  String compactifications on an orbi-folded torus with complex structure give
rise to chiral fermions, spontaneously broken CP, modular invariance. We show
that this allows simple effective theories of flavour and CP where: i) the QCD
angle vanishes; ii) the CKM phase is large; iii) quark and lepton masses and
mixings can be reproduced up to order one coefficients. We implement such
general paradigm in supersymmetry or supergravity, with modular forms or
functions, with or without heavy colored states.
