Click here to purchase the entire book in PDF format. Centre Frequency We can also calculate the middle of the passband using these two frequencies. It's not quite so simple as we'd like, however. Unfortunately, it's not just the frequency that's half-way between the low and high frequency cutoff's. This is because frequency specifications don't really correspond to the way we hear things. Humans don't usually talk about frequency - they talk about pitches and notes. They say things like ``Middle C'' instead of ``262 Hz.'' They also say things like ``one octave'' or ``one semitone'' instead of things like ``a bandwidth of 262 Hz.'' Consider that, if we play the A below Middle C on a well-tuned piano, we'll hear a note with a fundamental of 220 Hz. The octave above that is 440 Hz and the octave above that is 880 Hz. This means that the bandwidth of the first of these two octaves is 220 Hz (it's 440 Hz - 220 Hz), but the bandwidth of the second octave is 440 Hz (880 Hz - 440 Hz). Despite the fact that they have different bandwidths, we hear them each as one octave, and we hear the 440 Hz note as being half-way between the other two notes. So, how do we calculate this? We have to find what's known as the geometric mean of the two frequencies. This can be found using the equation $$f_{centre} = \sqrt{f_{c1} * f_{c2}}$$ (7.5)