|MadSci Network: Physics|
Hi, An octave equals multiplying frequency by 2, two octaves equals multiplying frequency by 2x2, three octaves equals multiplying frequency by 2x2x2, it means that moving up x octaves equals multiplying by x 2 (two to the power of x). X does not need to be an integer. One can raise to a real number, or to a fraction. For example, one cent is 1/1200th octave, so 1 cent up from a certain frequency equals multiplying with (1/1200) 2 To find the exponent if you know the base (in our case 2) is expressed as a logarithm. If x y=2 then x=log y (The base-2-logarithm of y) 2 Now, the two normally used logarithm bases are e (approximately 2.718) and 10 (for reasons of our using a 10-digit numeric system). Converting from, for example the base-e-logarithm (called the "natural" logarithm, written ln) simply is done as follows: ln y ln y log y = ---- = -------- 2 ln 2 0.693147 Kind regards, Bruno
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