Why Music Works: Chapter Six
The Harmonies of the Secondary Subdominant Contextual Sub-System
PREFACE to All Posts:
This is to be the culmination of the Musical Relativity series of posts I did back in 2006, which can be found to your right in the sidebar. Back then I was calling the series Musical Implications of the Harmonic Overtone Series. Even before that, I did a series of posts called Harmonic Implications of the Overtone Series that started this all. Here, I am presenting the final weblog version of the evolving book I've decided to publish with the intention of getting some feedback before I create the final print version, which I plan to put into the ePub format for iBooks. So, please feel free to ask any questions about anything that you think I haven't made perfectly clear, and don't hesitate to offer any constructive criticisms or suggestions. Since this project is the accidental result of several decades of curios inquiry - and many prominent and also relatively anonymous theorists and teachers have contributed ideas to it (Which I will credit where memory serves and honor dictates) - I am eager to get a final layer of polish from any and all who may happen to read this series and find it useful, or potentially so. Since I am creating these posts as .txt files first, revision should be a simple process.
Since my pre-degree studies at The Guitar Institute of the Southwest and my undergraduate work at Berklee College of Music looked at music theory from the jazz perspective, and then my master of music and doctor of musical arts studies at Texas State and The University of North Texas were from the traditional perspective, a large part of how I discovered the things in this book-in-progress was the result of my trying to reconcile those different theoretical viewpoints. Since I want this work to be of practical value, I have retained all of the traditional theoretical nomenclature possible, and only added to it where necessary to describe phenomena that have not heretofore been present in musical analysis. I have, however, standardized terminology into what I think is the most logical system yet devised, and that will be explained as the reader goes along. There is a lot of built-in review and repetition - something I've learned from my decades of private teaching - so even a once-through with this systematic approach to understanding musical phenomena ought to be of significant benefit.
Outright addition to traditional musical analysis is limited to the symbology required to label root motion and transformation types so that the root motion and transformation patterns are visible: This greatly facilitates comprehension, and since good and bad harmonic continuities are separated by the effectiveness or lack thereof in the root motion and transformation patterns, this also actually functions as an aid to composition. All symbology - old and new - has been worked out over the past three decades so that everything is readily available with the standard letters, numbers, and symbols found on a QWERTY keyboard.
Finally, for the contextual systems, I have used the Greek alphabet: The normal diatonic systems - those comprised of two minor seconds and five major seconds - are Alpha, Beta, and Gamma. The exotic diatonic systems - those that contain a single augmented second - are Delta, Epsilon, and Zeta, and finally, the alien diatonic systems - those that contain two augmented seconds - are Eta, Theta, and Iota. Since the theoretical writings that started western art music out were handed down from ancient Greece, I thought this would be a fitting tribute, as well as a handy and logical classification scheme.
Basically, if you have a baccalaureate-level understanding of music theory from either a jazz or traditional perspective, you should have no problem understanding anything in this straight-forward treatise.
INTRODUCTION to Chapter Six:
In chapter one, I demonstrated how the overtone sonority generates the three normal diatonic systems - those seven note systems that contain two semitones and five tones: Alpha, Beta, and Gamma - and then in chapter two we examined each of those systems in detail, discovering that the primacy of Alpha is due to the fact that all seven of its harmonies can be arranged in progressive order. In chapter three, we examined the contextualization of Alpha Prime, looking at the various different root progressions types it can exhibit, their various transformations, and through this we also started to look into the world of musical effect and affect. Chapter four was dedicated to examining how Beta Prime and Gamma Prime compared to Alpha, using the same musical proof formats developed in chapter three. Through those proofs, we discovered some very unusual harmonic effects that evoke the uncanny that are contained in the Beta and Gamma systems. Chapter five then took us out of the diatonic harmonic world and into the chromatic realm as we discovered the origins of the secondary dominant sub-system sonorities.
Now in chapter six, we will look at the secondary subdominant sub-system of harmonies. Whereas in the secondary dominant sub-system the harmonies were all overtone chords or altered overtone chords, in the secondary subdominant sub-system the harmonies are actually different genders of chords: Major sevenths, minor sevenths, and dominant sevenths.
