Saxophonist Pascal asked an excellent question concerning how to play by ear in different keys:
“Regarding exercises involving arpeggios, inversions, or scales on saxophone: When using movable DO, should I think of each tonality as if it were C Major? For example, when I play in E major, do I think, “DO RE MI FA SO LA TI DO”? Is it as if there were only one Major scale on each starting key? This is a revelation for me!”
Good question, Pascal. A major scale has the same specific form, regardless of which note is chosen to be DO. Here is that form shown as a schematic and on the piano keyboard:
From these pictures, you can see that the half-steps occur between MI & FA and between TI & DO. This is the rule, regardless of which key you’re in. There is a whole-step In between the other notes of the scale (DO-RE, RE-MI, FA-SO, SO-LA, & LA-TI). There are 12 major scales, each with a different DO. The form of every major scale is the same.
By way of illustration, pretend your drone is flying over a large field. You see a group of players come onto the field to set up a baseball diamond like this one:
Once you know where home plate is, you automatically know where the other bases are, because the distance from base to base is dictated by the rules of the game. In our case, home plate is like DO.
Now let’s pretend there are several other teams who also want to play on this property. Each team sets up its own diamond, and your drone captures this image:
In this picture, you see there are six baseball diamonds on different parts of the property. Each diamond is shaped the same as all the others. Once you know where home plate (DO) is, you know where all the other bases (RE, MI, FA, SO, LA, and TI) are.