therefore the whole tone scale has only 1 mode. Messiaen's mode 2, or the diminished scale, consists of semitone, tone, semitone, tone, semitone, tone, semitone, tone, which can only be arranged 2 ways, starting with either a tone or a semitone. Therefore mode 2 has two modes. Any scale having the same number of modes as notes is not a mode of limited transposition. Messiaen's list Messiaen's first mode, also called the whole-tone scale, is divided into six groups of two notes each. The intervals it contains are tone, tone, tone, tone, tone, tone – it has two transpositions and one mode. The second mode, also called the octatonic, diminished, whole-half, or half-whole scale, is divided into four groups of three notes each. It contains the intervals semitone, tone, semitone, tone, semitone, tone, semitone, tone – it has three transpositions, like the diminished 7th chord, and two modes: The third mode is divided into three groups of four notes each. It contains the intervals tone, semitone, semitone, tone, semitone, semitone, tone, semitone, semitone – it has four transpositions, like the augmented triad, and three modes. The fourth mode contains the intervals semitone, semitone, minor third, semitone, semitone, semitone, minor third, semitone – it has six transpositions, like the tritone, and four modes. The fifth mode contains the intervals semitone, major third, semitone, semitone, major third, semitone – it has six transpositions, like the tritone, and three modes. The sixth mode has the intervals tone, tone, semitone, semitone, tone, tone, semitone, semitone – it has six transpositions, like the tritone, and four modes. The seventh mode contains the intervals semitone, semitone, semitone, tone, semitone, semitone, semitone, semitone, tone, semitone – it has six transpositions, like the tritone, and five modes. Expansion and alteration of the modes Are there others? Messiaen wrote, "Their series is closed, it is mathematically impossible to find others, at least in our tempered system of 12 semitones." More modes can be found that fit the criteria, but they are truncations of the original seven modes. Truncation Truncation involves the removal of notes from one of the modes to leave a new truncated mode. Both the notes removed and the notes remaining must preserve the symmetry of the parent mode, and must therefore fulfill the conditions for limited transposition. For example, consider mode 1. C D E F G A Removing alternate notes creates a new truncated mode