Let Ω ⊂ ℝ² be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L²(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ² \ Ω. For which Ω the collection of such period sequences coincides with ℓ² We give an answer in terms of metric properties of holes in Ω.