The present paper studies the influence of the structural modulation on the low energy physics of the $S\!r_{14-x}C\!a_xC\!u_{24}O_{41}$ oxides, using ab-initio determination of the on-site and nearest neighbor effective parameters. The structural modulations appears 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.