Why Music Works: Chapter Eight
Root Motion and Transformation Types in the Delta, Epsilon, and Zeta Systems
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 Eight:
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. Previously, in chapter six, we looked at the secondary subdominant sub-system of harmonies, which completed a larger set of integrated chromatic systems, which we will look at in detail later.
Last time, in chapter seven, we went back a bit and looked at the exotic diatonic systems - those seven note contextual systems that contain a single augmented second: Delta, Epsilon, and Zeta - and now in chapter eight we'll look in detail at the root motion types they contain, and the unique harmonic effects that these unusual systems create.
*****
CHAPTER EIGHT:
EXAMPLE 40:
Listen to Example 40
Here we have the progressions and regressions in Delta Prime, using the same end-contextualized musical proofs I've presented earlier for Alpha, Beta and Gamma. One nice thing about using musical proofs that the reader can listen to, is that I really don't have to explain very much now that all of the elements of the contextual system concept have been previously presented. All of these transformations are direct, as the point now is to hear the various harmonies in isolation, so as to hear their uniqueness. The bVI(A5M7) is a hot sonority, and being entered via quadra-tone and exited by tritone - or the other way around in the case of the regressions - really puts it in stark relief here.
EXAMPLE 41:
Listen to Example 41
It really is difficult to even notice the augmented second movements in the transformational stratum unless you are careful to listen for them.
EXAMPLE 42:
Listen to Example 42
As I pointed out above, unusual harmonies more or less alternate with more normal seventh chords in this example. That's a nice resource. Now, on to the Epsilon system.
*****
EXAMPLE 43:
Listen to Example 43
This is the system normally referred to as harmonic minor, so some of these effects may be familiar to you. Since this should all be old hat now, I'll firmally dispense with the observations, unless something truly unique arises.
EXAMPLE 44:
Listen to Example 44
EXAMPLE 45:
Listen to Example 45
Now, on to the Zeta system, which is like melodic minor with a Phrygian minor second.
*****
EXAMPLE 46:
Listen to Example 46
NOTE: The D in the penultimate measure of the top system appears as a D-natural instead of the D-flat it ought to be. I corrected this when I was proofing the audio examples, but I'd already uploaded the JPEG files by then. So, it looks wrong, but it sounds right. A big part of this post series is to work the kinks out of the examples and more perfectly define the presentation order (More on that in a few minutes).
Note also that in the progressive root motion from the bIII(A5m7) - normally called an augmented seventh chord - that there is the augmented second in the transformation as the B-natural moves down to A-flat: This is why the so-called augmented seventh chords do not fit into the secondary dominant galaxy of sonorities - the augmented fifth has to move an augmented second down to get to the new root.
There are some very wicked sounding sonorities in this system. The vii(d3d5d7) is particularly cool.
EXAMPLE 47
Listen to Example 47
EXAMPLE 48
Listen to Example 48
Lots more interesting sonic resources in the exotic systems, but wait until we get to the alien systems (Those with two augmented seconds). I worked those out today - I could swear I did that before - and they are really, really creepy. One of the sub-contexts is the so-called Arabian or snake charmer scale, and that system creates some very bizarre sonorities. Next time, however, we are going to look at harmonic canons.
I think I have the final chapter outline done for the book now. Instead of presenting the secondary dominant sub-system and the secondary subdominant sub-system together, as I've done in this series, I'm going to break them up like so.
01] The Harmonic Series: Its Structure, Forces, and Primordial Resolution
02] Genesis of the Native Diatonic Contextual Systems: Alpha, Beta, and Gamma
03] Root Motion and Voice Transformation in the Native Diatonic Contextual Systems
04] Sonorities of the Secondary Dominant Contextual Sub-System
05] Genesis of the Exotic Diatonic Contextual Systems: Delta, Epsilon, and Zeta
06] Root Motion and Voice Transformation in the Exotic Diatonic Contextual Systems
07] Sonorities of the Secondary Subdominant Contextual Sub-System
08] Genesis of the Alien Diatonic Contextual Systems: Eta, Theta, and Iota
09] Root Motion and Voice Transformation in the Alien Diatonic Contextual Systems
10] Harmonic Canons, Musical Escher Morphs, and Musical Mobius Loops
11] Genesis of the Hybrid Nonatonic Contextual Systems: Kappa, Lambda, and Mu
12] The Integrated Chromatic Contextual Systems: Chi, Psi, and Omega
One thing I wanted to avoid, was putting all of the contextual systems together at the beginning. Not only can it get tedious that way, but spacing them out lends itself to the built-in review device that I like to use when teaching.
