#1
Improvising over a harmonic vamp. How do I go about it? (i.e. scales, modes)
Thank you
#2
There are so many approaches this is a really difficult question to answer at all. You really need to be more specific because right now essentially what you're asking is "teach me theory".
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#3
Play a note, if it doesn't sound good keep playing different notes until you find some that sound good.

However, if you learn some theory, you will learn how to work out which notes will sound good and why they sound good. There are loads of lessons on this site and others that should help get you started.