Most systems of music notation were developed as memory aids; they were never intended to define tone.  In terms of tabulature notation this works well: it is clear that the notation shows where to put your fingers on the guitar's fret board.  What actually sounds is ultimately at the player's discretion.  
Only as visual experience began to take precedence over auditory did the real confusion set in.  In order to teach musical syntax at the keyboard some fictionalized standard keyboard had to be the basis for the pitch sense.  But the piano never corresponded to that fiction.  Having more than one string per pitch gave its tone a chaotic fuzz.  The only way to believe that the theory was valid was to not listen to the actual sound of the instrument.
 
 


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