Second Mode

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.

Mode 2 is transposable three times. It is constructed by alternating half and whole steps. The three transpositions are:
It is the symmetry of these modes that limits the number of times they may be transposed. Even by beginning the scale with a whole step, the same limited set of transpositions is generated. The example below uses the same transposition number scheme as the one above so that you may easily see the relation:
In his book Breaking Free, Jeffrey Brillhart offers an entire chapter on the Second Mode with several characteristic harmonic progressions and many suggested ways to use the mode.