oh so you're distinguishing it from improvising on the melody (which is the key), and improvising on the harmony (which could be different scales). first time I heard that.

that last edit made alot of sense, thanks

take "misty" for example, look at the melody and you'll see it follows the changes more than the "home key"

@Some_Guy thanks for pointing that out. you made things alot clearer. so you're saying the melody itself is affected by all the different scales in the song.

@foreyez I'm saying that melody exists in a harmonic context, and that in most western music, that harmonic context includes both the pitch centre in general and also the harmony at that present time in the song. Part of what goes into a melody is choosing notes that outline that harmonic context, both of the home key, and the current harmony. So a melody might include notes that imply the chords, or it might deliberately choose notes that clash with or embellish the chords, but all of those notes will be heard in relation to both the chords and the key.

There are no "rules" here, it depends on the effect you want. But yes, often melodies (whether planned or improvised) will outline the chords of a song, and pick out notes that highlight the harmonic movement. But again, not always by any means.

Also, you have to realise that most songs will have chords that relate in some way to the home key at most points, and so whether your melody is following "the chords" or "the key" is a matter of perspective. And when songs use chords that noticeably fall outside the key, well you might write a melody to highlight those odd chords, or you might conversely do the exact opposite, sing or play a note from the home key to highlight the contrast, and then give a feeling of resolution when the chord gets back home. These are all options!

for an example of a song that includes lots of weird harmonic movements, and has a melody that dances around these weird movements, there is desafinado by Tom Jobim. It's literally called "out of tune" and is deliberately cleverly written to have a bizarre melody that only works because it implies an underlying (complex af) harmonic structure. On the opposite side "pyramid song" by radiohead works by essentially reusing the same notes in the melody again and again and re-contextualising them with new chords. Both approaches produce interesting effects and both can be (and are) used in a solo.

And if you're wondering "OK so why use scales at all", listen to this youtu.be/tCMhuN3053o and tell me whether you can sing even held whole notes that sound in tune with the chords just by ear. It's not easy to always find notes that fit when the harmony jumps around like that, and so employing scales can be a useful method to find the "good notes" in a given song; but they're just a tool, not a "rule". And personally, I prefer to only play songs I know well enough that I can just follow my ears, and if that means I don't play "giant steps" then personally I can live with that.

@Some_Guy consider creating an answer you have alot of important things youre writing and the mods might remove comments.

@foreyez I didn't realise how much I'd have to say. Please feel free to rip off these comments and create an answer (anyone)

difficult because the question is so broad, my comments might be too long for a comments section but I also don't think it's really comprehensive enough to "answer" your question, just an aspect of it.

Your last sentence - D Ionian may not be the same scale as A Mixolydian, but doesn't it contain exactly the same notes? So as far as improv is concerned, it's using the same 'scale' (as no-one just goes up and down the scale notes0.

@Tim in a different mode you concentrate on different notes. So in my example, your "strong" notes (1, 3, 5) and chords (I, ii, IV V) in D Ionian are going to be different in D Ionian than in A Mixolydian.

Lots of good comments on good answers mean a good question. Upvote the question, too, folks. :-)