Notes: C, D, Eb, F, Gb, Ab, A, and B - Key: C - Category: Nonatonic or Ennatonic Scales
The C Messiaen mode 2 inverse uses nine notes per octave. Because of this same reason it is a member of the so called Nonatonic or Ennatonic -scales that have Nine-note (or Nine-tone). On the piano keyboard, it is made up of three black keys: Eb, Gb, and Ab and five white keys: C, D, F, A, and B. This combination makes this scale - as well as the C Prometheus, C Prometheus Liszt, and C Prometheus Neapolitan - as great choices for composing or improvising music.
If we take a look a the key signature of the C Messiaen mode 2 inverse Scale we can find it has three flats and no sharps. Therefore, on sheet music you will find three accidentals on the score. The notes of this scale are: C, D, Eb, F, Gb, Ab, A, and B.