Composition Exercise One
You were probably expecting that the first composition exercise demonstrated here would have been a contrapuntal exercise, since I have spent so much time on that subject. So did I. However, I started writing a series of arpeggio studies for the guitar this month, and this morning over coffee I wrote the second in the series using the progression I analyzed in the Mechanics of Harmony post, so I decided to cover creating simple musical continuities out of harmonic progressions first.
It would be a good idea to review that previous post before continuing here.
As you can see, I started with a simple eight bar diatonic progression that uses all seven diatonic chords and that also has every type of diatonic root progression except for the TriTone as Retrogressive arrangement. The TriTone as Progressive root progression from the IV to the vii diminished divides the original progression into two halves that are mirror images of each other with respect to the root progression patterns: Where there is a Retrogression in the first four measures, there is a Progression in the second four; where there is a Strong Ascending progression in the first phrase, there is a Strong Decending in the second; the Mild Decending movement of the first section is answered by a Mild Ascending motion in the second. The only variation is that at the end of the second phrase there is a Strong Ascending progression from the IV to the V to turn the phrase around on itself. This two chord per bar harmonic rhythm will only appear three times and in this exact same form each time during the piece.
For the second eight bars, I isolated the root progression pattern of the first four bars of the original progression and repeated it in sequence still using the TriTone as Progressive root motion to link the to phrases of the progression. This creates an unusual non-dominant direct modulation to the parallel key a semitone below the tonic, but the previously established pattern makes it work seamlessly. I also changed the gender of the first phrase, making it in the tonic minor key, and I kept with that idea and have the second phrase in minor as well. The idea with this phrase, and the subsequent phrases not on the tonic, was to choose between major or minor by selecting the key closest to the original tonic of A major. So by that logic, G-sharp minor would be closer to A major than A-flat major would.
Just as there is a V to I Progressive root progression at the end of the original phrase, there is a similar progression at the end of the second eight bars. However, the one chord per bar harmonic rhythm is maintained throughout.
For the third phrase, I isolated the root progression pattern from the second four bars of the original progression and have it arranged as a mirror image of the second eight bar progression. It too sequences a semitone, but a semitone up versus the previous phrase's semitone down. It is also divided in half by a TriTone root progression, but this time the sole unused TriTone as Retrogressive form is employed, and so the list of possible diatonic root progressions is completed. Far from being a minor detail, this is a major structural point. I continued the first phrase of the third eight bar progression in the minor mode, but changed back to major for the last four bars of the third progression due to G major being closer to A major than G minor with all it's flats.
The modulation back to A major from G major is made exceedingly smooth by the last two bars having chords shared by both keys. I am actually quite delighted with the effect it has: The last two bars of the final eight bar phrase are in fact identical to the last two bars of the original progression, and here we have the second instance of the two chord per measure harmonic rhythm.
The final eight bars are an exact repeat of the original progression with a final two measures of tonic harmony at the end.
I used Schillinger's concept of Circular Transformation with only some minor adornments to arrange the top three voices of the piece: on the diatonic vii diminished triad I added a diminished seventh to give it the more dramatic color I wanted after the TriTone progression, and also to set up the later adornments in the same places in the third eight bar phrase. In measure 17 I use the same figure to get the sound of a minor triad with a major seventh, and in measure 21 I use the sound of a major triad with an added major seventh. These are only adornments and do not affect the purely triadic Circular Transformations of the top three voices in any way.
The bass voice is a slightly adorned Constant Root: Adding a constant root bass line to a properly transforming triadic or seventh chord progression will never result in forbidden parallels. This is a simple example of Schillinger's concept of Strata: The transforming triads in the upper three voices are one stratum, and the constant root bass line is another. You could concievably - and easily - have a third stratum of triads transforming opposite of their natural inclinations and still have no forbidden parallels with the resulting seven voices. Where there are Mild Decending or Mild Ascending root motions, I decorated the bass line with a passing seventh or a ninth in the bass respectively. Since I'm not using seventh or ninth chords, there is no danger of forbidden parallels with this embellishment. This relatively insignificant looking figure adds an unexpectedly large amount of dimension and depth to the resulting progressions in inverse proportion to it's appearance on the page.
Once I had all of these elements constructed in a whole note/half note voice leading sketch in C major, I selected the key in which it would fit most comfortably on the guitar. Since I do not want any open strings in the fingerings (So the piece can be moved to several pitch levels depending on what my performance set needs at any given time), the low note of F would have given A-flat major, but A major is a much more common guitar key, and it's easier to read with only three sharps as well, so that's where I put it.
