The P/I related pitch-class set of the opening movement of Webern’s op. 21 explores the following transpositions by nine semitones of the P and I forms of the twelve-tone row. The inversely proportional correspondence of the elements in the P/I related sets is characteristic of mirror-image symmetry. Note that the intervallic structure between P and I set elements remains fixed; however, the sequential melodic directions of the P and I sets proceed in opposite directions. On the other hand, the pitch structure of water-image symmetry may result in the alteration of intervallic structure by pien tone technique. The initial Modal Complex (mt’) and its three transformations of the first movement of Chou’s Streams provide a good example of water-image symmetry (Example 1).
Examining the original form (P) and its three transformations (R, I, and RI), we find that the intervallic content and direction between successive modes may alter. The pien tone (consisting of the interval of a minor second) and direction-sensitive properties in Chou’s modes are unlike the fixed intervallic relationship of the palindromic design of Webern’s sets.
As eight Trigrams form the eight basic units in the I-Ching, there are eight variable modes to form the basic modes in Chou’s modal system. These are: Heaven (h) [_ _ _], Lake [_ _ - -], Sun (s)[_ - - _], Thunder (t) [_ -- --], Wind (w) [-- _ _], Rain (r) [- - _ - -], Mountain (m) [--_--], and Earth (e) [-- -- --]. A modal complex, which forms the basic unit of modal structure in Cho’s music, is formed by combining any of the two modes (including the same mode in opposite direction).
In Example 2 the four subjects of the first exposition in the first movement also exhibit such alterations in intervallic content and direction. Here Chou uses five modes, “Mountain” (m), “Thunder” (t), “Sun” (s), “Lake” (l), and “Wind” (w), which are paired to form four modal complexes, mt’–ss’–tm’–lw’, in which the mode marked with an apostrophe designates the descending form of that mode.
The melodic flux that distinguishes the individual statements of the principal subjects arises from Chou’s application of water-image symmetry. In typical water-image symmetry, the yin-yang polarities, the dualities of changed/unchanged, fixed/unfixed, mobility/quiescence, simplicity/complexity, and temporal/spatial all take place concurrently. In this composition, Chou uses a nine-note skeleton set (C, D, E, E, F, G, G, B, B/C, A, B, A, G, F, F, D, E) and further arranges the skeleton set into the fugue subject (C, A, B, B, E, D, D, F, G/C, F, E, D, A, A, B, G, F).