I'm really confused about what Vincent Persichetti wrote in his book Twentieth Century Harmony, where he says speaking of primary chords in modes, "The Primary chords are the tonic, plus two dominant equivalents. These double dominants are those major or minor triads that include the characteristic scale step which produces the principal flavor of the mode."
Persichetti then goes on to show how in the mode D Lydian, (Characteristic flavor: Raised 4th step) the Primary chords are I, II and VII.
In another example, he shows the Primary chords in D Mixolydian, (Characteristic flavor: Lowered 7th step) the Primary chords are I, V and VII.
I'm confused by the wording you see in the quote, and can't seem to wrap my mind around the procedure for picking out the Primary chords in Modes.
Thank you all.