Re: What is the operation to convert Hertz to cents deviation in music pitch?

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