Deine Wellen umspielten mich (Your waves were playing around me) Josef (Matthias) Hauer

Use of the trope

Hauer's piano piece "Deine Wellen umspielten mich" (Your waves were playing around me) is based on the 31st trope. He uses a four-voice and a three-voice structural unit.

For the four-voice part Hauer exchanges the chromatic notes G flat (root note) and G. The chromatic neighbours G-G flat, A-B flat, B-C and E-F get a crotchet length, the notes A flat, D flat, E flat and D half the length of a minim:

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From this scheme (I) others can be derived, e.g. the following three two-bar units in four voices (II, III and IV) in which each voice of a trope half is assigned to one of the four voices of the movement.

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These four two-bar units, transposed to various root notes, form the first eight bars of "Deine Wellen umspielten mich". The process is as follows: the original two-bar unit (ex.I) is taken over, the next two-bar unit (ex.III) is transposed by a tritone (bars 3 and 4), a further two-bar unit (ex.IV) is transposed first by a minor seventh (bars 5 and 6) and then by a major third (bars 7 and 8).

In the three-voice structural unit the E flat (in the first half of the trope) is given the position of the first crotchet, D flat the second crotchet; in the second half of the trope D becomes the first crotchet, A flat the second:

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In this way four triads are created:

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As in the four-voice pre-fab structure the triads are used in different positions, e.g.:

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This two-bar unit is first transposed (and raised) by a third (bars 9 and 10) and then lowered by a full tone (bars 11 and 12) and taken over by the left hand. The right hand plays these chords in descending quaver triplets.