Lineal Study No. 1 is in G major, 4/4 time, and has the simplest possible texture of straight eighth notes, so I wanted this one to be in a different time signature and with a small added element of rhythm to it since the overall finished set of Lineal Studies is to be roughly progressive in terms of complexity and technical difficulty (I'm planning six to twelve of these little ditties). So, after I decided on 6/8 time I decided to use the rhythmic resultant of the interval of a perfect fourth, or the ratio of 4:3 (If you look back to the Relativity of Pitch to Tempo & Harmony to Rhythm post, you can see how these resultants of interference are worked out). I chose that because there is a compound tripple meter with four bar phrases, so it's a logical aspect of the composition as a whole. That resultant is 3+1+2+2+1+3, so I took the first half and decorated the first three eighth notes of every measure with it (3x1/16ths+1x1/16th+2x1/16ths), keeping the second group of three as the smaller term 3 but diminuted to the middle sized term of the resultant (An overblown way to say I left them straight eighth notes). I didn't use the second half of the resultant until the penultimate measure of tonic harmony, where combined with a slight ritardando it makes for a spectacularly effective close, despite the direct simplicity of the employment of it that I chose.
It is important to realize that there are many other possible permutations of this original progression available if you change the TriTone dividing progression to other forms, and with repeat schemes &c. this could have been made into an art song, or a movement for a chamber ensemble, or even a symphonic movement. I'm a guitarist and have no ensembles available to me, so I'm writing things that I can play and perform: MIDI renditions of larger stuff is only fun for so long for me. I want to play and perform the music that I write. Single line passages are also one of my technical weak spots, and I have neither the time nor the patience to work on scales and arpeggios, so these pieces will also serve a utilitarian purpose.
One final point: Different root progressions make the triadic voices move in different directions, either upward or downward. Strong Ascending progressions move the voices down, while Strong Decending progressions move the vioces up. Mild Ascending progressions also move the voices down while Mild Decending progressions move them up. And Retrogressions move the voices down, and Progressions move them up. Finally, TriTones move the voices up if they are in an as Progressive arrangement, or down if they are in an as Retrogressive relationship. Knowing this allows you to control where you want to have your voices move, and obviously an unbalanced progression can get you into trouble with ranges if you don't know what you're doing.
Now, the direction that voices move with seventh chords is an entirely different matter, and I'll wait to cover that until later, but you can certainly do some experiments and find that out for yourselves.
Even in small pieces with a modest scope - such as these Lineal Studies which are a minute or less in total playing time - it is not only possible but also highly desirable to construct them with a high degree of craftsmanship. By adhering to this philosophy of structural perfectionism and adding the necessary elements of inspired variety and detail, the resulting miniatures have a high degree of musicality. I always encourage my students to write many, many miniatures as this is the most effective way to master and develop the proceedures necessary to tackle continuities with a broader scope.
It would be a good idea to review that previous post before continuing here.
As you can see, I started with a simple eight bar diatonic progression that uses all seven diatonic chords and that also has every type of diatonic root progression except for the TriTone as Retrogressive arrangement. The TriTone as Progressive root progression from the IV to the vii diminished divides the original progression into two halves that are mirror images of each other with respect to the root progression patterns: Where there is a Retrogression in the first four measures, there is a Progression in the second four; where there is a Strong Ascending progression in the first phrase, there is a Strong Decending in the second; the Mild Decending movement of the first section is answered by a Mild Ascending motion in the second. The only variation is that at the end of the second phrase there is a Strong Ascending progression from the IV to the V to turn the phrase around on itself. This two chord per bar harmonic rhythm will only appear three times and in this exact same form each time during the piece.
For the second eight bars, I isolated the root progression pattern of the first four bars of the original progression and repeated it in sequence still using the TriTone as Progressive root motion to link the to phrases of the progression. This creates an unusual non-dominant direct modulation to the parallel key a semitone below the tonic, but the previously established pattern makes it work seamlessly. I also changed the gender of the first phrase, making it in the tonic minor key, and I kept with that idea and have the second phrase in minor as well. The idea with this phrase, and the subsequent phrases not on the tonic, was to choose between major or minor by selecting the key closest to the original tonic of A major. So by that logic, G-sharp minor would be closer to A major than A-flat major would.
Just as there is a V to I Progressive root progression at the end of the original phrase, there is a similar progression at the end of the second eight bars. However, the one chord per bar harmonic rhythm is maintained throughout.
For the third phrase, I isolated the root progression pattern from the second four bars of the original progression and have it arranged as a mirror image of the second eight bar progression. It too sequences a semitone, but a semitone up versus the previous phrase's semitone down. It is also divided in half by a TriTone root progression, but this time the sole unused TriTone as Retrogressive form is employed, and so the list of possible diatonic root progressions is completed. Far from being a minor detail, this is a major structural point. I continued the first phrase of the third eight bar progression in the minor mode, but changed back to major for the last four bars of the third progression due to G major being closer to A major than G minor with all it's flats.
The modulation back to A major from G major is made exceedingly smooth by the last two bars having chords shared by both keys. I am actually quite delighted with the effect it has: The last two bars of the final eight bar phrase are in fact identical to the last two bars of the original progression, and here we have the second instance of the two chord per measure harmonic rhythm.
The final eight bars are an exact repeat of the original progression with a final two measures of tonic harmony at the end.
