectively (And in combination for the tonic degree), and the canon is strict.
Secondary dominant sevenths are introduced on the third staff, and the French Sixth-derived V7(d5)'s dress up the lower canonic voices in the penultimate example.
In the final Dovetailing example, I used the delayed or interrupted crosswise transformation pattern associated with the secondary dominant example to begin the canon, but without the chromatically introduced leading tones, because the original diatonic canonic figure was so bland. The canonic elements are only two measures long since this is a double canon, so I didn't have to lengthen the progression. In fact, it could be shortened by a measure and all four of the voices would still have had the oportunity to fully participate in the canon, and that could have been even more effective. However, I wanted to demonstrate how a secondary V7(m9)/V could take the place of the vii(d7)/V I used in the triadic examples to achieve a similar effect in this virtual five-voice texture.
What these harmonic canon sketches remind me of when I listen to them (And, they are just sketches at this point, and require more levels of ornamentation to be employable in actual musical compositions), are some of the sketches of M.C. Escher that smoothly transform one element into another in a seamlessly logical way. In fact, this dovetailing harmonic canon technique is the exact musical equivalent of that visual art technique.
In the following posts I plan to present harmonic canons with two, three, and four different root progression types in their repeating patterns to further explore this idiom.
In the above series of examples we return to the progression I initially employed to demonstrate secondary dominant seventh chords, and with which I composed an accompanied Harmonic Double Canon. The top staff shows the diatonic triadic transformations over a constant root bass.
Though the progression does not sound inherantly canonic in this form, the diatonic framework for the canon is nonetheless present, simply awaiting the composer's attentions to bring it out. This diatonic canon is extracted on the second staff, and all that needs to be done to make it a strict canon is to create minor triads over the dominant and tonic degrees in measures six and seven of that example by employing B-flat and E-flat respectively.
The third stave presents the canon with that aforementioned modification in conjunction with chromatically introduced leading tones for a series of secondary dominant triads. At this point, the canonic nature of the upper stratum becomes easily perceivable to the astute listener. I also introduced a secondary diminsihed seventh in the final cadence figuration - the vii d7/V - to smooth out the voice leading and also to show how these sonorities are employed in this two-strata texture: The texture changes from three real parts to four momentarily to introduce and resolve the secondary diminished seventh, and then it goes back to triads over a constant root bass line.
On the fourth staff, secondary augmented triads are introduced. Note that since the target chords are of the minor gender, the augmented fifth is notated enharmonically as a minor sixth and is tied across the barline to become the minor third of that target chord. I also introduced a dominant seventh on the final quarter note to demonstrate that there is the oportunity to change to a tetradic texture in the upper stratum at this point. Introducing the seventh in a new voice while tying the root over to become the fifth of the target chord will start a series of crosswise transformations and is a highly effective technique.
Then, on the fifth staff from the top, I have changed the canon to 3/4 time to get a surface rhythm of constant quarter notes, and have also introduced a modulation to the relative minor with a second secondary diminished seventh at the end just to point out that it is there.
As nice as that example is, a much more artful way to introduce the canonic elements is one-by-one with a Dovetail device, as I have demonstrated in the final example of the progression. Since the canonic voice is three measures long, the first time through is the diatonic version, then the leader introduces the raised leading tone figure at the first repeat of the canonic element and the followers continue with that in strict canon, and finally the leader introduces the enharmonic secondary augmented triad's minor sixth for the third repeat of the canonic figure, and it too is copied in strict canon by the following voices: The strictness of the canon is never compromised. Note that because of the length of the canonic voice, the progression's series of falling perfect fifths/rising perfect fourths must be extended all the way to B-flat to give the third and final following voice the oportunity to fully participate in the canon. This increasing distance from the original tonic coupled with the piling up of increasingly dissonant secondary dominant sonorities creates a highly effective and highly charged canon, despite the simplicity of it on it's face. It also presented me with the oportunity to use a very Medieval-sounding cadence to return to the tonic that is quite tasty in this context (The mediant degree is lowered and minor, the subdominant degree is a dominant seventh with no fifth, and the dominant seventh is missing it's leading tone, which combine to create a hollow and primitive sounding cadential figure).
The same proceedure can be followed with a tetradic upper stratum of seventh chords, as I have demonstrated before, and have recapitulated above. In this instance, since all the transformations are crosswise or delayed/interrupted crosswise transformations, all four of the voices do not share all og the canonic elements, rather a Harmonic Double Canon is created with two voice pairs.
After the top stave's transformation blueprint, I have extracted the diatonic canonic framework beneath. Again, just change the seventh chords on the dominant and tonic degrees to minor sevenths with B-flat and E-flat respectively (And in combination for the tonic degree), and the canon is strict.
Secondary dominant sevenths are introduced on the third staff, and the French Sixth-derived V7(d5)'s dress up the lower canonic voices in the penultimate example.
In the final Dovetailing example, I used the delayed or interrupted crosswise transformation pattern associated with the secondary dominant example to begin the canon, but without the chromatically introduced leading tones, because the original diatonic canonic figure was so bland. The canonic elements are only two measures long since this is a double canon, so I didn't have to lengthen the progression. In fact, it could be shortened by a measure and all four of the voices would still have had the oportunity to fully participate in the canon, and that could have been even more effective. However, I wanted to demonstrate how a secondary V7(m9)/V could take the place of the vii(d7)/V I used in the triadic examples to achieve a similar effect in this virtual five-voice texture.
What these harmonic canon sketches remind me of when I listen to them (And, they are just sketches at this point, and require more levels of ornamentation to be employable in actual musical compositions), are some of the sketches of M.C. Escher that smoothly transform one element into another in a seamlessly logical way. In fact, this dovetailing harmonic canon technique is the exact musical equivalent of that visual art technique.
In the following posts I plan to present harmonic canons with two, three, and four different root progression types in their repeating patterns to further explore this idiom.
posted by Hucbald at 5:00 AM
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