*****
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 Eight:
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. Previously, in chapter six, we looked at the secondary subdominant sub-system of harmonies, which completed a larger set of integrated chromatic systems, which we will look at in detail later.
Last time, in chapter seven, we went back a bit and looked at the exotic diatonic systems - those seven note contextual systems that contain a single augmented second: Delta, Epsilon, and Zeta - and now in chapter eight we'll look in detail at the root motion types they contain, and the unique harmonic effects that these unusual systems create.
CHAPTER EIGHT:
EXAMPLE 40:
Listen to Example 40
Here we have the progressions and regressions in Delta Prime, using the same end-contextualized musical proofs I've presented earlier for Alpha, Beta and Gamma. One nice thing about using musical proofs that the reader can listen to, is that I really don't have to explain very much now that all of the elements of the contextual system concept have been previously presented. All of these transformations are direct, as the point now is to hear the various harmonies in isolation, so as to hear their uniqueness. The bVI(A5M7) is a hot sonority, and being entered via quadra-tone and exited by tritone - or the other way around in the case of the regressions - really puts it in stark relief here.
EXAMPLE 41:
Listen to Example 41
It really is difficult to even notice the augmented second movements in the transformational stratum unless you are careful to listen for them.
EXAMPLE 42:
Listen to Example 42
As I pointed out above, unusual harmonies more or less alternate with more normal seventh chords in this example. That's a nice resource. Now, on to the Epsilon system.
EXAMPLE 43:
Listen to Example 43
This is the system normally referred to as harmonic minor, so some of these effects may be familiar to you. Since this should all be old hat now, I'll firmally dispense with the observations, unless something truly unique arises.
EXAMPLE 44:
Listen to Example 44
EXAMPLE 45:
Listen to Example 45
Now, on to the Zeta system, which is like melodic minor with a Phrygian minor second.
EXAMPLE 46:
Listen to Example 46
NOTE: The D in the penultimate measure of the top system appears as a D-natural instead of the D-flat it ought to be. I corrected this when I was proofing the audio examples, but I'd already uploaded the JPEG files by then. So, it looks wrong, but it sounds right. A big part of this post series is to work the kinks out of the examples and more perfectly define the presentation order (More on that in a few minutes).
Note also that in the progressive root motion from the bIII(A5m7) - normally called an augmented seventh chord - that there is the augmented second in the transformation as the B-natural moves down to A-flat: This is why the so-called augmented seventh chords do not fit into the secondary dominant galaxy of sonorities - the augmented fifth has to move an augmented second down to get to the new root.
There are some very wicked sounding sonorities in this system. The vii(d3d5d7) is particularly cool.
EXAMPLE 47
Listen to Example 47
EXAMPLE 48
Listen to Example 48
Lots more interesting sonic resources in the exotic systems, but wait until we get to the alien systems (Those with two augmented seconds). I worked those out today - I could swear I did that before - and they are really, really creepy. One of the sub-contexts is the so-called Arabian or snake charmer scale, and that system creates some very bizarre sonorities. Next time, however, we are going to look at harmonic canons.
I think I have the final chapter outline done for the book now. Instead of presenting the secondary dominant sub-system and the secondary subdominant sub-system together, as I've done in this series, I'm going to break them up like so.
01] The Harmonic Series: Its Structure, Forces, and Primordial Resolution
02] Genesis of the Native Diatonic Contextual Systems: Alpha, Beta, and Gamma
03] Root Motion and Voice Transformation in the Native Diatonic Contextual Systems
04] Sonorities of the Secondary Dominant Contextual Sub-System
05] Genesis of the Exotic Diatonic Contextual Systems: Delta, Epsilon, and Zeta
06] Root Motion and Voice Transformation in the Exotic Diatonic Contextual Systems
07] Sonorities of the Secondary Subdominant Contextual Sub-System
08] Genesis of the Alien Diatonic Contextual Systems: Eta, Theta, and Iota
09] Root Motion and Voice Transformation in the Alien Diatonic Contextual Systems
10] Harmonic Canons, Musical Escher Morphs, and Musical Mobius Loops
11] Genesis of the Hybrid Nonatonic Contextual Systems: Kappa, Lambda, and Mu
12] The Integrated Chromatic Contextual Systems: Chi, Psi, and Omega
One thing I wanted to avoid, was putting all of the contextual systems together at the beginning. Not only can it get tedious that way, but spacing them out lends itself to the built-in review device that I like to use when teaching.
posted by Hucbald at 3:27 PM
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