When playing guitar,especially improvising,is it best to think of the notes a actual lettered notes or Scale degrees related to a tonic ? Since the keys are easily movable , I'm thinking that its better just to know the degree you want to play and knowing where that is related to the tonic.
With the guitar being a positional instrument, meaning one can play the same tune in many different keys but retain the same fingering and strings, merely moving where on the neck the tune is played, then knowing note names as the tune unfolds is not necessary. The relationship between the tonic and other notes, as far as where they are relatively speaking, fret and string, is easier to remember. In fact, there is often no need to reference from the tonic, but from the last note played. A lot of the time the next note will either be on the same string or an adjacent one, so knowing the various scale patterns is far more useful for improv. than the names of the notes. That's the academic side which (in my opinion) doesn't often come into play (sorry for the pun) during improvising.
Every guitar player is different so it depends. I have a friend who took piano lessons and read music before learning guitar and she would much rather know the names of the notes.
I play based on sound and feel and knowing where to put my fingers relative to where they are now to get to the note I want next relative to the note I am on.
But I have a musical ear. If you want me to play something, I would rather hear it than see it on tab. If you give me standard notation and ask me to play what is written I will get back to you in a few days. If I hear it, I can play it back immediately.
I personally have no need to know the names of the notes I am playing while I am playing them (I could tell you if I thought about it). I just need to know how to make what I hear in my brain translate to my instrument and the easiest way for me to do that is to start on the right note and go from there.
I am quite certain that if I was improvising and I tried to engage the part of my brain that would allow me to identify the notes I was playing, it would stifle my creativity and instinct. I think the best improvisers play by allowing their mind to engage with their soul and play what "feels" right. Thinking about the NAME of the note they wanted to play next - would short circuit that connection. Who cares what the note is called as long as it sounds good!
If you can improvise without knowing the names of the notes you are playing, your time will be better spent improving your craft by playing more - than by trying to learn to identify each note you are playing while improvising. That is my assessment based on my own personal playing style. Your mileage may vary.
Guitar is a three-dimensional instrument, where you are almost forced to know things in multiple locations. Here's something I think is of paramount importance: when you learn a tune on guitar, you should always practice playing chord and melody
together. That way you really learn to link the two things together. It has to become almost automatic. Then when you improvise, you should be able to see (and play) chords at almost any time as you go by. About note spelling when you play, I think it has to do with different areas of the brain. It's the same thing that happens when you speak another language. These are two different processes: one process is knowing and using that
language directly, without translating it. The other process is translating what you say into your own native language. That's what simultaneous interprets do. But they never do the two things together; always sequentially. So when you play, you bypass the names and go to the heart of things. If you really know these things, you won't need anything else. If you listened to music for enough time, you would tell most chords by ear, as if I’m listening to a D chord on the radio I know it’s D. And if I can hear their quality, find them on the fretboard, and play them, what else do I need?
I think it would be better to think the scale degrees.
For instance, let's say you play E (V) and then Am (i); if you think in scale degrees, then you will lead the notes that consist the V (E major chord) to the tonic chord (A minor). This way, you make the listener believe that there is some connection between the notes you play. They are two degrees of a scale.
If you only think the notes, then it might not give the best sound outcome (the chords might not sound connected with each other).
The notes will be the same, no matter how you think them, but the way you think, does affect the sound outcome.
It probably depends on how you 'hear' music.
For example ...
Absolute pitch :
I have recently been playing with a folk vocalist who doen'st play an instrument so we spent a bit of time getting the song into the right key for her. Her first choice was always pretty much the orignal key of a recording she'd learnt from - any other key felt 'odd', implying she might have something like perfect pitch. I think at that stage at least she's hearing music kind of in absolute terms : eg a C is a C , not a D even if you transpose. If your'e like this then perhaps it's more comfortable to work out the individual notes and get to know the fretboard that way. That's a lot to remeber though.
Relative to Tonic :
If you're able to hear the interval between the tonic and the notes of a tune (eg it's a 3rd. . then a 5th then a bent-up 7th rrelative to the tonic .. ) then maybe this is the way to think of your scales.
Relative to the last note :
Up two tones, down a full tone . .etc This seems a bit alien to me in that there's little notion of a "Home" note (ie the tonic) but if that's how you hear tunes then maybe this is a way forward.
To me, thinking in terms of an interval from the tonic is most intuitive as it means remembering only one instance of a scale, and is transferrable up and down the neck. The relevant scale becomes a "shape" of notes on the neck whcih makes life easier.
It also works on other instruments, although if you move to a piano you start to see that pianists may think in terms of absolutes, or have to remeber different 'shapes' for each key as the black/white notes translate to different patterns depending on the key.
I do think some of the answers so far are awesome. Let me please add by indicating something I was taught in music school.
The mode of a sequence of notes is also important, as the mode one is in can actually alter what the ear "hears."
For example the relative minor of CM is Am. The "notes" are exactly the same when no accidentals are present, yet we hear them differently when we look at the "root" note.
As I improvise, I often use modal shifts as a means of running from one key to another, or one section of the music to another (like at the end of a bridge). It's amazing what you can do by shifting run from (as above) CM to Am to AM when one rests on A as the "root" note for a moment before heading off into a key signature with 3 sharps.