For your Satin Doll song, if your chords of the beginning are /D-7 G7/D-7 G7/E-7 A7/E-7 A7/,so C key is the right key. Temporary modulation in a song don't change the basic key of a song. That is different if the whole chorus is transposed + half tone, in this case, the key should be changed. Regarding harmony rules, additional data can be found over the net or in many manuals.


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