Thank you for the excellent method, which I am truly enjoying.
I have a question with respect to naming/tagging notes within each harmonic environment. I understand that by naming the root note of each new environment relative to the overall key of the music, you want our brain to always maintain the connection to the major scale.
I have a difficulty here, in that over the years I have learned each harmonic environment naming their tonal centers always as note 1. For example rather than visualizing the natural minor as 6, 7, 1, 2, 3, 4, 5, 6 (which keeps your brain aware not only of the natural minor mood but also of the parent major scale), I am used to visualizing it as 1, 2, b3, 4, 5, b6, b7, 1.
In the same way my memory contains systems for each harmonic environment that you cover in the course (including key harmonic environments in the pentatonic systems, harmonic and melodic minor), I always visualize each environment as starting from note 1 and not from a note of the parent key.
I have noticed that most songs and jazz standards over which I want to improvise normally have just one concrete environment, and so it might be easier to name the notes as starting from note 1 rather than from a note of the parent key (e.g. note 6). Do you think it's necessary to have the nomenclature named in a way which always connects it back to its parent key?
This is important for me at this stage before I go further because maybe i am wrong and later I will regret not switching to the nomenclature as you have it in the course.
That's a good question and it's great that you're thinking deeply about it. I think the first thing to realize is that in IFR we actually study both points of view, and you should too. In the IFR courses, students learn the tonal view (minor tonal center = note 6) before they learn the modal view (minor tonal center = note 1 of a minor scale). By contrast, in your own experience it sounds like you gained confidence with the modal point of view first. The question of which point of view to learn first is really just a teaching decision. There are reasons why we teach the tonal point of view first, but it's certainly not a bad thing that you already have experience with the modal point of view.
Regardless of where you're starting from, through IFR you are going to develop confidence and mastery with both points of view, so that you can see very clearly where you are with respect to the tonal center of the moment and also with respect to the overall key.
Here's why it's important to add the tonal point of view to your skill set. You said that in the standards you normally play, it makes more sense to think of the tonal center as note 1 because this tonal center never changes. Whenever that's true, then that makes perfect sense. But the vast majority of standards use many chords from the same key, passing freely through both major and minor tonal centers. If you are limited to treating each new tonal center as a new "note 1", completely divorced from the rest of the composition, then you cannot see the big picture of how all of these progressions fit together. Instead you're imagining the song as an endless series of key changes, which forces you to continually switch to new scales and new naming systems, all of which is totally unnecessary.
Here is a blog post that tells a little more about this:
IFR Student Q&A: Why do you call it note 6?
But I think the most important thing to realize is that I'm not trying to "convert" you to any other way of thinking. Your own intellectual freedom is the most important principle here. If you prefer to consider each new tonal center a new "note 1" and manage all of the resulting key changes, that's up to you. Whatever supports you in creating your music in the most comfortable and enjoyable way is what you should do.
More importantly, both points of view are just different ways to describe the exact same reality. So at some point I think you will move beyond this distinction entirely. If I'm playing a standard that starts in what we might call the "six chord", and some other musician calls it the "one minor" chord, there is absolutely no conflict here. It's just a shift in coordinates. If I call it "one minor" then its dominant chord will be called "five dominant". If I call it "six minor" then its dominant will be called "three dominant". But we're talking about the SAME SOUNDS.
In other words, mastering this subject isn't about having a superior naming system. Mastery means being able to appreciate the logic of ANY naming system, because you understand the underlying musical material itself.
Here is a link to a related Q&A with a student that goes more deeply into this last point:
IFR Student Q&A: Should I be thinking about chord shapes or the overall key?
So remember that our goal is to truly understand this material so that we can effortlessly switch between the two points of view with no conflict. The tonal point of view isn't any "better" than the modal point of view. But since you already have a lot of musical knowledge based in the modal point of view, I think that mastering the tonal point of view would be a nice goal for you because it would add something new to your abilities.