There exists a related and impressive body of work towards understanding the geometric structure of elements of music theory, see e.g. https://www.google.com/ur

There exists a related and impressive body of work towards understanding the geometric structure of elements of music theory, see e.g. https://www.google.com/url?sa=t&source=web&rct=j&url=http://dmitri.mycpanel.princeton.edu/geometry.pdf&ved=0ahUKEwjPn6mK1PDNAhVl0oMKHYySC_4QFgggMAE&usg=AFQjCNE222eyXk0bv3DtrJdG28jY9DX7lQ https://www.google.com/url?sa=t&source=web&rct=j&url=http://... and references therein.