Why Music Works: Chapter Eleven
Root Motion and Transformation Types in the Eta, Theta, and Iota 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 Eleven:
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. After the secondary dominants, 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.
Then in chapter seven, we looked at the exotic diatonic systems - those seven note contextual systems that contain a single augmented second: Delta, Epsilon, and Zeta - and in chapter eight we looked in detail at the root motion types they contain, and the unique harmonic effects that these unusual systems create. With the exotic systems out of the way, in chapter nine, I was free to demonstrate a phenomenon that is an artifact of patterned root progressions, which I pointed out earlier, and that is harmonic canon. Depending upon how harmonic canons are developed and set up, I showed how they can also exhibit the phenomena I call Musical Escher Morphs and Harmonic Mobius Loops.
In the previous chapter, chapter ten, I introduced the alien diatonic systems - which are those seven note systems that contain two augmented seconds: Eta, Theta, and Iota - and with today's chapter eleven we will finish examining all of the nine master diatonic contextual systems and the total of sixty-three independent and dependent diatonic modes. All that is left is to look at and listen to the isolated root motion and transformation types.
*****
CHAPTER ELEVEN:
EXAMPLE 58:
Listen to Example 58
Here we have the progressions and regressions in Eta Prime, and you may find the effects other-worldly, as I do, which is what lead me to classify these contextual systems as alien: They are very, very far removed from the native systems, and even more foreign than the exotic systems.
EXAMPLE 59:
Listen to Example 59
These relatively smoother half-progressions and half-regressions can't do much to mitigate the strange harmonic effects that Eta Prime contains.
EXAMPLE 60:
Listen to Example 60
One of the problems with the augmented seconds is that - since there are two now - the listener is more likely to perceive them as minor thirds. That's pretty apparent in these super-progressions and super-regressions, where they are exposed in the bass.
*****
EXAMPLE 61:
Listen to Example 61
The Theta system is even stranger, as in addition to diminished thirds - which the listener is likely to perceive as major seconds - and the augmented seconds in the scale, we now have augmented thirds in the harmonies as well, which the listener will probably understand as perfect fourths. These distortions of native system realities can put listeners adrift, which is a nice way to affect them if that's the composer's desire. These systemic distortions of native reality are more compelling than the old techniques used in the serial systems of the century just passed, because a native system harmonic continuity can be progressively morphed into these alternate harmonic realities, and still retain their recognizability, as we will see in chapter twelve. One of the main criticisms of the various atonal methods is the, "any note could be replaced by any other note" feeling that listeners get, which is not an issue at all with systemic modifications from native, to exotic, and finally alien diatonic systems.
EXAMPLE 62:
Listen to Example 62
The funky thirds are quite apparent with the third movements in the bass with these half-progressions and half-regressions, but the connection to modal reality, though tenuous, is never entirely broken. This is far more effective than simply emerging listeners into total chaos, which they usually object to (And rightly so, in most instances). The exceptions, as always, involve situations such as film and stage vehicles, where there are extra-musical contextual defining elements at work. But for absolute music, especially, the alternate contextual morphologies available with exotic and alien systems are a great way to evoke the uncanny while still anchoring the listener to a modal locus.
EXAMPLE 63:
Listen to Example 63
The bizarre nature of Theta Prime is nicely exposed by the super-progressions and super-regressions.
*****
EXAMPLE 64:
Listen to Example 64
The minor tonic of Iota Prime adds even more darkness to the character of this alien system.
EXAMPLE 65:
Listen to Example 65
By the way, if you have been listening to all of the examples as we have progressed through the nine diatonic contextual systems, your brain is being hacked by them: Since almost nobody other than myself has ever listened to them systematically like this, I can tell you that this exposure will alter your conception of what musical reality can be. This is all leading up to the next chapter, where we will take an harmonic Mobius loop and morph it through all nine systems. If you have a musically sensitive mind, this will be very enlightening for you.
EXAMPLE 66:
Listen to Example 66
And so, all nine of the diatonic contextual systems have now been presented: Alpha, Beta, and Gamma for the three native systems; Delta, Epsilon, and Zeta for the three exotic systems; and finally Eta, Theta, and Iota for the alien systems. The total of sixty-three modal contexts and sub-contexts provide many more sonic resources than the old common practice guys were ever aware of, and even more than more modern jazz composers ever conceived of, all in a simple and intuitive system that can be applied to any diatonic theme a composer comes up with.
There are systems outside of the diatonic realm of course - which I have briefly alluded to previously - and we will begin to look at those in chapter thirteen.
