What are cents in music?

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

Pitagorean major third:

$c e n t s = (l o g_{2} (329.06) - l o g_{2} (260)) * 1200$

Base 2 logarithms of 329.06 and 260 are:

$l o g_{2} (329.06) = 8.36220685522536$

$l o g_{2} (260) = 8.02236781302845$

We substitute the values and calculate:

$c e n t s = (8.36220685522536 - 8.02236781302845) * 1200$

$c e n t s = 0.33983904219691 * 1200 = 407.8$

Just intonation major third:

$c e n t s = (l o g_{2} (325) - l o g_{2} (260)) * 1200$

Base 2 logarithms of 325 and 260 are:

$l o g_{2} (325) = 8.34429590791582$

$l o g_{2} (260) = 8.02236781302845$

We substitute the values and calculate:

$c e n t s = (8.34429590791582 - 8.02236781302845) * 1200$

$c e n t s = 0.32192809488737 * 1200 = 386.3$

Type the frequency of two notes and click Calculate cents to find out the cents that separate them: