Tenney–Euclidean temperament measures: Difference between revisions

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 ||J \wedge M||'_{RMS} = \sqrt{\frac{n}{C(n,r+1)}} det([v_i \cdot v_j - na_ia_j])</math>
-Again, Graham Breed defines the simple badness differently, skipped here because, by that definition, it is easier to find TE complexity and TE error first and derive the simple badness from their relationship.
+A perhaps simpler way to view this is to start with a mapping matrix <math>V</math> and add an extra row <math>J</math> corresponding to the JIP; we will label this matrix <math>V_J</math>. Then the simple badness is:
+<math>\displaystyle
+||J \wedge M||'_{RMS} = \sqrt{\frac{n}{C(n,r+1)}} det(V_J V_J^T)</math>
+So that we can basically view the simple badness as the TE complexity of the "pseudo-temperament" formed by adding the JIP to the mapping matrix as if it were another val.
+Graham Breed defines the simple badness slightly differently, again equivalent to a choice of scaling. This is skipped here because, by that definition, it is easier to find TE complexity and TE error first and multiply them together to get the simple badness.
 == TE error ==