Re: [Harp-L] Tremolo harmonicas

[Vern <jevern@xxxxxxx>]

Since we are splitting hairs (or semitones), here is the formula for Cents.

Where:  fo is a base frequency 
              f  is a different frequency
              C  is the change in cents
              1200 is the number of cents in an octave
Then:

C = 1200 / log(2) * [log(f) - log(fo)]

Note that when f < fo, C is negative.

and 

f = fo * 2^(C/1200)

This is derived from the definition of a semitone where (in equal temperament) the frequency ratio of adjacent semitones is the twelfth root of two.

f = fo * 2^(1/12)

To be fair…Small values of C approximate the % of the frequency difference of a semitone.  Although C(f) isn't linear, a short distance along the curve approximates a straight line.

Vern 

On May 26, 2013, at 10:03 AM, Winslow Yerxa <winslowyerxa@xxxxxxxxx> wrote:

> ……..Actually, your formula is incorrectly stated. Cents are not based on 1/100th of the frequency. They are based on 1/100th of the semitone, which itself does not have a direct linear relationship to frequency……....