Seeing as you asked my opinion... (although I might be repeating some of the above)...
Originally Posted by Jeansen
A sequence like Am-G-F is a standard sequence in A natural minor (A aeolian). There would normally be no good reason to switch scales. (a) it would sound wrong; and (b) it makes it more difficult! (You want more reasons?? )
To say it's "in A minor" or "in A aeolian" just means that A will sound like the tonal centre, like the chord you want to finish on. It has no impact on scale pattern choice.
You could choose any pattern of the C major scale - call it what mode you like - it makes no difference.
Or, to be more precise, it will make a difference, but not a modal one.
Whatever pattern you choose it will sound like A aeolian on Am, G mixolydian on G, F lydian on F - but you may not notice those sounds (esp if the chords don't last more than a bar), and it doesn't really matter.
If you want to underline those modal sounds, you would accent the F note on the G chord (and on the Am), and the B note on the F. But (a) you may or may not like the sounds you get that way; and (b) that strategy may work against building good melodic lines across the chords, which is what matters.
What should govern your choice of scale pattern is:
1. how high or low on the neck do you want to go?
2. which pattern offers the easiest ways to play the arpeggios of the chords?
3. which pattern offers the easiest ways to play phrases you like?
#2 is the most important. Any mode/pattern of the C major scale (any neck position) contains the requisite arpeggios, but some lend themselves better to playing off those arpeggios.
The fact that it's in A aeolian means you will probably want to play off the A notes in whatever pattern you choose. Phrases ending on A will sound finished. A is the "period" on any musical sentence in that key/mode. Think of A as the gravitational centre, that you can pull away from for effect, but need to return to eventually. (Stay on it too long, you sound "grounded". Stay away from it too long, you are "flying", but may also sound lost or aimless.)
The secondary notes are any other chord tone (on the current chord). After that, other scale notes (which are all chord tones from the other chords) are best as passing notes.
The fact that Am and F share 2 notes means that most of what you can play over Am will also work well over F. In fact, the whole A minor pent sounds good over F - and obviously over Am too. But it won't work over G.
CHORD ARPEGGIO PASSING NOTES
Am A C E B D F G
G G B D A C E F
F F A C G B D E
So you need to start from arpeggio notes - because they always fit. Obviously this means knowing how to find the arpeggios in each scale pattern - which in turn means knowing all your CAGED movable chord shapes.
Plan a phrase to land on a chord tone on the next chord. Eg, on the Am chord, you could think of B as a target note on the G. You could start from A, C or E, play a scale line, and if it ends on B (or G or D) as the G chord starts, it will sound good. Plan something similar to get you from the G to the F chord, then from the F back to Am.
A great example of simple lead phrases using this concept, over this very sequence, is Neil Young's "Like A Hurricane". Listen to the intro melody (actually the same as the vocal melody). It plays off chord tones on the Am (with passing scale notes between); hits a target D note on the G, plays a similar line from (and between) G chord tones; then plays a line on the F very like the first line on the Am. An element of sophistication is that the phrase on the F begins with an E note. That's the maj7 of the chord, which adds a special "wistful" character.
and here it is on keyboard, a little clearer:
(The 4th chord is Em, btw, then another G before going back to Am.)
This is basic stuff. Once you've done a few of these kind of exercises, you get an idea of what works, and of the effect of particular chord tones. (Eg, a 3rd has its own sound or character, diifferent from a 5th, and both are different in impact from a root.) So you start to get a vocabulary of expression. Then you can "push the envelope" - maybe go for non-chord tones. Hold (or repeat) a single note across all the chords, see if it works (some will, some won't). Add chromatic notes (outside the scale) in passing - see if you can get away with that (or look for strategies that let you get away with it - jazz players know them all ).
You will also start to get an idea of what is "right" for any particular song. A phrase that sounds good on a blues or heavy rock number, might not work on a ballad (and vice versa), even tho the chords are all the same.
You don't need rules spelled out for this, because you know what those kinds of music sound like. You know - at least once you've got past beginner-level improvisation - when you hit a note (or idea) that's wrong.