Transposing and Modulation
 How do transposition and modulation relate? Are they the same? In this newsletter we’re going to take a look at both of them and see what makes them tick.
I’m sure that you have had the experience sometime in your piano-playing life when someone asks you to play a song — but in a different key than in which it is written. It might be a singer wanting you to lower the song a step so he/she doesn’t screech. It might be a song leader wanting you to play a song in a more comfortable keys for a congregation or group. It might be a trumpet player looking over your shoulder and wanting to play along with you — but when he/she plays the same note you are playing, it sure doesn’t sound the same!
So….it’s your job, as pianist, to get that song moved to a different key. That’s transposition — playing or writing a song in a different key than in which it was originally written.
   Modulation is similar but different — modulation means the process of getting from the old key to the new key. In other words, if I’m playing in the key of C, and then want to play in the key of Eb, I have to learn to modulate — move smoothly from one key to another without being too abrupt and jarring.
Continued at https://www.playpiano.com/Articles/25-transpose&modulate.htm