The best thing for me (in tonal music) is to think of a major scale as an ordered collection of notes. You can start the scale anywhere in that collection, and go up to the next octave. Those are the modes.
And you can build chords on every scale step. Just skip every other one, and when you have four there's the seventh chord built on that step. Those are your arpeggios, in root position. If you play the _chord_ notes starting on any note other than the bottom (the one you built it from by skipping over notes), those are the inversions of that chord.
Hey, simple is good--for me at least. But srsly, I find that approach helps me see the modes and arpeggios on the fretboard.
And you can build chords on every scale step. Just skip every other one, and when you have four there's the seventh chord built on that step. Those are your arpeggios, in root position. If you play the _chord_ notes starting on any note other than the bottom (the one you built it from by skipping over notes), those are the inversions of that chord.
Hey, simple is good--for me at least. But srsly, I find that approach helps me see the modes and arpeggios on the fretboard.