Let Ω⊂R² be a countably-connected domain. In Ω, consider closed differential forms of degree 1 with components in L²(Ω). Further, consider sequences of periods of such forms around holes in Ω, i.e. around bounded connected components of R²∖Ω. For which domains Ω the collection of such a period sequences coincides with ℓ²? We give an answer in terms of metric properties of holes in Ω.