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There are two basic ways of learning Major scale along the full fretboard. Using the CAGED system or using a 3-notes-per-string system.
Using CAGED (actually it should be EDCAG as pattern 1 gives rise to the E chord shape) the 5 patterns look like this:
The CAGED system is intrinsic to these shapes.
Look at pattern 1 - do you see how an E-shape chord sits within?
Look at pattern 2 - do you see how a D-shape chord sits within?
Look at pattern 3 - do you see how a C-shape chord sits within?
Look at pattern 4 - do you see how an A-shape chord sits within?
Look at pattern 5 - do you see how a G-shape chord sits within?
In learning & practicing you should always start and end on the lowest root note, cycle around each scale shape several times, and listen for the sound of the root note.
Also listen for the sound of the intervals. The formula for the Major scale is:
Tone, Tone, Semitone, Tone, Tone, Tone, Semitone
Whole, Whole, Half, Whole, Whole, Whole, Half
Each shape has 17 notes. This means that when practicing to a metronome, playing 16th notes, with 4 notes between each click, you should always land back on the low root note on the beat.
Start with a down pick and try playing alternate picking. With these patterns you should find you end up on the lowest root note with a down pick each time.
With regard to using the Major scale to improvise ...
It is a melodic scale, and really moves in different paths to the blues-rock minor pentatonic scale. It's not so much about using licks ... it's more about building melody lines. The vocal melodies of millions of songs are Major scale melodies.
'Seasonal' thought ... using just pattern 1 of the Major scale how many Christmas song melodies can you play, just by ear and a little bit of experimenting?
Folk and traditional songs tend to be Major scale melodies for the most part too.
Here is me ... a little while ago, having learned all 5 patterns of the Major scale, having a bit of an improv to a Major scale backing track in G. I'm not saying it's perfect - it isn't and my technique is not fantastic either - but it may help to illustrate the melodic nature of the scale.
Notice, in a few places, a slightly bluesy-sound comes in ... that's me running out of ideas and inspiration and 'cheating' ... thinking in terms of E minor pentatonic (which is contained entirely within the G Major scale).
I think these sections are really noticeable and also help to illustrate the differences between these two scales and their use.
See below ...