*****
CHAPTER SIX:
Secondary dominants are more well known than secondary subdominants, but both contextual sub-systems offer sonic resources that the composer ought to be aware of. The intuition of many rock music writers has lead them to the secondary subdominant major triads over the years - most notably to me, Pete Townshend of The Who - and this is partly explained by the fact that major triads sound so good with overdriven guitar amps. But, secondary subdominant major triads also produce a unique sonic environment that can't be duplicated in any other way. For example, The Real Me from The Who's Quadrophenia album is just loaded with them - as are many of the songs in that rock opera concept - and this is exactly where I started to figure them out when I was back in high school: I was positively addicted to those records.
Traditionally, the secondary subdominant major triads and major sevenths have been justified through the concept of modal interchange, which is borrowing harmonies from modes parallel to whichever one you have nominated as home. While this is a very useful compositional concept - I use it all the time - in this chapter we will see how the origin of these harmonies is better explained by the progressive resolutional paradigm established by the overtone chord.
In the modal interchange model, if we are in Alpha Prime - traditional major, or Ionian - the idea is to borrow the subdominant Lydian chords from the other Alpha System parallel modes. With I(M7) as the Ionian tonic, we get the bII(M7) Lydian chord from the parallel Phrygian, the bIII(M7) from the parallel Dorian, the IV(M7) is the native Ionian subdominant, bV(M7) comes from Locrian, the bVI(M7) comes from Aeolian, and finally, the bVII(M7) comes from Mixolydian. This creates a hybrid system of all subdominant chords surrounding a tonic much like the secondary dominants create a hybrid system of all dominants surrounding a tonic (And you can just as easily justify secondary dominants through modal interchange too). Later, when we look at integrated chromatic contextual systems, we will find that the secondary subdominants progressively leading away from the tonic create a grand subdominant preparation for the most remote of the secondary dominants, which then lead back to the tonic. Taking musical gravity into account, this creates a descending barber pole loop that spirals ever downward.
For now, we will simply look at the different genders of secondary subdominant, and where they came from.
EXAMPLE 28:
Listen to Example 28
As you can now see, the secondary subdominants are also generated by the resolutional paradigm established by the primordial resolution of the overtone sonority. Previously, with the secondary dominants, we were seeing overtone chords and altered overtone chords on the diatonic degrees progressively moving toward the tonic, whereas here, we see Lydian harmonies progressively leading away from the tonic, and so into the chromatic realm, at bVII(M7) and on. Where the connection between the secondary dominant sub-system and the secondary subdominant sub-system occurs is at the enharmonic progressive root motion that would be from the bV(M7) - the most remote of the secondary subdominants - to the V(d5m7)/iii - the most remote of the secondary dominants. Since G-flat is the enharmonic of F-sharp, this would lead to B-natural in the Alpha Prime on C here. As I mentioned above, we will look at this when we get to integrated chromatic contextual systems.
OBSERVATIONS:
1. The secondary subdominant major seventh chords are Lydian sonorities extending progressively away from the tonic.
2. This is opposed to the secondary dominant Mixolydian sonorities and altered Mixolydian sonorities, that approach the tonic progressively.
3. Upper structure tones for secondary subdominant major sevenths are: Major ninth, augmented eleventh, and major thirteenth.
4. As the iv(m7) chord in the penultimate measure shows, secondary subdominants can also me minor seventh chords.
Obviously, the minor subdominant was a better choice here because of all of the flatted notes in the bV(M7), which would have produced two augmented seconds going into a major chord on the fourth degree with the normal clockwise transformation that a super-regression carries.
5. Secondary subdominant major sevenths are generated by Alpha Prime (Ionian/Pure Major).
6. So, secondary subdominant minor sevenths will be generated by Alpha 6 (Aeolian/Pure Minor).
7. Therefore, secondary subdominant minor sevenths will be Dorian sonorities.
*****
EXAMPLE 29:
Listen to Example 29
This is example twenty-eight in the Alpha 6 independent sub-context.
