Let 0 < a < 1, 0 ≤ b < 1 and I = [0, 1). We call contracted rotation the interval map φ_{a,b}: x ∈ I → ax+b mod 1. Once the parameter a is fixed, we are interested in the family φ_{a,b}, where b runs on the interval I. We use the fact that, as in the case of circle homeomorphisms, any contracted rotation φa,b has a rotation number which depends only on the parameters a et b. We will discuss the dynamical and diophantine aspects of the subject. In particular, we will show that, if a and b are algebraic numbers, the rotation number is rational using a transcendance theorem about the value of the Hecke-Mahler series at an algebraic point. The talk is based on a joint work with Michel Laurent.