of limited transposition. C E G Removing two notes for every one kept creates a new truncated mode of limited transposition. C F Keeping two notes for every one removed creates another truncated mode of limited transposition. C E F A Only Messiaen's mode 7 and mode 3 are not truncated modes: the other modes may be constructed from them or from one or more of their modes. Mode 7 contains modes 1, 2, 4, 5, and 6. Mode 6 contains modes 1 and 5. Mode 4 contains mode 5. Mode 3 contains mode 1. Pure intervallic truncations Tritones, truncation of modes 1, 2, 3, 4, 5, 6 and 7: augmented fourth, augmented fourth – 1 mode and 6 transpositions Major thirds, truncation of modes 1, 3, 6 and 7: major third, major third, major third – 1 mode and 4 transpositions. See Augmented triad Minor thirds, truncation of modes 2, 4, 6 and 7: minor third, minor third, minor third, minor third – 1 mode and 3 transpositions. See Diminished seventh chord Whole tones (mode 1), truncation of modes 3, 6 and 7: tone, tone, tone, tone, tone, tone – 1 mode and 2 transpositions Other truncations Truncation of modes 2, 4, 6 and 7: semitone, tone, minor third, semitone, tone, minor third – 3 modes, 6 transpositions. (Modes are "mirror" inversions of Petrushka Chord modes.) Truncation of modes 1, 2, 3, 4, 5, 6 and 7: major third, tone, major third, tone – 2 modes, 6 transpositions. See French Sixth and Dominant seventh flat five chord Truncation of modes 2, 3, 4, 5, 6 and 7: perfect fourth, semitone, perfect fourth, semitone – 2 modes, 6 transpositions. See 1:5 Distance model Truncation of mode 3: minor third, semitone, minor third, semitone, minor third, semitone – 2 modes, 4 transpositions. See augmented scale Truncation of modes 2, 4, 6 and 7: minor third, tone, semitone, minor third, tone, semitone – 3 modes, 6 transpositions. See Petrushka Chord Use and sound Messiaen found ways of employing all of the modes of limited transposition harmonically, melodically, and sometimes polyphonically. The whole-tone and octatonic scales have enjoyed quite widespread use since the turn of the 20th century, particularly by Debussy (the whole-tone scale) and Stravinsky (the octatonic scale). The symmetry inherent in these modes (which means no note can be perceived as the tonic), together with certain rhythmic devices, Messiaen described as