Different rotations of the same necklace are used across cultures, as well as within the same musical tradition. For example, the above rhythm is referred to as Tresillo in Cuba when started on the first onset, as Samhyon Toduri in Korea when started on the second onset, and as Nandon Bawaa Ghana when started on the third onset. Examples of necklace rotations like these and many more can be found in this paper on The Distance Geometry of Music.