Let v be a grid path made of north and east steps. The lattice TAM(v), based on all grid paths weakly above v and sharing the same endpoints as v, was introduced by Preville-Ratelle and Viennot (2016) and corresponds to the usual Tamari lattice in the case v = (NE)(n). Our main contribution is that the enumeration of intervals in. TAM(v), over all v of length n, is given by 2(3n+3)l/(n+2)1 (2n+3)1. This formula was first obtained by Tutte (1963) for the enumeration of non separable planar maps. Moreover, we give an explicit bijection from these intervals in TAM(v) to non-separable planar maps. (C) 2016 Elsevier Ltd. All rights reserved.