  Generalizing the scaling limit of Martelli and Sparks [hep-th/0505027] into
an arbitrary number of spacetime dimensions we re-obtain the (most general
explicitly known) Einstein-Sasaki spaces constructed by Chen, Lu, and Pope
[hep-th/0604125]. We demonstrate that this limit has a well-defined geometrical
meaning which links together the principal conformal Killing-Yano tensor of the
original Kerr-NUT-(A)dS spacetime, the Kahler 2-form of the resulting
Einstein-Kahler base, and the Sasakian 1-form of the final Einstein-Sasaki
space. The obtained Einstein-Sasaki space possesses the tower of Killing-Yano
tensors of increasing rank, underlined by the existence of Killing spinors. A
similar tower of hidden symmetries is observed in the original
(odd-dimensional) Kerr-NUT-(A)dS spacetime. This rises an interesting question
whether also these symmetries can be related to the existence of some
"generalized" Killing spinor.
