Recently I've been doing an exercise that makes me feel sorry for anyone who happens to be listening. I pick a song that I know by heart. Recently I played Autumn Leaves, Pennies from Heaven, and I Could Write a Book on the flute. I start in the key the were written in and then transpose them, moving around the circle of fifths (C-F-Bb-Eb- etc.) until I cover all twelve keys. Things get somewhat difficult when I reach the keys with a lot of sharps and flats, and I occasionally have to stop and think - and LISTEN to myself.
My ear isn't so great, and my musical memory is also weak, so I often have to remind myself, let's say, that a melody moves up and spells a half-diminished chord (as in Pennies from Heaven), or shifts briefly into another key. But I'm sure this exercise is doing me good.
When I read music, I don't listen to what I'm playing in the same way as when I play by heart or by ear. By forcing myself to play in all the keys, I'm hearing better and moving my memory of the tune from my fingers to my mind. By listening to what degree of the scale the song starts on (Autumn Leaves is in a minor key and starts on the tonic; I Could Write a Book is in a major key, starts on the third degree, and jumps to the seventh before we actually hear the tonic note), I hope I'm training my ears to hear what key the song is in. With some songs, like Desafinado, you don't hear what key it's in until the very end.
Jazz musicians were (are still?) expected to transpose easily, because vocalists often required a lower or higher range than the original key of a song. I have read that Coleman Hawkins was often so bored with the standards he was playing on a club date, that he called them in unexpected keys, making things tough for the musicians he was playing with. It's more or less standard procedure to play Mack the Knife in a new key every chorus, moving up chromatically.
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