There are hundreds of scales and many different types of chord. Trying to calculate a way through this library is not going to work when you step onto stage or the record light goes on. Applying learned formulas as a way of navigating these complex harmonic combinations is going to limit your imagination.
So how can one know, which of the many notes, in which of the many scales to play over which of the many types of chord?
You have to do this in the twinkling of an eye. How can this be done?
The answer is simple. You need to use your ear.
Your ear is connected directly to your heart and your imagination.
Formulas, and calculations are not.
The problem is, that the term “playing by ear” has more than one meaning. If one is playing by ear in the true sense, one is playing directly from the imagination and the heart on the instrument. Each note is the note you want to hear at that moment to express how you feel about the music.
The other common meaning of “playing by ear” is something else entirely. It refers to a someone, who doesn’t have any real understanding of what each note will sound like before they play it. They don’t really understand music theory either, nor do they really know their instrument that well, but they manage to make what they play “fit in” ok despite this. They will typically rely on preset fingering patterns which they already know will sound ok, but have no real connection to what they hear in their head. This is not playing by ear in the true sense and it is ultimately a very restrictive and unsatisfying approach for both player and listener.
Learning to use your ear in the true sense of the word is the most important thing you can do as a player. In terms of making great music, it trumps any level of technique. For many players, and certainly for improvisors, being able to truely play by ear, is the only way to real musical satisfaction.
This is one major area of study and practice. This is one of what I call the Three Cornerstones which we look at in detail in private teaching as well as workshops.