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From the application of combinatorics we know that there are in total $$\left(\begin{matrix}12\\3\\\end{matrix}\right)-\left(\begin{matrix}11\\3\\\end{matrix}\right)=\frac{12!}{\left(12-3\right)!\ \cdot\ 3!}-\frac{11!}{\left(11-3\right)!\ \cdot\ 3!}=55$$ different triads to one and the same root note (12 over 3 minus 11 over 3, which do no start with the root note).

The 55 triads can be clustered into 19 groups of three because there are two inversions to each triad. In this way, the following complete list of all triads possible within an octave is obtained:

  • Note: The chord names will be introduced later.

  • The Excel file can be downloaded here as a reference.