I frequently use this scale in Jazz to create movement through the chords. Barry Harris is the expert on it. He calls it the “6th diminished scale.” The reason why he includes the flat 6 is because he believes that scales come from two different four note chords. In this case, we have C major 6 CEGA and Bdim7 BDFAb. Put those two chords together and there you have the scale! The coolest thing about this scale is that if you harmonize it in four note chords then you get C6 - Ddim7 - C6 in first inversion - Fdim (inversion of Ddim7) and so on. The entire scale is just inversions of C6 and Ddim7. This goes much further than this, and is what I consider to be the best way at tackling theory.
