#### How do we calculate the cents that separate two notes?

We have found two formulas to calculate the cents knowing the frequencies of two notes:

$cents = ( log_2(f_2)-log_2(f_1) ) * 1200$

$cents = log_2 \left( \frac{f_2}{f_1} \right) * 1200$

Let's calculate the cents of the major thirds that we discussed earlier.

Pitagorean major third:

$cents = ( log_2(329.06)-log_2(260) ) * 1200$

Base 2 logarithms of 329.06 and 260 are:

$log_2(329.06) = 8.36220685522536$

$log_2(260) = 8.02236781302845$

We substitute the values and calculate:

$cents = ( 8.36220685522536 - 8.02236781302845 ) * 1200$

$cents = 0.33983904219691 * 1200 = 407.8$

Just intonation major third:

$cents = ( log_2(325)-log_2(260) ) * 1200$

Base 2 logarithms of 325 and 260 are:

$log_2(325) = 8.34429590791582$

$log_2(260) = 8.02236781302845$

We substitute the values and calculate:

$cents = ( 8.34429590791582 - 8.02236781302845 ) * 1200$

$cents = 0.32192809488737 * 1200 = 386.3$