  We make explicit Serre's generalization of the Sato-Tate conjecture for
motives, by expressing the construction in terms of fiber functors from the
motivic category of absolute Hodge cycles into a suitable category of Hodge
structures of odd weight. This extends the case of abelian varietes, which we
treated in a previous paper. That description was used by
Fite--Kedlaya--Rotger--Sutherland to classify Sato-Tate groups of abelian
surfaces; the present description is used by Fite--Kedlaya--Sutherland to make
a similar classification for certain motives of weight 3. We also give
conditions under which verification of the Sato-Tate conjecture reduces to the
identity connected component of the corresponding Sato-Tate group.