OBSERVATIONS:
1. Secondary subdominant minor seventh chords are Dorian sonorities extending progressively away from the minor tonic.
2. This is opposed to the secondary dominant Mixolydian sonorities, which approach the tonic progressively.
3. Upper structure tones for secondary subdominant minor sevenths are: Major ninth, perfect eleventh, and major thirteenth.
4. The direct half-step resolution of the enharmonic V(d5m7m9)/V justifies the jazz subV7 practice.
Just as I was providentially able to present a minor subdominant in example twenty-eight, I was able to work in a V(d5m7m9)/V harmony here (The point of origin for the German Augmented Sixth in paleo-terminology). That sonority is enharmonic because of the tied G-flat, which would otherwise be an F-sharp. The resulting structure in the transformational stratum therefore reads like an A-flat dominant seventh chord, which jazz theorists call a subV7/V (Which shares its tritone with the dominant on D-natural), and all four notes move down by semitone into the primary dominant in this direct transformation. So, a jazz substitute secondary dominant resolving down by semitone in parallel is actually a V(d5m7m9/0) notated enharmonically and transforming directly. Pretty funny.
5. However, that direct resolution of the enharmonic V(d5m7m9)/V also nullifies jazz subV7 theory.
6. Additionally, that resolution of the V(d5m7m9)/V also nullifies traditional "German Sixth" theory.
If you could even say that the traditional German Augmented Sixth nomenclature rises to the level of a theory.
7. Both traditional and jazz theories are wrong here, but at least the traditional notation is correct.
8. Secondary subdominants can also be overtone sonorities generated by Beta Prime.
This is, in a way, out of bounds for the pure secondary subdominants generated by Alpha Prime and Alpha 6, but since Alpha 6 is combined with Beta Prime to create the traditionally so-called melodic minor nonatonic hybrid contextual system, I thought I'd go ahead and present them.
*****
EXAMPLE 30:
Listen to Example 30
This is example twenty-eight with secondary subdominant overtone chords.
OBSERVATIONS:
1. Secondary subdominant M(m7) chords are Mixolydian Augmented-fourth sonorities.
2. These are the chords actually generated by the harmonic series to partial eleven.
3. Secondary subdominant M(m7) chords are not considered dominant because they don't target degrees of Alpha Prime.
4. In context, if these chords target degrees of Alpha 6 or Beta Prime they may be considered dominant.
This is the way many paleo-theorists have done it in the past, but since Alpha Prime is, well, Alpha Prime, no overtone chord that doesn't come from a natural degree of Alpha Prime targeting a natural degree of Alpha Prime is a functional dominant harmony.
5. All of the altered dominant forms are available as subdominants as well.
6. The secondary dominant and secondary dominant sub-systems join to create a downward spiral of overtone sonorities.
7. That downward spiral of overtone chords covers the entire circa 144 semitone range of human hearing.
8. That pattern is imprinted in the subconscious of every human being, probably while they are still in the womb.
This why in absolute music - where music creates its own context - there has to be a musical contextual system or sub-system present that is independently functional. I'll present an example demonstrating this at the end of the first part of this book that describes the complete harmonic system. It really does sound like something that is deeply engrained, perhaps even at the genetic level.
*****
EXAMPLE 31:
Listen to Example 31
Of course, these examples can also transform directly.
OBSERVATIONS:
1. This is example twenty-eight with the harmonies transforming directly.
2. The continuous high surface tension provided by constant M(M7) chords is quite dissonant.
*****
EXAMPLE 32:
Listen to Example 32
OBSERVATIONS:
1. This is example twenty-nine with the harmonies transforming directly.
2. The increased surface tension provided by continuous m(m7) harmonies is much more mellow.
*****
EXAMPLE 33:
Listen to Example 33
OBSERVATIONS:
1. This is example thirty with the secondary overtone chords transforming directly.
2. While the M(M7) and m(m7) transformations were diatonic from chord to chord, these include chromaticism.
As the major thirds descend to minor sevenths in the target chords, as we also saw with direct transformations of secondary dominants.
3. The constant chromatic side-slipping creates a vaguely jazzy effect.
Though Mozart was no stranger to side-slips.