I used Schillinger's concept of Circular Transformation with only some minor adornments to arrange the top three voices of the piece: on the diatonic vii diminished triad I added a diminished seventh to give it the more dramatic color I wanted after the TriTone progression, and also to set up the later adornments in the same places in the third eight bar phrase. In measure 17 I use the same figure to get the sound of a minor triad with a major seventh, and in measure 21 I use the sound of a major triad with an added major seventh. These are only adornments and do not affect the purely triadic Circular Transformations of the top three voices in any way.
The bass voice is a slightly adorned Constant Root: Adding a constant root bass line to a properly transforming triadic or seventh chord progression will never result in forbidden parallels. This is a simple example of Schillinger's concept of Strata: The transforming triads in the upper three voices are one stratum, and the constant root bass line is another. You could concievably - and easily - have a third stratum of triads transforming opposite of their natural inclinations and still have no forbidden parallels with the resulting seven voices. Where there are Mild Decending or Mild Ascending root motions, I decorated the bass line with a passing seventh or a ninth in the bass respectively. Since I'm not using seventh or ninth chords, there is no danger of forbidden parallels with this embellishment. This relatively insignificant looking figure adds an unexpectedly large amount of dimension and depth to the resulting progressions in inverse proportion to it's appearance on the page.
Once I had all of these elements constructed in a whole note/half note voice leading sketch in C major, I selected the key in which it would fit most comfortably on the guitar. Since I do not want any open strings in the fingerings (So the piece can be moved to several pitch levels depending on what my performance set needs at any given time), the low note of F would have given A-flat major, but A major is a much more common guitar key, and it's easier to read with only three sharps as well, so that's where I put it.
Lineal Study No. 1 is in G major, 4/4 time, and has the simplest possible texture of straight eighth notes, so I wanted this one to be in a different time signature and with a small added element of rhythm to it since the overall finished set of Lineal Studies is to be roughly progressive in terms of complexity and technical difficulty (I'm planning six to twelve of these little ditties). So, after I decided on 6/8 time I decided to use the rhythmic resultant of the interval of a perfect fourth, or the ratio of 4:3 (If you look back to the Relativity of Pitch to Tempo & Harmony to Rhythm post, you can see how these resultants of interference are worked out). I chose that because there is a compound tripple meter with four bar phrases, so it's a logical aspect of the composition as a whole. That resultant is 3+1+2+2+1+3, so I took the first half and decorated the first three eighth notes of every measure with it (3x1/16ths+1x1/16th+2x1/16ths), keeping the second group of three as the smaller term 3 but diminuted to the middle sized term of the resultant (An overblown way to say I left them straight eighth notes). I didn't use the second half of the resultant until the penultimate measure of tonic harmony, where combined with a slight ritardando it makes for a spectacularly effective close, despite the direct simplicity of the employment of it that I chose.
It is important to realize that there are many other possible permutations of this original progression available if you change the TriTone dividing progression to other forms, and with repeat schemes &c. this could have been made into an art song, or a movement for a chamber ensemble, or even a symphonic movement. I'm a guitarist and have no ensembles available to me, so I'm writing things that I can play and perform: MIDI renditions of larger stuff is only fun for so long for me. I want to play and perform the music that I write. Single line passages are also one of my technical weak spots, and I have neither the time nor the patience to work on scales and arpeggios, so these pieces will also serve a utilitarian purpose.
One final point: Different root progressions make the triadic voices move in different directions, either upward or downward. Strong Ascending progressions move the voices down, while Strong Decending progressions move the vioces up. Mild Ascending progressions also move the voices down while Mild Decending progressions move them up. And Retrogressions move the voices down, and Progressions move them up. Finally, TriTones move the voices up if they are in an as Progressive arrangement, or down if they are in an as Retrogressive relationship. Knowing this allows you to control where you want to have your voices move, and obviously an unbalanced progression can get you into trouble with ranges if you don't know what you're doing.
Now, the direction that voices move with seventh chords is an entirely different matter, and I'll wait to cover that until later, but you can certainly do some experiments and find that out for yourselves.
Even in small pieces with a modest scope - such as these Lineal Studies which are a minute or less in total playing time - it is not only possible but also highly desirable to construct them with a high degree of craftsmanship. By adhering to this philosophy of structural perfectionism and adding the necessary elements of inspired variety and detail, the resulting miniatures have a high degree of musicality. I always encourage my students to write many, many miniatures as this is the most effective way to master and develop the proceedures necessary to tackle continuities with a broader scope.
posted by Hucbald at 2:08 AM
1 Comments:
Hi Robert. Progressive root motion is the most common or "normal" motion and it occurs when the root falls by perfect fifth, or the inversion of that, rises by perfect fourth. Retrogressions are the opposite of Progressions and the root rises by perfect fifth or falls by perfect fourth in those relationships. If you set up a series of chords in a Progressive relationship and then play them backwards, you get Retrogressions, which do indeed sound like they are gowing backwards, which is why they got that name. The V to I is the primordial Progression and first appeared at cadential points during the 15th century. That progression was elongated with secondary dominants over the course of the seventeenth century when harmony proper first started getting recognized by theorists. Look back to the "Harmonic Progression Mechanics" post for a full explaination.
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