  The auxiliary/dynamic decoupling method of hep-th/0609001 applies to
perturbations of any co-homogeneity 1 background (such as a spherically
symmetric space-time or a homogeneous cosmology). Here it is applied to compute
the perturbations around a Schwarzschild black hole in an arbitrary dimension.
The method provides a clear insight for the existence of master equations. The
computation is straightforward, coincides with previous results of
Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity
in either the definition of variables or in fixing the gauge. We note that the
method's emergent master fields are canonically conjugate to the standard ones.
In addition, our action approach yields the auxiliary sectors.