I like that photo, even though she bears an uncanny resemblance to my ex-wife.
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 Eleven:
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. After the secondary dominants, 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.
Then in chapter seven, we looked at the exotic diatonic systems - those seven note contextual systems that contain a single augmented second: Delta, Epsilon, and Zeta - and in chapter eight we looked in detail at the root motion types they contain, and the unique harmonic effects that these unusual systems create. With the exotic systems out of the way, in chapter nine, I was free to demonstrate a phenomenon that is an artifact of patterned root progressions, which I pointed out earlier, and that is harmonic canon. Depending upon how harmonic canons are developed and set up, I showed how they can also exhibit the phenomena I call Musical Escher Morphs and Harmonic Mobius Loops.
In the previous chapter, chapter ten, I introduced the alien diatonic systems - which are those seven note systems that contain two augmented seconds: Eta, Theta, and Iota - and with today's chapter eleven we will finish examining all of the nine master diatonic contextual systems and the total of sixty-three independent and dependent diatonic modes. All that is left is to look at and listen to the isolated root motion and transformation types.
CHAPTER ELEVEN:
EXAMPLE 58:
Listen to Example 58
Here we have the progressions and regressions in Eta Prime, and you may find the effects other-worldly, as I do, which is what lead me to classify these contextual systems as alien: They are very, very far removed from the native systems, and even more foreign than the exotic systems.
EXAMPLE 59:
Listen to Example 59
These relatively smoother half-progressions and half-regressions can't do much to mitigate the strange harmonic effects that Eta Prime contains.
EXAMPLE 60:
Listen to Example 60
One of the problems with the augmented seconds is that - since there are two now - the listener is more likely to perceive them as minor thirds. That's pretty apparent in these super-progressions and super-regressions, where they are exposed in the bass.
EXAMPLE 61:
Listen to Example 61
The Theta system is even stranger, as in addition to diminished thirds - which the listener is likely to perceive as major seconds - and the augmented seconds in the scale, we now have augmented thirds in the harmonies as well, which the listener will probably understand as perfect fourths. These distortions of native system realities can put listeners adrift, which is a nice way to affect them if that's the composer's desire. These systemic distortions of native reality are more compelling than the old techniques used in the serial systems of the century just passed, because a native system harmonic continuity can be progressively morphed into these alternate harmonic realities, and still retain their recognizability, as we will see in chapter twelve. One of the main criticisms of the various atonal methods is the, "any note could be replaced by any other note" feeling that listeners get, which is not an issue at all with systemic modifications from native, to exotic, and finally alien diatonic systems.
EXAMPLE 62:
Listen to Example 62
The funky thirds are quite apparent with the third movements in the bass with these half-progressions and half-regressions, but the connection to modal reality, though tenuous, is never entirely broken. This is far more effective than simply emerging listeners into total chaos, which they usually object to (And rightly so, in most instances). The exceptions, as always, involve situations such as film and stage vehicles, where there are extra-musical contextual defining elements at work. But for absolute music, especially, the alternate contextual morphologies available with exotic and alien systems are a great way to evoke the uncanny while still anchoring the listener to a modal locus.
EXAMPLE 63:
Listen to Example 63
The bizarre nature of Theta Prime is nicely exposed by the super-progressions and super-regressions.
EXAMPLE 64:
Listen to Example 64
The minor tonic of Iota Prime adds even more darkness to the character of this alien system.
EXAMPLE 65:
Listen to Example 65
By the way, if you have been listening to all of the examples as we have progressed through the nine diatonic contextual systems, your brain is being hacked by them: Since almost nobody other than myself has ever listened to them systematically like this, I can tell you that this exposure will alter your conception of what musical reality can be. This is all leading up to the next chapter, where we will take an harmonic Mobius loop and morph it through all nine systems. If you have a musically sensitive mind, this will be very enlightening for you.
EXAMPLE 66:
Listen to Example 66
And so, all nine of the diatonic contextual systems have now been presented: Alpha, Beta, and Gamma for the three native systems; Delta, Epsilon, and Zeta for the three exotic systems; and finally Eta, Theta, and Iota for the alien systems. The total of sixty-three modal contexts and sub-contexts provide many more sonic resources than the old common practice guys were ever aware of, and even more than more modern jazz composers ever conceived of, all in a simple and intuitive system that can be applied to any diatonic theme a composer comes up with.
There are systems outside of the diatonic realm of course - which I have briefly alluded to previously - and we will begin to look at those in chapter thirteen.
posted by Hucbald at 2:27 AM
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