As a drum teacher I feel that the four core rudiments are single stroke, double stroke, paradiddle, and buzz role.  I teach how to hold the sticks then apply the rudiments; but it is buzz role that consolidates the actual correct stick holding technique.  This is because it is impossible to do a buzz role until one holds the sticks correct.
From West London Drum Tutor, drum lessons in Harrow, Greater London, UK
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