Equations and formulas for musical calculations

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The following equation represents the amount of unique combinations of music intervals:

    \[ t = \sum_{r=0}^{n}\left\{\binom{n}{r}-k \right\}×\left\{ \frac{1}{r+1}\right\}+\frac{k}{k}\scriptstyle (k>0) \]

Remember the binomial coefficient, otherwise known as n choose r :

    \[ \binom{n}{r}=\frac{n!}{r!(n-r)!}=\binom{n}{n-r} \]

We can evaluate k with the following expression:

    \[ k=\binom{n}{r}mod(r+1) \]

The frequency of a pitch is calculated using:

    \[ f =r\left ( \sqrt[12]{2}\times n \right )=r\left ( 2^{\frac{n}{12}} \right ) \]