A dynamical r-matrix is associated with every self-dual Lie algebra \A
which is graded by finite-dimensional subspaces as \A=\oplus_{n \in \cZ}
\A_n, where \A_n is dual to \A_{-n} with respect to the invariant scalar
product on \A, and \A_0 admits a nonempty open subset \check \A_0 for
which \ad \kappa is invertible on \A_n if n=0 and \kappa \in \check
\A_0. Examples are furnished by taking \A to be an affine Lie algebra
obtained from the central extension of a twisted loop algebra \ell(\G,\mu) of
a finite-dimensional self-dual Lie algebra \G. These r-matrices, R: \check
\A_0 \to \mathrm{End}(\A), yield generalizations of the basic trigonometric
dynamical r-matrices that, according to Etingof and Varchenko, are associated
with the Coxeter automorphisms of the simple Lie algebras, and are related to
Felder's elliptic r-matrices by evaluation homomorphisms of \ell(\G,\mu)
into \G. The spectral-parameter-dependent dynamical r-matrix that
corresponds analogously to an arbitrary scalar-product-preserving finite order
automorphism of a self-dual Lie algebra is here calculated explicitly.Comment: LaTeX2e, 22 pages. Added a reference and a remar