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The writing needs to be improved. For example, there is this sentence: "Thus, for example, all other properties of the string being equal, to make the note one octave higher (2/1) one would need either to decrease its length by halve (1/2), to increase the tension to the square root (√2), or to decrease its mass per unit length by the inverse square root (1/√2)."
"...decrease its length by halve..." should be "decrease its length by half...."
"...increase the tension to the square root..." should be "...increase the tension by a factor of the square root of two..."
"...or to decrease its mass per unit length by the inverse square root..." should be "...or to decrease its mass per unit length by a factor of the inverse square root of two...."
And then near the end, "Similar laws where not developed for pipes..." should be "Similar laws were not developed for pipes..." ("were" instead of "where")