Bilateral Keyboard Symmetry in the Music of Einojuahni Rautavaara

20th-century Finnish composer Einojuhani Rautavaara’s fascination with symmetry played an integral role in his compositional evolution. Inherent in 12-to-the-octave composition, pitch symmetry has been exploited by many twentieth-century composers. One type of visual symmetry—bilateral keyboard symmetry—influences Rautavaara’s compositions in both piano and non-piano settings. Bilateral keyboard symmetry organizes the piano keys into a symmetrical plane creating axes at pitch classes {2} and {8}. Every note consequently has a complement in mirrored respect to the axes (i.e., {7} complements {9} and {1} complements {3}) which can then be used to generate harmonies and melodies. These harmonies and melodies coincide with tonal and aesthetic choices in the music of Rautavaara yielding triadic relationships such as D-major complementing G-minor. This non-transposing type of symmetry is not based upon auditory organization of pitches, but of visual organization of piano keys and is used with mir- rored physiological motions of the hands at the piano. This system can also be found in many non-piano pieces such as Ballad for Harp and Strings and Sonata for Solo Cello no. 1, which feature sections resembling bilateral keyboard symmetry. Using a novel system of analytic notation, bilateral keyboard symmetry can be examined on local and global levels