Another way of using mathematical ideas to create musical structures is to try to describe an image musically.
In the drawing by M.C. Escher above, a leitmotiv can be associated with the end figure of each section, for instance, the third from top in the left column: hexagons and fish. The question becomes how, musically, to continuously transform one into the other. In mathematics this procedure is called ‘homotopy’.
One or more parameters can be set for the beginning and end of the piece (e.g. minor to major, loud to soft, staccato to legato), with a seamless transformation process between them.
Can the timbre of an oboe be continuously transformed into the voice of a soprano? This can be achieved digitally if the instrument or human voice is synthesized by means of signal processing tools, but it might be possible with live performers too, with careful doubling and dynamics.