In conventional Common Western Notation (CWN) there are different notations styles for flags and beams, evolved historically. We present a classification based on an algorithm which sets beams according to positions in a musical metric space. This algorithm contributes to more clarity also for the human discussion of the historic phenomena thanks to its stratified architecture: (a) assignment of canonical beaming to nodes of the metric tree, then (b) data transformations coming from pauses, dotted notations, etc., (c) breaking of beams according to further parameters like motifs, playing techniques, etc., and finally (d) transformations according to the needs of graphic appearance. For phases (a) and (b) an exact algorithm is presented; for (c) and (d) a semi-formal classification grid.