If you play fingerstyle, Martin Taylor has an interesting way of teaching the building up of chords starting from the bass note, harmonizing it with 10ths (3rds up an octave) and then adding 7ths to supplement the sound. The intuition is that you really only need the root note and 3rds to form the chordal tonality (major/minor).
I found this quite interesting to fully understand the fretboard, from a horizontal scale perspective instead of CAGED.
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