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.
Interesting view on the whole tone scale. Is it influenced by early 20th century Russian harmony like Yavorsky?
Now the next step would be interesting to see this diatonic interpretation applied to whole tone passages. The main contradiction would be that commonly the six tone scale is regarded not to possess a root/ground note. Thinking of Debussy I mostly perceive a tonic feeling. Maybe you can argue for a tonic by your model?
Thank you for this remark! I’ll need to deal with Yavorsky’s modal theory in greater detail, but it seems as if his conception of tritone relations prevents him to accept the enharmonic identity of the augmented fourth and diminished fifth (which is crucial to my proposed construction of the whole-tone scale).
I agree that whole-tone scales are frequently applied in music with the clear notion of a stable root (for example, in the Prelude of Debussy’s Pour le piano). I would even go so far and say that there might be a ‘functional’ air to the two modes (or transpositions) of the hexatonic scale—a tonic and a dominant form, with the former containing the root and the latter the leading tone(s). If we transpose my model up or down by a perfect fifth, we’d get two different ›dominant forms‹ centered around F or G, and comprising both B / C-flat and C-sharp / D-flat. This might be a possible application of the model to argue that there are possible roots in whole-tone scales. I’ll have to think this over …