Equations and formulas for musical calculations

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:

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

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