Let me respell your blues scale (enharmonic the same as yours except this is the way it's traditionally lettered)
C Eb F Gb G Bb C
Most don't harmonize that scale as chords are in thirds and that scale skips and adds some tones, but if you did you'd get...
Cm7,
Ebmaj,
Fmaj7add9(no third),
Gbmaj6(no fifth) or Ebm/G ,
For the G note I get Cm(#11)/G,
For the Bb note Ebm6/Bb
However, most would think of the blues scale as a derivative of the Mixolydian scale...
Mixolydian C, D, E, F, G, A, Bb, C
Blues C, Eb, F, Gb, G, Bb, C
Harmonizing mixolydian:
C7
Dm7
Em7b5
Fmaj7
Gm7
Am7
Bbmaj7
If you add the additional tones of the blues scale to the above you can get a lot of other chords, like:
C7 or C7#9 or C7#9b5 or C9b5, C13 etc
Dm7, D7 (spelled enharmonically) D7#9, Dm9
etc |