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The notational principles of imperfection and alteration, intrinsic to the mature mensural system of the later Middle Ages, are generally still learnt by students and scholars. Ronald Woodley explores the wider 15th-century intellectual and mathematical mental apparatus that underpins this particular aspect and argues that the explanations of imperfection, alteration and the dot (point) with which most students and scholars today are familiar, are seriously incomplete and in some places actually inaccurate or misleading, at least with respect to the 15th-century.

Biography of LaMarr Woodley, currently Linebacker at The Pittsburgh Steelers, previously Youth Football Camp at LaMarr Woodley and Youth Football Camp at LaMarr Woodley.

Biography of Allan Ronald, currently Professor at University of Manitoba, previously Emeritus Distinguished Professor at University of Mantoba;Health Sciences Centre;St Boniface Hospital.