 part. By developing this tool, composers were allowing themselves more complex methods to organize their ideas as well as communicate more information and more complex information to the performer, theorist, and eventually ensemble coordinator (conductor). Before score notation, it was more difficult, given only the independently notated polyphonic parts of a piece, to determine how one part would fit precisely with another and what the combination of these parts would ultimately communicate. With score notation, it became much easier to a priori internally audiate and understand a piece of music before it was ever unencrypted by performers in performance or rehearsal. (see Figure 10 and 11)
Figure 10: Below is the original manuscript of Alexander Agricola's (1457/58 - 1506) "Agnus Dei" from his "Missa in Myn Zyn." Here you can see the Soprano voice's part on the top of the left page, the "alto" (tenor 1) voice on the bottom of the left page, the "tenor" (tenor 2) on the top right, and the bass on the bottom right. While this edition is fine for performances purposes, it would be difficult to select any random note from one part and know immediately to which notes it corresponds in the other parts, since these parts are not temporally synchronized in this notation (e.g. the first note in the second line of the soprano does not necessarily correspond to the first note in the second line of any of the other parts).
Figure 11: Below is a video transcription with recorded performance of the above music manuscript. With the "score notation" it is much easier to see how each part harmonically and rhythmically fits together at any one moment.
There is no specific “light-bulb” moment for this innovation; no particular person is easily given the sole credit. Such notation in various forms appears in isolation throughout the Middle Ages and Renaissance, especially in theoretical treatises,  which perhaps realized the pedagogical utility of such a presentation of information. However, when only performance is the aim of musical 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 exam