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Duke Ellington plays a beautiful solo Take the A Train in 1956 [see youtube live performance is awesome] I think it's in C and most transcripts are in C. But there is a video of him playing with the band years earlier and he calls out: "A Train in A flat".
What's going on, does this have to do with band vs solo ? Horn transposing ? How do they decide the key ?
Different instruments (and the voice, which is different on everybody) have strengths in different ranges. Usually, key choice is meant to capitalize on some particular characteristic of the instrument in question.
This is most obvious with the voice. Let's say we're writing a song for a singer whose highest solid note is an A. We have a melody where the triumphant high note at the end is the 5th of the scale. Putting the piece in D makes that high note our singer's nice high A. Or we could key it in C to make it come out a little easier. This is why musical theater is full of such awkward keys--the original singer's best high note was a G-flat, and the high note is the tonic, so G-flat major it is!
With saxophone, the core range is (written) D4-F6. The full range does extend past that in both directions, but that's generally where you want to hang out. So if you have control of the key, and you have a good idea of what you want to with it and where those notes should sit on the instrument, you can pick the key strategically. Concert A-flat is an alto sax's F, which is a pretty nice key to play in.
In jazz, musicians make a habit of being able to play their tunes in all keys. In order to “hang” this is something you just need to know how to do. Part of the reason they did this was because they played the same tunes all the time and it kept them fresh and interesting to play and listen to. The fact that he called out Ab that one time is most likely arbitrary.
