Definitions
"Musical Distance" (MD): the performer's relationship to a written part.
By written, I mean one or several of the following:
1) orally conceived and passed on
2) notated
3) recorded
in other words: any way(s) of setting the part in stone!
Degrees
Of course, since a given performer could position himself anywhere in between rendering a part exactly (and even then, the music would differ from one musician playing the part to the next) and improvising freely, the notion of "Musical Distance" is extremely loose. However, I'd like to submit 5 very general positioning possibilities to your consideration:
1: part interpreted
2: improvisation based on part
3: improvisation based on part context (the context could be one or several of the following: key(s), chord changes, meter(s), feel(s)...)
4: improvisation not obviously related to part
Application
In a group setting, it could be interesting to implement this idea by assigning a given MD degree to each band member. Different levels of interaction (between the musicians in the band) could thus be achieved using different combinations of MDs (e.g. at a given point in a tune and in the case of a trio: MD for the pianist could be 3, MD for the bassist could be 2, and MD for the drummer could be 1.) Each particular section of a tune could be assigned a particular MD combination if desired, which would give the composer an extra tool to participate in controlling the level of musical interaction throughout the piece. Conversely, MD combinations needn't be planned at all shall the composer wish to delegate this responsibility to the performers entirely.
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