We show that the basic bijection \Psi of a diagram which has been introduced in [DS3] (see also [DS2]) to unify the known combinatorial proofs of the so called cyclotomic identity (cf. [DS1,MR1,MR2,VW]) and which provides moreover a setting for bijections concerning primitive necklaces, defined and studied by Viennot [V], de Bruijn and Klarner [dBK], and Gessel [DW], may be viewed as a special instance of a more general bijection defined for arbitrary cyclic sets. Indeed, if this more general bijection is applied to the cyclic set P(A) of periodic functions on the integers with values in the set A, one gets the bijection discussed in [DS2,DS3].