(I just posted an answer to this sort of question...which if I have been asked once I have been asked a thousand times over the years...on my own brass discussion site, The Open Horn. It seems to me to be a pretty good overview of my own approach to the idea, so I thought that I would post it here as well. In it I recommend that the questioner purchase my book for a more thorough answer, but since I have not yet managed to finish a treble clef/valved instruments edition of that book I cannot yet recommend the same thing to any but the most advanced trumpet players, people who will be easily able to translate trombone concepts to their own instruments. Nevertheless, the links to several of my articles on Carmine's ideas might come in useful to people here, so read on if you are interested.)
The "goal" of the Six Notes exercise?Hey Sam, I've been wondering lately, someone has told me in the past about "The Six Notes" excercise from Carmine, but honestly I never gave it too much attention. Now that I've grown up a bit and discovered potential of Caruso excercises I know, I started wondering - what's the goal of "The Six Notes"? How should I practice it and what does it help me with?
I could write a book.
In fact...I already have.
Time, Balance And Connections.
Achieving a good balance between you and your equipment through the use of time-based exercises to provide the possibility of good connections through all registers of the instrument. A pretty good survey of everything that Carmine taught.
For starters, read my article Carmine Caruso-A Brief Overview. Then read this one, which I have not yet gotten around to updating and posting on my own site-Carmine Caruso and the Six Notes.
How should you practice the exercise and how will it help me you?
Well, the very basic version that I present in that second article...if done right, something that I have literally never heard from any student who told me that they "knew" the Six Notes but had not either studied with Carmine or with one of his better students...is the single best prelude to warming up that I have ever found. Bar none. I often say that all I have essentially done is throw a grenade into Carmine's exercises, picked up the pieces and found that all of them function the same way as did the originals. Read the short article Carmine Caruso, Mandelbrot sets, and me for more on that idea.
I use it...highly individualized... as a prelude to every examination of any particular set of ranges in which I am about to practice.
So the best long-story-short answer to your question that I can offer would probably be "Buy my book and find out." There are 265 pages in it and almost every one of them is in some way "about" the ideas behind that one masterfully simple exercise of Carmine's.
Sorry, Peter. That is about the best answer that I can offer. If you were sitting here in front of me I could show you what I mean in about 20 minutes. But you are not, so...there it is.
Read the articles and get back to me if you have any more questions.