In his book The Technique of My Musical Language, Olivier Messiaen identifies seven modes of limited transposition. Within the chromatic system of twelve sounds, Messiaen has identified groups of pitches which after a certain number of transpositions are no longer transposable. These modes may be used both melodically and harmonically and give the impression of several tonalities without polytonality. The first of these modes is the whole tone scale. The second mode is probably the best known of the modes Messiaen identifies as it is also known as the octatonic scale.
The third mode is transposable four times just like an augmented triad. The mode is constructed in tetrachords (groups of four notes) following the interval pattern whole step-half step-half step. The four transpositions are shown below.
With nine pitches in Messiaen’s mode three, the possibilities for harmonic complexity advance dramatically.
For the ecclesiastical mode three, see the Phrygian mode.