#1
So I think I've got a fairly good grasp on improvising now. I just get a little confused when it comes to chord progressions that are more than I-IV-V etc.

Say for example, I'm playing over Am-Em-C-D. Any of the notes in those respective chords will work over those chords--but if the changes between chords are quick, then we can't really play a different scale over each chord, right ? So we need one scale that will work for all of them-- in this case, the tonal center is Gmaj or Em. Why not Am? 

So if that holds true, we can basically play Em pentatonic the entire time, right? Or Em Aeolian, G Ionian and the various modes therein, right? 

I'm just trying to get this all into my mind. It's difficult. If anyone could point me in the right direction for learning more about this specific bit of theory, I'd appreciate it a lot. Cheers. 
#2
Forget theory, scales, modes, or finding tonal centers... 

Improvisation is about having something to express that sounds good.

This means two things:

- it does not come from "searching", figuring out, crafting, or constructing - it comes from something musical already within you needing to get out and be expressed

- that something is coming from your ears' interaction with the music; not from calculations, patterns, or shapes - if you don't already hear what to do, none of the reading, writing, and math are going to reveal it to you

Just listen to a lot of different kinds of music until you begin to have musical ideas you hear in your mind and feel compelled to express.
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#3
Yeah, the thing you need to do is shift your mindset...always remember that the guitar is a musical instrument first and foremost.

So try to get out of the habit of approaching playing the guitar as a physical exercise and start approaching it as a musical one ...start thinking about scales and chords as the sounds they're made up of, not the shapes and patterns they create.

So listen to your backing and simply play a note. And ask yourself the question "do I like the way that sounds?" If you don't then okay something else, if you do then you need to ask yourself "what sound do I want to hear next?", then figure out where to find it on the fretboard. A good understanding of their and a good ear are what make finding that next note easier, but you've still go to have an idea in your head before you can really make music.

Play the guitar, don't let the guitar play you.
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#4
As others have said, use your ears. There's really no right and wrong. What sounds good is good.

But I think it makes sense to have some kind of a reference point. Am Em C D is a diatonic chord progression (so one scale will work over all of the chords). What key is it in? Well, that depends on the context, but the notes in the Em scale will work over all of the chords because all of those chords use notes in that scale.

Knowing scales and chords definitely helps you with finding the notes that you want to play. But I would suggest treating them as a way of navigating on the fretboard, not as a rule that you need to follow. It's pretty easy to fall into the trap of "letting the guitar play you" and just moving your fingers randomly in a scale shape. That's not what you want to do.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#5
Thanks guys. I get where you're going. I agree that improvisation and lead guitar in general should be more musically based than "mathematically", so to speak. I've even found in my own playing that the better I get technically, the easier it is to fall into trappings of scales and speed and flash rather than focusing on musicality. 

That said, I posted this question for advice on music theory and improving my understanding of what works where and why. I know what SOUNDS good but I want to learn why it sounds good. I have a rudimentary understanding of music theory that I'm trying to take to the next level. I want to be able to say "right, this lick works here because it's in E minor pentatonic over a change from Cmajor to D major, etc. 
#6
I think understanding what you are playing over is important. That's really the best way of determining what will most likely work. So if you haven't already learned about functional harmony, I would suggest learning about it - you want to understand the chord progression. Another thing is thinking about how the notes that you play relate to the chords. You want to play over the changes, and this means knowing when the chords change and what notes are in those chords.

Learn about consonance and dissonance, and tension and release. Chord tones are always consonant. Some non-chord tones are more dissonant than others. Dissonance is not necessarily a bad thing, but it usually needs to be resolved to sound good. So you want to be aware of the notes that create tension, and you want to know how to release that tension. You can actually try this just by playing non-chord tones over a chord and using your ears to tell where the tension wants to resolve.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
Laney VC30
Tokai TB48
Yamaha FG720S-12
Yamaha P115
#7
When you listen to music don't just bang your head and play air drums, but invent lines in your head that go along with the song, then when you get back to your guitar, play those lines out. You'll find out that oftentimes, in your own melodies and leads other people write, a single phrase of a solo will use notes from major and minor scales simultaneously. Or the solo may be primarily in a major scale, but one key note may be a minor third(or whatever depending). Why? Because it sounds good, and this is why it is considered a bad thing to fall into a habit of strictly playing certain scales over certain chords.