I came close to having a "natural E" eighth note bounce in on the right side, but then all the "see sharp" and "be flat" jokes came to mind.
I always hated logarithms, but at least I could understand what base 10 was. How do you have a base where you don't even know what the number is? Why not 2? Why not pi? Oh, yes, because this irrational number was "natural"!
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Now, this is how I understand it, although I am not sure that this is the general case.
e is the only number where the derivation of the function e^x is the same function. This doesn't work with any other number. The derivation of 10^x is ln 10 . 10^x.
So the base is for the exponential function and well, logarithms are the inverse function for exponentials, so it makes sense that the same base will be the main one.
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