(From Berklee Jazz Theory and Harmony)
Most textbook explanations of modal harmony warn you to beware of the diatonic tritone in each mode, lest it pull you into the relative major key. This warning is valuable, but it can be somewhat limiting, especially in jazz composition. Since the characteristic note of each mode is also a note in the diatonic tritone of that mode, it stands to reason that the tritone may actually have a role in helping to establish the sound of that mode. Play the examples below on the piano and you will see and hear that these voicings, as simple as they are, are potential I chords in D Dorian, E Phrygian, F Lydian, G Mixolydian, A Aeolian, and B Locrian respectively. Note that the respective tritones are given strong support from each modal tonic in the bass clef. This helps anchor thr tritone and ensures modal rather than tonal orientation.
The problem with the tritone in modal harmony is not so much the interval itself but the placement of that interval in a voicing in thirds. Voicings in thirds (triads and seventh chords) are so identified with the major and minor modes that their very use promotes tonal rather than modal identity. Bill Evans and Miles Davis must have understood this instinctively at the Kind of Blue recording sessions, because Bill Evans makes extensive use of voicings in fourths throughout, especially on “So What." Voicings in fourths have a more ambiguous quality than voicings in thirds. A quartal “triad” (three-note voicing in perfect fourths) doesn't sound major, minor, augmented, or diminished. In fact, any of the three notes in such a voicing might be the “root” of the chord! This ambiguity has intrigued jazz musicians for more than forty years and is at the heart of the use of these voicings by players and composer/arrangers who hope to sound “modern.”