Moving the E Shape, Fret by Fret
First, we move the shape, as is, fret by fret, leaving the 6, 2, & 1 strings open. At each fret, let’s make a thumbs up or down for the way the chord rings.
For thumbs up, the chord will need to resonate in a way that is somewhat consonant. For thumbs down, it will sound like a scary movie chord. Thumbs down doesn’t mean unusable, just dissonant. The scary movie chords, when arpeggiated, can sound pretty cool. For our purposes here, we are thinking about strumming.
These chords are labeled by the tones which are being fretted. Obviously, with the 6, 2, and 1 strings ringing, some of the chord names will be different. The exception is the E chord. We aren’t overly concerned with their technical names; we are just seeking out cool sounds. Many of them actually work for what they are named. Example: G is actually a G6/E, but will work fine when we see a G. We’ve chosen flat names for the sharp/flat. Most of the sharp/flat Major triads have flat names [F# and Gb are both].
If the system is closed [no open strings/only the 5, 4, & 3 fretted], the chord name is the name of the chord, & the chord will sound fine everywhere.
On some, like the F, we can control the low E with our fretting hand thumb. By doing this, we can not let it ring as loud, or mute it out completely.