Understanding the function of each note in a chord will help you unleash the fretboard and your guitar playing!
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I’d never thought about why there is no minor G or C chord in the open position before, but this got me thinking about it! I worked through the notes in each chord and came to the conclusion that you can’t play G or C minor in the open position as they both have a third which falls on an open string, which you can’t lower to a flat. They also both have another third which you can lower, but if you do so it sounds horrible (as it clashes with the non-flat third). Anyone else reach this conclusion too, or is there something else I’ve missed here?
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Hi @Wrangl3r,
You’re correct there. If I want play a Gm with a fingering close to the open G, I use 3x03x3 where I mute the A and B strings.
Hello @Wrangl3r welcome to the Community.
You are spot on with your analysis and thinking - kudos and good vibes to you.
There are some awkward fingerings that can give you minor chords in open position but they are too awkward to contemplate mostly.
There are five open position major chords, A, C, D, E, G only. B and F require barre chords. Hey presto! Shake up the alphabetical order, rearrange and you have CAGED. The beautiful CAGED system.
The minor chords have a similar story - open position minor chords are Am, Dm, Em only. Bm, Cm, Fm and Gm require barre chords.
Cheers 
| Richard_close2u | JustinGuitar Official Guide & Moderator
Yes I’d never thought about this either until today! Makes total sense now - thank you