PREFACE to All Posts:
This is to be the culmination of the Musical Relativity series of posts I did back in 2006, which can be found to your right in the sidebar. Back then I was calling the series Musical Implications of the Harmonic Overtone Series. Even before that, I did a series of posts called Harmonic Implications of the Overtone Series that started this all. Here, I am presenting the final weblog version of the evolving book I've decided to publish with the intention of getting some feedback before I create the final print version, which I plan to put into the ePub format for iBooks. So, please feel free to ask any questions about anything that you think I haven't made perfectly clear, and don't hesitate to offer any constructive criticisms or suggestions. Since this project is the accidental result of several decades of curios inquiry - and many prominent and also relatively anonymous theorists and teachers have contributed ideas to it (Which I will credit where memory serves and honor dictates) - I am eager to get a final layer of polish from any and all who may happen to read this series and find it useful, or potentially so. Since I am creating these posts as .txt files first, revision should be a simple process.
Since my pre-degree studies at The Guitar Institute of the Southwest and my undergraduate work at Berklee College of Music looked at music theory from the jazz perspective, and then my master of music and doctor of musical arts studies at Texas State and The University of North Texas were from the traditional perspective, a large part of how I discovered the things in this book-in-progress was the result of my trying to reconcile those different theoretical viewpoints. Since I want this work to be of practical value, I have retained all of the traditional theoretical nomenclature possible, and only added to it where necessary to describe phenomena that have not heretofore been present in musical analysis. I have, however, standardized terminology into what I think is the most logical system yet devised, and that will be explained as the reader goes along. There is a lot of built-in review and repetition - something I've learned from my decades of private teaching - so even a once-through with this systematic approach to understanding musical phenomena ought to be of significant benefit.
Outright addition to traditional musical analysis is limited to the symbology required to label root motion and transformation types so that the root motion and transformation patterns are visible: This greatly facilitates comprehension, and since good and bad harmonic continuities are separated by the effectiveness or lack thereof in the root motion and transformation patterns, this also actually functions as an aid to composition. All symbology - old and new - has been worked out over the past three decades so that everything is readily available with the standard letters, numbers, and symbols found on a QWERTY keyboard.
Finally, for the contextual systems, I have used the Greek alphabet: The normal diatonic systems - those comprised of two minor seconds and five major seconds - are Alpha, Beta, and Gamma. The exotic diatonic systems - those that contain a single augmented second - are Delta, Epsilon, and Zeta, and finally, the alien diatonic systems - those that contain two augmented seconds - are Eta, Theta, and Iota. Since the theoretical writings that started western art music out were handed down from ancient Greece, I thought this would be a fitting tribute, as well as a handy and logical classification scheme.
Basically, if you have a baccalaureate-level understanding of music theory from either a jazz or traditional perspective, you should have no problem understanding anything in this straight-forward treatise.
INTRODUCTION to Chapter Six:
In chapter one, I demonstrated how the overtone sonority generates the three normal diatonic systems - those seven note systems that contain two semitones and five tones: Alpha, Beta, and Gamma - and then in chapter two we examined each of those systems in detail, discovering that the primacy of Alpha is due to the fact that all seven of its harmonies can be arranged in progressive order. In chapter three, we examined the contextualization of Alpha Prime, looking at the various different root progressions types it can exhibit, their various transformations, and through this we also started to look into the world of musical effect and affect. Chapter four was dedicated to examining how Beta Prime and Gamma Prime compared to Alpha, using the same musical proof formats developed in chapter three. Through those proofs, we discovered some very unusual harmonic effects that evoke the uncanny that are contained in the Beta and Gamma systems. Chapter five then took us out of the diatonic harmonic world and into the chromatic realm as we discovered the origins of the secondary dominant sub-system sonorities.
Now in chapter six, we will look at the secondary subdominant sub-system of harmonies. Whereas in the secondary dominant sub-system the harmonies were all overtone chords or altered overtone chords, in the secondary subdominant sub-system the harmonies are actually different genders of chords: Major sevenths, minor sevenths, and dominant sevenths.
