Which chords can be used in this Vietnamese pentatonic scale?

[fantasyvn]

Could you pls help?
I'm studying this Vietnamese pentatonic scale: C D F G A .
Which chords can be used in this scale?
As I understand, the chords are based on the notes of the scale.
C: ?
D: D (D F A )
F: F (F A C)
G: ?
A: ?
Thank you for your kind help.

[MadBrain]

Which note is the root? (in what key is this scale? what is the "first" note?)

There are two different pentatonic scales with these notes (but different roots):
- F major pentatonic (F G A C D), uses the same chords as F major
- D minor pentatonic (D F G A C), uses the same chords as D minor

F MAJOR CHORDS:
BASIC:
F (F A C)
Gm (G Bb D)
Am (A C E)
Bb (Bb D F)
C (C E G)
Dm (D F A)

EXTENDED:
Fmaj7 (F A C E), Fmaj9 (F A C E G), Fadd9 (F G A C)
Gm7 (G Bb D F), Gm9 (G Bb D F A), G7 (G B D F), G9 (G B D F A)
Am7
Bbmaj7, Bbmaj9, Bbadd9
C7 (C E G Bb), C9, Csus4 (C F G), Bb/C (C Bb D F)
Dm7, Dm9
Eb, Edim (E G Bb)



D MINOR CHORDS:
BASIC:
Dm (D F A)
F (F A C)
Gm (G Bb F)
A (A C# E), Am (A C E)
Bb (Bb D F)
C (C E G)

EXTENDED:
Dm7 (D F A C), Dm9 (D F A C E)
Em7b5 (E G Bb D), E7, Eb, Ebmaj7, Ebmaj9
Fmaj7, Fmaj9, Fadd9
Gm7, Gm9, G, G7, G9
A7 (A C# E G), Am7 (A C E G), Am9, Asus4, G/A (A G B D)
Bbmaj7, Bb7, Bb9
Cadd9

[jancivil]

Which note is the root? (in what key is this scale? what is the "first" note?)

There are two different pentatonic scales with these notes (but different roots):
- F major pentatonic (F G A C D), uses the same chords as F major
- D minor pentatonic (D F G A C), uses the same chords as D minor

Actually the scale the OP has is a basic mode of Vietnamese traditional music. "The Bac scale system is also that commonly used in Chinese, Mongolian, Korean and Japanese music. The above-mentioned Bac scale (Ex, 1-a) corresponds to the Chinese scale called Zhi (in Vietnamese: Chuy)."

http://lyrichord.com/linernotes/LAS7396US.pdf

I can't know why the OP has selected this particular object, but as itself it is neither of those two. If he or she doesn't really know, why not, deal w. the familiar and slap some chords on it.

[MadBrain]

True, I have to admit that what I gave is the western version of the pentatonic scale.

For a melody using the C D F G A scale with the root on C, I'd try harmonizing it as C dorian (C D Eb F G A Bb). C minor (C D Eb F G Ab Bb) also seems to sortof work, but you have to be careful not to use chords with Ab when the melody plays A. That means I'd try using chords like:
Cm (C Eb G)
Dm (D F A)
Eb (Eb G Bb)
F (F A C)
Gm (G Bb D)
Bb (Bb D F)
plus Fm (F Ab C) and Ab (Ab C Eb) whenever the melody isn't playing A.

Unfortunately western theory doesn't really have an answer on how to put chords on a C D F G A scale in the key of C... it kinda needs a E or Eb to work (which is why western musicians favor the C D E G A and C Eb F G Bb scales over other pentatonic scales in C). With C D F G on the root chord, it tends to act as a dominant chord (Bb/C) and instantaneously modulate up to F major pentatonic (F G A C D).