  In this article, we introduce the notion of {\it concentric twin cotorsion
pair} on a triangulated category. This notion contains the notions of
$t$-structure, cluster tilting subcategory, co-$t$-structure and functorally
finite rigid subcategory as examples. Moreover, a recollement of triangulated
categories can be regarded as a special case of concentric twin cotorsion pair.
  To any concentric twin cotorsion pair, we associate a pretriangulated
subquotient category. This enables us to give a simultaneous generalization of
the Iyama-Yoshino reduction and the recollement of cotorsion pairs. This allows
us to give a generalized mutation on a set of cotorsion pairs defined by the
concentric twin cotorsion pair.
