![]() Divisions of time at phrase and section are proportional to underlying fundamental frequencies. Piano notes are proximate to harmonic relationships, up to the 96th partial. Thus, The resulting tonic chord at the end of the piece is about a minor third higher than the (functionally) Same chord at the beginning. The sound file presents just-tuned common-tone chord progressions that, With each iteration, Shift higher in frequency by the interval of a Syntonic Comma. Incongruity (for piano and fixed media) Refers to the meshing of seemingly incommensurate systems: Harmonic (or Extended Just Intonation), Represented by fixed media, And Equal-Tempered, Represented by the piano part. ![]() 2010 composition competition notes and bios winners and finalists:
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