Here are a couple of figures from the introduction by Craig Ayrey to "Musical fact and the semiology of music" by Jean Molino:
The footnote "6" (in "Fig 26") points to Jean-Jacques Nattiez, Musicologie générale et sémiologie, Paris: Christian Bourgois, 1987, page 38. There's an English translation, Music and Discourse: Toward a Semiology of Music. Translated by Carolyn Abbate (1990). Princeton University Press.
Reversing the second arrow (in the move from Fig 1 to Fig 2) seems like an interesting move, insofar as it seems to make the musical "trace" into something like a shared space. Maybe this Nattiez-ian way of thinking is something we can use for thinking about phatics?