  We show that for an infinite set X, if L is a completely distributive
algebraic lattice with not more completely join irreducible elements than the
size of the power set of X, then there is a monoidal interval in the clone
lattice on X which is isomorphic to 1+L, which is L plus a new smallest element
added. Concerning cardinalities of monoidal intervals this result implies that
there exist monoidal intervals of all cardinalities of at most the size of the
power set of X, as well as monoidal intervals of cardinality 2^k, for all
cardinals k which are not greater than the power set of X.
