Private research

Martin Schlumpf has long conducted research privately into polyrhythms and polymeters. Various handwritten formulae and tables on these subjects can be obtained here in the form of Adobe PDF files.

The author is very grateful to receive feedback on the issues touched on here.

The following formulae govern the relations between the variables “number of beats” (i.e. basic metrical units) / tempo / duration and metronomic or acceleration factor with 1) constant tempo relations and 2) constant geometrical accelerando / ritardando.

sketch paper 1
sketch paper 2