ON REPRESENTING CONSONANCE STRUCTURES

We consider the representation of consonance structures in music, and consider two families of examples. We thus derive pieces of music which are similar to existing ones, via generalised tunings. In the first family of examples, certain representations define interpretations of two part compositions, written on a stave. The relevant consonance structures are quivers, built from consonances between notes that are close in the score, as determined by a certain algorithm. We present some interpretations of Bach’s Invention No. 9 in F minor. Special cases of our interpretations are certain tunings to equal temperament and just intonation. In the second family of examples, we represent consonance structures found in one part compositions written on the stave with contrapuntal pieces, with harmonics of notes in the one part composition corresponding to motifs in the contrapuntal pieces. We present an example where the one part composition is the first twelve crotchets of the folk song ‘The False Bride’.