I notice that at least in the beginning of your method, you don't talk about chord types like major, minor, dominant, diminished. You describe everything only as the "1 chord" the "2 chord", etc. So how will I know how to improvise over songs with chord symbols like "A-7b5"? Do you help us make this translation eventually? Or do we switch over to the other system at some point? Or am I supposed to just learn to recognize all of these sounds by ear so that I don't need the chord symbols?
That's a great question. You are exactly right that in the IFR method, we start by learning to visualize each note and chord within the overall key of the music. This is where those expressions like the "1 chord" and the "2 chord" come from.
But as our palette of sounds becomes more advanced, we will naturally expand our focus to include the intervalic relationships that you're talking about. Specifically, we begin to study the chord shapes you mentioned like major, minor, dominant, etc. In the book "Improvise for Real", you will find these exercises in the chapters leading up to IFR Exercise 4: Mixed Harmony.
The result is that when you're working at the level of Exercise 4, you will have both points of view thoroughly integrated in your mind. For example when you are playing the "2 chord", you will see very clearly that you are playing notes 2, 4, 6 and 1 on your tonal map, but you will ALSO see the minor seventh chord shape that these notes create.
If you want to see some examples of how this works, I invite you to take a look at IFR Standards Workout 1. This volume contains five of the most common jazz tunes played in jam sessions, explained in IFR tonal language so you can see exactly how this translation works.
Your final thought also brings up a great point. Part of our IFR practice is learning to recognize these sounds by ear. So very often I will find that the fastest way for me to understand the harmony of a song is to simply listen to it for a chorus or two. But sheet music and chord symbols are also a very helpful tool, especially when the harmony of a song is unusual or very complex. So it's important to be able to understand these symbols for yourself and relate them to the harmonic concepts that we study in IFR. I encourage you to do this with every tune you play. If you ever get stuck or have a question about how to analyze a particular tune, feel free to send us a message and we will be happy to analyze it with you.