The pentatonic scale often has chords that are 4 or 5 semitones apart (CEA, GCE, etc.). How do you describe these chords? Is the only way to describe them as major/minor chords but with a different lower note (C/G, etc.)?
It's better to think of the Pentatonic scale as a 'cut down' scale. In the minor Pentatonic it's notes 1,3,4,5 and 7(missing 2 and 6). The chords of the pentatonic scale are the same as the standard minor, so they'd be Im, IIIM, IVm, Vm and VII.
I believe you mean if you take the 1st, 3rd and 5th notes of pentatonic, what chords you would get then? Correct me if i'm wrong,
1 = 1 2 = 3 3 = 4 4 = 5 5 = 7
So in this case let's take the chords you'd get(in the a minor pentatonic)
1 = 135 = 147 = adg = A7sus4(no 5th) 2 = 246 = 351 = cea = Amin/C 3 = 357 = 473 = dgc = CM7/D(no 3rd) 4 = 468 = 514 = ead = Asus4/E 5 = 579 = 735 = gce = CM/G
I hope that helps. the problem with analysing chords like this is that you're kind of in a system of music that's not got a formal naming structure. Usually the 7 notes of the scale are the basis for scale theory, so when you remove 2 of them, but apply the 7 note convention of moving up the scale you get some funkily named chords as you can see. It's similar to when a 12 tone system is used, only going the other way. Another way to think of it is like operating with a different base system.(if you're a mathmetician)
I'm not sure if there's a system for describing them in a similar way to the 12 tone stuff, but I hope my answer has given some understanding into why it's not generally considered. If my answer is based on false assumptions, please let me know in the comments and I'll Update :)
The pentatonic actually has less chords that are 4 - 5 semitones apart as there is simply less instances of these two intervals than nearly all other scales (which mostly have seven notes).
Cmaj pent C D E G A C
C Ionian C D E F G A B C
I assume what you really meant to say in your first sentence was "Chords built from the pentatonic scale often have consectutive chord tones that are 4 or 5 semitones apart (CEA, GCE, etc.)"
As for naming chords built from pentatonic scales such as the two you mention they are named as you would for all chords: using the normal conventions. e.g.
CEA = C6 or Am (1st inversion or Am/C) or Esus4#5/C
GCE = C (2nd inversion or C/G) or G6sus4 or Em#5/G
Which name you should use depends on the context they appear in, you'll very rarely (or never) find G6sus4, Esus4#5/C or Em#5/G to be the appropriate names when you use these chords.
In general, there are five types of three-part chords. This applies to pentatonic scales as well as to heptatonic (7-note) scales. These types are
That's all there is. Of course many three-pitch chords can be interpreted in several ways, but with the above list I'm referring to a standard classification used e.g. in Creative Chordal Harmony for Guitar by Mick Goodrick and Tim Miller.
Let's have a look at the C major pentatonic scale and see which three-part chords it contains. Since it is a scale with five notes, there are exactly 10 different three-part chords:
cde - cluster cdg - quartal (Gsus4) cda - 7th (no 3): Dm7 (no 3) ceg - triad (C) cea - triad (Am) cga - 7th (no 5): Am7 (no 5) deg - 7th (no 5): Em7 (no 5) dea - quartal (Asus4) dga - quartal (Dsus4) ega - 7th (no 3): Am7 (no 3)
Obviously, different inversions do not count as different chords. It might seem odd to call a chord "minor 7 (no 3)", because it's the third that determines whether a chord is major or minor. But the rationale behind it is that we are in the key of C major and in this key we normally have a Dm7 chord (the same holds for Am7).