Music is an unexpected alliance of “rivers” in our head and body of very ancient and very modern forces that reflect the way we operate inside and the social/cultural milieu we swim in and share.

Music reflects motion and travel, and obstacles giving us resistance, and the sight of objects promising us rewards.

Music reflects a sense of the effort it takes to do these things — where to turn, when to wait, how hard to work to scale a steep terrain, how to proceed carefully. The underlying meaning of music comes from how to do these things, not how to describe a scene but how to react emotionally to interaction with a scene. This traces back to our animal nature, but the process is superimposed on our experience of aesthetic emotion, a product of our civilization and humanity, and our spatial sense of traversal and transformation.

So we have at least several forces at work in our experience of music:

• Animal emotion and its tie to effort and life-preserving traverse. (Kevin Behan basing his ideas on animal emotion researcher, Jaak Panksepp).
• Experience of inner tension and release as projected by a spectrum of harmonic relationships in a melody. (Carol Krumhansl and others)
• Aesthetic emotion, a refinement and enjoyment of complex and transforming relationships between artistic elements. (Virtually spatial; rhythmic; textural)

Melody, I and others believe, is experiencing the effects of such a path.

Path Mathematics:  Mathematically, the trace of  line intervals resulting from moving and traversing along from significant point to significant point, is called a graph. The theory of constructing these and analyzing them is called graph theory. The points are called nodes and the connecting intervals are called edges. The theory is  applied to choices of paths, often along the edges of a solid 3D figure such as a tetrahedron (4 equal sides) or more complex shapes, such as a dodecahedron (12 sides).

Somewhere within our cognitive apparatus, I believe, may be a capacity to carry on such activities — to construct, store, remember, and transform such graph paths. Our “river” components catalyze it — travel, effort, animal emotion, and aesthetic emotion.

Gilles Baroin, in his dissertation at the University of Toulouse (2011), shows how to construct such graph paths to represent melodies, using quaternion objects and computer representation to create a picture of visual turning and observation of a melody graph. It does not directly incorporate perceptual experimentation involving music (psychophysics), but does show how a path system can be built around quaternion objects and relationships.

For several quotes and references from researchers, go to page Rivers and Paths.