OP you’re going to hear an onslaught of different explanations from music theory enthusiasts who want it explained their way.
The basic gist is that the sharps/flats system is not only incredibly *more* efficient because of the way music is organized (both on instruments and in the way our brains process sound) but it’s almost unimaginable once you learn basic music theory that it could be notated any other way.
Not all notes of the available 12 are treated equally when it comes to putting them together. A certain pattern, a subset of the 12, is what you might call the “primary colors” or basic elements of the set. The sharps/flats system is necessary to communicate according to the terms of this foundational aspect of sound.
The reason I can’t say “which notes makes up the primary subset” is because it’s all relevant to what you select as your *reference point* ( in math terms maybe you’d call it the origin or x=0). The subset would be described like a function —> where you give me x and I’ll tell you the various other notes based on the x you gave me.
The notation here, again, is absolutely a given once you learn the basics.
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