The hexatonic or whole-tone scale (Messiaen’s mode 1) is not actually diatonic but a symmetrical scale, constructed from an equidistant division of the octave in six portions, which results in scale degrees separated by two half-tone steps from one another. This contradicts the common definition of diatonicism as a sub-category of heptatonicism, requiring seven discrete scale degrees in unambiguous alteration. However, it is possible to derive a whole-tone scale from diatonic material, which I am going to show here.
To this end I will make use of tetrachordal theory. A tetrachord consists of four adjacent diatonic pitches in the range of a perfect or augmented fourth, coming in four possible variants which differ by the existence and position of half-tone steps: Ionian (2 2 1), Dorian (2 1 2), Phrygian (1 2 2), and Lydian (2 2 2: no half-tone step). If we conceive every diatonic mode as a combination of two disjunct tetrachords transposed by a perfect fifth, there are seven combinations making up the seven diatonic modes—for instance, the Aeolian mode consists of a lower Dorian and an upper Phrygian tetrachord, while the Mixolydian mode consists of a lower Ionian and an upper Dorian tetrachord. The eighth combination, though, joins two Lydian tetrachords to a non-diatonic whole-tone scale, provided we allow the upper tetrachord to transpose by a diminished (instead of a perfect) fifth. The resulting scale (2 2 2 0 2 2 2) has six pitches, but makes use of all seven scale degrees, with a diminished second F-sharp / G-flat at the center. In the plagal variant, the scale covers the range of an augmented seventh G-flat / F-sharp.
