A couple people were saying in a previous post, how for ear training one should think in scale degrees and not intervals. So if I'm on the note E and I want to get to the note G, then I shouldn't think of a "minor third", rather I should think of going from ^3 to ^5 in the key of C.
I always thought that intervals were of utmost importance, since if I randomly pick a note on the keyboard, I could play any melody I wanted to regardless of if I even knew what key I was on, just by committing the sound of an interval to muscle memory on the piano.
Also each interval has a specific function and I'm not sure if scale degrees do. But now after I read what they were saying about scale degrees, I'm thinking maybe that's the better approach because it sounds more efficient. I'm not sure.
So, in what situations would you use intervals vs. scale degrees, especially when it comes to playing by ear and improvisation?