Somewhat unrelated: I’m looking for a comprehensive overview of why the CAGED system works on guitar. I see lots of mechanical explanations of how to use it to play various chords down the neck, but nothing explaining the theory behind it.
Using a 6-string bass as an example: https://bradleyfish.com/the-notes-on-the-6-string-bass-guita...
You can find a 2D pattern in the white notes (green notes in the pic) that you can use to understand how the pattern will extend from a given point. For example notice EF+BC always appear in the same 2x2 box shape. Also how those boxes repeat in a diagonal line, and how boxes are connected vertically by a "strip" of 3 notes ADG
The only difference for guitar is that you have to correct for the G/B strings which are separated by a 3rd instead of a 4th, by scooting the pattern on the B+E strings up by one fret
- those 5 chords are the first you learn, and mechanically easy to play in open position, so you know them by heart
See this diagram (https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F...):
- the CAGED 'order' (C then A then G etc) matches the order in which octaves of the same root appear as you go up the neck, therefore CAGED is a good way of visualising octaves (see how in the 'C-shapes' column the chords 'share' root notes when played in that order up the neck)
- each chord matches a root note position (C: top part of the neck box on the 5th string, A: bottom part of the neck box on the 5th string, etc), therefore if you're playing a scale, no matter what position you're playing it in, you can choose a CAGED chord to overlay on it and easily find the root, third, and fifths (see how in the 'C major scale' column, you can overlay each chord onto one way of playing the C major scale)
- learning these mnemonics should eventually help you 'unlock' the guitar neck, ie have an intuitive knowledge of what intervals you're playing and how to build melodic lines with them
Generally, music theory 'works' because it describes why things sound good. It's not theory that informs what sounds good, rather theory attempts to describe what sounds good and build patterns which will help theory learners, in turn, make music which sounds good.
By the way I think the most difficult thing about CAGED is that it's way too overhyped. It promises too much (scales?) but delivers too little. (Doesn't even have minors)
The book I'm reading (recommended in another comment) does talk about minor forms of CAGED forms, though - pentatonic scale patterns, arpeggio patterns, and chord forms.