Onr of the most daunting tasks of my musical endeavors has been learning (and memorizing) the fourth movement of Philippe Manoury's Le Livre des Claviers, a vibraphone solo. Analyzing the harmonic structure of the piece has made it more approachable.
One of the hexachords used multiple times through the piece is (013579), which is the prime form. It has 1 degree of transpositional symmetry and 0 degrees of inversional symmetry, meaning there are 12 possible transpositions. It’s close proximity to the whole tone scale is responsible for the dream-like, celestial, or other-worldly nature of the piece. Since there are only two varieties of the whole tone scale, there is not much potential for transposition. However, Manoury modifies the whole tone scale by replacing one whole step with a half step. This allows for twelve different transpositions. (013579) is transferred from different styles throughout the piece: pointillistic, sustained, heavy, quiet, rubato, and nebulous. It is transformed through transposition and inversion, rarely repeating the same normal form. This is demonstrated plenty of times in the first page of the piece.
The interval class vector for this hexachord is: 142422
All hexachords used in the first page:
(013579) - Scriabin “Mystic” chord. IC vector: 142422. Symmetry: 1, 0
(023579) - all-combinatorial (B). IC vector: 143241. Symmetry: 1, 0
(023468) - all-combinatorial (B). IC vector: 242412. Symmetry: 1, 0
(023469) - all-combinatorial (B). IC vector: 234222. Symmetry: 1, 1
(02468T) -Whole-tone; maximally even. IC vector: 060603. Symmetry: 6, 6
(012479) - all-trichord hexachord. IC vector: 322332. Symmetry: 1, 0