What are cents in music?
José Rodríguez Alvira
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:
\[ cents = ( 8.34429590791582 - 8.02236781302845 ) * 1200 \]
\[ cents = 0.32192809488737 * 1200 = 386.3 \]
Cents Calculator
Type the frequency of two notes and click Calculate cents to find out the cents that separate them:
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