  The present paper studies, using ab-initio calculations, the influence of the
incommensurate structural modulations on the low energy physics of the
$Sr\_{14-x}Ca\_xCu\_{24}O\_{41}$ oxides. On-site, nearest-neighbor and
next-nearest-neighbor effective parameters were computed within a $t-J+V$ model
based on the copper magnetic orbitals. The structural modulations appear to be
the key degree of freedom, responsible for the low energy properties such as
the electron localization, the formation of dimers in the $x=0$ compound or the
anti-ferromagnetic order in the $x=13.6$ compound.
