The video above was filmed at the Royal Conservatory in The Hague, NL. It is part of a collection of video chronicling workshops that were given by pianist Barry Harris between 1989 and 1998. That collection can be found on the Barry Harris Videos channel on YouTube. There is a lot of great information there. Dr. Harris’s career has spanned over half a century and at the age of 85, he continues to perform and teach.
In the video, Harris outlines and demonstrates a set of rules for dealing with descending dominant (Mixolydian) scales. The basic concept is that in particular circumstances, the addition of half steps is necessary to insure that chord tones (1, 3, 5, b7) occur on downbeats instead of upbeats.
In the handout below, I wrote out the rules outlined by Dr. Harris in the video. Harris briefly talks about rules for the Major scale, but only mentions the use of a half step going from 6 to 5 before returning to the discussion of the dominant (Mixolydian) scale.