Nice to hear that you're digging into Ted's lesson pages. There's several lifetimes worth of material to work on, and one has to be selective if he wants to remain a little bit sane in the study process.
I believe that Ted developed exercises or studies that focused on certain string sets for several reasons. Mostly I think they were meant to be vehicles for learning new chords and seeing how chords can be connected up and down the guitar neck, as opposed to across the neck. They help one to build a wider arsenal of chords to play wherever one wants - top, middle, or bottom strings. After gaining a lot of experience with the examples he gives, then one can choose according to need of a given situation.
Often Ted would take one comping study and write it out on the top strings, then write it out again with the exact same voicings but on the middle strings. Learning these variations helps the student to see how different chord forms can be modified slightly when moved onto different string sets. He called this system "String Transference." This was a fundamental point he taught all students. (See the "Fundamentals" section for 5 lesson pages from Ted, and also check out the "From Students" section for Bob Holt for his explanation). Moving chord the same chord (or group of chord progressions) around on the neck also forces one to learn the notes all over the neck.
Another factor for the different string sets is the tone differences. Compare the tone of a triad voiced on the top 3 string and the same notes on the bottom 3 string up high on the neck. For Ted this was an important aspect to be considered. Also, by playing these chord forms on different sets, one gets exposed to forms that might be unusual or unfamiliar...and challenging for the fingers. Ted was all about breaking old fingering habits, expanding the boundaries, and exhausting the possibilities. These were meant as teaching vehicles, but if one is so inclined he could certainly play these at a gig. It's just that the purpose of all of this is to bring you to the point where you have much more freedom that just memorizing a collection of chord moves.
As far as the "cumulative" question, here is what was written in the July 2018 TedGreene.com Newsletter:
July 2018 • TedGreene.com Newsletter
This month we have 12 new lesson pages for the Fundamentals section. Most of these pages come from a couple of folders in Ted’s teachings file cabinets that he listed as “Cumulative Teaching Program.” What the heck is that?
Cumulative: Merriam-Webster defines this as, “Increasing by successive additions; made up of accumulated parts; and formed by the addition of new material of the same kind.” This is a term Ted used several times (mostly during the 1980’s) for describing how to approach either learning or teaching new concepts. The idea is to expose the student with a small bite-size chunk of information first. Once that is learned, he would then add another small chuck to the first. Then another after those two were grasped, and so on. Thus, the pieces were absorbed accumulatively. The brain seems to better understand, absorb, and retain information gathered this way.
Sometimes Ted presented the cumulative method by introducing a basic chord form, then made slight modifications to it, one note at a time, thus resulting in a large collection of different chords all based off the original starter chord form. You can see this at work in some of the lessons presented this month, particularly the “Cumulative Chords - 5th String Root, Middle Strings, 4-Noters” page.
Since most of these “cumulative” lesson sheets deal with basic building blocks for chords, we have put them in our Fundamentals section. On some pages the cumulative process is not always clear. Perhaps it was Ted’s job as the teacher to explain what was going on in each lesson. Since we don’t have Ted to do this, you’ll be required to think deeply and analyze each lesson: play thru the examples, try to see what’s going on, and use some intuition to unlock the ideas. The concepts will come to you.
On some of Ted’s cumulative chord pages he has a symbol in the upper left corner with at number, a dot, and interval and an arrow or arrows. For example: 5•R→ shows that the 5th string is the bass note and is the Root of the chord. If the arrow is pointing downward, that indicates that the chord forms are built on the frets above the bass note (towards the guitar bridge). If the arrow is pointing upward, then this shows that chords are built on the frets lower on the neck (towards the guitar nut). If the arrow is straight, then the chords are built straight across from the root. I believe these symbols were mainly meant for Ted himself, not the students, so you can ignore them if you wish….but it will give some idea about the organization of the lesson page. All of Teds’ little symbols and notes have a reason behind them.
This all may be an oversimplification of what Ted meant by the cumulative process, but at least it serves as a starter for you understand what these pages are all about. Next month we’ll be presenting another batch of similar cumulative pages. Please keep in mind that although most of these lessons are placed in the Fundamentals section, they’re not all just for beginners only. Even the veteran player may find something useful, or see new ways of looking at the guitar fingerboard, etc. So, give these pages a quick review – you may be surprised.
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I hope this explanation sheds more light that causes more confusion.