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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=(log2(f2)log2(f1))1200

cents=log2(f2f1)1200

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

Pitagorean major third:

cents=(log2(329.06)log2(260))1200

Base 2 logarithms of 329.06 and 260 are:

log2(329.06)=8.36220685522536

log2(260)=8.02236781302845

We substitute the values and calculate:

cents=(8.362206855225368.02236781302845)1200

cents=0.339839042196911200=407.8

Just intonation major third:

cents=(log2(325)log2(260))1200

Base 2 logarithms of 325 and 260 are:

log2(325)=8.34429590791582

log2(260)=8.02236781302845

We substitute the values and calculate:

cents=(8.344295907915828.02236781302845)1200

cents=0.321928094887371200=386.3

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