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...Proc nati acad sci usa vol pp february physics fractal geometry of music melody kenneth j hsu and andreas hsut eidgenossische technische hochschule zurich switzerland tkonservatorium und musikhochschule contributed by october abstract critics have compared bach s to sounds in combination harmony ofsounds spaced a the precision mathematics what temporal succession rhythm is supposedly are questions for curious scientist series single notes deliberately arranged pattern purpose ofthis short note suggest that chosen from preexisting has been handed down at least part mandelbrot preci tradition or accepted as convention theory sion deviation log og linear plot taught us successions not random frequency distribution ofi chaotic musicuntilthe th century was oneofthefourmathematical mathematical expression this order disciplines quadrivium beside arithmetic astronomy cause consonance terms aris totelian analysis stated be numerous sonorus studying natural catastrophes one harmonic number rati...