CHAPTER SIX:
Secondary dominants are more well known than secondary subdominants, but both contextual sub-systems offer sonic resources that the composer ought to be aware of. The intuition of many rock music writers has lead them to the secondary subdominant major triads over the years - most notably to me, Pete Townshend of The Who - and this is partly explained by the fact that major triads sound so good with overdriven guitar amps. But, secondary subdominant major triads also produce a unique sonic environment that can't be duplicated in any other way. For example, The Real Me from The Who's Quadrophenia album is just loaded with them - as are many of the songs in that rock opera concept - and this is exactly where I started to figure them out when I was back in high school: I was positively addicted to those records.
Traditionally, the secondary subdominant major triads and major sevenths have been justified through the concept of modal interchange, which is borrowing harmonies from modes parallel to whichever one you have nominated as home. While this is a very useful compositional concept - I use it all the time - in this chapter we will see how the origin of these harmonies is better explained by the progressive resolutional paradigm established by the overtone chord.
In the modal interchange model, if we are in Alpha Prime - traditional major, or Ionian - the idea is to borrow the subdominant Lydian chords from the other Alpha System parallel modes. With I(M7) as the Ionian tonic, we get the bII(M7) Lydian chord from the parallel Phrygian, the bIII(M7) from the parallel Dorian, the IV(M7) is the native Ionian subdominant, bV(M7) comes from Locrian, the bVI(M7) comes from Aeolian, and finally, the bVII(M7) comes from Mixolydian. This creates a hybrid system of all subdominant chords surrounding a tonic much like the secondary dominants create a hybrid system of all dominants surrounding a tonic (And you can just as easily justify secondary dominants through modal interchange too). Later, when we look at integrated chromatic contextual systems, we will find that the secondary subdominants progressively leading away from the tonic create a grand subdominant preparation for the most remote of the secondary dominants, which then lead back to the tonic. Taking musical gravity into account, this creates a descending barber pole loop that spirals ever downward.
For now, we will simply look at the different genders of secondary subdominant, and where they came from.
EXAMPLE 28:
Listen to Example 28
As you can now see, the secondary subdominants are also generated by the resolutional paradigm established by the primordial resolution of the overtone sonority. Previously, with the secondary dominants, we were seeing overtone chords and altered overtone chords on the diatonic degrees progressively moving toward the tonic, whereas here, we see Lydian harmonies progressively leading away from the tonic, and so into the chromatic realm, at bVII(M7) and on. Where the connection between the secondary dominant sub-system and the secondary subdominant sub-system occurs is at the enharmonic progressive root motion that would be from the bV(M7) - the most remote of the secondary subdominants - to the V(d5m7)/iii - the most remote of the secondary dominants. Since G-flat is the enharmonic of F-sharp, this would lead to B-natural in the Alpha Prime on C here. As I mentioned above, we will look at this when we get to integrated chromatic contextual systems.
OBSERVATIONS:
1. The secondary subdominant major seventh chords are Lydian sonorities extending progressively away from the tonic.
2. This is opposed to the secondary dominant Mixolydian sonorities and altered Mixolydian sonorities, that approach the tonic progressively.
3. Upper structure tones for secondary subdominant major sevenths are: Major ninth, augmented eleventh, and major thirteenth.
4. As the iv(m7) chord in the penultimate measure shows, secondary subdominants can also me minor seventh chords.
Obviously, the minor subdominant was a better choice here because of all of the flatted notes in the bV(M7), which would have produced two augmented seconds going into a major chord on the fourth degree with the normal clockwise transformation that a super-regression carries.
5. Secondary subdominant major sevenths are generated by Alpha Prime (Ionian/Pure Major).
6. So, secondary subdominant minor sevenths will be generated by Alpha 6 (Aeolian/Pure Minor).
7. Therefore, secondary subdominant minor sevenths will be Dorian sonorities.
EXAMPLE 29:
Listen to Example 29
This is example twenty-eight in the Alpha 6 independent sub-context.
