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So, I had to leave and I finished that last comment quickly.
I reread your comment, and I want to respond more directly than I did in the mini theory dissertation.
Yes, you can solo in G major over Em, because they have the same notes, as you said. However, that’s why they can’t be different keys. The notes are the key. So the 2 “scales”, G major and E minor, are in the same key. One key.
By the way, there are only 12 keys. C, G, D, A, E, B/Cb, F#/Gb, Db/C#, Ab, Eb, Bb, and F. I just went around the circle of 5ths from C back around to F. There are 3 enharmonic keys, meaning there are 15 key “signatures” even though there are 12 keys.
Each of the 12 keys have 7 modes. That’s the basic system. Beyond that, there are variations they use in jazz, variations in blues, and of course the many variations of international music.
Music theory is a puzzle that you have to look closely at for quite a while until you finally “see” it. When you see it, you wonder why it was so hard to see as then it appears quite simple.
MG 😀
