Theory of scales in piano improvisation

Question

I'm learning the piano and just learned two scales, A and C (and the theory as to how to make the other keys: WWHWWWH).

Other than learning how to make major/minor/dim etc chords how else can I use the scale?

For example: On youtube I saw guys talking about improvisation on the piano and they hit a C chord with their left (bass) hand and the right hand they pick certain notes that "go well" with that chord, I'm guessing there is some theory there as to what would sound good (eg: a 1 and 3 or a 1 and 6 etc) but I can't really find it.

As you might have guessed, I am very much a beginner so feel free to throw in any pointers to anything else.

Answer 1

There is a jazz scale theory, coming mainly from the modal period, with contributions from the jazz theorist George Russell, that approaches improvisation by viewing "every chord as having one or more scales that can be played over it" (www.jazzstandards.com/theory/modal-jazz.htm).

Here's a possible chords-scales correspondence (this chart is my attempt at summarizing lessons from the course Jazz Improvisation by Gary Burton; any mistake is my own fault):

Approaches by other performers and theorists may vary from this chart in some details and consider additional scales, like pentatonic and so on.

So in principle, selecting a scale as per this chart will provide, for each chord, notes that sound "good". I suppose this may answer strictly the question asked, but of course it's an over simplification and anyway only a small part of the improvisation process. And it's a rather complex subject in it self, requiring many hours of study to understand the theory behind these chords and scales and master all the different scales in all (or at least most) of tonalities.

Anyway, studying the major (= the Ionian) and minor (the natural minor = the Aeolian) scales is always the place to start, so you're on a good track by beginning to understand and play the major scales.