Based on experimental observations of modulated magnetic patterns in a Co_0.5Ni_0.205Ga_0.295 alloy, we propose a model to describe a (purely) magnetic tweed and a magnetoelastic tweed. The former arises above the Curie (or Néel) temperature due to magnetic disorder. The latter results from compositional fluctuations coupling to strain and then to magnetism through the magnetoelastic interaction above the structural transition temperature. We discuss the origin of purely magnetic and magnetoelastic precursor modulations and their experimental thermodynamic signatures.