We study the disturbance attenuation problem in a heterogeneous mass chain where both the number of masses and the mass distribution may change. The paper studies the scalar transfer functions from the disturbance at a boundary point to a given intermass displacement. It is shown that these transfer functions can be represented in the form of composition sequences generated by Möbius transformations. The framework aims at devising a method of designing the interconnection impedances in the mass chain in a scale-free manner. That is, the resulting design guarantees certain performance criteria for mass chains of any length and any mass distribution. A graphical method is provided for such an interconnection design problem.