sical data, it is understandable that the composer or music publisher only concern themselves with writing or printing performance parts. If one were to look at music from the Renaissance during the mid to late 16th century, bar lines do begin to appear relatively frequently in some sources; one notable source that uses bar lines and “score notation” is the Baldwin Manuscript, produced in Elizabethan England during the last decade of the 16th century (see Figure 12). As larger and more varied ensembles begin to emerge at the dawn of the Baroque, barlines and score notation begin to become more ubiquitous across Europe due to difficulties with and the necessity of ensemble coordination. Perhaps no other innovation in notation, barring pitch and rhythmic notation, was more influential in fostering the prolific complexification of Western music between the 17th and 21st centuries.  The score afforded greater and greater levels of coordination among larger and larger ensembles.
Figure 12: The first musical piece from the Baldwin Manuscript ("Baldwin's Commonplace Book"), which shows the beginning of a five-voiced motet in score notation with barlines. Here, you see two "systems" of the score (two macro-lines of five-parted music; the first five staves being sung before the second macro-group of five staves below). This fashion of score notation continues throughout most of the book.
What might be worth taking from this innovation, however, are the benefits of not writing music with a score. If the score affords coordination, then it might actually be a hindering tool if one’s goal in composition is non-coordination. By feeling compelled to produce a score, even in the cases of purely electronic music,  one might ultimately be subject to purely irrelevant musical dimensions that encumber their present creative process. While we should recognize the power of the score, it might also be important to recognize its relative infancy and the limitations it places upon us in our ability to communicate certain ideas. For example, if Conlon Nancarrow had required himself and his music to serve the limitations of the score, the “notation” of a piece like Study No. 40a (canon e/pi) or Study No. 33 (canon 2:sqrt(2)) would have been impossible since the polyphonic parts of these pieces essentially never coincide in time. If the score is predicated on coincidences in time, any piece predicated on the lack of such coincidence cannot rely on the score as traditionally understood. (see Figure 13)
Figure 13: Nancarrow's "Study No 33" for player piano, which contains two musical strata at two different tempos in the ratio of 2 against the square-root of 2. Since the square-root of two is an irrational number, this tempo is simply an approximation, but essentially these two musical strata should theoretically never coincide in time, since 2 cannot be equally divided by the square-root of 2. This goes against all conventions of score notation, making any conventional score notation somewhat absurdist. Here, as designed, this piece is realized by a player piano, since a human performance is extremely difficult, if not impossible, if the piece is to be at all a close approximation.
These innovations in pitch, rhythm, and time notations, perhaps ironically, lead to the third and last innovation in musical communication I will address herein: non-prescriptive notation. Since the precision innovations of the score suggested the limitations it places on our ability to express free and incommensurate musics, the next innovation I wish to address is the return to non-prescriptive systems of musical notation. Thus far, this essay has been entirely concerned with the development of greater and greater levels of prescriptiveness in musical encryption. Perhaps 1000 years has finally lead us full circle in the 20th and 21st centuries, as some composers have realized that the representation of some sonic ideas cannot be encoded with pitch-rhythm-time prescriptions.
In the 20th century, composers, perhaps realizing many of the issues addressed above, sought to 