We continue the study of centralizers on Köthe function spaces and the commutator estimates they generate (see [29]). Our main result is that if
X
X
is a super-reflexive Köthe function space then for every real centralizer
Ω
\Omega
on
X
X
there is a complex interpolation scale of Köthe function spaces through
X
X
inducing
Ω
\Omega
as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, all real centralizers can be identified with derivatives of complex interpolation processes. We apply our ideas in an appendix to show, for example, that there is a twisted sum of two Hilbert spaces which fails to be a
(
UMD
)
({\text {UMD}})
-space.