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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.

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According to Persichetti, the primary chords of a mode are the tonic, and two other major or minor triads that include the mode's characteristic scale step. The focus here is on the modes that are different from the standard major and (natural) minor scale, and locrian is also excluded because of its diminished tonic triad. As you probably know, the characteristic scale steps of the remaining four modes (dorian, phrygian, lydian, mixolydian) are the notes that distinguish the mode from the common major or minor scales. For dorian it is the natural sixth, for phrygian the minor second, for lydian the raised fourth, and for mixolydian the minor seventh.

Now there are always three triads in the scale including the characteristic scale step, because that note can appear as the root, the third, or the fifth of a chord. However, one of those triads is always a diminished triad, so there remain only two major or minor triads including the characteristic scale step. For dorian, the (major or minor) triads including the natural sixth are ii and IV. For phrygian you get II and vii, for lydian II and vii, and for mixolydian v and VII.

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