OBSERVATIONS:
1. Secondary subdominant minor seventh chords are Dorian sonorities extending progressively away from the minor tonic.
2. This is opposed to the secondary dominant Mixolydian sonorities, which approach the tonic progressively.
3. Upper structure tones for secondary subdominant minor sevenths are: Major ninth, perfect eleventh, and major thirteenth.
4. The direct half-step resolution of the enharmonic V(d5m7m9)/V justifies the jazz subV7 practice.
Just as I was providentially able to present a minor subdominant in example twenty-eight, I was able to work in a V(d5m7m9)/V harmony here (The point of origin for the German Augmented Sixth in paleo-terminology). That sonority is enharmonic because of the tied G-flat, which would otherwise be an F-sharp. The resulting structure in the transformational stratum therefore reads like an A-flat dominant seventh chord, which jazz theorists call a subV7/V (Which shares its tritone with the dominant on D-natural), and all four notes move down by semitone into the primary dominant in this direct transformation. So, a jazz substitute secondary dominant resolving down by semitone in parallel is actually a V(d5m7m9/0) notated enharmonically and transforming directly. Pretty funny.
5. However, that direct resolution of the enharmonic V(d5m7m9)/V also nullifies jazz subV7 theory.
6. Additionally, that resolution of the V(d5m7m9)/V also nullifies traditional "German Sixth" theory.
If you could even say that the traditional German Augmented Sixth nomenclature rises to the level of a theory.
7. Both traditional and jazz theories are wrong here, but at least the traditional notation is correct.
8. Secondary subdominants can also be overtone sonorities generated by Beta Prime.
This is, in a way, out of bounds for the pure secondary subdominants generated by Alpha Prime and Alpha 6, but since Alpha 6 is combined with Beta Prime to create the traditionally so-called melodic minor nonatonic hybrid contextual system, I thought I'd go ahead and present them.
EXAMPLE 30:
Listen to Example 30
This is example twenty-eight with secondary subdominant overtone chords.
OBSERVATIONS:
1. Secondary subdominant M(m7) chords are Mixolydian Augmented-fourth sonorities.
2. These are the chords actually generated by the harmonic series to partial eleven.
3. Secondary subdominant M(m7) chords are not considered dominant because they don't target degrees of Alpha Prime.
4. In context, if these chords target degrees of Alpha 6 or Beta Prime they may be considered dominant.
This is the way many paleo-theorists have done it in the past, but since Alpha Prime is, well, Alpha Prime, no overtone chord that doesn't come from a natural degree of Alpha Prime targeting a natural degree of Alpha Prime is a functional dominant harmony.
5. All of the altered dominant forms are available as subdominants as well.
6. The secondary dominant and secondary dominant sub-systems join to create a downward spiral of overtone sonorities.
7. That downward spiral of overtone chords covers the entire circa 144 semitone range of human hearing.
8. That pattern is imprinted in the subconscious of every human being, probably while they are still in the womb.
This why in absolute music - where music creates its own context - there has to be a musical contextual system or sub-system present that is independently functional. I'll present an example demonstrating this at the end of the first part of this book that describes the complete harmonic system. It really does sound like something that is deeply engrained, perhaps even at the genetic level.
EXAMPLE 31:
Listen to Example 31
Of course, these examples can also transform directly.
OBSERVATIONS:
1. This is example twenty-eight with the harmonies transforming directly.
2. The continuous high surface tension provided by constant M(M7) chords is quite dissonant.
EXAMPLE 32:
Listen to Example 32
OBSERVATIONS:
1. This is example twenty-nine with the harmonies transforming directly.
2. The increased surface tension provided by continuous m(m7) harmonies is much more mellow.
EXAMPLE 33:
Listen to Example 33
OBSERVATIONS:
1. This is example thirty with the secondary overtone chords transforming directly.
2. While the M(M7) and m(m7) transformations were diatonic from chord to chord, these include chromaticism.
As the major thirds descend to minor sevenths in the target chords, as we also saw with direct transformations of secondary dominants.
3. The constant chromatic side-slipping creates a vaguely jazzy effect.
Though Mozart was no stranger to side-slips.
posted by Hucbald at 2:27 AM
1 Comments:
Where are the pipes, mon?
Cheers
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