The only reason you would have to pay an artist is if you are creating a "derivative work". The US government's position on what a derivative work is here. They identify as an example "A musical arrangement of a preexisting musical work". One can check relevant US case law here pertaining to "fair use" (a likely defense in case "copying" was found). The statutory definition of "derivative work" at 17 USC 101 is that it is
a work based upon one or more preexisting works, such as a
translation, musical arrangement, dramatization, fictionalization,
motion picture version, sound recording, art reproduction, abridgment,
condensation, or any other form in which a work may be recast,
transformed, or adapted. A work consisting of editorial revisions,
annotations, elaborations, or other modifications which, as a whole,
represent an original work of authorship, is a “derivative work”.
One may presume that the map is "based on" a protected work, so the question is whether it is recast, transformed of adapted: presumably, it is. A rhythm can be an element in a finding of infringement (Dorchester Music v. National Broadcasting Company 171 F. Supp. 580: melody and rhythm were fund to be substantially similar). However, many rhythms are centuries old or more, e.g. Dhruva Tala, Scandinavian polska. This resource may also be useful in sorting out musical infringement questions. The essential question is whether the map "copies" a protected element of a composition, and that depends on what the map "is".
Whether or not this matters to you depends mostly on whether you are creating the possibly infringing work (a map). If you are just creating a program that allows people to do something with what they already have, then there is no liability for infringement (just as a person who creates a program allowing sound to be recorded or sound files to be manipulated is not liable for infringement if someone uses the program to infringe on copyright). There are ample non-infringing uses for such a program.