The extended augmented scale
(Messiaen mode number 3)

The basic augmented scale is a six-note mode created by alternating the interval of a minor third with semitone steps. However, it offers fairly limited harmonic resources, and can be extended by the addition of a third augmented triad. By this means the scale retains its transpositional possibilities - it can be transposed four times, like any augmented triad - but gains harmonic flexibility.

The resulting mode is listed as one of the possible "modes of limited transposition" by Messiaen. It has three modes. Below I give the parallel harmonies derived from various values for mode I. I'll be uploading some more work on this subject.