The following is something I wrote in a Facebook group in response to a young player who was seeking methods to develop his transposition skills:
The ability to transpose is an essential weapon in the aresenal of any working musician. There are a number of different methods to develop this skill. Personally, I’m a big believer in transposing functionally, meaning using the Solfege system of Moveable DO (where the tonic is DO) to understand the line from a functional standpoint (as opposed to Fixed DO, where C is always DO). I also use a LA-based minor. Allow me to explain:
When I practice scales on any instrument, I sing solfege in my head along with the scale so that my muscle memory relates to the function of the notes in the scale (i.e. if I’m in A major, in my head I’m thinking “DO, RE, MI, FA, etc.” rather than thinking “A, B, C#, D, etc.”). Whenever I read a line or play a melody, I’m either sightsinging or singing it in my head by function. Since I have practiced my scales functionally, and hear them as such, I can tell my fingers: “Play in the key of Eb major,” or “Play in the key of B major,” and because I have done the prep work, not only do I play the right notes in the key required, but I also understand their function and am able to optimize their function for a better performance of the line (i.e. leading tone resolution to tonic, subdominant resolution to mediant, adjusting pitch on certain chord tones to tune the ensemble, etc.).
I understand that intervallic transposition is a tried-and-true method, and many of my colleagues teach that way. However, my issue with intervallic transposition is that not only does it require that you do math on every single note, but it also negates the understanding of function.
Is it a lot of prep work to get to this point? Sure. But the benefits to your musicianship are immeasurable, because not only will you be playing the correct notes, you will also have a greater ability to interact with your fellow musicians on the fly. And besides, who wants to play everything in the same key all the time? Not only is that boring, but it doesn’t challenge you as a musician. Why rest on your laurels if you can constantly push yourself to get better?