  In this paper we introduce and study the relative cyclic subgroup
commutativity degrees of a finite group. We show that there is a finite group
with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$
and we indicate some classes of finite groups with few relative cyclic subgroup
commutativity degrees. Using this new concept, we are able to show that the set
containing all cyclic subgroup commutativity degrees of finite groups is not
dense in $[0, 1]$.
