The partition relation A→(P)^μ_λ, despite its brevity, is remarkably expressive. This fundamental combinatorial principle asserts that every λ-coloring of μ-sized subsets of A is constant on a subset in the class P. By adjusting the parameters A, μ, λ, and P, one can express a wide variety of large cardinal principles, including weak compactness, Ramsey-ness, and even supercompactness. In this talk, we focus on the case where A is an uncountable cardinal κ and P is the class of stationary subsets of κ. By work of Baumgartner 1977, it turns out that this corresponds to certain ineffability properties of κ. We also describe how this fits into a different hierarchy of ineffability properties described in current joint work with Matthew Foreman and Menachem Magidor.