The idea of "theory" in science, math, and music
Not to be pedantic, but I would imagine it was in development for quite awhile, and then he eventually published that book outlining it. But since you were wondering about a philosophical bent, I would argue that the
concept of the limited modes existed for as long as it existed in his head before he published the treatise (obviously in an evolving state, conceptually). So I'm still not grasping the idea of it coming into existence at the exact time that it...came into existence? Maybe I'm missing something.
Otherwise, as far as a more philosophical angle on this, I'm not well versed in math or science to add that angle; all I can point to is what I mentioned earlier; that music theory is essentially aesthetic theory. So if music theory is the technical information for musicians, then aesthetic theory is that information applied to philosophy.
EDIT: ...or rather, if music theory is the technical information for musicians, then aesthetic theory is the same information but viewed from a remote perspective, from which philosophical claims can be made. But it helps to know the information from the technical perspective first before removing oneself to a perspective from which the information is seen as remote.