We study spectral measures of different rescalings of some flows on surfaces, i.e. some translation flows and flows with symmetric logarithmic singularities.

We show that for any r\in \Q\setminus\{1\}, spectral measures of (T_t) and (T_{rt}) are mutually singular. This in particular implies that non-trivial rational rescalings are disjoint in the sense of Furstenberg. Joint work with P. Berk.